The Principles and Practice of Modal Counterpoint.pdf

The Principles and Practice of Modal Counterpoint

Covering modal music from Gregorian chant through the seventeenth century, The Principles and Practice of Modal Counterpoint is a comprehensive textbook combining stylistic composition, theory and analysis, music history, and performance. By supplementing a modified species approach with a wealth of complete musical examples and historical information, this textbook thoroughly joins principle with practice, providing a truly immersive experience in the study of modal counterpoint and familiarizing students with modal repertoire. Features: • A balanced approach to learning counterpoint combining technique, style, and composition • Synthesizes the species approach and also the direct approach in an original way • Includes many complete musical scores • Provides self-tests and exercises throughout each chapter Douglass M. Green (1926–1999) was a founding member of the Society for Music Theory. He last taught at the University of Texas at Austin, where he was Professor of Music Theory until his death. Widely known as an expert in the music of Debussy and Berg, Green was the author of many articles and books on musical form and harmony, including the seminal analysis text Form in Tonal Music. He won several honors throughout his lifetime, including appointment as a Fulbright Scholar to Italy, the ASCAP-Deems Taylor Award, and the E.W. Doty Professorship of Fine Arts at UT-Austin. Green’s counterpoint classes remain legendary among his students. Evan Jones is Associate Professor and Coordinator of Music Theory and Composition at the Florida State University College of Music. He has received a Sproull Fellowship from the University of Rochester, a Doctoral Fellowship from the Social Sciences and Humanities Research Council of Canada, and the Alfred Mann Dissertation Prize from the Eastman School. He has published research on music by Lassus, Quantz, Schubert, and Xenakis in peer-reviewed journals and essay collections, and has edited a two-volume collection of essays on twentieth-century string quartets.

The Principles and Practice of Modal Counterpoint

Douglass M. Green and Evan Jones

First published 2011 by Routledge 270 Madison Avenue, New York, NY 10016 Simultaneously published in the UK by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2011. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. © 2011 Taylor & Francis All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data Green, Douglass M. (Douglass Marshall), 1926–1999. The principles and practice of modal counterpoint / Douglass Green and Evan Jones. p. cm. Includes bibliographical references and index. 1. Counterpoint. I. Jones, Evan. II. Title. MT55.G814P75 2011 781.2'86–dc22 2010005907 ISBN 0-203-84655-9 Master e-book ISBN

ISBN13: 978–0–415–87821–0 (hbk) ISBN13: 978–0–415–98865–0 (pbk) ISBN13: 978–0–203–84655–1 (ebk)

Contents

Foreword by Jonathan C. Santore Preface Chapter 1 Modes and Monophony 1.1 1.2 1.3 1.4

Authentic and Plagal Melodies in Folksong Scales and Modes Plainsong The Problem of Ionian and Aeolian

Chapter 2 The Single Line 2.1 Species Counterpoint 2.2 The Melodic Line 2.3 Melodic Intervals Chapter 3 Counterpoint During the Middle Ages 3.1 Early Organum 3.2 Voice Interchange 3.3 Music Without a Plainsong Basis Chapter 4 First Species in Two Voices 4.1 Harmonic Intervals: Consonance and Dissonance 4.2 Types of Motion 4.3 Adding a Counterpoint Against a C.F.

ix x 1 1 2 4 12 17 17 18 20 24 24 26 28 33 33 35 40

vi

Contents

Chapter 5 First Species in Three Voices 5.1 Harmonic Intervals 5.2 Characteristics of First Species in Three Voices Chapter 6 Counterpoint During the Fourteenth Century 6.1 6.2 6.3 6.4 6.5

Fourteenth-Century Textures and Rhythms Canon and Hocket Cadence Types Fauxbourdon The Style of John Dunstable

46 46 47 54 54 58 62 64 64

Chapter 7 Second Species in Two Voices

75

Chapter 8 Second Species in Three Voices

81

8.1 Intervals and Focal Points 8.2 Parallels on Successive Strong Beats 8.3 Cadences Chapter 9 Counterpoint During the Renaissance 9.1 9.2 9.3 9.4 9.5 9.6

Introduction Secular Pieces in Three-Part Counterpoint Sacred Music in Four and Five Parts Dissonance Meter Mensuration Canons

Chapter 10 Fourth Species in Two Voices 10.1 10.2 10.3 10.4 10.5

Consonant and Dissonant Syncopes Suspension Types Summary of Fourth Species Application of Fourth Species An Approach to Writing Fourth Species

Chapter 11 Fourth Species in Three Voices 11.1 11.2 11.3 11.4

Addition of a Third Voice to a Two-Voice Suspension Relationship Between First and Fourth Species Suspension Possible Only in Three or More Voices Cadences

81 82 82 87 87 88 98 107 107 110 117 117 120 121 122 124 130 130 134 136 137

Contents

Chapter 12 Texture, Melody, and Meter 12.1 12.2 12.3 12.4 12.5

Further Characteristics of Renaissance Music The Cadential Suspension Meter in the Single Line Imitation and Fore-Imitation The Bicinium

Chapter 13 Further Aspects of Species Counterpoint 13.1 Mixture of the Species 13.2 Species Counterpoint in Four Voices 13.3 Summary of Dissonance, Use in Second and Fourth Species

vii

141 141 149 154 155 156 164 164 165 169

Chapter 14 The Melodic Line

170

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11

170 171 172 175 178 180 182 185 187 190 191

Introduction to Modal Counterpoint Notation Melodies in Quarter-Notes and Longer Values Melodies with Eighths and Sixteenths Setting Latin Words Mode The Single Eighth-Note and the Sixteenth-Note Pair Isolated Eighth-Notes in Pairs Eighth-Notes in Groups of Three or More Use of Accidentals Melodic Curve

Chapter 15 Modal Counterpoint in Two Voices 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8

The Dissonances The True Cadence The Initial Phrase in Two Voices Interior Phrases Method for Writing a Two-Voice Phrase The Consonant Cadence Analysis of a Bicinium Writing a Bicinium

Chapter 16 Modal Counterpoint in Three Voices 16.1 16.2 16.3 16.4 16.5

Texture Cadences Motives and Imitation Victoria’s Et Misericordia Ejus: Cadential Treatment Victoria’s Et Misericordia Ejus: Motivic Treatment

195 195 199 201 202 204 208 209 211 214 219 220 225 226 230

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Contents

16.6 16.7 16.8 16.9 16.10 16.11

Part Writing Consonant Harmonies Unaccented Dissonance Accented Passing Tones Suspensions An Alternative Example

Chapter 17 Modal Counterpoint in Four or More Voices 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8

Texture Doubling in Consonant Sonorities Suspensions in Four Voices The Final Cadence Initial Notes Types of Imitation Triple Time Some Notes on Writing in Five or More Voices

Chapter 18 The Rise of Tonality in the Seventeenth Century 18.1 18.2 18.3 18.4 18.5 18.6

Dissonance as Expression in the Early Seventeenth Century Dissonant Chords Before the Seventeenth Century Seventh Chords in the Seventeenth Century Nonchordal Dissonance: Notes of Adjacency Nonchordal Dissonance: Time Extensions Diminutions

232 233 234 235 238 241 244 244 249 250 256 259 260 263 267 268 268 269 270 271 273 276

Epilogue: The Nature of Counterpoint Answer Boxes for Self-Tests Appendix A: Some Latin Texts Appendix B: Pronunciation of Church Latin Appendix C: Tones and Text of the Magnificat: The Canticle of the Blessed Virgin Mary (Luke 1: 46–55) Appendix D: Facsimile of Parts for Palestrina’s Missa Sine Nomine, Agnus II

281 283 293 295 297 299

Notes Select Bibliographies Index of Rules for Species Counterpoint Index of Rules for Modal Counterpoint Index of Musical Examples

302 306 313 314 316

Foreword

When Douglass M. Green passed away in 1999, his magnum opus, The Principles and Practice of Counterpoint, was almost completely finished, with only the final chapter of the second volume left unwritten. The present volume is the first of two. Throughout his long and distinguished career as a theorist, composer, organist, and church musician, counterpoint was always his primary interest. He began work on Principles after moving to The University of Texas at Austin in 1977; early iterations of the text were used by hundreds of Doug’s students at UT-Austin and Indiana University (where he taught during a sabbatical), many of whom have gone on to teaching in their own counterpoint classrooms, and making do with faded photocopies of Doug’s text. I first made Doug’s acquaintance as one of those students; later (after getting through those courses successfully!), I summoned up the courage to ask his daughter out on a date, and eventually became his son-in-law. Doug’s heirs turned to me, as a family member with expertise in the field, after his death to shepherd the book through the publication process. Extensive discussions about Principles with his friends, colleagues, and former students made it clear that, while Doug’s innovative approach to contrapuntal pedagogy was as fresh and valid as ever, the prose of the text would require some editing for a more contemporary audience. This was a difficult prospect for all of us who loved Doug and were reluctant to change his final work. On the other hand, I strongly felt that the best testament to Doug’s memory would be the publication and continuation of Principles as a living text, meeting the evolving needs of contemporary counterpoint teachers and students. For these reasons, when Constance Ditzel at Routledge expressed an interest in an updated version of Principles, I suggested that we find a co-author who respected Doug’s pedagogical aims, but would not feel constrained by his memory, someone who was an active counterpoint teacher with a sympathetic but independent pedagogical approach. I believe we’ve found this person in Evan Jones. On behalf of Doug’s family, I’d like to thank Evan Jones, Constance Ditzel, and Routledge for introducing his work to new generations of counterpoint students, and for keeping alive the memory of an esteemed and beloved teacher, mentor, and friend. Jonathan C. Santore, Ph.D. Professor of Music Theory and Composition and Chair Department of Music, Theatre, and Dance Plymouth State University (New Hampshire)

Preface

It was an honor to be asked to prepare Douglass Green’s two-volume manuscript, which he collectively entitled The Principles and Practice of Counterpoint, for publication. I was immediately impressed by the breadth and depth of the present volume, extending from Gregorian chant through seventeenth-century developments, and including a great number of complete pieces of music. Professor Green’s incisive stylistic observations and his unique pairing of “principles and practice” provide an expert introduction to musical developments over quite a lengthy historical span.

FEATURES Species Counterpoint

Combining the study of stylistic composition, theory and analysis, music history, and performance, a course in modal counterpoint is without doubt a multifaceted endeavor. Students face the challenge of composing not only “correct” but also musically convincing examples of a centuries-old style, and teachers face the challenge of finding an efficient way of transmitting the necessary knowledge and assessing compositional attempts. The long-standing popularity of Johann Joseph Fux’s “species” approach to modal counterpoint indicates its success in this regard. Fux’s eighteenth-century treatise, Gradus ad Parnassum, established the species approach as the dominant instructional paradigm for over two hundred years. Species counterpoint sets a series of developmental stages for budding contrapuntists to encounter in turn, gradually attaining a more and more elaborate compositional result. Complete Musical Works

Unfortunately, many species-oriented books (starting with Fux’s own, of course) have neglected to provide a substantial quantity of complete musical works by modal composers, perhaps expecting too much of the method itself and underestimating the importance of studying such issues as text setting. A number of recent textbooks have modified or abandoned the progressive organization of the species approach, aiming instead to extract stylistic rules with reference directly to the musical literature, but have sacrificed something of the pedagogical clarity of Fux’s method. In supplementing a modified species approach with a wealth of complete musical examples and historical information, the present volume keeps the promise of its title, joining principle with practice in an unusually thorough and sensitive way.

Preface

xi

Interwoven Organization

The particular ordering of components in this volume has been chosen so as to achieve the maximum connection between historical, theoretical, and practical dimensions. I share Professor Green’s conviction that Fux’s third species (four notes against one) should be delayed until after fourth species (syncopes); the introduction of smaller note values thus coincides with the study of melody and rhythm in Palestrina, Lassus, and Victoria, beginning in Chapter 14. Professor Green was less certain about the ideal ordering of material before that point in this volume. From certain anomalies of example numbering in Professor Green’s manuscript, it was apparent that at one point he had begun with all the species-based chapters in a row, and had later decided to begin with all of the historical chapters. Neither of these, however, was a perfect solution. Instead, I have arrived at an interwoven ordering of historical chapters and species-based chapters that reinforces certain topics and skills from different perspectives along the way. The introduction to modal melody and plainsong in Chapter 1 is followed by a consideration of melodic line from a Fuxian perspective in Chapter 2; the survey of medieval polyphony in two and three parts is followed by an introduction to Fuxian first species in two and three parts; and the evolving nature of consonance and dissonance in the music of early Renaissance is complemented by Fux’s presentation of dissonance treatment in second and fourth species. Even though Fux approached these issues from an eighteenth-century point of view, and was primarily focused on the style of Palestrina rather than the music of earlier centuries, this volume integrates the gradual introduction of the species and the intervening historical and analytical chapters so that they reinforce each other very fruitfully, and can be pursued in tandem.

TO THE STUDENT The study of the rules and norms of modal music necessarily exists in a symbiotic relationship—indeed, in a kind of counterpoint—with the study of real musical literature. Students will of course become acquainted with the strictures that are discussed and illustrated, but should also aim to achieve a more intuitive awareness of the expressive, affective character of the music being studied. This is only possible if the musical repertoire can be experienced through listening and performance. Even when considering the most technical, abstract details of the style, it is also crucial to recognize a connection to the particulars of compositional practice and to the musical effect that results. I believe this volume strikes this balance in a useful and accessible manner, and provides a truly immersive experience of modal music. Although most musicians are more familiar with eighteenth- and nineteenth-century classical music than with earlier styles, the study of modal counterpoint provides a direct path to the understanding and appreciation of many different eras of modal music. The traditions and practices that developed toward well-loved examples of sacred sixteenth-century vocal music may initially strike the beginning student as somewhat foreign in sound, and will probably prove difficult to imitate compositionally at first. Following the pluralistic program of study in this volume, however, will bring the student into a closer relationship with modal repertoire, will certainly enhance an awareness of many of its aspects, and will equip the student to compose in a stylistically faithful manner. Further, since the composers of modal music established ideas of consonance and dissonance, harmonic sonority, melodic gesture, and textual treatment that persisted through later centuries, the rewards of studying this subject are similarly long-range in scope.

xii

Preface

ACKNOWLEDGMENTS I have many people to thank in connection with this project. First, I would like to thank Constance Ditzel (at Routledge) and Jonathan Santore for selecting me to co-author this volume and its companion, and for providing immeasurable assistance along the way. This volume has also benefitted greatly at various stages from the help of Mhairi Baxter and Denny Tek at Routledge, Maggie Lindsey-Jones, Emma Wood, and others at Keystroke, and John Banks. Musical examples were expertly realized by Chris Burton and Jeff Yunek. I would like to thank all my colleagues at the Florida State University College of Music for their support, and all the students who have taken my counterpoint classes over the years. My parents, Peter and Helen Jones, and my parents-in-law, David and Barbara Ferguson, have been extremely supportive and generous during my work on this project. I am also grateful to my wife, Kim, for her patience, her selflessness, and for the pleasure of her companionship. Finally, I owe a debt that can never be repaid to my esteemed co-author, with whom it has been my very great privilege to collaborate in the manner that we have. Evan Jones July 2010

Chapter 1

Modes and Monophony

1.1 Authentic and Plagal Melodies in Folksong Beginning on a low C (C3 for men, C4 for women),1 sing the melody of “Home on the Range” (it starts “Oh, give me a home”). You will be in the key of F and you will end on the note F. Starting again from the F, in the same key, sing the melody of “On Top of Old Smokey.” You probably noticed that the first one was easy to sing while the second one was uncomfortably high. It would seem more natural for the second tune to be transposed down a perfect fourth or a perfect fifth to begin on low C (C3 for men, C4 for women) or even low Bb (Bb2 for men, Bb3 for women). Now try “Home on the Range” beginning on F4 (F3 for men). Unless you have an unusually high voice, you will wish you were in a lower key. The easiest singing range for the untrained voice is about an octave, C3–C4 for men, an octave above that for women, C4–C5. Most people can go fairly easily a third below and a second above this octave. By putting “Home on the Range” in the key of F and “On Top of Old Smokey” in the key of C, all these songs can be comfortably sung by anyone. Folksongs generally have a range of about an octave, rarely more than a tenth. In order to accommodate folksongs to a singable range, the accompanist has to be able to play in at least two keys, a fourth or fifth apart. Most folksongs can be placed into one of two categories: those whose prevailing ranges lie within the octave formed by the tonic notes and those whose prevailing ranges lie within the octave formed by the dominant notes. The former is referred to as an authentic range, or simply an “authentic melody,” and the latter as a plagal range, or a “plagal melody” (Example 1-1). EXAMPLE 1-1

In relation to the keynote, a melody with a plagal range lies lower than does a melody with an authentic range, for the tonic note lies approximately in the middle of its compass.2

2

Modes and Monophony

EXERCISE 1.1 Sing as many of the following songs as you know. Which are plagal and which authentic? 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

“I’ve Been Working on the Railroad” (“The Eyes of Texas”) “Camptown Races” “When Johnny Comes Marching Home” “Alouette” “On Top of Old Smokey” “The Streets of Laredo” “Old Folks at Home” “Oh Dear, What Can the Matter Be?” “Doe, a Deer” “Greensleeves” (or “What Child Is This”)

1.2 Scales and Modes A thorough discussion of scales and modes, their origins, their tunings and temperaments, their functions and uses throughout music history would be an enormous undertaking. For our purposes here it is enough to describe the chief modes and their scales without inquiring closely into the chain of events that led to their development in the first place. The notes of plainsong can be abstracted to form diatonic scales. A diatonic scale has one and only one note for each letter name, seven different notes in all. The notes of each diatonic scale can be rearranged to form an uninterrupted seven-note segment of the cycle of perfect fifths. Starting arbitrarily on Bb, the cycle of fifths is shown in Example 1-2 along with the possibilities for various diatonic scales. (Some “fifths” are shown as fourths, in order to keep the pitches within a narrower range on the staff.) EXAMPLE 1-2

Ionian (major) = notes 2–8, beginning on C Dorian = notes 2–8, beginning on D Phrygian = notes 2–8, beginning on E Lydian = notes 2–8, beginning on F Mixolydian = notes 2–8, beginning on G Aeolian (minor) = notes 2–8, beginning on A Transposed Ionian (major) = notes 1–7, beginning on F Transposed Dorian = notes 1–7, beginning on G Transposed Phrygian = notes 1–7, beginning on A Transposed Lydian = notes 1–7, beginning on Bb

Modes and Monophony

3

Transposed Mixolydian = notes 1–7, beginning on C Transposed Aeolian (minor) = notes 1–7, beginning on D Other major scales = notes 3–9, beginning on G; notes 4–10, beginning on D; notes 5–11, beginning on A; etc. Other minor scales = notes 3–9, beginning on E; notes 4–10, beginning on B; notes 5–11, beginning on F#; etc. You may already have guessed that a scale in itself gives you neither key nor mode. One note of the scale must be selected as the tonic (or final) and the other notes arranged in ascending or descending order if you are to speak of the “scale of C major” or the “scale of Bb Lydian.” We can take any one of the sevennote segments from the cycle of fifths and, selecting each of the seven notes in turn, construct the scales of seven different keys and modes (see Example 1-3). EXAMPLE 1-3

In each instance the half-steps occur between different scale degrees. Thus, each one is a different mode, with no cases of the same mode being transposed. The names are those that have come to be attached to these particular modes through tradition.3 Although the mode on B has been given the name Locrian (among others) it is not a mode that has ever really been in use, at least not until the twentieth century. It has always seemed defective because its fifth degree forms the interval of a diminished fifth with the tonic. Thus it has no true dominant, nor does it have a consonant tonic triad. Folksongs tend to divide the octave into two unequal parts consisting of a perfect fifth and a perfect fourth, but the Locrian mode does not lend itself to this kind of division. The lower fifth outlines the diminished fifth and the upper fourth outlines the tritone.4 The Lydian mode, though accepted by theorists as a viable mode, tended to be shunned by composers until the twentieth century, at least in its pure form. The tritone between the first and fourth scale degrees sounds so rough that composers have regularly lowered the latter by a half-step to form a perfect fourth. But to do this consistently turns the Lydian mode into a transposed version of Ionian, the major mode. It

4

Modes and Monophony

is only when scale-degree 4^ is kept well away from scale-degree ^1 that a satisfactory pure Lydian mode can be maintained.

SELF-TEST 1.1 Fill in the blanks. 1. The range of a plagal melody is approximately from scale-degree ______ to scale-degree ______. 2. “Joy to the World” is an example of ________________ melody. ^ 3. The Phrygian scale is distinct from the other modes in that the distance from scale-degree 1 to scaledegree ^ 2 is a ___________-step rather than a ___________-step. 4. Using only the white keys of the piano, the diatonic scale beginning on G is called ________________ and the one beginning on D is ________________. ^ and between ^ ^ is the _______________. 5. The scale with half-steps between scale-degrees ^ 3 and 4 7 and 8 This scale is also called ________________. 6. The Aeolian (natural minor) scale has half-steps between scale-degrees ______ and ______ , and between scale-degrees ______ and ______. ^ is called ________________. 7. The scale that is similar to major except for the raised scale-degree 4 8. The scale that is similar to minor except for the raised scale-degree ______ is called ________________. 9. The difference between major (Ionian) and Mixolydian is in scale-degree ______.

1.3 Plainsong Medieval theorists found that they could accommodate most of the plainsong repertory in eight categories. Separating the authentic ranges from the plagal ranges gives two large groups. Within each of these groups there are four modes: Dorian, Phrygian, Lydian, and Mixolydian.5 The names indicate the authentic group. The plagal group uses the same four names with the prefix “hypo-.” During the Middle Ages, as in modern times when dealing with plainsong, it was more usual to denote the modes by numbers than by names. Odd numbers refer to the authentic modes and even numbers to the plagal modes.

Modes and Monophony

5

Psalms and other scriptures tended to be chanted mainly on a single pitch. This pitch is called the reciting tone. In the table above it can be seen that the reciting tone is always F, A, or C except in Mode 7 where it is D. It would have been unthinkable to recite on a B, since in relation to the other notes of the scale B would necessarily be pulling against the F, a tritone away. In the authentic modes, then, the reciting tone is a perfect fifth above the final unless that perfect fifth would put it on a B. The reciting tones of the plagal modes are a third below those of the corresponding authentic modes, except in the case of Mode 8 where C replaces B.6 The range of Mode 4 violates the pattern of the other plagal modes for the same reason. All the other modes are shown with a range of a fourth below the final to a fifth above the final, but the typical range of Mode 4 extends from C to C instead of B to B.

EXERCISE 1.2 Examples 1–4 through 1–16 comprise a small anthology of plainsong in every mode. Sing through these several times each, trying to get a feel for the quality of each mode.7 It is important to keep in mind that the notated pitches are not absolute but only relative. Music was not written with various key signatures but only in “white” notes, although B could be either natural or flatted. You may sing these, then, at any comfortable pitch level. As you sing, take note of the melodic intervals and ask yourself these questions: 1. 2. 3. 4.

Do the melodic intervals include leaps of thirds, fourths, or fifths? Do the examples include leaps of octaves and/or sixths? Are the gaps produced by leaps invariably followed by melodic motion in the opposite direction? Are there two successive leaps in the same direction? Also take note of other characteristics.

1. In a large number of chants it is easy to perceive that the melody revolves around the reciting tone of the mode, even though the music is by no means a simple case of reciting a psalm or scripture reading on a single pitch. In many others either the note around which the music revolves is not the reciting tone of the mode or else the music does not concentrate on any one note. 2. Notice how the final cadence is approached. Is it by step from above or below, or is it approached by leap? 3. Finally, think about the form of the piece. Does it divide into clear-cut sections? Does one section seem to be based on one of the authentic modes while another section has the plagal version of the same mode?

6

Modes and Monophony

EXAMPLE 1-4 MODE 1: From the Ordinary of the Massa Dorian (transposed Aeolian)

Lord, have mercy. Christ, have mercy. a

Up to the asterisk the music is sung by a solo voice (cantor or priest). The choir joins in at that

point.

EXAMPLE 1-5 MODE 1: Ambrosian hymn (Second Vespers of Christmas) Dorian

Christ, the Redeemer of all, from the Father, the only one of the Father, who alone ineffably was born before the beginning.

Modes and Monophony

7

EXAMPLE 1-6 MODE 1: Antiphon (Second Vespers of Christmas) Dorian (transposed Aeolian)

Today Christ is born: today the Savior has appeared: today on earth the angels sing and the archangels rejoice: today the just exult, saying: Glory to God in the Highest, Alleluia.

EXAMPLE 1-7 MODE 2: Introit (First Mass of Christmas) Hypodorian

The Lord said to me, “You are my Son; today I have begotten you.” (Psalm) Why do the nations rage so furiously, and the people think vain things?

8

Modes and Monophony

EXAMPLE 1-8 MODE 3: Hymn (feast of Corpus Christi) Phrygian

Let my tongue tell the mystery of the glorious Body and of the precious Blood which, for the ransom of the world, the fruit of a noble womb, the King of the nations, has shed.

EXAMPLE 1-9 MODE 4: Antiphon (Second Vespers of Trinity Sunday) Hypophrygian

Let praise to God the Father, and to His equal, the Son, and with unceasing zeal to thee, Holy Spirit, resound from our mouth through all ages. (Psalm) Praise the Lord, ye children: praise the name of the Lord.

Modes and Monophony

9

EXAMPLE 1-10 MODE 5: Antiphon (first Sunday of Advent at Vespers) Lydian

Behold, the Lord will come, and all his saints with him: and there will be on that day a great light. Alleluia.

EXAMPLE 1-11 MODE 5: From the Ordinary of the Mass Lydian (transposed Ionian)

Lamb of God who takest away the sins of the world, have mercy upon us.

EXAMPLE 1-12 MODE 6: Hymn (Seven Sorrows of the Blessed Virgin Mary, Second Vespers) Hypolydian

The grieving mother stood in tears next to the cross where her Son was hanging.

10

Modes and Monophony

EXAMPLE 1-13 MODE 6: Introit (Mass for the Dead) Hypolydian

Grant them eternal rest, O Lord, and let perpetual light shine upon them.

EXAMPLE 1-14 MODE 7: Communion (Mass on the feast of the Sacred Heart of Jesus) Mixolydian

One of the soldiers pierced his side with a spear, and at once there came out blood and water.

Modes and Monophony

11

EXAMPLE 1-15 Before Sunday Mass Mixolydian

Thou shalt sprinkle me with hyssop, O Lord, and I shall be cleansed; thou shalt wash me, and I shall be made whiter than snow. (Psalm) Have mercy on me, O God, according to thy great loving-kindness.

EXAMPLE 1-16 MODE 8: Hymn (Whitsunday at Second Vespers) Hypomixolydian

Come, Creator Spirit, visit thy minds: fill with celestial grace the hearts which thou hast created. Amen.

12

Modes and Monophony

1.4 The Problem of Ionian and Aeolian You may be wondering why the medieval theorists recognized only four different modes with their authentic and plagal versions. What about Aeolian and Ionian modes such as seem to occur in Example 1-4, 1-6, and 1-11? There are two possible answers to this question. First, because of the problem of the tritone with F, it was always possible to use Bb instead of B-natural. But the use of Bb can alter the character of a mode. In Example 1-4 and much of Example 1-6, for instance, the stress on F calls for Bb, to avoid the F–B tritone. It would not be strictly necessary to recognize the mode on A (Aeolian) as a separate entity, since music with Aeolian characteristics could be easily explained as Dorian-with-Bb transposed up a perfect fifth. Similarly, when Lydian used Bb, as it often did, it did not have to be explained as a different mode (Ionian) since it could be sufficiently understood as Lydian-with-Bb, the flats being there for the purpose of correcting the tritone. Another answer to the question has to do with the medieval concept of the organization of the modes. They were not thought of as scales of seven different pitch classes spread throughout an octave. Rather, each mode was considered to consist of a perfect fifth and a perfect fourth placed conjunctly—that is, the same pitch served as the upper extreme of the perfect fifth and the lower extreme of the perfect fourth, or vice versa. Authentic modes had the perfect fifth on the bottom, plagal modes the perfect fourth. Each fifth and each fourth was characterized by the placement of the intervals between their extremes. Thus each mode had its particular type of perfect fifth and its particular type of perfect fourth, as demonstrated in Example 1-17. Notice the location of the half-steps. In the first four modes the half-step placement in the fifth corresponds to that in the fourth. EXAMPLE 1-17

Modes and Monophony

13

It is true that Dorian and Mixolydian share the same type of fourth. Since a fourth offers only three possible placements of the half-step, it is inevitable that two of the four fourths would be alike. But their fifths are unique. The Aeolian and Ionian modes on the other hand have neither unique fourths nor unique fifths. Aeolian is a mixture of Dorian and Phrygian, Ionian a mixture of Mixolydian and Lydian. (See Example 1-18.) Not until the Swiss theorist Heinrich Glarean published his treatise Dodecachordon in 1547 were Aeolian and Ionian accepted as modes in themselves.8 EXAMPLE 1-18

SELF-TEST 1.2 Mode numbers Reciting tone

Final

Fill in the mode number (1–8)

A

F

Mode no. _____

A

E

Mode no. _____

A

D

Mode no. _____

F

D

Mode no. _____

C

F

Mode no. _____

C

G

Mode no. _____

C

E

Mode no. _____

D

G

Mode no. _____

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Modes and Monophony

SELF-TEST 1.3 Fourths and fifths 1. The Dorian fifth has half-steps between its ______________ and ______________ notes. It appears not only in Dorian mode, but also in ______________ and Hypo______________. 2. The fourth with a half-step between the first and second notes is called the ______________ fourth. It appears in the ______________, the Hypo______________, and the ______________ modes. 3. Aeolian mode consists of a ______________ fifth and a ______________ fourth. 4. Ionian mode consists of a ______________ fifth and a ______________ fourth.

EXERCISE 1.3 Answer the following questions about each of the four pieces given. 1. 2. 3. 4. 5.

What is its mode? Can the music be said to revolve around the traditional reciting tone of its mode? Which is more prevalent, motion by step or motion by leap? Generally speaking, does the motion turn downwards after an upward melodic leap, and vice versa? How are the cadences approached, by stepwise motion or leap? From above or below?

A. Antiphon in honor of the Blessed Virgin Mary

Hail Mary, full of grace, the Lord is with thee. Blessed art thou among women and blessed is the fruit of thy womb, Jesus. Holy Mary, Mother of God, pray for us sinners now and in the hour of our death. Amen.

Modes and Monophony

B. Hymn for Vespers, First Sunday of Advent

Nurturing Creator of the stars, eternal light of believers, Jesus, Redeemer of all, hear the suppliants’ prayers.

C. Hymn before Benediction (Stanza 5 of Example 1-8) Spanish chant

Therefore, prostrate, we revere such a great sacrament: and the old teaching yields to the new rite: let a supply of faith surpass the insufficiency of the senses.

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Modes and Monophony

D. Hymn of St. Thomas Aquinas in honor of the Blessed Sacrament

Godhead here in hiding, whom I do adore Masked by these bare shadows, shape and nothing more, See, Lord, at thy service low lies here a heart Lost, all lost in wonder at the God thou art. (Translated by Gerard Manley Hopkins)

Chapter 2

The Single Line

2.1 Species Counterpoint During the sixteenth century a number of treatises dealing with counterpoint were written. Several authors, among them Gioseffo Zarlino and Thomas Morley, used an approach in which the simplest steps were presented first, then modifications and difficulties were gradually introduced one by one. Characteristic of this approach was the presentation to the student of a given unchangeable melody, called the cantus firmus (“fixed song”), against which the student wrote counterpoints. At first only one note was placed against each note of the cantus firmus—note against note, or in Latin, punctus contra punctum. After this step was mastered, two notes were placed against one, and so forth in various combinations called species. This pedagogical approach, known today as “species counterpoint,” was thoroughly systematized by Johann Joseph Fux in his famous Latin treatise Gradus ad Parnassum. His book is known to have been admired by J. S. Bach, whose pupil Lorenz Mizler translated it into German. It became the basis of contrapuntal study for virtually all eighteenth-century composers, including Haydn and Mozart. When Mozart taught counterpoint to his English pupil Thomas Attwood, Fux’s treatise was the basis of their lessons. Haydn and Albrechtsberger both had recourse to it when teaching their most famous pupil, Ludwig van Beethoven. The value of the method is indicated in the title “Steps to Parnassus” (Mount Parnassus is the mythical home of the muses). The student is asked to take one step at a time. Difficulties are isolated from each other so that one does not have too much to contend with at any given moment. But the method has a drawback, too, for if followed systematically through all five species, first in two voices, then in three, then in four and more, the time normally allotted for the study of counterpoint in the usual college curriculum will long have gone by. Only artificially contrived counterpoint will have been dealt with and the music of the great composers bypassed. For this reason, we will use the species approach only up until Chapter 13 of this book, for the purpose of introducing and practicing only the most essential concepts of counterpoint. Although species counterpoint is intended to acquaint the student with contrapuntal principles rather than with any particular historical style, it was developed at a time when Palestrina’s manner was looked on as the epitome of the strict sacred vocal style. The practice of species counterpoint, then, is an excellent introduction to composition according to the aesthetic of the Roman School of the late sixteenth century. This music was done almost entirely in strict diatonicism either with no key signature or with a signature of one flat. Accidentals are strictly limited:

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The Single Line

1. When no key signature is present one may, under certain circumstances to be explained later, alter a Bnatural to a Bb. With a signature of one flat, one may alter an E-natural to an Eb. 2. When cadencing on D, G, or A, one should create a leading-tone by raising the seventh degree of the scale. To cadence on D, use C# instead of C-natural. Similarly, to cadence on G or A, use F# or G# respectively. 3. When ascending through the leading-tone one may raise the sixth degree of the scale in order to reach the seventh degree by step (e.g., F#–G#–A). In summary, the only accidentals available in this style are Bb, C#, F#, and G#. With a key signature of one flat, Eb is also available, but G# is unavailable. It is important to remember that accidentals may not be used arbitrarily. Sharps are used only to produce a leading-tone for a cadence. Flats are used only to avoid the tritone (explained in 2.3 below). With this limited spectrum of pitch classes, exercises can be done in any of the standard church modes. The modes were discussed in detail in Chapter 1. For now, we need to remember especially the following: 1. The Dorian mode beginning on D uses the scale D–E–F–G–A–B–C–D with no signature. It can be transposed up a perfect fourth by using a key signature of one flat and beginning the scale on G: thus, G–A–Bb–C–D–E–F–G. 2. The Phrygian mode beginning on E uses the scale E–F–G–A–B–C–D–E. It can be transposed up a perfect fourth by using a key signature of one flat and beginning the scale on A: A–Bb–C–D–E– F–G–A. The Phrygian mode differs from the others in that it never uses a raised seventh degree of the scale in order to cadence. The move into the tonic from below is by whole step, D-natural to E or, if transposed, G-natural to A. 3. The Lydian mode beginning on F uses, like the other modes, only those pitches with unaltered letter names (white keys of the piano). Transposed to Bb, it has a signature of one flat. 4. Mixolydian uses the “white notes” on G. Transposed up a fourth, its scale is C–D–E–F–G–A–Bb–C. 5. Aeolian is the same as natural minor on A; transposed up to D, it uses one flat in the signature. 6. Ionian is the same as major on C; transposed up to F, it uses one flat in the signature. In modal terminology the note on which the scale is built is known as the final. In Dorian, the final is D; in Phrygian it is E, and so on. The word “final” is analogous to the word “tonic” as used in the analysis of tonal music.

2.2 The Melodic Line Sing the cantus firmus in Example 2-1, play it, then sing it again.1 As you perform this and the following melodies, try to notice which specific intervals occur melodically. When there is a leap, how is it approached and left? EXAMPLE 2-1 Fux

The Single Line

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The eleven pitches comprise seven stepwise motions and three leaps (notes 1–2, 4–5, and 6–7). Although other melodies may have a greater proportion of leaps, on the whole this ratio is about normal— two-thirds stepwise motion and one-third leaps. This is not surprising when we remember that a melody is not simply a number of notes sung or played one after another. Rather, it has something about it that makes these notes hang together in such a way that we can refer to them in the singular: we say “a melody,” not “some notes.” One of the qualities that brings about this coherence is the fact that most of the notes in the melody move to other notes that are close by. There is a second fact about Fux’s cantus firmus (hereafter referred to as C.F.) that plays a part in producing a coherent quality: the melody has a single climax. This is note 7, higher than the other pitches in the melody. But the simple fact that it is the highest pitch is not enough to cause it to serve as a climax. Rather, it is due to notes 2 and 5, which prepare the climax by leading the ear upward, and notes 8 through 11, which bring about a gentle descent.2 In other words, a high or low note cannot act as a focal point if it is isolated from the other notes of the melody. Rather, such isolated notes will simply not seem to be a part of the line. Sing and play the “bad” examples given in Example 2-2. The notes marked X are isolated. Only by altering the notes or adding others can the melodies of Example 2-2 be made satisfactory. EXAMPLE 2-2

EXAMPLE 2-3

In the case of melody (a) in Example 2-3 the zenith is not led up to as it was in Fux’s C.F., Example 2-1. Nevertheless, the climactic C5 is well enough incorporated into the line because of the descending stepwise motion, which fills in the gap created by the leap from note 3 to note 4.3 In the case of melody (b) in Example 2-3, the second note (B3), though highest, sounds less like the climax than part of a circular motion around the pitch G3 (notes 1 and 4). Rather, it is the low D3 (note 5) that seems to be the focal point of the melodic line. A negative climax like this is called a nadir. In melody (a) of Example 2-3, the gap between notes 3 and 4 was filled in by stepwise motion in the opposite direction. A similar means of filling-in occurred in melody (b) after the gap produced by notes 4 and 5. But motion in the opposite direction serving to fill in a gap does not necessarily have to be by an immediate step. It is enough that the gap is compensated for in some way. Melody (c) inserts an extra note

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The Single Line

(4a), which moves by leap in the opposite direction. Melody (d) reverses notes 6 and 7, yet the gap between notes 4 and 5 is satisfactorily filled in. Sing-play-sing all the melodies of Example 2-3 several times. Do the same with the melodies in Example 2-4. Which are satisfactory? Whenever one seems unacceptable, try to determine precisely what makes it so. DO NOT READ THE SUBSEQUENT PARAGRAPH UNTIL YOU HAVE DONE THIS. EXAMPLE 2-4

You probably noticed that melody (a) of Example 2-4 was extremely static, owing to the back-and-forth motion of notes 2 through 6. This motion also means there is no single climax, neither zenith nor nadir. Melodies (b) and (c) are satisfactory. In the latter, notice how note 2 is brought into the mainstream by notes 9 and 12. These three notes together form an ascending scale (G3–A3–B3) which is fulfilled by the final C4. Melody (d) would be acceptable if only it began with note 2. But the first note, A2, is isolated from the rest of the line. Note 8 is raised, of course, in order that it may move by whole step into the leading tone, as in the melodic minor scale.

2.3 Melodic Intervals Here are more C.F.s to be sung, then played, then sung again (do not neglect this triple performance!) (Example 2-5). EXAMPLE 2-5

The Single Line

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In performing these and the previous C.F., you may have made some or all of the following observations: 1. Species counterpoint is strictly diatonic. No chromatic half-steps appear and the only accidentals are those necessary to create a leading tone or to avoid an augmented second in approaching the leading tone from below. Two half-steps in succession must be avoided: for instance, Bb–A–G#. 2. Occasionally a note is repeated, but rarely more than once. 3. Only easily sung melodic intervals are employed. No leaps of augmented or diminished intervals, no leaps larger than a perfect fifth and minor sixth except for the octave. Minor sixths occur only very occasionally and always in ascending, never descending, motion. Major sixths are entirely avoided. 4. Melodies end on the final of the mode. The final is approached by step either from above or from below. Although in these examples all melodies also begin on the final, this is not a strict rule. If not the final, the first note will probably be the fifth degree of the scale. 5. Approach to the cadential ^2 is usually by step from above. When the final is approached by step from above, that is, from scale-degree ^2, this note is itself approached by step or by a descending third. In other words, the last three notes will be ^3–^2–^1, ^1–^2–^1, or ^4–^2–^1. Of these, ^3–^2–^1 is the most common. 6. A melodic leap must be compensated for in one way or another. Either the note immediately preceding or the note immediately following a leap should move in the opposite direction to the leap itself. That is, leaps must be either approached or left by motion in the opposite direction. While leaps may be both approached and left by movement in the opposite direction, this contour is not a requirement except in the case of large leaps—the ascending minor sixth and the octave, ascending or descending (see item 7 below). The compensating movement in the opposite direction does not necessarily have to be by step. The rule for leaps of a major or minor third, perfect fourth, or perfect fifth may be put this way: when a leap occurs it is either at the bottom of a line in a single direction or at the top, not somewhere in the middle. 7. Large leaps are both approached and left by contrary motion. The ascending minor sixth and the octave are considered large leaps. For the sake of balance in the line, the notes both preceding and following must lie within the gap produced by these leaps. (See Example 2-5(b), notes 6–8; Example 2-5(c), notes 4–6; and Example 2-5(e), notes 2–5 and 7–11.) 8. Occasionally double leaps occur. Two successive leaps in the same direction occur twice in Example 2-5(a), notes 4–6 and 8–10. In this case the double leap must be both preceded and followed by motion in the opposite direction. Moreover, the double leap itself must outline a major or minor triad (not diminished or augmented). Or, the two leaps may outline an octave—a perfect fifth as the lower leap, a perfect fourth as the upper leap (as in Example 2-5(d), notes 1–3). A general principle regarding double leaps is that the smaller leap is never the lower one.

22

The Single Line

9. A high or low note is not isolated by register from the other notes, but is incorporated into the line by means of notes a step or a third away. SELF-TEST 2.1 The following are intended to help you reinforce this information. Directly above each melody, write “good” or “bad” with the numbers 1 through 7 of the observation that it illustrates or ignores.

There is one more observation very important to an acceptable melodic line in species counterpoint. This has to do with the avoidance of the stressed tritone. In everyday language the word “tritone” is often used to mean either the augmented fourth or the diminished fifth. When correctly used, however, the term applies only to the augmented fourth, which indeed comprises three (whole) tones: hence, “tri-tone.” The diminished fifth, on the other hand, is made up of two half-steps, one at either end, and two whole tones. Of course the total number of semitones in either case is six, but the effect in tonal and modal music of a tritone is very different from that of the diminished fifth. In illustration, sing, play, and sing the melodies given in Example 2-6. DO NOT READ FURTHER UNTIL YOU HAVE DONE THIS. EXAMPLE 2-6

The Single Line

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You probably noticed a certain difficulty in singing note 5 of melody (b), or at least in singing it exactly in tune. There is a slight roughness here since note 5 is the lower end of a tritone begun with note 2. Although notes 5–7 in the same melody also produce a tritone, the fact that the melodic line continues on upward to the C4 (note 8) smoothes out this roughness so that the latter part of the melody is acceptable. Similarly notes 2–4 in melody (c) cause a difficulty. On the other hand, melody (a) offers no problems whatever, notes 2–6 comprising not a tritone but a diminished fifth. We can, then, formulate Observation No. 10. 10. The last three or four notes of a passage in a single direction should not outline a tritone (an augmented fourth).

SELF-TEST 2.2 The following should help to reinforce the observation regarding the tritone. Write “good” or “bad” directly above each melody. If the melody is “bad,” indicate which notes comprise the offensive tritone.

Principle

In species counterpoint the single melodic line is simple and coherent. Practice

Simplicity of line is produced by limiting the pitches to those occurring in the diatonic scales, by stressing stepwise motion, and by ending with a stepwise approach to the tonic. Coherence is produced by compensating for leaps by subsequent contrary motion, and by providing a clear focal point, zenith or nadir.

EXERCISE 2.1 Review Section 2.2 (“The melodic line”). Then write twelve melodies in whole notes, very carefully following Observations 1–10 as listed in Section 2.3. Use (at least) two different clefs. The melodies should be in various ^ ^ modes, some transposed (one flat in key signature) and some not. Always begin on scale-degree 1 or 5 and ^ end on 1. Sing-play-sing each one before deciding you are satisfied with it. Remember, your best friend is your eraser.

Chapter 3

Counterpoint During the Middle Ages

A thorough account of counterpoint from the tenth century through the sixteenth century must inevitably deal with virtually all part music written during this period of more than five hundred years. Such accounts are presented to varying degrees of detail in music history books and musical dictionaries. Our purpose here is to highlight some of the aspects of counterpoint from that period, especially aspects that have a bearing on the contrapuntal writing of later periods.

3.1 Early Organum About the end of the ninth century, theorists began to describe a way of singing portions of plainsong in more than one part. There is reason to believe that the practice of singing secular music in at least two parts had, for a long time, been practiced in some places, but we have no authoritative written accounts of such activities. A segment of plainsong would be sung by one voice, the vox principalis, while another voice, the vox organalis, would double it at the fourth or fifth below. Perhaps two higher voices would double the principal and organal voices at the upper octave. Much of the piece would move along this way in parallel fourths and/or fifths. The voices generally began with a unison and spread out through a second or third to the fourth or fifth and reversed the process for cadences. In his treatise entitled Micrologus (c. 1025), Guido of Arezzo talks about these approaches to the cadential unison, showing that theorists of the time were interested in how two-part cadences could be achieved. Example 3-1 is a piece found in a handbook of music, the Musica Enchiriadis, an anonymous work dating from around 900. EXAMPLE 3-1


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In addition to the dominating parallel motion, it includes oblique motion at the beginning of phrases and two or three instances of contrary motion. By the next century, contrary motion in organum was being both practiced by composers and advocated by some theorists. In the twelfth century in certain places in Spain and France, another type of organum was being practiced, which has come to be called florid or melismatic organum. The organal voice, rather than moving note-against-note with the principal voice, sings a melisma in an improvisatory manner above the slowermoving notes of the plainsong. Thus what had originally been the chief tune, the plainsong itself, was now more of a foundation made up of a series of long sustained notes acting as a support for the fantastic arabesques in the upper voice (Example 3-2).1 EXAMPLE 3-2

Since the manuscripts, found in the monastery of St. Martial in south-central France and the monastery of Santiago de Compostela in northwestern Spain, are by no means consistently clear as to precisely where the simultaneities occur, we cannot draw hard-and-fast conclusions regarding consonance and dissonance treatment in melismatic organum. What is interesting for us in this study is the texture of this music— two melodic lines performed simultaneously but maximally contrasted to each other. By the late twelfth century, composers may have felt the need for a notation by which they could indicate the rhythms of the two voices more precisely. Over a period of years the practice of notating by means of rhythmic modes came into being. Each of the six modes provided a basic rhythmic pattern similar to those found in poetry, and means were worked out by which slight variations of these patterns could be notated. Example 3-3 is based on the first rhythmic mode, long-short, here transcribed as a quarter-note followed by an eighth-note.

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EXAMPLE 3-3 From Gaude Maria Leonin

As might be expected, phrase endings formed the interval of an octave or perfect fifth. Rarely one might find a perfect fourth. More often than not, phrases also began with one of these perfect consonances, but they did not do so consistently. They might even begin with dissonances. Leonin’s Gaude Maria (Example 3-3) begins its first two phrases (not shown) with a minor seventh and a major ninth, respectively, both moving immediately into an octave. In twelfth-century counterpoint there was often a great deal of parallel motion, particularly parallel perfect fifths.

3.2 Voice Interchange The anonymous work given as Example 3-4 is a fascinating motet from the thirteenth century. The text itself is amusing. It interrupts the word “Alleluya” by inserting other words between its second and third syllables, at each repetition adding length to this interruption. Finally, as a kind of coda, we hear the word in its normal form. EXAMPLE 3-4 Alle, psallite Anonymous, 13th c.


Alle-

Allesing with -luya. Allenoisily sing with -luya to God with a full heart sing with Alleluya.

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-luya

The tenor sings a bit of melody, which may or may not be taken from plainsong, three measures in length. Above this a second voice, the duplum, sings a counterpoint, virtually note-against-note. Above this a third voice, the triplum, sings a slightly more florid counterpoint. These three measures are immediately repeated, the sole difference being that the duplum sings what the triplum previously had, and the triplum sings what the duplum previously had. This type of voice interchange, also known by the German

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term Stimmtausch, is common in medieval music. The exchange is at the identical pitch level so that the repetition is essentially the same, although of course there will be some difference in timbre between the two singers. The second phrase, extended to four measures, is similarly repeated with voice interchange, as is the third phrase, five measures in length. Two voices always rest at the end of a phrase while the other voice artfully bridges the gap between phrases. Each phrase ends with a perfect fifth above a diminished third, the final of the mode. Harmonically, the piece is quite static. Such is not always the case, but many thirteenth-century pieces tend in this direction. The famous rota from thirteenth-century England, Sumer is icumin in, makes elaborate use of voice interchange while being even more harmonically static than the motet Alle, psallite. Its correct performance takes six voices, four to sing the round itself, and two for the ostinato pes (“foot”) which supports it. Example 3-5(a) shows this pes; Example 3-5(b) shows the essential harmony of the entire piece. EXAMPLE 3-5

3.3 Music Without a Plainsong Basis Not all sacred music used plainsong as a foundation. One of the chief musical types in the thirteenth century was the conductus, a piece normally composed of newly invented melodies. The prevailing, though not the only, texture for the conductus was basically note-against-note, so much so that musicologists today speak of such texture as “conductus style.” Example 3-6 is the beginning of a hymn in conductus style for two voices. EXAMPLE 3-6

Born for us today of the Virgin Mary . . .

Mark the harmonic intervals, noticing where consonances and where dissonances occur. Is there any voice crossing? Do all types of motion appear? Are there parallel octaves, unisons, and/or fifths? What is the rhythmic relationship between the voices?


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Example 3-7 is the first stanza of the complete conductus Orientis partibus. It is a three-voice setting of the Song of the Ass, a tune that existed in various versions and may still be familiar today as the Christmas carol “The Friendly Beasts.” This conductus was performed as part of a ceremony celebrating the flight of the Holy Family into Egypt, during which a young girl dressed as the Virgin Mary rode a donkey into the church. It is known to have been performed regularly in France at Beauvais and Sens, and probably also in Madrid. The tune is in the lowest voice. EXAMPLE 3-7

Out from lands of Orient was the ass divinely sent; strong and very fair was he, bearing burdens gallantly, Heigh, Sir Ass, oh heigh! (Translated by Henry C. Greene)

Perform the piece several times by singing the tune and playing the upper voices. Then ask yourself the same questions asked in reference to Example 3-6. If you did this carefully, you probably made some or all of the following observations: 1. The chief consonant sonority is the perfect fifth, which begins and ends each phrase and dominates the strong beats within the phrase. 2. Voice crossing is quite common, even below the lowest voice. 3. Parallel perfect fifths, perfect octaves, and perfect unisons are all to be found. 4. The upper voices are slightly more rhythmically active than the lowest voice.

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Secular music, of course, did not use plainsong as a basis. The instrumental dance illustrated in Example 3-8 uses the first rhythmic mode in both voices. Since it is a dance it has a regular metric structure that transcribes into modern notation as four-measure phrases. The second phrase is similar to the first except that its ending is altered to conclude on the final of the Lydian mode, while the first phrase ended on the second scale degree. Thus the two phrases together form what we would call today the antecedent and consequent of a period. In the thirteenth century, the era of this dance, the phrase that begins the period was called “open” and the phrase that ended it was “closed.” EXAMPLE 3-8

The remainder of the piece consists of four more “periods” on the same tune but with varying counterpoints. Beginning with the third “period” the tune is transferred to the upper voice and, consistent with the lack of key signature in that voice, transposed up a perfect fifth.2 The last time, the theme itself is varied. The style of the estampie is similar to that of a two-part conductus. The intervallic structure between the two voices is grounded solidly in the sonority of the perfect fifth. Not only do most phrases begin and end with the perfect fifth, but so do most measures begin with it. Dissonances tend to be a step away. Play the estampie fragment several times, listening carefully to the effect of the Bb3 in the lower voice and the B3 in the upper voice. Although the B-natural occurs but once in the first period (m. 7) it gives a very distinctive sound to the passage. It leads to the upper voice cadence on C as a leading-tone to scale-degree ^ The quality of this 5^ of the mode, while the E3 in the lower voice acts as leading-tone to scale-degree 1. double leading-tone became very prominent in later thirteenth-century music and permeates the sound of fourteenth-century music, occurring in a much more obvious way than in this estampie (see Chapter 6). The trouvère Adam de la Halle, to whom our Example 3-9 is attributed, composed a number of rondeaux in three parts that are fairly typical of thirteenth-century conductus style. Notice how the two upper voices consist, for the most part, of parallel fourths in opposition to the lowest voice. A rondeau consists of two parts, A and B, both parts being performed according to the scheme AB aA ab AB. Capital letters indicate identity of the poetic line as well as the musical. In Tant con je vivrai, B consists of three phrases, each three measures in length, and all closely related motivically. Example 3-9(b) shows a summary outline of the four cadences in this piece. In the first two cadences, two voices move stepwise into the cadential note and its fifth, while the third voice jumps to the octave of the cadential


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note. The last two cadences are forerunners of what became known as the clausula vera, the “true” or “authentic” cadence, in which two voices move by step—one up and one down—into the cadential note. In the thirteenth and fourteenth centuries the third voice normally ascends by half-step into the fifth above the cadential note. This is the double leading-tone cadence. EXAMPLE 3-9 (a) Rondeau: Tant con je vivrai Adam de la Halle, 13th century

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EXAMPLE 3-9 (b)

Tant con je vivrai is also typical of much thirteenth- and fourteenth-century music in that no particular mode is made manifest. The overall tonal organization is not without logic, however, as is shown in Example 3-10. The first part moves from an 85 on A down to an 85 on G. The second part begins again on A and moves through G to conclude on F. EXAMPLE 3-10

The feeling of conclusion at m. 14 is not due to the melodic lines having reached a “tonic.” It is more likely due to their having simultaneously arrived at a low point. The listener senses an affinity with the natural law of gravity.3

SELF-TEST 3.1 Circle the correct words or figures. 1. In early organum the vox principalis sang a segment of plainsong that sounded above / below the vox organalis. 2. In the late twelfth / thirteenth century composers such as Leonin organized their music rhythmically by the use of rhythmic modes. 3. In the motet Alle, psallite cum luya the German term Stimmtausch refers to the insertion of text within a word / the repetition of material in a new voice. 4. Sumer is icumin in is a conductus / rondeau / canon. 5. It is true / false that all music of the Middle Ages was built on a plainsong basis. 6. Orientis partibus is a conductus / rondeau / canon. 7. The estampie is an instrumental dance with a texture similar to florid organum / a rota / a conductus. 8. It is true / false that medieval music is always written in one of the modes.

Chapter 4

First Species in Two Voices

4.1 Harmonic Intervals: Consonance and Dissonance For two reasons the definition of consonance and dissonance1 has changed over the years: (1) from time to time opinions as to which intervals are consonant and which dissonant have varied; and (2) the precise meaning of the terms themselves has not had a uniform explanation from writers on music.2 For instance, in 1597 Thomas Morley defined a consonant sound as one which “delights” the ear, a dissonant sound as one which “offends.”3 Many other writers, especially those writing before the nineteenth century, also speak of “pleasantness” and “unpleasantness” as aspects of consonance and dissonance respectively. In our own time, writers often describe the difference in terms of relative stability or instability. A consonance sounds relaxed, not particularly demanding further motion: it is more or less stable. A dissonance sounds tense, demanding resolution to a more stable sound. A slightly different point of view is that a dissonance is a sound that needs explanation—in order to understand it the listener must depend on its resolution to a consonance. To complicate matters still further, intervals that are generally acknowledged to be consonant are not necessarily perceived to be equally so. Thirds and sixths are both considered consonant intervals, yet the third is stable enough to end a piece of music while its inversion, the sixth, is not. And the perfect fourth has, over the years, been in the ambiguous position of being consonant in some contexts and dissonant in others. Until the eighteenth century theorists regarded as most consonant those intervals whose ratio was made up of the smallest numbers. For example, if one vibrating string produces the note C2, a string half its length will produce C3, an octave higher. The ratio of the two pitches’ frequencies is 2:1, and the resulting octave is a perfect consonance. If the ratio between two frequencies is 3:2, a perfect fifth results. It is called a perfect consonance, but is slightly less stable than the octave. The ratio 4:3 gives the perfect fourth, which is the inversion of the perfect fifth and less stable than the fifth. The imperfect consonances are given by the other ratios: 5:4 and 6:5 result in the major and minor third respectively, and their inversions are the minor and major sixths, ratios 8:5 and 5:3.4 Sixths are less stable than thirds. It might appear, then, that the “stability” of an interval is in direct proportion to the ratio that produces it—that is to say, the ratio made up of two adjacent lower numbers gives a more consonant interval than does a ratio deriving from higher numbers or from numbers not adjacent. Thus, the perfect fifth (3:2) is more stable than the major third (5:4), but the major third is more stable than the major sixth (5:3). It was during the seventeenth century that the laws of vibrations of strings were discovered. When a string vibrates it does so not only in its full length but also in halves, thirds, quarters, and so on. Not only

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is the fundamental pitch of the string produced, but also overtones in increasingly smaller intervals. The same is true of the column of air in an organ pipe or a wind instrument. Thus the early theorists with their consonances based on small-numbered ratios were justified since the first—and therefore most prominent —overtones correspond exactly to these ratios. A pitch produced by a musical instrument is a complex sound, made up of various pitches. We speak of the fundamental as the first partial, the first overtone as the second partial, and so on. (See Example 4-1.) EXAMPLE 4-1 THE OVERTONE SERIES

The first six partials correspond to the pitch classes of a major triad, but beyond that some of the partials do not correspond very closely with the pitches used in Western music. The seventh and eleventh partials, for instance, are perceptibly lower than the notated Bb4 and F#5 in Example 4-1 (hence the minus signs above them). Moreover, the overtones from the seventh partial upwards are too close together to be perceived as consonances, for they are notes of adjacency—a whole step or smaller. Therefore tradition has it that the first six partials along with their octave replicas give us our consonances, as shown in Example 4-2.5 The fifth and eighth partials produce the minor sixth, the third and fifth partials the major sixth. EXAMPLE 4-2

Consonances, then, are the perfect intervals and major and minor thirds and sixths. But it is not quite so simple as this, for there is a problem regarding the perfect fourth. Beginning in the fourteenth century, composers have tended to treat the perfect fourth as a consonance only when it appears between two upper voices. When the lower of the two notes comprising the perfect fourth is the lowest-sounding voice, this interval has been perceived as so unstable as to be for all intents and purposes a dissonant interval, and has been used as such by composers. Possible reasons for this rather odd phenomenon are demonstrated in Example 4-3.


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EXAMPLE 4-3

In (a), (b), and (c), the chord in brackets represents the pitch G2 and its overtones. In (a) the lower note of the perfect fourth (A3) clashes with the overtones of G2 that resonate from the perfect fifth that precedes it. In (b) it is the upper note of the perfect fourth that clashes with the overtones of G2. The C4 is felt to have a strong downward pull into the B3. In (c) the perfect fourth is in the two upper voices, corresponding to the overtones of G2. Undoubtedly the explanation given above is both incomplete and over-simplified. It is offered as at least a partial explanation for the fact that the perfect fourth, when it is formed from the lowest voice upwards has been usually (but not always) treated as a dissonance.6 One final fact regarding consonant intervals needs to be mentioned: it is generally agreed, and has been for hundreds of years, that the perfect consonances are distinguished from the imperfect by a decided difference in quality. While writers through the ages have used various words to describe this difference, most people today refer to the perfect consonances as having a “hollow” or “empty” sound as opposed to the imperfect, which are described as “full” or “rich.” As one goes higher up the partials of the overtone series one senses a corresponding increase in the opposition of the notes making up an interval: the unison (1:1) carries no opposition, the octave (2:1) almost none, the perfect fifth (3:2) very little and so forth. When we come to the major second (9:8) or the minor second (16:15), the two notes are so opposed that we call the result dissonance. Between these extremes lie the imperfect consonances evincing considerable opposition and yet still consonant, the major third (5:4) more so than the minor third (6:5), and both types of third more so than their inversions the sixths (8:5 and 5:3). The reason it is important to remark on the distinct sonority of a perfect consonance as contrasted with the imperfect consonance is that the sound of the latter has traditionally called for a treatment different from that of the former. In the remaining sections of this chapter it will be noticed that the “hollow” sounds of the perfect unison, perfect octave, and perfect fifth call for special ways of approaching them.

4.2 Types of Motion Following an ancient tradition, Johann Joseph Fux wrote his Gradus ad Parnassum as a dialogue between a master, Aloysius (representing Palestrina)7 and a pupil, Joseph (representing Fux himself ). Aloysius presents his pupil with a C.F., the lower line in Example 4-4, first presented as Example 2-1. He instructs Joseph to compose a note-against-note counterpoint above it. Joseph’s solution, approved by Aloysius, is the upper line.

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EXAMPLE 4-4

The resulting bit of two-voice counterpoint demonstrates the four types of motion possible between any two dyads: oblique (one voice is stationary while the other moves), parallel (both voices move in the same direction and the same number of steps), contrary (the voices move in opposite directions), and similar (the voices move in the same direction but not the same number of steps).

SELF-TEST 4.1 Look at Example 4-4 again and mark the type of motion that occurs between each pair of adjacent dyads. (Actually write it down: don’t merely think it!) Sing-play-sing Example 4-4. In singing two parts, sing the upper note of each dyad, then the lower note of the same dyad, then the upper note of the next, followed by its lower note, and so on. For the second singing, begin with the lower note. You should also try to find a friend to sing one of the parts simultaneously with you. There is no substitute for this kind of musicianship training.

Only consonant intervals may occur in first species (note-against-note). Since in two parts one of the pitches of any perfect fourth is bound to be the lower voice, all perfect fourths are excluded from first species along with the other dissonances. Example 4-4 happens to include all the available consonant dyads except the minor sixth and the perfect unison (P1). The perfect unison is used in first species only at the beginning or the end. Within the phrase, the perfect unison gives the effect either of a premature cadence or of the sudden disappearance of one of the voices. Careful observation of Example 4-4 will reveal that, while all types of motion are present, parallel motion is confined to thirds and sixths. Moreover, perfect fifths and perfect octaves are not approached by parallel or similar motion—in every case the perfect fifths (notes 4 and 6) and the perfect octave (note 11) are approached by contrary motion. Nevertheless, the perfect intervals may be approached by oblique motion also. All these observations may be summarized by one rule, which should be memorized: In two-voice counterpoint, all motions are correct except parallel or similar motion into a perfect consonance. Example 4-5 illustrates the correct motions. Beneath them are some that are incorrect. In Example 4-5, (a) through (d) are illustrations of correct parallel thirds and sixths, (e) through (g) show correct similar motion to a third or sixth, (h) through (j) correct contrary motion to any type of consonance, (k) through (m) correct oblique motion to any type of consonance. Parallel perfect unisons, perfect fifths, and perfect octaves are shown in (n), (o), and (q). Approach to a perfect consonance by similar motion, called “direct” or “hidden” fifths, octaves, or unisons, is illustrated by (p), (r), (s), and (t). The direct unison is a double fault for it inevitably produces overlapping, a situation in which a lower voice is on a higher pitch than the upper voice’s immediately preceding note, or vice versa, as shown in (t).


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EXAMPLE 4-5

Overlapping is shown below in other contexts. Though one occasionally comes across it in music of the great composers, it is considered somewhat ungainly and difficult to sing. Overlapping should be avoided when possible, but tolerated if by its presence a melody may be improved. However, in species counterpoint it is forbidden (Example 4-6). EXAMPLE 4-6

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SELF-TEST 4.2 Here are eight examples of three motions each. Identify the two examples that have no errors in them. The others contain at least one error, perhaps more.

There are four more points to be made regarding motion in first-species counterpoint. The first is that the rule against parallel perfect unisons, perfect fifths, and perfect octaves applies to consecutive perfect consonances even when they are approached by contrary motion: if the two voices are sounding a perfect fifth they may not move to a perfect twelfth (a perfect fifth displaced by an octave) even though this would be done by motion in the opposite direction. The same is true of unisons and octaves (Example 4-7). EXAMPLE 4-7

The second point is that there is an exception to the stricture against the direct perfect fifth. A third may move by descending similar motion to a perfect fifth provided the upper note progresses by step. This motion, known as the “horn fifth,” is in imitation of natural brass instruments. Similarly, a sixth may move


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by ascending motion to a perfect fifth with the same provision: the upper note progresses by step. Of the two motions, the descending one is better and more common (Example 4-8). EXAMPLE 4-8

Special note should be taken of the fact that this leniency is given only to the direct perfect fifth, not the direct octave or unison. The third point is that in two-voice species counterpoint, the parts may not cross. At each moment the upper voice must remain literally above the lower voice. In the next chapter we will observe that crossing does sometimes occur between upper voices in a three-part texture, but very rarely does a voice cross below the bass. In two-voice writing, of course, any crossing is necessarily with the bass (i.e., the lower voice). Such strictness limits available choices and thus helps the student’s development. Be careful to distinguish between crossing and overlapping. Voices are crossed when the lower voice moves above the upper voice so that at a given moment the lower voice is actually higher. Voices are overlapped when the lower voice moves to a pitch higher than the previous note of the upper voice. In overlapping there is no moment when the lower voice is literally higher than the upper voice.

Finally, to ensure independent melodic curves between the voices, no more than three parallels (thirds or sixths) may occur in succession. The rules regarding first-species counterpoint in two parts may be summarized as follows: 1. Only consonances may occur as harmonic intervals: perfect fifths, perfect octaves, major and minor thirds and sixths. The perfect unison may appear as the first or last interval only. All dissonances and the perfect fourth are excluded. 2. Oblique motion is always good. With the exception of consecutive perfect fifths and perfect octaves, contrary motion is also always good. 3. Parallel (consecutive) perfect fifths, perfect octaves, and perfect unisons are forbidden. 4. Similar motion into a perfect interval is forbidden except in the case of the “horn fifth” (descending from a third to a perfect fifth or, less often, ascending from a sixth to a perfect fifth with upper voice moving by step). 5. Overlapping is to be avoided—that is, do not allow the pitch of a lower voice to be higher than the immediately preceding pitch of the upper voice, or vice versa. 6. Crossing of voices is not allowed. 7. We are limited to three parallel thirds or three parallel sixths in succession. 8. For the most part the two voices should remain within the space of an octave of each other, never more than a twelfth.

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9. Each voice cadences by step on the final. Thus, the last two dyads form either a minor third moving to a perfect unison, or a major sixth moving out to a perfect octave. 10. Avoid cross-relations; that is, a note in one voice should not be immediately preceded or followed in another voice by an altered version of the same note. For example, if the upper voice has a C-natural, the lower voice should not follow it with a C#.

4.3 Adding a Counterpoint Against a C.F. Two-voice counterpoint consists of two melodies that ideally are of equal melodic interest but which, while producing good harmony, are opposed to each other in some way. In later chapters we will see that this opposition is generally a matter of rhythm. For the time being, writing only in whole notes, the opposition is expressed mainly in ensuring that the two focal points do not replicate each other. In other words, the climaxes should appear at different times or be of differing types, e.g., a zenith vs. a nadir. Before beginning to write a counterpoint against a given C.F., then, it is best to sing the C.F. several times, noting its mode and the melodic curve displayed. Since the perfect fourth is not an available harmonic interval, the opening must produce a unison, a perfect fifth, or perfect octave. Each voice must begin on either scale-degree ^1 or ^5. This means, then, that if the C.F. is the upper voice, the counterpoint must also begin on ^1 in order to form a consonant interval. After writing the first note, skip to the end and write the last three notes of the cadence. Then plot a curve that will get you from the first note to the beginning of the cadence and that will provide a curve differing from that of the C.F. (See Example 4-9.) EXAMPLE 4-9

We might choose a G5 for the zenith, producing an octave with the C.F. at note 6. In that case we can easily lead up to the zenith as shown in Example 4-10. We now have a satisfactory counterpoint to the C.F., since the curve of each line is independent of the other and only approved harmonic intervals occur. Moreover, as a melody the counterpoint is as acceptable as the C.F. EXAMPLE 4-10


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On the other hand, suppose we had chosen to make a zenith on G5 at note 4 rather than note 6. We would have had difficulty choosing suitable fifth, sixth, and seventh notes (Example 4-11). EXAMPLE 4-11

The lesson to be learned, then, is this: when working with a C.F. one cannot be rigid about one’s original choice of the curve for the counterpoint. If we had been determined to use note 4 as our zenith and had a G5 in mind for this zenith, we would have had great difficulty in writing a really good counterpoint against it. The student must always be flexible about original decisions, setting them down tentatively only. Still, it is important to plot the curve. Long-range planning is essential if melodies are to be musically coherent, but one’s mind must be constantly open to possible alterations. Counterpoint beneath the C.F. must begin on scale-degree ^1, since ^5 would form a perfect fourth with the C.F. However, if the counterpoint begins after a rest, it might well start on ^5.

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EXAMPLE 4-12

Sing-play-sing all the melodies of Example 4-12. Since the voices may not overlap or cross, the range of the alto C.F. effectively prevents a high zenith in the tenor. Therefore counterpoint (a) uses a nadir for a focal point (note 6). In (b) the tenor’s fifth note is also a nadir, but the whole melody is constrained to lie within the very narrow range of a perfect fourth and the end is static. Putting the counterpoint into a bass voice gives more room to maneuver, as in (c) and (d).

SELF-TEST 4.3 Point out all errors in the following:


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Melodic Principle

When two melodic lines sound together in first-species counterpoint, their curves are opposed to each other. Harmonic Principle

When two melodic lines sound together in first-species counterpoint, they produce a series of consonant intervals that maximize the full sound of the imperfect consonances while stressing, at the beginning and end, the stability of the perfect consonances. Practice

Phrases in first species, two voices, begin with a perfect unison, perfect fifth, or perfect octave and end with a perfect unison or perfect octave. When perfect consonances within the phrase are approached by similar or parallel motion, they do not draw undue attention to themselves. Since descending motion, seeming more relaxed, tends to call less attention to itself than does ascending motion, the exceptional case of “horn fifths” (a perfect fifth approached by similar motion) is better by descent than by ascent.

EXERCISE 4.1 Write counterpoints as indicated against the given C.F. Begin on scale-degree ^ 1 or ^ 5 and cadence with (#)^ 7–^ 1. Fux

Fux

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Plainsong

EXERCISE 4.2 Write one counterpoint above the following C.F. and another below it. The C.F. is to sound with one or the other of the parts you write—not all three together (notice the brackets). Morley


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EXERCISE 4.3 Write three examples of first-species counterpoint in two voices without a C.F. Each example should be in a different mode and at least ten notes in length. One example should be in Phrygian, either original or transposed. Begin with a note or two in each voice, then write the cadence in both voices. After this, plot the curves each voice will follow, then fill in the remaining notes.

Chapter 5

First Species in Three Voices

5.1 Harmonic Intervals A brief illustration of three-voice counterpoint in first species is given as Example 5-1, the numbers representing harmonic intervals. The analysis is done in four steps. 1. Identify the interval between the two upper voices and write it above the middle voice. 2. If the upper voices are crossed, indicate this crossing by an X.1 3. Identify the intervals above the lowest voice and write them below that voice, placing the larger number above the smaller (regardless of which voice it refers to). 4. Reduce compound intervals to simple ones by subtracting an octave. EXAMPLE 5-1

Example 5-2 shows three illustrations of first species in three voices using a C.F. These are taken from Fux’s Gradus ad Parnassum. The C.F. is placed first in the soprano, then in the alto, and finally in the bass. Analyze these for harmonic intervals in the manner of Example 5-1. DO NOT READ FURTHER UNTIL YOU HAVE DONE THIS.


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EXAMPLE 5-2

5.2 Characteristics of First Species in Three Voices You probably noticed some or all of the following observations regarding three-voice counterpoint in first species.

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Vertical Sonorities

A. Vertical sonorities are of two main types: 1. The full chord—three different pitch classes produce the 53 or the 63, that is, a triad in root position or in first inversion. 2. Two different pitch classes are sounded, one voice doubling another at the unison or the octave; various combinations such as 85, 83, 55, 86, etc., are produced. In addition, it is allowed for the initial or the final sonority to have only one pitch class, tripled (see Example 5-2(a), note 11). B. The rule against writing a unison within a phrase does not hold for three-voice counterpoint since there is now ample opportunity for fuller sonority. But all three voices must not sound the same pitch class except as the final sonority or the first sonority of a phrase. C. You may have noticed that none of the illustrations in Example 5-2 begins or ends with a full chord (53 or 63). This result is inevitable. Since each voice begins on ^1 or ^5 of the mode, the initial sonority cannot have more than two pitch classes. (Remember, the lowest voice, unless it begins with a rest, must begin on scale-degree ^1.) The goal of the cadence, the final sonority, must be led into by stepwise motion in two of the voices: (#)^7–^1 and ^2–^1. The remaining voice may sound a major third above the final, the perfect fifth above the final, or the final itself. D. The penultimate chord is always a full triad. When the two stepwise motions into the final are both in the upper voices, as in Example 5-2(a), the lowest voice will be on scale-degree ^5, producing a 53 (the equivalent of a root-position dominant triad, V, in tonal music). When the leading tone is in the lowest voice, as in Example 5-2(b), the third voice will again be on scale-degree ^5, producing a 63 (labeled as V6 in tonal music). When scale-degree ^2 is in the lowest voice the third voice must not sound the ^5. If it did, there would be an incorrect perfect fourth with the bass, a 64 chord. Therefore, in this case the third voice sounds the fourth degree of the scale, producing a 63 chord (labeled as viiº6 in tonal music) as in Example 5-2(c).2 In short, the penultimate chord will be either a major triad in root position or a major or diminished triad in first inversion.3 It must not be a diminished triad in root position. These chords are produced automatically by following the rule of stepwise motion into the final through the leading tone in one voice and scale-degree ^2 in the other, along with the remaining voice sounding either the fifth or the fourth degree of the scale. Melodic Curve

A. The bass line of the first illustration, Example 5-2(a), tends to lose its melodic quality toward the end. That is, the last four notes, moving by leaps of the perfect fourth and perfect fifth, are there more for the purpose of producing desirable harmony than for the elegance of their melodic curve. (This is also typical of bass lines in tonal music that lead to a root-position V chord in the cadence.) Notice that this does not occur in the other two illustrations, where the bass line leads by step into the final. B. The focal points of each of the voices must be in different places or at least be of different types. Motions

A. The rule against parallel fifths applies to parallel perfect fifths but not to unequal fifths. In Example 5-2(c) the dyads above notes 9 and 10 move from a perfect fifth to a diminished fifth. This is perfectly correct, as is the reverse—a diminished fifth to a perfect fifth—although the latter is much less


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common. Naturally, unequal fifths occur in upper voices only, since one may not write a diminished fifth with the bass. Parallel perfect fourths between upper voices, as occur at notes 5 and 6 of Example 5-2(a), are correct and are quite common. B. In Example 5-2(a), the first dyad in the upper voices, a perfect fourth, moves in an ascending direction to a perfect fifth. This is not in accordance with the rule learned in the last chapter regarding similar motion into a perfect fifth. The reason is that the restriction against similar motion into a perfect interval holds for outer voices only. In two-part counterpoint both voices are, of course, outer voices. But in this case, one is an inner voice. The stricture against similar motion into a unison still holds since overlapping would inevitably occur.

C. In a cadence hidden perfect octaves may occur in outer voices when scale-degree ^2 in the top voice and scale-degree ^5 in the bass both move down to ^1.

Spacing

A. For the best sound in performance there should be no more than an octave between the two upper voices except perhaps for one or two notes at a time. See the second note of Example 5-2(c). There should be no more than a twelfth between the lowest two voices. In Example 5-2 the largest interval with the bass is a tenth. Ordinarily there should be no problem about spacing if you are careful to write in the proper range for each voice and choose the same or adjacent voice types: soprano, alto, and tenor, for instance, or two sopranos and alto. Soprano, alto, and bass is not a difficult combination to write for; nor is soprano, tenor, and bass. But do not call for two sopranos and bass, or for two basses and soprano. B. Voices may cross provided they do not cross below the bass (i.e., whichever voice type is acting as the bass in the phrase).

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SELF-TEST 5.1 1. For ease of reading, the first two phrases are notated on two staves. Locate errors or questionable places in all three.

2. Fill in the notes missing from these cadences.


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Harmonic Principle

When three melodic lines sound together in first-species counterpoint they produce consonant sonorities which should contain the full sound of thirds and sixths whenever possible. Practice

Full consonant triads occur as often as possible, and always as the penultimate chord of a phrase. These are major triads in root position or major or diminished triads in first inversion. When a vertical sonority consists only of two pitch classes, one doubled, it is best to include an imperfect consonance. Thus, 83, 86, 33, etc., are preferable, except as the initial or final sonority of a phrase. But since a third is preferable to a sixth, 83 is preferable to 86, and 33 is preferable to 66. A tripled pitch class may occur only as the initial or final sonority of a phrase. In three-voice counterpoint, first species, the melodic principle and practice remain the same as in two voices except that sometimes the bass voice, in seeking harmonic support for the two upper voices, tends to become unmelodic as it nears the cadence. EXERCISE 5.1 Write first-species counterpoint in three voices as indicated. Decide first upon the last three notes in each voice. Then plot tentative curves for the voices and fill in the remaining notes. The last two are to be done without a C.F. Notice key signatures in the third exercise. Which mode has the C.F. become by this change?

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Chapter 6

Counterpoint During the Fourteenth Century

6.1 Fourteenth-Century Textures and Rhythms The rondeau by Adam de la Halle given in Example 3-9 has a simpler texture than most music of its time. As we get into fourteenth-century music we find much that is quite elaborate. The composition of music with complicated textures and rhythms freed from the constraints of the rhythmic modes was made possible by advances in notation. About 1325 Philippe de Vitry dealt with these notational innovations in a treatise entitled Ars Nova (“The New Art”) and this term has come to be used in reference to the entire fourteenth century. Guillaume de Machaut was both the chief composer and the chief poet of fourteenth-century France. He composed monophonic pieces as well as works for two, three, and four voices. Example 6-1 is a rather elaborate rondeau for a solo voice and three undesignated instruments. Notice that the cantus’s treble clef has an “8” beneath it, indicating that the vocal line should sound an octave lower. Thus all four parts are placed quite close together with a good deal of crossing. Nevertheless, you should be able to play the triplum, tenor, and contratenor on the piano while singing, or listening to a friend sing, the vocal line. It is important not merely to listen to recordings of the music we are studying but, as much as possible, to perform it yourself. If the music is in your ear, that is to say in your mind, your analysis will be all the better.


EXAMPLE 6-1 Rondeau: Rose, lis, printemps, verdure Guillaume de Machaut

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* Ms: B-natural


* * Ms: Eb


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Rose, lily, spring, verdure, flower, balm, and sweetest fragrance, Lovely one, you outdo them in sweetness. And all the gifts of nature are yours, so I adore you: Rose, lily, spring, verdure, flower, balm, and sweetest fragrance, And if all creatures were to exceed your worth Still would I say, and on my honor: Rose, lily, spring, verdure, flower, balm, and sweetest fragrance, Lovely one, you outdo them in sweetness.

First play each line of Example 6-1 by itself, noting its range, its modal characteristics (if any), cadences, and whether there is a motivic organization to the line. Then play the lines together, noticing harmonic aspects of the cadences and consonance/dissonance treatment. After you have done this, compare your observations with the following: 1. The ranges of the triplum and cantus are the same, as are those of the tenor and contratenor. The former are plagal, the latter authentic (Example 6-2). Considering the overall piece, the Ionian mode is represented by the stressed notes within these ranges with accidentals obscuring the mode as noted in Item 2 below. EXAMPLE 6-2

2. The opening of the piece (mm. 1–11) is clearly Ionian, cadencing in m. 10 with a double leading-tone cadence on the final, C. The next phrase (mm. 12–18) introduces Ebs and Bbs, eliminating the Ionian quality and substituting the feel of the Aeolian mode transposed to G (that is, G natural minor). Measure 19 begins again as if in Ionian mode, but quickly reverts to the Bb and Bb, ending with a kind of Phrygian cadence on D, based on mm. 16–17. Part A of the rondeau, then, has an “open” ending, like a gigantic expansion of the idea of the antecedent in the estampie (Example 3-8). Part B takes up where Part A left off, but moves quickly to a double leading-tone cadence on the pitch-class C (m. 30), similar to the cadence in m. 10. The last phrase re-introduces the flats, and, following the motivic structure of mm. 20–25 rather closely, manages to alter the ending so as to cadence on the final C with another double leading-tone cadence. Thus Part B “closes” at m. 30 and this close is reiterated at mm. 36–37. A summary outline of the overall harmonic organization would look something like Example 6-3. Thus, the modal qualities are by no means stressed in details. To the extent that any modal aspects are at all prominent, however, they are precisely the two modes not theoretically recognized by medieval writers, Ionian and Aeolian.

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EXAMPLE 6-3

3. Parallel unisons, fifths, and octaves continue to appear frequently. There seems to be no feeling against the doubling of the leading tone, which itself causes parallelism in most cases. 4. The first beat of the measure is generally consonant, but these consonances now frequently include the third or sixth above the lowest-sounding note. Almost half of the first beats of a measure include at least one imperfect consonance. Measure 9 begins with a perfect fourth between the cantus and tenor, the only time the fourth has a prominent position in this piece. Measure 24 begins with a dissonance and, according to the manuscript, m. 27 does too. But the latter does not have the logic of that in m. 24, and it seems likely that Machaut must have intended the first note of m. 27 to be an A3, as given in our version. 5. Types of dissonance are limited to notes of adjacency and to pitch reiteration: that is, every dissonance is either a suspension, an anticipation, or is prepared and/or resolved by step. There appear to be no special rules regarding particular placement of the dissonances within the measure other than, as previously mentioned, the general avoidance of dissonance on the first beat of a measure.

6.2 Canon and Hocket Fourteenth-century composers produced some music in which canon plays a significant role. Canon occurs when one voice is totally derived from another voice by some kind of rule (the word canon means “law” or “rule”). The rule should indicate to the performer precisely what must be done to derive another part from the part given: therefore it should indicate what pitch level one is to begin on and when to begin on it, as well as whether the melody is to be sung in the same way as by the original voice or to be altered in some way. The simplest canons are rounds, in which all voices enter with the same melody at the same pitch level and after the same time interval. One fourteenth-century canon seems to have started as a kind of parody on the words of the thirteenthcentury motet. In the motet one voice had a text beginning, “I have been seized by the ability to sing of her whom I have loved so much . . . ” The canon, which is a three-part round, begins, “I have been seized by the ability to sing like the cuckoo.”1 The latter part of the round includes many rests that separate the cries of the cuckoo. When sung as a round these rests are filled in by similar cuckoo cries from one of


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the other voices, producing the hocket effect, a device characterized by short groups of notes separated by rests that are filled in by short groups of notes in another voice. Example 6-4 is an excerpt from the round Talens m’est pris. EXAMPLE 6-4

This particular round, presented as Example 6-5, was known all over Europe.2 At first sight this seems to be a simple two-part canon, the rule being that the second voice, the comes (“follower”), shall imitate the first voice, the dux (“leader”), after a time interval of seven measures. When the dux is finished, at m. 42, the comes has reached its thirty-fifth measure. These notes make a suitable cadence, so the piece is over. But with closer acquaintance the listener realizes that mm. 22–42 of the dux are in fact a retrograde of both the pitches and the rhythm of mm. 1–22. Inevitably, the same is true of the comes, from m. 29 on. A canon by retrograde motion is known as a canon cancrizans (“crab canon”). This canon, as we have seen, qualifies as an ordinary canon by direct imitation and also as a canon by retrograde motion (Example 6-5). EXAMPLE 6-5

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There is a famous three-part rondeau by Guillaume de Machaut to the words “Ma fin est mon commencement et mon commencement ma fin” (“My end is my beginning and my beginning my end”). Not surprisingly he sets this in such a way as to make maximum use of retrograde motion. It can best be described as a musical palindrome, since Part B of the rondeau is an exact reversal of Part A. The two upper parts are interchanged (Stimmtausch) for the reversed playing, while the contratenor reverses itself. Example 6-6 is the end of Part A and the beginning of B.


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EXAMPLE 6-6

While not ceasing to be a palindrome, Ma fin est mon commencement is also a canon, since the three voices of Part B can all be derived by a rule from Part A. As a matter of fact, in the manuscript Machaut does not write out the whole piece at all. There is one long line covering both A and B. This is to be read straight through by the instrumentalist playing the duplum. The tenor who sings the words simply sings this line backwards. This is indicated in the manuscript by placing the words in reverse order. The contratenor has a part only half as long, to be played forward, then backwards. The rule, then, is this: Tenor sings duplum in retrograde; contratenor repeats his part in retrograde. This shows that all canons are not necessarily a matter of one voice imitating another in the sense of leader and follower. A canon is simply a rule by which a performer’s part can be derived from music that has been notated in an obscure way. Returning to the hocket present in the round Talent m’est pris (Example 6-4), it should be mentioned that the hocket technique had been in use since the twelfth century. It even appeared in church music, though not without complaint from some scandalized churchgoers. An English writer of the twelfth century produced the following diatribe: Sometimes thou mayst see a man with an open mouth, not to sing, but as it were to breathe out his last gasp, by shutting in his breath, and by a certain ridiculous interception of his voice to threaten silence, and now again to imitate the agonies of a dying man, or the ecstasies of such as suffer.3 In our Examples 6-4 and 6-5 the hocket is appropriate to the words—a descriptive device representing cuckoo calls. Similarly, Example 6-7 shows a segment of hocket from a fourteenth-century French threevoice canon having to do with falconry. The hocket is a bit of tone painting representative of the excited cries of the falconers. It is not insignificant that the canons of Examples 6-4, 6-5, and 6-7 have words dealing with cuckoos and falcons. During the fourteenth century there was a genre of composition called the chace in France (in Italy the caccia), which set poems dealing with outdoor life to music as canons. Despite the name, Se je chant’ mains seems to be the only French chace that actually deals with hunting as a theme. Many chaces and caccie, while maintaining a three-voice texture, consisted of a two-voice canon over a slower-moving free tenor.

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EXAMPLE 6-7 Chace “Se je chant’ mains” Anonymous, 14th c.

Ho, hou, houp! Hou, It’s on the wrong course, God willing! Houp, ha-hau, hou . . . pick it up! Ha-hau ha-ha . . . it’s dead—now let’s feed our falcons.

6.3 Cadence Types Study the cadences in Example 6-8, observing how each voice approaches its final note and the harmonic intervals produced by these voices. EXAMPLE 6-8 Phrygian type:


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Authentic type:

The two cadential types shown are not limited to the fourteenth century, nor was the fourteenth century limited to those two types. Nevertheless, these are so much more prevalent in the Ars Nova (fourteenth century) than others that they must be considered standard cadences for that era. The Phrygian can appear on other cadential notes than E: by using Bb it can be transposed to A; with Bb and Eb it can cadence on D, as we saw in Example 6-1. Similarly, the authentic type can cadence on any pitch class except E or B by the addition, where necessary, of appropriate sharps. You probably noticed that the three-voice “authentic type” cadences shown in Example 6-8(d) invariably move from scale-degree ^2 to ^1 in the lowest voice. Other arrangements are to be found now and then— occasionally there is even a ^5 in the lowest voice—but the cadences as given are the most common. The last cadence in Example 6-8(d), marked “under-third,” jumps up a third to reach the final by inserting the sixth degree of the scale between ^7 and ^1. The common nickname for this cadence, the “Landini sixth,” is quite inappropriate: although it is characteristic of Landini’s music, one comes across it often enough in the music of other composers, including earlier than Landini. Our Example 3-7, for instance, ends with such a cadence, and dates from at least one hundred years before Landini’s birth. The only standard cadence shown with inevitable parallel octaves is the Phrygian type without the seventh degree, as shown in Example 6-8(a). In four voices, however, the others are very likely to include parallel octaves by a doubling of the ^7–^1 progression in the fourth voice. Parallel fifths will occur even in three voices with the double leading-tone cadence whenever the #^4–^5 is above the ^7–^1. In Example 6-1, for instance, this happens with all the double leading-tone cadences.

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6.4 Fauxbourdon During the Middle Ages, types of organum other than that practiced on the continent were being sung in Great Britain, especially in Wales and in the north. The most remarkable feature of much two-part English music of the thirteenth to the fifteenth centuries is frequent successions of parallel imperfect consonances, particularly parallel thirds. In three-part music, as early as the end of the thirteenth century, we find extended successions of 63 chords. Example 6-9 is a typical segment from an anonymous setting of the Te Deum found in a late thirteenth-century manuscript. The plainsong melody is in the tenor, the lowest voice.4 EXAMPLE 6-9

Music consisting of many 63 chords in succession interspersed with an occasional 85 is popularly called fauxbourdon (the original and precise meaning of the term is not clear). Because of the prevalence of imperfect consonances in such passages and the closeness of the voices to each other, the sound of this music is fuller and richer than the typical sonorities of Machaut, Landini, and their predecessors on the continent.

6.5 The Style of John Dunstable Some passages in the music of the English composer John Dunstable (c. 1385–1453) have fauxbourdon characteristics. Example 6-10 is the opening of one of his better-known compositions, the antiphon Quam pulchra es for three voices.5 This work bears some resemblance to the conductus in that all parts are freely composed rather than incorporating a plainsong C.F., and much of it moves in approximate note-againstnote texture.


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EXAMPLE 6-10

How lovely and graceful you are, dearest, for pleasures; Your stature is as a palm and your breasts like its clusters. (Song of Solomon 7: 6–7)

Measures 12–14 are almost completely pure fauxbourdon, although the rest of the piece has no more than two or three 63s in a row. The quoted section of the piece includes three cadences: mm. 8–9 on C, mm. 14–15 on F, mm. 17–18 on C. The second one, on F, is our familiar double leading-tone cadence. In the other two, scale-degree ^4 is not raised to #^4 to act as a leading tone to ^5. The result is a more euphonious sound, the same as that which later came to be called the “leading-tone cadence” (viiº6–I). Notice the sixteenth-note passing tone that fills in after the under-third in m. 8. This ornamentation appears in several cadences throughout this piece. The tonal organization of Quam pulchra es is very much like Guillaume de Machaut’s rondeaux Rose, lis, printemps, verdure and Ma fin est mon commencement in broad outline. Though not having the repetition scheme of the rondeau, Quam pulchra es is in two parts. Part A (mm. 1–30) establishes the Ionian mode very clearly in its first phrase (mm. 1–9), then moves on to close with a cadence on D (mm. 28–29, not shown here). Part B (mm. 31–58) begins where A left off and returns to cadence on C, Ionian mode. The overall tonal motion of all three pieces may be summarized as in Example 6-11.

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EXAMPLE 6-11

Dunstable’s rhythms are somewhat more regular and his harmonies more consonant than those of French and Italian composers who were writing at the end of the 1300s and the beginning of the 1400s. His melodies may seem “smoother” than, say, Machaut’s, but this description applies only to the rhythms of the melodies, not to the melodic intervals employed. If anything, Dunstable’s melodic intervals are somewhat less stepwise than Machaut’s, stressing small jumps of thirds as they do. We are speaking here of the treble voice. The tenor (downward stems in Example 6-10) and contratenor (upward stems) are often quite jagged, particularly the contratenor. In late medieval music, the real purpose of the contratenor was not so much linear as it was harmonic. It served to enrich the sonorities implied by the two-voice framework of tenor and treble. Looking back at the contratenor of Example 6-1 (pages 55–57), for instance, we see the awkward leap from m. 19 to m. 20. Still, this kind of thing occurs only once in Machaut’s piece, whereas in Quam pulchra es the contratenor often moves in very awkward lines. Example 6-12 is another piece by Dunstable, a textless motet apparently intended for instrumental performance. The manuscript, in the British Library, gives only the following for the tenor:

with a rhyming Latin rubric: A dorio tenor hic ascendens esse videtur Quater per genera tetrachordum refitetur. (Starting from Dorian, this tenor seems to be ascending, Let it be repeated four times in the [four] species of tetrachords.) In other words, the tenor is a kind of abstract representation of the tetrachord consisting of scale-degrees ^ ^ ^ 2– ^ 1. ^ This tetrachord will sound first in Dorian, then Phrygian, Lydian, and Mixolydian. The treble 1–4–3– voice and contratenor are written out in full, the treble being a melody whose phrase structure divides the work into two halves. Between the second and third statement of the tenor’s tetrachord the treble voice rests. Otherwise its phrases overlap the beginnings and endings of the tenor’s reiterated statements. The suppleness of this treble melody is quite engaging. Examine it above all for its contour (Example 6-12).


EXAMPLE 6-12 Textless motet John Dunstable

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Except for the under-third (“Landini sixth”) the final cadence looks and sounds to modern ears like a V–I authentic cadence. It is not, however, essentially different from the standard authentic cadences shown in Example 6-8 (pages 62–63). The treble and tenor move outward by step to the octave. The contratenor adds a consonant pitch to the sonority. Usually this third voice moves from scale-degree ^4 or #^4 to ^5. In ^ The structure of the cadence is in the other two voices, a major sixth moving this case it moves from 5^ to 1. outward to an octave.

SELF-TEST 6.1 1. Stimmtausch / caccia / round is a canon in which all voices enter with the same melody at the same pitch after the same time interval. 2. Most chaces or caccie are compositions with a text having to do with the sacred liturgy / courtly love / outdoor life. 3. A canon cancrizans is built on the principle of recurrence of a refrain / retrograde motion / contrary motion. 4. When one voice sings a single note or short groups of notes with interspersed rests that are filled up by another voice, we speak of voice interchange / cancrizans / hocket. 5. It is true / false that in both types of cadence—Phrygian or Authentic—the two-voice framework of the cadence consists of a major sixth moving outward to an octave. 6. Fauxbourdon is a term that may indicate passages moving in parallel fourths / 6s / octaves. 3 7. The progression symbolized today by “viiº6–I” is never / always / sometimes found in late medieval music.

EXERCISE 6.1 Without looking back at Example 6-8, write typical fourteenth-century Phrygian cadences on A and D in three voices. Write authentic cadences in fourteenth-century style ending on G and on C. Use the under-third cadence for one of these.


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EXERCISE 6.2 Study the fourteenth-century ballata Gram piant’ agli ochi by Francesco Landini (pages 70–72). Draw conclusions as to: 1. 2. 3. 4. 5. 6. 7.

its texture (i.e., the relationship between the voices) its modal qualities, if any the advantage of its partial signature its cadences (where do they occur and what types are they?) its consonance/dissonance treatment the melodic intervals used in the voice part as contrasted with those used in the instrumental parts occurrences of parallel perfect octaves, perfect fifths, or perfect unisons.

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Ballata: Gram piant agli’ ochi Francesco Landini


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Tears pour from my eyes, heavy grief is in my heart; my soul is overwhelmed and I die. Because of the bitter, harsh separation, I call on death who does not want to hear me; life goes on against my will, and I must suffer a thousand deaths; but although I live I never want to follow, if you do not wish it, bright star and sweet love.

EXERCISE 6.3 Analyze the accompanied song O rosa bella (below), which stems from the early fifteenth century. It has been attributed both to John Dunstable and to John Bedyngham. In addition to the questions raised for Exercise 6.2, you should consider the overall form and tonal organization of the work as well as its motivic aspects. Begin by playing the tenor and cantus alone. O rosa bella


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O beautiful rose, O my sweet soul, do not let me die in paying court to thee. Alas, alas, must I end in sorrow though serving well and loving loyally. O God of love, who punishes me with this love, I’m forever dying because of that faithless woman. Help me now in my suffering, heart of my body, don’t let me die!

Chapter 7

Second Species in Two Voices

In second species two notes are written against one. In the traditional notation of species counterpoint this means two half-notes against one whole-note. Since repeated half-notes are essentially the same as a whole-note, there must be no half-note repeats. At this point it is convenient to begin using barlines and setting a 2/2 meter. This way it is clear that the first half-note is stressed, acting as a downbeat. The second is unstressed, an upbeat. In Gradus ad Parnassum Fux presents the teacher Aloysius as explaining to Joseph that the stressed half-note occurring on beat 1 of each measure must form a consonance with the C.F. whole-note. The unstressed half-note on beat two may be either a consonance or a dissonance, but if it is a dissonance it must be a passing tone (p.t.). A passing tone fills in the gap of a third by stepwise motion. That is, it moves by step from a consonance and continues in the same direction to another consonance. It does not matter whether the passing tone is consonant or dissonant. Repeated notes are excluded from the voice with halfnotes (Example 7-1). EXAMPLE 7-1

After this brief explanation Joseph is told to write a counterpoint against a given C.F., which he does with this result (Example 7-2). EXAMPLE 7-2

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Sing-play-sing Example 7-2, then between the staves write in the number of each harmonic interval. DO NOT READ FURTHER UNTIL YOU HAVE DONE THIS. You will have noticed that the downbeats of mm. 8, 9, and 10 all begin with the perfect fifth. Aloysius explains that the ear will perceive a succession of parallel perfect fifths here (see Example 7-3). The same would, of course, be true in the case of octaves. EXAMPLE 7-3

Joseph then corrects the passage as in Example 7-4, and this version is acceptable to Aloysius. EXAMPLE 7-4

Measures 8 and 9 have been altered to produce sixths rather than fifths on the downbeats. Although neither Joseph nor Aloysius comments further on the changes made, it is readily noticeable that the upper line has been much improved beginning on the second beat of m. 5. The first version was without a focal point of any kind. The second version has a build-up from m. 5 to a zenith in m. 8. In second species the voice in half-notes begins on the first beat or after a half-note rest. It must start with scale-degree ^1 or ^5. Here is an example with half-notes in the lower voice (Example 7-5). EXAMPLE 7-5

Sing-play-sing Example 7-5, then write in the harmonic interval between the staves. You probably noticed immediately that the half-note motion ceases with the last two measures. When the voice with half-notes is the lower voice, it is often difficult to achieve a cadence without moving into first species at the end (see Example 7-6). For this reason, the last two notes in second species may both be whole-notes.


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EXAMPLE 7-6

You may also have noticed that in Example 7-5 there are only two passing tones (m. 4 and m. 6). Although sometimes passing tones are consonant, these are both dissonant. In the case of passing tones, consonance or dissonance is not an issue. What is essential is that they pass by step from one note to a different note. This different note is, then, by necessity a third away. See Example 7-7(a), (b), and (c). Dissonant neighbor notes are incorrect in second species, although consonant ones are acceptable. See Example 7-7 (d) and (e). EXAMPLE 7-7

One final point: on the second half of a measure, a unison is acceptable. Of necessity it will be arrived at by oblique motion, mitigating the effect of the sudden disappearance of a voice. Nor does it produce the quality of a premature cadence (Example 7-8). EXAMPLE 7-8

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SELF-TEST 7.1 1. Name the mode and find the errors.

2. Name the mode and fill in the missing notes.

Principle

In second species, two notes against one serve to increase the rhythmic opposition between the two voices while maintaining a general effect of consonance. Practice

A consonant note may leap to another consonant note and may be metrically either weak or strong. A dissonant note must be metrically weak and it must be a passing tone. The passing note fills in the space of a third, passing from one consonant pitch to another by stepwise motion. Successive strong beat intervals should not be perfect consonances of the same size or the ear will perceive them as undesirable parallels.


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EXERCISE 7.1 Add counterpoint in two-part second species to the following C.F. Write the cadence first—at least the last three or four notes. The staves with overlapping brackets are written that way purely for the sake of convenience. One counterpoint is to be written above the C.F. and another below. The three voices do NOT sound together: this is still two-voice counterpoint. Sing-play-sing everything you write, checking not only for correct harmonic and melodic intervals, but for the elegance of the melodic curve as well. If a passage is difficult to sing, there is probably an error somewhere.

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In addition, write two examples of second species without a C.F. When writing the cadence, remember to approach ^2 by step or by leap of a descending third.

Chapter 8

Second Species in Three Voices

8.1 Intervals and Focal Points Sing-play-sing each voice in Examples 8-1 and 8-2, then play them (or sing them with two friends) simultaneously. Mark the passing tones with a “p.t.” Indicate the intervallic structure of the remaining vertical sonorities as you did for first species in three voices. EXAMPLE 8-1

EXAMPLE 8-2

As in previously discussed species, focal points are either at opposing points in the melodic curves of the different voices, or of differing types. Only consonant sonorities are available, except that half-note passing tones may occur on weak beats.

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8.2 Parallels on Successive Strong Beats It will be noticed that in Example 8-2 at mm. 5–6 the tenor and bass have parallel octaves on successive downbeats. In three voices the rule against parallel perfect fifths and parallel perfect octaves on successive downbeats has traditionally been relaxed providing: (1) the intervening note is a consonance; (2) an inner voice is involved; (3) the voice in half-notes moves in contrary motion to the voices with whole-notes. Example 8-3 illustrates. EXAMPLE 8-3

The reason parallel octaves, fifths, or even unisons are not objectionable under these conditions has to do with the listener’s perceptions. When one hears fifths or octaves on two successive downbeats as parallel fifths or octaves, it is because one is making a mental connection from the beginning of a measure to the beginning of the next. If one voice is an inner voice, the parallels are not so obvious to the ear. Moreover, an intervening consonance enables the listener to perceive beats 1 and 2 of a measure as a single harmony in two positions. The move to the next measure, especially if accomplished with contrary motion, will be heard as a move from beat 2 of one measure to beat 1 of the next measure, and the effect of parallels is dissipated. Should the intervening note be dissonant, however, it will not have the effect of changing the position of the chord, but will merely be a passing tone within a single position and the effect of parallels will remain.

8.3 Cadences With two voices in whole-notes and one in half-notes, it is sometimes difficult to make harmonically effective cadences. It is therefore permissible to move into first species for the last two measures, as occurred in Examples 8-1 and 8-2. Nevertheless, it is possible to produce all the cadences without sacrificing half-note movement. (See Example 8-4.)


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EXAMPLE 8-4

Examine the cadences carefully. Just as in first species, every three-voice cadence includes the standard two-voice cadence. One voice approaches the final via scale-degree ^7 or #^7, that is, stepwise from below. The other approaches the final via scale-degree ^2, stepwise from above. These are the cadential voices. When both are the upper voices, the third voice sounds scale-degree ^5 beneath them. When the cadential voice with scale-degree ^2 is the lowest voice, the third voice must sound scaledegree ^4 above it—otherwise a dissonant six-four chord will result. When the cadential voice with scaledegree 7^ or #7^ is the lowest voice, the third voice must sound scale-degree 5^ above it—otherwise a dissonant diminished fifth with the bass will result.

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SELF-TEST 8.1 1. Which of the following fragments are correct? If incorrect, give the reason. Note: with the exception of (c), these fragments are to be considered as occurring within the phrase. Only (c) represents a cadence.

2. In each of the following cadences, fill in the two missing notes.


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Principle

Second species in three voices follows the same melodic and harmonic principles as first species in three voices and second species in two voices. The only principle unique to this chapter deals with the perception of parallel octaves, unisons, and fifths on successive downbeats. This is: Under certain conditions the effect of parallel perfect consonances can be mitigated. Practice

When two strong beats in succession have a perfect unison, perfect fifth, or perfect octave in the same two voices, the listener will hear objectionable parallels unless 1. one of the voices involved is an inner voice 2. one of the voices moves in an opposite direction to the others, and 3. the half-note on the weak beat is consonant.

EXERCISE 8.1 1. Complete:

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2. Write a passage of second species in three voices without a C.F.

Chapter 9

Counterpoint During the Renaissance

9.1 Introduction There is no clear-cut stylistic division between music of the late Middle Ages and music of the early Renaissance. As with other style periods, the change from one to the next is fraught with currents and cross-currents, and the change from one practice to another is often very gradual. In many ways much of Dunstable’s music is so similar to what we think of as late medieval practice that some scholars consider him to be the last of the great medieval composers. On these grounds he was included in our Chapter 6. In other ways his music shares characteristics traditionally thought to be typical of the early Renaissance, so that he may be placed among the first composers of that era. The song O rosa bella, which you analyzed as part of the exercises at the end of Chapter 6, if not by Dunstable, is at least contemporaneous with him. This piece shares several of the characteristic practices of the first of the Netherlandish composers, comprising the so-called Burgundian School. During the fifteenth century, the duchy of Burgundy was quite large, including eastern France, the Netherlands, and Belgium. The city of Dijon, where the court was located, and the city of Cambrai were among the leading musical centers of Europe. Of the many composers who were either Burgundians themselves or who lived and worked there, the two who stand out the most were Guillaume Dufay (c. 1400–1474) and Gilles Binchois (c. 1400–1460). The greatest composer of the generation after Dufay and Binchois was Johannes Ockeghem (c. 1430–1495), who was born in Hainaut in Flanders. Very well known and admired by his fellow musicians, he worked in various places in what is now Belgium and France. We will study several of his pieces. The generation after Ockeghem was dominated by another Flemish composer, Josquin des Prez (c. 1445–1521), believed by many today to be the greatest composer of the entire Renaissance. As a youth he went to Italy, working as a musician at the cathedral in Milan, later in Rome, Florence, and Modena. There is an undated letter to the Duke of Ferrara from his secretary recommending that the duke hire Heinrich Isaac rather than Josquin. The letter says, in part: [Isaac] is more good-natured and companionable, and he will compose new works more often. It is true that Josquin composes better, but he does it when it suits him and not when one wants him to.1 Nevertheless, Josquin worked in Ferrara in 1499 and again in 1503 and composed a famous mass based on the vowels in the Duke’s name:2

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H E R C U L E S re ut re

D U X ut

F E R R A R I Æ re fa mi re

These syllables, of course, translate to the notes D–C–D–C–D–F–E–D and serve as a cantus firmus for the mass. Later, Josquin also worked for Louis XII of France, and ended his days in Brussels. The late fifteenth century and the first half of the sixteenth century have often been called the Golden Age of music, not only because of the large number of excellent composers and the many first-rate compositions written, but also because of the esteem in which music was held by all educated people. Among the many other composers of the time, we will have occasion in this chapter to consider Pierre de la Rue and the German composer Arnolt Schlick. During the sixteenth century three events occurred in the history of the Church that were very important for music. The first began in 1517 with Martin Luther’s public announcement of his ninety-five theses. The importance for music of the subsequent Protestant Reformation can hardly be overestimated. We will study two settings of Lutheran chorales by Johann Walter (1496–1570) who worked closely with Luther in providing music and liturgy for church services. The second event was effected by Henry VIII of England—the Church of England’s break with Rome in 1534. Thomas Tallis (c. 1505–1585) was perhaps the most important English composer of the midsixteenth century, composing both Latin and English church music of remarkable variety, including the famous Spem in alium for eight five-voice choirs, forty independent parts in all. We shall study one of his small church works in English. The style of sacred music in English was influenced by the fact that composers were urged, in the words of Thomas Cranmer, Archbishop of Canterbury, to write in such a way that the music “would not be full of notes, but, as near as may be, for every syllable a note, so that it may be sung distinctly and devoutly.”3 The third event in the history of the Church was the Council of Trent, which began in 1545 and lasted until 1563. This Council brought about the so-called Counter-Reformation and had much to do with encouraging the style of music best exemplified by the sacred works of Palestrina, Lassus, and Victoria. We shall postpone discussion of this Roman School until subsequent chapters, when we consider the music of Palestrina in some detail and even learn to imitate it.

9.2 Secular Pieces in Three-Part Counterpoint Dufay’s rondeau Je requier a tous amoureux is shown in Example 9-1. Sing-play-sing the tenor line through. Do the same with treble and tenor together, noting the harmonic intervals and cadences. Don’t overlook the partial signature. Then play or sing the contratenor through. Does it have as good a line as the treble and tenor, or does it seem more in the tradition of contratenors of the late Middle Ages, mainly there for harmonic purposes? DO NOT READ ON UNTIL YOU HAVE DONE THIS.


EXAMPLE 9-1 Rondeau: Je requier a tous amoureux Guillaume Dufay

Essential features of the cadences in this piece are summarized in Table 9-1.

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TABLE 9-1 Cadences in Dufay’s Je requier a tous amoureux Scale degree, cadential note

Type of cadence (treble and tenor)

Scale degrees of added notes (contratenor)

Ornamentation

PART A 3–4 8–9

^ F 1, ^ 5, C

Authentic Authentic

^ 5–^ 5 of F ^ 4–^ 5 of C

Under-third Under-third with ^ insertion of 1 between ^ 6 and ^ 7

PART B 13–14

^ 3, A

Phrygian

^ 7–^ 4 of A

18–19

^ F 1,

Authentic

^ 5–^ 5 of F

Under-third with ^ insertion of 1 between ^ 6 and ^ 7 Under-third with ^ insertion of 1 between ^ 6 and ^ 7

Measure

While none of these cadences is entirely new to us, the effect they produce is rather different from typical medieval cadences. There are no double leading-tone cadences, and the Phrygian cadence has been made to sound plagal by the falling perfect fourth in the lowest voice. The cadences of the tonic (mm. 3–4 and 18–19) are similar to the one that ends Dunstable’s O rosa bella. This cadence became so prevalent during the fifteenth century that it is known as the Burgundian cadence. The contratenor’s octave (from a low scale-degree ^5 to a high ^5) causes the sonorities to sound to modern ears like a progression from V to I, both in root position, when the work is played on the piano. But with different timbres one can follow the actual linear movement and hear the tenor/treble’s major sixth moving outward to the octave. The sound of Je requier a tous amoureux is rather modern. It seems like F major, cadencing on the tonic in m. 4 and in the dominant key at m. 9. Measure 14 gives the effect of the submediant (D minor) followed by a close in the tonic. While study of this rondeau may give the impression that tonality was on its way in, such was by no means the case. More than 150 years had yet to elapse before the modal system began to disappear and major-minor tonality became a principle of organization.4 In fact, although pieces in major mode similar to Je requier a tous amoureux appear rather frequently around Dufay’s time, they tended to disappear as time went on, and we find that much of the sixteenth century was devoted to a more strictly modal music. A confusing aspect about modality in medieval and early Renaissance music is that scholars have not been able to find hard-and-fast rules for musica ficta, the unwritten accidentals that contemporaneous performers were trained to put in. Modern editors indicate these accidentals above rather than before the note whenever they think the music should not be purely diatonic. If musica ficta is applied lavishly according to whim, the music’s mode can easily be altered. Though there are certainly a number of instruction books from the late Middle Ages and early Renaissance dealing with the rules of musica ficta, it is still not always possible to know with certainty whether a note should be sung as written or whether it should be raised or lowered a half step. For example, turn back to Example 6-10 (page 65). At m. 14 beat 2, the lowest voice has a flat in front of the B3. This position of the flat indicates it was written by


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the composer himself. On beat 3 the middle voice has a natural in parentheses. This is a cautionary sign necessary because we have written the tenor and contratenor on the same staff. In the original they were written on separate staves and the notation was a plain B3 at that point. We have followed the editor of Musica Britannica, Volume 8 (Bukofzer) in assuming Dunstable intended B-natural on beat 3, producing a double leading-tone cadence. But another editor (Besseler) has inserted a small flat over that B3 in his edition, indicating his belief that a simple leading-tone cadence is called for. Who is right? There seems to be no doubt that the double leading-tone cadence had pretty well died out by the beginning of the sixteenth century, but for fifteenth-century music it is by no means clear when it should be called for. For example, the opening phrase of the rondeau by Dufay in Example 9-2 is supplied with an editorial B-natural causing a double leading-tone cadence. To some it might seem more in keeping with Dufay’s secular style to retain the Bb for a simple leading-tone cadence. EXAMPLE 9-2 Ce moys de may Guillaume Dufay

Dufay’s ballade Se la face ay pale (“If my face is pallid”), shown in Example 9-3, was extremely popular during the fifteenth century. Apparently he intended it for two singers and one instrumentalist, though it can be performed with two instrumental parts and one singer (the tenor). Play or sing through each part separately before attempting them together. DO NOT READ ON UNTIL YOU HAVE DONE THIS. EXAMPLE 9-3 Chanson: Se la face ay pale Guillaume Dufay

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If my face is pallid, the cause is love. It is the chief [cause], and to love is so bitter That I could drown myself in the sea. As the fair one whom I serve well knows, I can know no joy, nor live without her.

There are several noteworthy features about this piece. Tonality and Cadences

The piece is in Ionian mode (C major), but it seems less “modern” than Je requier (Example 9-1) because the clear-cut internal cadences are, like the final cadence, on C rather than on the dominant or subdominant. Internal cadences occur at m. 10 and m. 25. The first of these is an authentic cadence with the under-third. The second is not a standard cadence. Although the two upper voices move stepwise into the tonic, as is normal, the bass moves from ^4 down to ^1 rather than the usual ^5 down to ^1. There is also an unusual cadence at mm. 17–18. If Dufay himself had not written the accidentals Bb and C# in the lower voices of m. 17, one would assume a leading-tone or double leading-tone cadence on G. But the Bb accidental makes an F# in the superius unlikely. The result is a cadence in which the cadential voices— superius and tenor—do not form a major sixth before moving into the octave. Instead they form a minor sixth (A3 and F4), ornamented with an under-third, while the contratenor moves from #^4 to ^5. Melodic Intervals

At mm. 14–15 Dufay has written an Eb4 in the contratenor. With the B-natural on the last beat of m. 14 and the presumable Eb4 in m. 15, a diminished fourth is outlined, redolent of the harmonic minor scale. Although this interval was not infrequently used by some sixteenth-century composers, for Dufay, writing in the fifteenth century, it was quite unusual. Perhaps there should be an editorial Bb on beat 3 of m. 14. This would also eliminate the questionable diminished fifth between outer voices, but, at least to modern ears, the B-natural sounds better. Postlude

The textless passage at the end functions as a postlude. In the past, scholars have believed textless passages to be intended for instruments alone, but the current prevailing belief is that these were vocalized. It is possible, even likely, that instruments played along with the singers all the way through.

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Function of Contratenor

The contratenor of Se la face ay pale is, in spite of its wide range, more linearly conceived than the pieces we have considered so far. It even participates rhythmically in the piece, filling in barren spots (mm. 8 and 18) and providing motion, especially in the final textless postlude. Imitation

So far, except for canons and O rosa bella, we have seen only a very sparse use of imitation. Se la face ay pale, on the other hand, includes several small “points of imitation,” conspicuous at m. 13 and at mm. 15–16 between superius and tenor, and at mm. 25–26 in all three voices. Imitation is somewhat free but still noticeable at mm. 21–22 between superius and tenor. It is important to take note of the fact that when a texted part is imitated by another texted part, the words as well as the pitches and rhythm are kept intact as part of the imitating motive. Fauxbourdon

The piece includes a short passage of fauxbourdon in mm. 16–17. Here the middle voice is lowest and, by eliminating the retardation, we have:

Dufay sometimes wrote extended passages of fauxbourdon. The entire communion antiphon of his Missa Sancti Jacobi has such a texture.5 Indeed, so thoroughgoing is the fauxbourdon that Dufay did not notate the middle voice but instructs the singer to perform his part by transposing the superius down a fourth. The interval of a fourth between the two top voices has the advantage of making possible both 63 and 85 sonorities. Short passages of fauxbourdon, such as that found in Se la face ay pale, occur from time to time well into the sixteenth century, but in music of that time they impart a slightly old-fashioned flavor. Ockeghem’s Fors seulement, another three-part secular piece, is given as Example 9-4. Play it through several times, then answer the questions on Self-test 9.1. EXAMPLE 9-4 Chanson: Fors seulement Johannes Ockeghem


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Save only the expectation of my death, No hope remains in my weary heart, For my unhappiness torments me so very strongly. There is no grief which I do not feel on account of you, For I am sure of losing you.

SELF-TEST 9.1 Cadences, or patterns suggestive of cadences, are found at mm. 4–5, 14–15, 19 (with extension to beat 4 of m. 20), 23, 30, and 34–35. 1. Mark the two cadential voices, i.e., those that move stepwise into the cadential note. Then observe what the third voice is doing at that moment. If it is not resting, what scale degree is it on? (Count ^ the cadential note, whatever it is, as scale-degree 1.) 2. What mode is the piece in? 3. On which scale degrees of this mode are the cadences? 4. Mark each appearance of the motive consisting of a descending tetrachord with the rhythm of a dotted quarter followed by two sixteenths.

Some further comments on Fors seulement are called for.


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Melodic Contour

Fors seulement is outstanding for the beauty of its melodies, not only the superius, but also the tenor and bass. Perhaps this is the reason for its great popularity, testified to by the numerous pieces Renaissance composers based on it: more than thirty chanson settings, masses by Obrecht, Pierre de la Rue, and others, as well as one by Ockeghem himself. Each phrase of the superius has both a high and a low point. Singplay-sing through the superius. How would you describe the curve of each phrase? How does Ockeghem’s melody compare with the rules for melodic lines given by Fux for species counterpoint? DO NOT READ ON UNTIL YOU HAVE DONE THIS. The melody of the superius is particularly striking in Part Two of the song. The first two phrases (mm. 23–27 and 27–30) both begin with or near their high notes and gently curve downwards to a low point. The final phrase (mm. 30–35) begins with its low note, D4, ascends a seventh to C5, falls a fourth (m. 32), then climbs to D5, an octave above its initial note, coming to rest on A4, midway between the extremes of the octave D4–D5. The lower voices, though perhaps not so perfectly rounded as the superius, are no less carefully fashioned. Notice, for instance, the gradual descent of the tenor from its initial A4 down a perfect fifth to D4 (m. 5), then moving on in the next phrase, continuing its descent to a low A3 reached just in time to be supported by the D3 of the entering bass. From m. 9 to m. 13 it climbs up to Bb4, its highest note yet, then, after another descent reaches a climactic C5 in m. 18. In the second part, this C5 is picked up in mm. 22 and 24 and rises to a D5, the high point of the entire piece for the tenor. It makes a gradual descent (mm. 27–31) to its low A3 and remains in that register for the ending. The suppleness of the individual voices is achieved not only by the rise and fall of the lines but by the rhythmic variety. Only rarely do two adjacent measures have the same rhythmic pattern. The lower voices, with their many syncopations and other special groupings, are contrived to obscure metric regularity. There is a highly sophisticated subtlety to the rhythms of the lower lines which you will appreciate by playing and singing them through several times. The whole piece exhibits only one exact sequence: in the superius, m. 24 is repeated in sequence in m. 25. Other seeming sequences are varied in some way, as shown in Example 9-5. EXAMPLE 9-5

Texture

Texture is the aspect of music that has to do with the relationship between the voices. In this piece, though all three voices are linearly conceived, it is clearly the superius that has the smoothest and most attractive melody; the lower voices, active as they are, provide contrapuntal accompaniment to it. (Significantly, it is the superius that Ockeghem used as a C.F. in his Missa Fors seulement, a portion of which we will shortly be

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examining.) Perhaps one reason for the impression of accompaniment conveyed by the lower voices is that they act as an introduction to each part of the piece. Measures 1–4 prepare and anticipate the entrance of the superius at m. 5. The first part of the piece ends with a cadence on the tonic at mm. 19–20. The second part is introduced by the lower voices in mm. 21–23. Finally, the character of the lower voices, with faster moving notes and more irregular rhythmic patterns in mm. 14–20, 22, and 23, seems instrumentally conceived. Another aspect of the texture of Fors seulement is that the voices are for the most part grouped homorhythmically into pairs, the tenor acting as upper voice to form a pair with the bass, and acting as lower voice to form a pair with the superius. This explains why the tenor has so little opportunity for rests, in contrast to the superius and the bass. At times the odd voice rests while the pair is heard alone, but at other times the pair is pitted against the odd voice. For instance, at m. 15 it is superius and tenor versus bass; at m. 16 superius and bass versus tenor; at m. 24 superius and bass versus tenor; at mm. 25–26 superius and tenor versus bass. Imitation

Fors seulement depends even more on motivic imitation between the voices than did Dufay’s Se la face ay pale. When the superius enters in m. 5 it begins as an imitation of what the tenor had at the start. The bass of m. 5 is imitated by the tenor of m. 6. Beginning in m. 10 with the tenor, all three voices have the ascending scale fragment in quarter-notes. Among the other points of imitation, the most conspicuous is at the pickup to m. 24 (“Qu’il n’est douleur . . . ”) where the very expressive line of the superius is imitated at the unison by the tenor. Mark all imitations in the piece.

9.3 Sacred Music in Four and Five Parts While the distinction between sacred and secular music did not extend to the number of voices used, there was a tendency, particularly in the fifteenth century, to write secular music in three parts and sacred music in four. During the sixteenth century it became common to enrich the texture with more parts. Four- and five-part music, sacred or secular, became the norm and six parts was common enough. Generally speaking, sacred music tended to employ a greater number of parts than did secular. In this section of the chapter, we will consider excerpts from three fifteenth-century masses that have characteristics of what musicologists have categorized as the cantus firmus mass, the parody mass, and the paraphrase mass. In the first type, a pre-composed melody appears in one of the voices (the tenor, as a rule) to be used as a C.F. acting as a foil for the contrapuntal activity of the other voices. This C.F. might be a familiar melody—L’homme armé was frequently chosen—or a contrived or abstract formula, a hexachord or the derivation used by Josquin on the name of the Duke of Ferrara (see pages 87–88). More often, it was the tenor of a secular chanson. The parody mass, on the other hand, used not just one line of a pre-composed work but the entire texture, woven into the newly composed work in an original way. The paraphrase mass was not necessarily based on any pre-composed work, but had a prominent motive that ran through all movements as a unifying factor. Dufay wrote a mass based on his own Se la face ay pale (Example 9-6). He takes the tenor of the ballade and incorporates it as a C.F. in most, but not all, of the movements of the mass. Example 9-6 is the opening of the first Kyrie. It will be immediately noticed that the tenor is in 3/2 time while the other voices are in 3/4. The inscription beneath the tenor reads: Canon: Tenor crescit in duplo Rule: the tenor increases by twice as much


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It was not customary for the composer to indicate the precise underlay of the text. Dufay simply wrote “Kyrie eleison” at the beginning and left it up to the singers to place the syllables where they saw fit, liturgical correctness demanding that the words be pronounced three times in all. Instruments were probably employed along with the singers or possibly instead of some of them. Try to play the two top voices and the bass on the piano while singing the tenor line. Or get a friend to sing or play the tenor for you. Be sure to compare the tenor with that of the original ballade (Example 9-3). EXAMPLE 9-6 Missa Se la face ay pale, Kyrie Guillaume Dufay

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The superius in this mass begins with a nine-note motive (mm. 1–3) which reappears frequently at important spots in the mass. Though it may be altered in some way, this motive is always clearly recognizable. Thus, Dufay’s Missa Se la face ay pale is both a C.F. mass and a paraphrase mass. It also has two passages that are suggestive of parody technique: these occur at the end of the Gloria and the end of the Credo. A comparison of the last fifteen measures of the Credo (Example 9-7) with the last twelve measures of Example 9-3 will make clear the distinction between a C.F. treatment and a parody treatment. Measure 186 to the end of the Credo are identical in the tenor to mm. 19–30 of the ballade. But from m. 186 to m. 191 there is no resemblance in the other voices between the ballade and the mass setting. Beginning with m. 192 the superius and contratenor take their cue from the corresponding voices in the ballade. The same sort of thing happens at the end of the Gloria and both passages, when performed with voices and instruments, make exciting culminations to their respective movements. While these passages are not as extended or thoroughgoing as many later parody masses, the essential technique is the same. EXAMPLE 9-7 Missa Se la face ay pale, ending of Credo Guillaume Dufay


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Like Dufay’s Missa Se la face ay pale, the Missa Fors seulement of Ockeghem, though ostensibly a C.F. mass, in many respects foreshadows the parody mass. Compare the first Kyrie (Example 9-8) with the chanson on pages 94–96. The Ockeghem Kyrie is also shown in facsimile.

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EXAMPLE 9-8 Missa Fors seulement, Kyrie Johannes Ockeghem


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Note the remarkable way in which Ockeghem has contrived to present the superius of the chanson at its original pitch level (starting on A4) as the comes in a canon at the perfect fifth, the dux being the contratenor starting in m. 1 on D4. (The slight alterations at mm. 5 and 7 in the comes are not to make the canon work—the voices fit together without them.) As if this weren’t enough, the canon is placed above the original chanson bass, which has been transposed, like the contratenor, down a perfect fifth. The ranges are all extremely low. All church music was intended for male performers exclusively, high treble parts being taken by boys, the others by grown men. Male altos or countertenors have a range up to and beyond C5. But this piece is unusually low even for Ockeghem who is known for his low ranges. The five parts are fairly close together and often cross, resulting in a very rich, full sound. Cadences are

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few and far between, in Example 9-8 only at mm. 10–11 and the end. It is often difficult to follow the individual lines. It may well have been the composer’s intention that listeners should feel themselves bathed in a full, flowing mass of sound reverberating through the church, rather than intellectually following the contrapuntal lines. Such may also have been Ockeghem’s intention in his Missa Mi-Mi from which the beginning of the Agnus Dei is presented as Example 9-9. This mass is known as an excellent example of Ockeghem’s nonimitative counterpoint, since no imitation of importance is present. Instead, a unified feel is evoked by the motto E3–A2–A2, found at the beginning of important sections.6 Play through this example several times on the piano, and DO NOT READ ON UNTIL YOU HAVE DONE THIS. EXAMPLE 9-9 Missa Mi-Mi, Agnus Dei Johannes Ockeghem

Like the Missa Fors seulement, the Missa Mi-Mi is low in pitch and there are very few cadences. The few cadences are de-emphasized by an entering voice or one or more voices running through the cadential


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spot. Other than the motto from which the mass gets its name, no melodic fragment stands out as a motive. Instead, there is an unhindered flow of free, supple melodic lines—a joy to sing and an unforgettable experience for the listeners who allow themselves to be caught up in the overall sonority.

9.4 Dissonance This passage from the Missa Mi-Mi affords a good opportunity to consider dissonance treatment at this time in history. Dissonances can be divided into two main groups: (1) notes that are adjacent to consonances, and (2) notes that are time extensions, either forward or backward, of consonances. In the first category are those dissonances commonly called passing tones, neighbors, escape tones, and appoggiaturas. All these approach and/or leave the consonance by stepwise motion. In the second category are suspensions and anticipations. The suspension originates as a consonance that is extended into the “timeslot” of another note, a consonance one step below, thus for a time becoming dissonant. The anticipation is the opposite: it is as if the voice with the anticipation moves too soon to its next consonance. Any of the dissonant types in either the first or second group may occur as a consonance, the contour and rhythm marking it as a kind of suspension, anticipation, passing tone, etc. (the 6–5 “suspension” or the 5–6–5 neighbor, for instance).

9.5 Meter SELF-TEST 9.2 In Example 9-9 a circle has been placed wherever a dissonance appears. Mark each circle with a 1 or a 2 depending on whether the dissonance belongs in the first category noted above or the second.

Theorists of the thirteenth to the sixteenth centuries distinguished between musica plana (plainsong) and musica mensurata (measured music). In the former the rhythm was fairly free, in the latter each note has a specific duration relative to the other notes. Musica mensurata was made practical by a notational system devised by Franco of Cologne in his treatise Ars cantus mensurabilis (“The Art of Mensurable Music”), published toward the end of the thirteenth century. We refer to this system as mensural notation or Franconian notation. With alterations it remained in use until the end of the sixteenth century and the system we use today is, to some extent, based on it. Detailed understanding of notation from the thirteenth to the sixteenth centuries is a study in itself. For our purposes we need to know only a few essential features of notation as it appeared after the middle of the fifteenth century, written mostly in white notes rather than the earlier black notes. There were eight symbols for single notes: Maxima (Mx)

Minima (M)

Long (L)

Semiminima (Sm)

Brevis (B)

Fusa (F)

Semibrevis (S)

Semifusa (Sf )

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Of these, the essential notes for understanding mensuration are the B, S, and M. The system worked by means of signatures indicating the relationship of these notes to each other. Unlike modern notation, the larger-value note could equal either twice or three times the value of the smaller. The terms perfect and imperfect were used to express the ratio. “Perfect” indicated triple or divisible by three—in homage to the perfection of the Holy Trinity—whereas “imperfect” meant duple or divisible by two. The terms tempus or prolatio indicated which notes’ values were involved. For instance, in perfect tempus (time), three S = one B ( = ), but in imperfect time two S = one B ( = ). In perfect prolatio (prolation) three M = one S ( = );in imperfect prolation two M = one S ( = ). A circle represented triple or perfect time, a dot triple or perfect prolation. A half circle represented duple or imperfect time, and the absence of a dot duple or imperfect prolation. The usual possibilities can be summed up in Table 9-2. TABLE 9-2

In transcribing into modern notation we use note values that appear smaller than those used in white Franconian notation. We either halve the values (ratio 1:2) or quarter them (ratio 1:4). Examples of these notes in modern notation would look as in Table 9-3.


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TABLE 9-3

When transcribing into modern notation, then, we can use 2/4 or 2/2 for , 3/4 or 3/2 for , 6/8 or 6/4 for , and 9/8 or 9/4 for . These time signatures, however, are not always the exact equivalent of the Franconian time signatures. In modern notation, 6/8 normally means two beats in a measure, each beat divisible by three; 3/4 means three beats in a measure, each divisible by two. The listener hears 3/4 or 6/8 . But means merely that two M take the time of one S, and therefore six M take the time of three S. There is no indication of grouping by pulse or accent, nor did music make use of barlines. (See facsimiles on pages 104 and 105.) Therefore six M in could be transcribed into modern notation as or as . If a 6/8 measure sounds like three groups of two, today we call it a hemiola and consider it a metrical abnormality. But in the music of the Renaissance various groupings are constantly to be found and are not in the least abnormal. In fact, one reason for the interest that this music evokes is its constantly shifting metric quality and the possibility of various interpretations. For instance, turn back to Example 9-1 (page 89). The treble line at m. 8 could be sung as 6/8 or as 3/4 . Similarly, the contratenor at m. 16 could be transcribed (as here) as 3/4 or as 6/8 . Turn back also to Example 6-12 (pages 67–68) and consider the rhythm of the treble line, particularly in mm. 12–15 and 26–31. Is more than one metrical interpretation possible for each of these passages? These four mensurations are alla semibreve: each tactus (beat) has the value of a semibrevis ( ). It was also possible to let each tactus have the value of a brevis ( ). In this case, referred to as alla breve, a vertical line was drawn through the signatures and so they looked like this: and . In the sixteenth century alla breve notation became the norm. Since the tactus, generally speaking, was always performed in a tempo of about 50–60 beats per minute, music written alla breve moved approximately twice as fast as music written alla semibreve. The signatures having triple prolations, and , could be changed to alla breve by the addition of a 3 to the duple alla breve signatures: and . In modern notation with reduction by 1:4 or 1:2 is as shown in Table 9-4. With the addition of a dot the duration of a note could be lengthened by one half of its duration, just as we do today.

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TABLE 9-4

9.6 Mensuration Canons Composers of the fifteenth century seem to have been intrigued by the game-playing possibilities inherent in musical notation. Their mensuration system made it possible to devise canons that would be difficult if not impossible to notate in another system. Example 9-10 is one of the easier mensuration canons from a Missa L’Homme armé composed by Josquin des Prez and first published in 1502, though probably composed much earlier.


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EXAMPLE 9-10 Missa L’Homme armé, Agnus Dei Josquin des Prez

The Latin heading, “Out of one voice, three,” is not really a helpful clue to the solution of the canon since the three time signatures are sufficient evidence that this is to be a three-voice piece. There are also two signa congruentiae (signs of congruence), one above the third note from the end of the first staff, and the other above the eleventh note from the end of the second staff. These signs indicate the “points of agreement” between the voices—that is, when the slower-moving voices reach these points they should hold their notes and the three voices will come to an end together. The signatures let it be known that the top voice will move alla breve in duple time, triple prolation, the middle voice alla semibreve in duple time, duple prolation, and the lowest voice alla breve, duple time, duple prolation. What is not indicated is the pitch level for two of the voices. The clef just to the left of the signatures tells us that C4 is the second line from the bottom and therefore the written notes begin on D4. But if this pitch level is applied to all three voices, horrendous harmonic clashes occur before long. Josquin simply leaves it up to the performers to find the pitch level that will work. One way to set about the problem is this: since the signs of congruence are given, we know which notes are going to be sounding at the end of the piece. The top voice, alla breve in three, will be moving fastest and therefore will be the only voice to perform the entire piece. Judging from the clef, the top voice ends on an F4. At this point the lowest voice, next fastest, will have reached the second sign of congruence, a notated D4. This is possibly the correct pitch since the two form a consonance. But the middle voice, the slowest moving, will end at the first sign of congruence, a notated G4. Obviously the middle voice is intended to be transposed. If it were to be transposed down a perfect fourth, it too would end on D4. This is a possibility that needs to be checked out by beginning the piece with the middle voice transposed down a perfect fourth, starting on A3. Unfortunately, this puts it below the lowest voice, forming a dissonant perfect fourth between A3 and D4. But if the lowest voice were sung at the lower octave, the piece would

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begin (bottom to top) D3–A3–D4 instead. This is a very normal way to begin a Renaissance piece, two notes on scale-degree ^1 and one on scale-degree ^5, and it results in good vocal ranges. We are still dealing with a hypothesis and must wait for corroboration from the rhythmic point of view. As it turns out, these pitch levels are satisfactory, and, since they correspond to normal voice ranges, they are undoubtedly what Josquin had in mind. Indeed, other transpositions result either in unacceptable dissonance or in extended voice crossings, which would cancel out Josquin’s indication as to which mensuration should be on top, which in the middle, and which on the bottom. We now have to write out a score of the three-part canon according to the three mensuration signatures given. In the alla breve top and bottom voices, each tactus will correspond to a brevis ( ); in the upper voice this brevis will correspond to three semibreves and in the lower voice it will correspond to two semibreves. Since the middle voice is alla semibreve, each tactus will correspond to a semibrevis ( ). It must be remembered that the tactus, or beat, is the same for all mensurations. We can make a score, then, using Josquin’s own note shapes and marking the tactus by means of vertical lines between the staves. Example 9-11 shows the beginning of such a score. EXAMPLE 9-11

A score in modern notation can easily be made from this by reducing the note values by a 1:2 or 1:4 ratio and settling on a time signature by which all parts can be expressed. One such modern score, taken from the Historical Anthology of Music,7 is given here as Example 9-12. Naturally, for a modern transcription the ratio of the alla breve voices has to be different from the ratio of the alla semibreve voice. Here, the editors transcribed the alla breve voices with a 1:4 ratio, and the alla semibreve voice with a ratio of 1:2. EXAMPLE 9-12


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Josquin’s great forerunner, Johannes Ockeghem, composed a mass known as the Missa Prolationum, which consists in its entirety of mensuration canons. It is possible that Ockeghem was not simply attempting to appear ingenious by writing his mass in this way, but that he wrote it to be used in teaching or examining his choristers in the various mensuration systems. One reason some scholars consider this a possibility is that many of the most complicated parts from the mensural point of view apply to the rests rather than to the sung notes! The situation for the performers is far more complex than it might seem from the listener’s standpoint. A facsimile of an early manuscript of the Sanctus and Osanna from this mass is presented on pages 114–115. We will concern ourselves with the Osanna only, notated as the last two staves on each of the two pages. What we have here is a double canon—that is, the page on the left gives us one notated melodic line with two mensuration signatures, on the top space and on the bottom line, a clear indication of a two-voice canon. The page on the right gives us another melodic line with two mensuration signatures and two F clefs an octave apart: another two-voice canon to sound simultaneously with the first. ( Just as a single canon has at least two voices, so a double canon must have at least four.) None of the mensuration signatures is alla breve, and all four are of different types, representing the main types listed on page 108. The soprano clef of the page on the left indicates the higher voice to be what today we would call 2/4 or 2/2 time and the lower voice to be in 3/4 or 3/2 time—that is, both are in duple prolation, but only the higher voice in duple time. The right-hand page with the F clefs gives us the two lower voices, evidently to sound an octave apart: these will be tenor (T) and bass (B). (The upper clef, of course, refers to the bass, the lower clef to the tenor.) The mensuration signatures show the T to be in what we today would call 6/8 or 6/4 time and the bass in 9/8 or 9/4 time. That is to say, both are in triple prolation, but only the lower voice is in triple time. Although all necessary clues for the solution of this canon are given, it would not be possible for us at this stage to make an accurate score of it because we have not taken up a detailed study of fifteenth-century notation as regards ligatures and coloration. A ligature is a single sign that indicates two or more notes, as can be seen in the upper canon’s Osanna immediately to the right of the four initial breves. Near the end of the lower canon are two black diagonals, ligatures that have been subjected to coloration. Generally speaking, the blackening of a note or ligature that would ordinarily be white reduces its value by one-third. If you examine the upper canon carefully you will notice that beginning with the fifth sign all the notes

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are either of small value or have been blackened. This is also true of the lower canon. Before going on, you should look through the solution of this double canon given as Example 9-13. What is the relationship between superius and contratenor and between tenor and bass? Is the same relationship maintained throughout? ANSWER THESE QUESTIONS BEFORE READING ON. You will have noticed that the Ct begins with note values one-and-one-half times as long as those of S, but at m. 10 both voices move in identical note values. A similar situation prevails between T and B. The reason for this is that, in fifteenth-century notation, if a passage uses only short notes (M or smaller) or blackened L, B, and S, the notes of a voice in triple time lose one-third of their value, thus putting them at the same speed as a voice in duple time. Ockeghem apparently wanted to begin the piece with all voices simultaneously, but after a while to have two voices (S and T) act as leaders and two (Ct and B) as followers. To accomplish this, he began with long note values that, in the various mensuration systems, would result in notes of varying duration. When the melodic lines in each pair of voices were the desired time interval apart, he switched to short values and blackened notes, producing the same durations in both duple and triple time. In this way, owing to the peculiarities of the fifteenth-century notational system, Ockeghem could compose an “irregular” canon and notate it very simply.8


EXAMPLE 9-13 Missa Prolationum, Osanna Johannes Ockeghem

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Chapter 10

Fourth Species in Two Voices

After Fux’s fictional student Joseph learns to handle two notes against one, he is instructed in third species: four quarter-notes against one whole-note. Third species, however, deals with details of the melodic line rather than with basic concepts. For that reason it seems best to postpone the introduction of smaller note values to Chapter 14, in which we will be studying melody and rhythm in the style of Palestrina. For now we can go on to fourth species: the introduction of syncopes along with the concept of the suspension. A syncope is a note that begins on a weak beat and is held over to a strong beat.

10.1 Consonant and Dissonant Syncopes Joseph’s teacher Aloysius presents him with two examples, the first illustrating consonant syncopes, the second dissonant syncopes. Identify each harmonic interval (Example 10-1). DO NOT READ ON UNTIL YOU HAVE DONE THIS. EXAMPLE 10-1

It will be readily observed that to produce a consonant syncope one must find a note that is consonant with two adjacent notes of the C.F. In Example 10-1(a), for instance, the initial C5 in the syncopated line forms an octave with the first note of the C.F. and a perfect fifth with the second note. To produce a correct dissonant syncope—that is, a suspension—one must be able to move the dissonant note to a consonance by means of a descending second. In Example 10-1(b), the note on the first beat of each measure is dissonant.

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It moves down by step to a consonance on the second half of the measure. Such a move is termed the resolution of the dissonance. The resolution also acts as the preparation for the dissonant syncope immediately following. Aloysius goes to some pains to make sure Joseph understands the essential nature of dissonant syncopes. “You should know that the notes held over and, as it were, bound with fetters, are nothing but retardations of the notes following.” If the retardations were removed, the result would be a passage of note-againstnote consonances (Example 10-2). EXAMPLE 10-2

It follows, then, that the dissonant syncopes in Example 10-3(a) are necessarily incorrect, since if the passage is written without the retardations the actual progression would be no more than parallel perfect octaves. See Example 10-3(b). EXAMPLE 10-3

Such is not the case with consonant syncopes, since here there is an acceptable harmonic interval on each beat. Example 10-4(a), then, is satisfactory. It is NOT the same as 10–4(b) with retardations.


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EXAMPLE 10-4

In Example 10-4(a), the fifths appear on the weak beat of each measure. By the same token, a series of fifths on the strong beats of a syncopated passage is acceptable. Since the fifths are separated by consonances, they will not be heard as objectionable parallels (Example 10-5). The same holds true for octaves and unisons providing there are no more than two in a row (Example 10-6). EXAMPLE 10-5

EXAMPLE 10-6

Joseph wants to know why the resolutions of a suspension cannot be made by ascending motion. Aloysius is stumped and pretends that the answer would be too difficult for Joseph to comprehend at this stage. He replies: You raise a problem that is harder to untangle than the Gordian knot. I shall deal with it later because, being still at the threshold of the art, you would not now wholly understand it. Although it may seem to be a matter of indifference whether if you remove the retardation a series of thirds ascends or descends, yet there remains a certain distinction. This, as I said, will be explained sometime separately.

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Luckily for Aloysius, Joseph apparently forgets this question. At least he does not raise it again and, as far as we know, is never provided an answer. Actually, during the eighteenth and nineteenth centuries, suspensions did sometimes resolve upwards, especially when they could do so by half step with a leadingtone quality. We will come to this in the companion volume to this book. Species counterpoint, like music of the sixteenth century, knows only the descending resolution of the suspension.

10.2 Suspension Types The most satisfying suspensions are those that resolve “euphoniously,” that is, to the full sound of an imperfect consonance. When the C.F. is in the lower voice, then, the suspensions that produce the best effect are the 7–6 and the 4–3. The 9–8 and the 2–1 are less attractive but still tolerable. The 6–5 is also acceptable but, of course, is not to be counted as a dissonant suspension. See Example 10-7. EXAMPLE 10-7

Example 10-7(e) a case in which the suspension is an augmented fourth. Although this is perfectly good, it is of infrequent occurrence. Diatonically, when there is a key signature of one flat, it can happen only between the notes Eb and A or between Bb and E. With no key signature it can happen between F and B or between Bb and E. When the C.F. is in the upper voice, the possibilities for suspensions are drastically limited. They amount to the 2–3 and its octave transposition, the 9–10 (Example 10-8).1


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EXAMPLE 10-8

Joseph hesitantly asks why Aloysius has not included the 7–8 as a possible lower voice suspension. Again, Aloysius is at a loss. He can only cite the example of the great masters who avoided it altogether. Even in music of the eighteenth and nineteenth centuries one can almost never find the 7–8 as a lower voice suspension in two-voice counterpoint, except where the tempo is so fast that the roughness of the sound is scarcely to be heard (as in the final movement of Mozart’s String Quartet in G major, K. 387, m. 7).

10.3 Summary of Fourth Species Fourth species is made up of consonant syncopes and dissonant syncopes. Consonances can leap freely, if need be, to other consonances, consistent with the rules of melodic motion as presented in Chapter 2. Dissonances take the form of suspensions with their preparations and resolutions. The preparation must be consonant and it occurs on the second beat of a measure, the weak beat. It is held over to the first beat of the next measure and becomes dissonant as the C.F. moves to a different note. This dissonance is then resolved to a consonance by moving the syncope by descending stepwise motion. One more point may be made here. In working out an exercise, Joseph—who is indeed a remarkable student—decides it is worthwhile for the sake of the line to break the chain of syncopes, inserting one or two plain half-notes, as in second species. Aloysius approves of this maneuver if by so doing one can improve the line and cause it to be easier to sing.

SELF-TEST 10.1 Which of the following are incorrect? Give reasons.

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10.4 Application of Fourth Species Example 10-9 shows two fourth-species exercises by Joseph. Mark all the intervals before reading on. EXAMPLE 10-9 Fux


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Fux

Aloysius seems to be more indulgent toward his pupil than are many counterpoint teachers toward theirs. Although he does not praise Joseph, neither does he fault him, remarking only that this is good enough for the present. Yet Example 10-9(a) is hardly counterpoint at all, for after m. 1 it consists of a string of 2–3 suspensions. If we remove the retardations, we find that the two lines are not in opposition to each other. Rather, the syncopated line duplicates the C.F. at the third below. The second example is much better, although the lack of a zenith is not compensated for by the ineffectual nadir in the third measure. Note should be taken of the cadences. As in all two-voice counterpoint, the tonic is reached by stepwise motion in both voices. This means that when the syncopes are in the upper voice, the penultimate measure will contain a 7–6 suspension at the cadence. When the syncopes are in the lower voice, the cadence will include a 2–3 (or 9–10) suspension. In both cases the resolution of the suspension will be the leading tone (Example 10-10). EXAMPLE 10-10

Here are two illustrations of fourth-species counterpoint containing a mixture of consonant and dissonant syncopes. Don’t forget Joseph’s maneuver: it is sometimes prudent to break the syncopation pattern for a note or two if by doing so one can achieve a better line or one more independent of the contour of the C.F. (see Example 10-11(b), mm. 4–5). Play-sing-play these and write the harmonic intervals between

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the staves. You will probably have observed before now that in fourth species the unison may be used within the phrase since it will by necessity occur by oblique motion. EXAMPLE 10-11

10.5 An Approach to Writing Fourth Species The most practical way to approach these exercises is to work from both ends toward the middle. Since there is little choice as to the last three cadential notes, these should be written in first, thus setting up the goal to be reached. The beginning should then be decided upon and a tentative curve planned. Since we are now dealing with syncopes, the likelihood of simultaneous climaxes is greatly reduced. Keep in mind the option of breaking the chain of syncopes for one or two notes. In illustration, consider the C.F. in Example 10-12. Since the syncopes are to be in the lower voice, we can write in the 2–3 suspension for the cadence at once. The lower voice’s opening note will have to be the first scale degree. But if we begin with a rest and tie this Bb4 over to the next measure we will have an incorrect perfect fourth. So we begin on beat 1 and immediately move to a consonant syncope. By following this contour we arrive at Example 12-13. EXAMPLE 10-12


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EXAMPLE 10-13

Although measures 4 and 5 both begin with the interval of an octave, these do not constitute incorrect parallel octaves because they are separated by a consonant interval (see Example 10-6). However, mm. 3–5 are not very euphonious, consisting as they do of four perfect consonances within a span of five beats. By changing the contour of the lower voice and breaking the chain of syncopes, one may arrive at Example 10-14. EXAMPLE 10-14

This is a satisfactory alternative and, having a larger proportion of imperfect consonance, its sound is richer. It does break one rule of species counterpoint by crossing voices (m. 3), a practice limited to three or more parts in this pedagogical system. (Actual music by the great composers indulges in part crossing fairly often, even in two voices.)2 Let us try for one final version of this counterpoint, a version that will avoid crossing of parts, that will have a large proportion of imperfect consonances, and that still will maintain a good line (Example 1015). This version has a zenith in m. 2 and a nadir in m. 6, includes a good share of full sounds, and it breaks no rules of species counterpoint. Still, it might be faulted: except for the cadence there is not a single suspension. It is the dissonant sound of the suspension and the gratification of its resolution that gives fourth species its special character. The only excuse that can be offered is that when the syncopated voice is beneath the C.F., the possibilities of suspensions are greatly reduced, since the only acceptable lower voice suspension is the 2–3 (9–10). EXAMPLE 10-15

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SELF-TEST 10.2 A summary of the rules for writing fourth species in two parts would include the following: 1. To produce fourth-species counterpoint in two voices one writes (against a C.F.) a voice consisting mainly of a series of consonant or dissonant syncopes / suspensions / half-notes. 2. Octaves, unisons, or fifths may occur on successive strong beats provided there is a dissonance / consonance on the weak beat between them. 3. Octaves, unisons, or fifths may occur on successive weak beats provided there is a dissonance / consonance between them. 4. A series of 9–8 or 2–1 suspensions would be incorrect because in essence the two lines would be moving in direct / parallel / hidden octaves or unisons. 5. A complete suspension figure has three parts to it: the preparation which must be dissonant / consonant, the suspension itself which is dissonant / consonant, and the resolution which is dissonant / consonant. 6. When the C.F. is the lower voice, the available suspensions are 2–3 (9–10) / 7–8 / 7–6 / 4–3 / 6–5 / 2–1 (9–8). 7. With a 4–3 suspension the 4 may / may not be an augmented fourth. 8. When the C.F. is the upper voice, the available suspensions are 2–3 (9–10) / 7–8 / 7–6 / 4–3 / 6–5 / 2–1 (9–8). 9. When the C.F. is the lower voice, the cadential suspension will inevitably be 2–3 (9–10) / 7–6 / 4–3. 10. When the C.F. is the upper voice, the cadential suspension will inevitably be 2–3 (9–10) / 7–6 / 4–3. 11. In fourth species, dissonances are always on strong / weak beats.

SELF-TEST 10.3 Fill in the missing notes in these cadences:


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SELF-TEST 10.4 Mark the errors:

Syncopation Principle

When one of two melodic lines moves in syncopes, the essential harmonic intervals produced are the same as in first species. However, the syncopated voice delays its motion to each successive note of the line by one beat. Suspension Principle

In delaying its motion to the next note, the syncopated voice may, by the movement of the other voice, become dissonant. This dissonance can be resolved only by descending stepwise motion on the part of the syncopated voice. Practice

The syncope, beginning on a weak beat, must be consonant. It holds over to a strong beat and is then either consonant or dissonant. If consonant on the strong beat, it moves by step or leap to another consonance on the next beat, the weak beat. If dissonant on the strong beat, it moves down by step to a consonance on the next beat, the weak beat. If the syncope is in the upper voice it is best for the dissonance to be either a 7 or a 4 because the resolutions will then be to the full sound of an imperfect consonance (7–6 and 4–3). If the syncope is in the lower voice, the dissonant interval must be a 2 or its octave displacement, a 9.

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EXERCISE 10.1 1. Write suspensions as indicated. The first one is done for you as a model.

2. Using the approach suggested in Chapter 10.5, write two syncopated voices above and two below each of the following C.F. Comment on the merits and defects (if any) of your work. Note: Up to this point only two types of dissonance are available. A dissonance on a strong beat must be a suspension; a dissonance on a weak beat must be a passing tone. Do not write any other type of dissonance.


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Chapter 11

Fourth Species in Three Voices

11.1 Addition of a Third Voice to a Two-Voice Suspension Explanation of suspensions in three voices is simplified if we have a name for each of the three voices involved. In two-voice fourth species we simply referred to the “syncopated voice” and to the C.F. But in three parts it is important, when dealing with dissonant suspensions, to be clear about the function of each of the three voices. We shall refer to the voice with the syncope—the suspension itself—as the suspension voice. The voice against which the suspension is dissonant is called the accompanying voice. The remaining one is the third voice. In Example 11-1 sing each voice while playing the other two. Do this several times, listening carefully to yourself. Then play all three parts together. EXAMPLE 11-1


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It is important to be able to distinguish between the accompanying voice and the third voice. In Example 11-1(a), the bass is the accompanying voice because it is the bass note D3 that causes the C5 in the suspension to be dissonant. In Example 11-1(b), the soprano is the accompanying voice because its B4 causes a dissonant ninth with the suspension. While it is true that the third voice (the alto) is also dissonant with the suspension, 9–10 is a viable two-voice suspension, while 4–5 is not. In Example 111(c) and (d) the bass is the accompanying voice because it causes a ninth and a fourth, respectively, with the suspensions in the alto. Whenever the suspension voice is dissonant against the bass, it is the bass that is considered to be the accompanying voice, even though another dissonance with an upper voice may be present. The suspension voice and the accompanying voice are the same for three-part suspensions as for twopart. The question to be asked is, “What note is appropriate for the third voice?” There are two basic rules that govern the determination of its pitch at the moment of the suspension: 1. The third voice’s note must form a consonance with the other two voices at the moment of the suspension’s resolution. This means the third voice and the accompanying voice must be consonant with each other. (Remember that the augmented fourth or diminished fifth in the upper voices of a diminished triad count as consonant, as well as the perfect fourth in upper voices.) 2. The third voice must not have the same pitch class as the resolution of the suspension. The principle behind the first rule has to do with Aloysius’ statement regarding the harmony resulting from the resolution of a dissonant syncope. We know that the dissonances in themselves are altogether lacking the grace and charm of harmony; and that whatever pleasantness and beauty they may give the ear have to be attributed to the beauty of the succeeding consonances to which they resolve. Behind the second rule is the principle of fulfilled expectation basic not only to music but to any temporal art—drama, film, fiction, or poetry. A situation is set up which arouses certain expectations on the part of the listener, reader, or viewer, this expectation subsequently being fulfilled or frustrated. In Western music, much of the interest comes about because of this principle. If the third voice anticipates the note of resolution, it is as if the listener is not given a chance to experience the expectation. The situation is somewhat akin to hearing the punch line of a joke prematurely. Of course, in the case of the 9–8 or 2–1 suspension, the pitch class of the resolution is indeed sounding. But this is a different situation, for here it is the accompanying voice, the voice that causes the dissonance in the first place, that is sounding the pitch class of resolution. The rule stipulates that the third voice must avoid it. A glance back through Example 11-1(a), (b), (c), and (d) will confirm these rules. In each case the third voice is consonant with the other two voices at the moment of resolution (and therefore inevitably consonant with the accompanying voice at the moment of suspension). This consonant note is never the same pitch class as the resolution. If these rules are followed mistakes will not occur. But certain intervals are nevertheless preferable to others. A careful perusal of suspensions as practiced from the sixteenth to the nineteenth centuries will reveal certain tendencies on the part of the best composers. Example 11-2 shows the various suspensions with different pitches in the third voice. The preferred simultaneity is placed first in the list and marked with an asterisk.

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EXAMPLE 11-2



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A glance down the preferred sonorities (with asterisks) reveals that, when the suspension is in the upper voice the preferred note for the third voice is a third above the bass. The inevitable exception is the 4–3, for the third above the bass would anticipate the note of resolution. The preferred tone for the 4–3 is a perfect fifth above the bass rather than the sixth, as the former produces a stronger dissonance for the suspension. Though the six-four is possible, it is quite a mild dissonance and, as we shall see shortly, its very mildness makes it possible to act, under certain conditions, as a consonance. When the suspension is in the lowest voice, the perfect fourth or perfect fifth above the bass are both about equally dissonant and both result in resolutions to full triads. The less preferred sonorities should be used only when necessary to avoid incorrect progressions or to produce an improved melodic line.

SELF-TEST 11.1 1. Name each voice (suspension voice, accompanying voice, third voice) in the following three-part suspensions.

2. Indicate the intervals in all the suspension figures above. Place a hyphen between the two numbers that represent a suspension and its resolution. If an interval is retained for more than one beat, draw 7— 6. a line after its number. The first one, (a), is done for you here as a model: 5 33

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3. Fill in the third voice according to the preferred sonority.

11.2 Relationship Between First and Fourth Species In introducing three-voice fourth species to Joseph, Aloysius, as before, stresses the essential similarity between a passage of first species and the same passage with retardations (fourth species). He shows Joseph the illustrations given in Example 11-3. EXAMPLE 11-3

He goes on to show a three-voice passage with syncopes in the lowest voice, indicating that it is correctly done. See Example 11-4(a).


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EXAMPLE 11-4

Joseph musters his courage to protest: From this statement, dear master, a doubt occurs to me which I should like to express if you don’t mind. . . . If in [Example 11-4(b)] without the retardations, an immediate succession of several fifths results, [Example 11-4(a)] with the retardations is for the same reason faulty if the retardations be disregarded. Aloysius, though pleased with Joseph’s perspicacity, shows himself to be unprepared to give a clear answer. He replies at length but, after appealing to the authority of the great masters, tends to skirt the issue. It is likely that the full sound of the complete triads mitigates the effect of parallelism that would be troublesome with a thinner sonority. Moreover, parallel fifths do not strike the ear so plainly as octaves or unisons. A further case of what might be taken for incorrect parallel perfect fifths (between the upper voices of Example 11-5) occurs during one of Joseph’s exercises and is approved by Aloysius. EXAMPLE 11-5

Such a passage would not be acceptable if the parallels were octaves or unisons, since in that case they would be much more noticeable. See Example 11-6. EXAMPLE 11-6

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In this respect, Aloysius points out that although unisons, octaves, and fifths are all perfect consonances, the unison is “more perfect” than the octave and the octave than the fifth. The greater the perfection of a consonance, the less “harmony” it has. Since the pleasant quality of the suspension figure comes about through the resolution of its dissonance into a euphonious harmony, it follows that a dissonance resolving into a perfect fifth is better than one resolving into a perfect octave and still better than one resolving into a unison. (Of course, the resolution to an imperfect consonance is still better than to a perfect fifth.) In passages such as our Examples 11-4(a) and 11-5, the resolution of the suspension is to a full triad containing both a perfect fifth and an imperfect consonance. The completeness of the harmony, in conjunction with the fact that the fifths do not literally move at the same time, mitigates any objectionable quality they might otherwise have possessed.

11.3 Suspension Possible Only in Three or More Voices Occasionally Joseph shows remarkable astuteness. In one of his exercises he produced Example 11-7 simply, as he admits, because he could not think of anything else to do and he remembered having seen such a passage in the works of the great masters. Identify the intervals. EXAMPLE 11-7

You undoubtedly noticed an unusual occurrence in m. 3. On the first beat the “suspension” is a perfect fifth above the bass and on the second beat the “resolution” is a perfect fourth—seemingly a reverse placement of consonance and dissonance. What has actually happened on beat 1 of m. 3 is an inversion of the 73—6 suspension. The third voice has been dropped to the lowest position. The result is that the suspension voice is now a perfect fifth above the bass, and the accompanying voice is a sixth above the bass. We speak of this sonority as a six-five chord suspension. (The word “chord” indicates a simultaneity rather than a succession and thus it is distinguished from the 6–5.) In fourth species the “resolution” of the six-five chord suspension is necessarily to a six-four chord. Normally, as we have observed several times before, a six-four is so unstable as to be thought of and treated as a dissonance. But in this case the six-four on beat 2 of m. 3 becomes, with no change of the bass note, a 54—3 on beat 1 of m. 4 which then resolves to a 53 on beat 2. The following conditions prevail. 1. The bass note remains the same for two full measures, similar to a pedal point. It begins before the sixfour and continues after it. 2. The perfect fourth above the bass is approached by step and resolves by step. In this case, D5 moves down stepwise to C5 and C5 moves down stepwise to B4. 3. Immediately following the six-four, the third voice moves from the sixth above the bass to the perfect fifth above the bass, resulting in a 54—3. We call this six-four a consonant fourth (abbreviation: Con4) because, by comparison with the 54—3 to which it moves, its dissonance is mild enough to make it seem sufficiently consonant to prepare a


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suspension. If the fourth above the bass in the six-four is an augmented fourth, however, the dissonance will be too sharp to serve as a Con4. The Con4 does not necessarily follow a six-five chord suspension as it did in Joseph’s example. Example 11-8 shows how it might occur in other circumstances, still keeping to the three conditions listed above. EXAMPLE 11-8

Example 11-8(a) shows that the Con4 may be approached by step from below rather than from above. In Example 11-8(b) the Con4 is not part of a six-four sonority. This is less usual since the fullness of the triadic harmony is lacking, but it occurs when necessary for the sake of the line. In all cases the Con4 must immediately be turned into a 54—3 suspension.

11.4 Cadences Example 11-9 offers a comparison of first- and fourth-species cadences. Add Arabic numerals to indicate the intervallic structure of each sonority. It will be noticed that it is possible to assign Roman numerals to these cadences, just as if they were cadences in the major-minor system: Example 11-9(a) and (b) can be understood as V—I, Example 11-9(c) as V6—I, Example 11-9(d) as viiº6—I. EXAMPLE 11-9

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The close relationship between first and fourth species is especially noticeable when comparing cadences (review page 48, item D). Fourth species is similar to first except that the voice with the leading tone must include a retardation of that leading tone. In other words, the leading tone acts as the resolution of a suspension. Since the resolution is always a step lower than the suspension, the preparation and the suspension itself must be one step higher than the leading tone—that is, scale-degree ^1, the final. As shown in Example 11-9, when turning first species into fourth, the third-from-the-last note is altered when necessary to provide for the preparation and suspension. In Phrygian the procedure is similar to Example 11-9(d) in that ^2, a diatonic half-step above the final, occurs in the lowest voice. One of the upper voices resolves the 7–6 suspension to ^7, a whole-step below the final. The third voice, of course, has the third above the bass (Example 11-10). EXAMPLE 11-10

The designations “accompanying” and “third voice” apply to a single suspension figure only. A part may thus be the third voice at one point in the phrase and accompanying voice in another. In Example 11-11, for instance, for mm. 2, 3, and 7 the soprano is the accompanying voice and the alto the third voice; for m. 4 the reverse occurs. EXAMPLE 11-11

SELF-TEST 11.2 1. The consonant fourth (Con4) is a special type of suspension / preparation possible only in three or more voices. 2. To produce a correct Con4 the middle voice / top voice / lowest voice must be stationary and sounding both before and after the Con4. 3. In a Con4 configuration, the fourth itself must / need not be approached and left by stepwise motion. 4. Suspensions that can occur only in the lowest voice are the 6–5 / 2–3 / six-five chord suspensions.


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5. In the six-five chord suspension figure, the suspension voice is the bass / sixth above the bass / fifth above the bass. 6. In fourth species the six-five chord suspension inevitably resolves to a 5 / Con4 / 6 . 3 3 7. The last two chords of a three-part cadence in fourth species are similar to first-species cadences in that they can be analyzed by the Roman numerals V—I / vi—I / IV—I / viiº6—I / V6—I. 8. The leading tone is / is not / may be the resolution of a suspension in fourth-species cadences. 9. The last three notes of the third voice / suspension voice / accompanying voice in a three-part ^ ^ ^ fourth-species cadence are inevitably scale-degrees 1, 7, and 1. 10. In three-part species counterpoint, the penultimate chord of a cadence is sometimes / never / always a full triad.

Suspension Principle

In fourth-species counterpoint, three melodic lines produce harmonies similar to those in three-voice first-species counterpoint. The unique suspension principle has to do with the arousal of the listener’s expectations when a dissonant suspension is heard. This principle is: The resolution of a dissonant suspension will sound as a consonant sonority. This consonant sonority gratifies the listener’s expectations. Practice

With a 2–1 (9–8) or 7–6 suspension, the third voice generally sounds the third above the bass. With a 4–3 suspension, the third voice sounds the fifth above the bass. With a six-five chord suspension, the resolution is to a Con4, which then continues with a 4–3 suspension. With a lower voice suspension (2–3 or 9–10), the third voice generally sounds either the fourth or the fifth above the bass.

EXERCISE 11.1 Complete the following as indicated:

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Write a similar passage in Aeolian mode without a C.F. Include a 6 Con4 5 5 4

—3.

Chapter 12

Texture, Melody, and Meter

12.1 Further Characteristics of Renaissance Music For sheer beauty and expression of sorrow, Josquin’s five-part lament on the death of Ockeghem (in 1497) stands out as one of the supreme masterworks of the Renaissance. A short score of this work is given as Example 12-1. In this score the tenor is removed from its normal place and appears at the top. The reason for this change from usual practice will become clear when the music is examined. Before reading on you should play through the four other voices both separately and together, either omitting the tenor line at the top or singing it as you play. Or, as was suggested in connection with Example 9-6 (pages 99–100), get a friend to sing or play the tenor on another instrument while you perform the four other voices. DO THIS BEFORE READING ANY FURTHER. EXAMPLE 12-1 Déploration sur le trépas de Jean Ockeghem (Nymphes des bois) Josquin des Prez

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Nymphs of the woods, goddesses of the springs, skilled singers of every nation, Change your clear and lofty voices to sharp wails and lamentations, For the molestations of Atropos have sternly trapped your Ockeghem. Music’s true treasure and master can from death no more escape And, great pity, lies buried in earth. (1.) Don your clothes of mourning: Josquin, Brumel, Pirchon,a Compère, (2.) And weep great tears from your eyes: you have lost your good father. Tenor: Eternal rest grant unto them, O Lord, and let perpetual light shine upon them. a

Pierre de la Rue (c. 1452–1518).

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Déplorations (laments) on the deaths of famous people were not uncommon during the Renaissance. The poem used by Josquin is a version of an epitaph by the poet Jehan Molinet and was set to music by at least one other composer. It is typical of the Renaissance mind to combine Christian and pagan images. (One thinks of Michelangelo’s painting of the Holy Family with nude Greek youths exercising in the background, or the ceiling of the Sistine Chapel with seven Old Testament prophets confronted by five Greek sibyls.) In this piece the Christian aspect of mourning is represented by the tenor, who sings the words of the Introit of the Requiem Mass using the traditional plainsong. This tune was presented as Example 1-13 (page 10). If you turn back and sing it through you will recall that it is in Mode 6 (Hypolydian) and sounds like major mode. In his manuscript Josquin wrote it in Mode 6 but transposed it up a perfect fourth with one flat in the key signature. If sung as notated, then, it would sound in Ionian (or major) mode. Apparently taking an idea from Molinet’s poem (“change your clear and lofty voices to sharp wails”), Josquin writes the following instructions: Canon: ung demi ton plus bas Rule: one semitone lower Rather than starting on Bb, the singer must start on A. It is not a matter of transposing each note of the plainsong down a half-step. What Josquin is asking is that the plainsong be sung not in Mode 6 as written, but in Mode 4 (Hypophrygian) transposed up a perfect fourth to begin on A. The new mode distorts the character of the music, changing a major-mode sound to Phrygian: something “clear and lofty” becomes a “wail.” Against this peculiar cantus firmus in the tenor, the other voices sing a French chanson speaking of Ockeghem’s death in images taken from Greek mythology—nymphs, goddesses, Atropos (one of the three Fates who cuts the thread of life with her shears). The main part of the piece is over at m. 55, complete with a transposed Phrygian cadence at mm. 51–52: Bb3 in the tenor moves down to A3 while the G4 in the contratenor moves to the A4 an octave higher. The other voices turn this into a deceptive progression and continue with an extension ending in m. 55 with a plagal cadence. The tenor having completed his plainsong introit, the remainder of the piece may be thought of as an epilogue. The music becomes extremely simple, almost homorhythmic, and the sequences of triads in mm. 60–63 are very moving. Josquin’s Déploration for Ockeghem can serve as a reference piece for pointing out some of the characteristic details of Renaissance music. Five-Voice Texture

The rich sonority made possible by writing for five voices was very much admired during this time and became more and more common in the sixteenth century. The fifth part was called just that: Quinta Pars, or later simply Quintus (Q). Sometimes Q was a second tenor, as in this piece. At other times it was a second alto or bass, the voice range being obvious from the clef used for Q. The Canzona Motive

Very prominent throughout is the repeated-note motive with a rhythm of a half-note followed by two quarter-notes (see mm. 6–8, 13, 15, 16, 19, 20, 23, 24, 35, 36, 40, 45, 56, and 64). We have come across this motive before, as the head motive of Ockeghem’s chanson Fors seulement (Example 9-4, pages 94–96). It even plays a prominent role in O rosa bella (pages 72–74) where it begins the second part (m. 27). We will soon meet it again as the head motive of a chanson in Flemish by Pierre de la Rue. In the sixteenth


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century, this same motive became a standard opening for the French chanson and its Italian counterpart the canzona, and continued as a stereotype for the instrumental canzona da sonar. One still finds it very frequently in instrumental canzone of the seventeenth century. The Nota Cambiata

Another motive that appears frequently in fifteenth-century music is the escape tone leaping down a third. In Example 12-2(a) it is a three-note figure. Example 12-2(b) shows it as a four-note figure. In the fournote version it became a cliché of the sixteenth century, dealt with in a later chapter. During the fifteenth century it could take either the three-note or four-note form. In the Déploration it appears in mm. 38–39 (B imitated by Q) and in mm. 48–50 (Ct imitated by S).1 In the latter half of the fifteenth century the rhythm is almost always a dotted quarter-note followed by an eighth-note (assuming that the modern notation represents the tactus by a half-note). The eighth-note is usually, but not always, dissonant. The note to which it leaps must be consonant. Since the eighteenth century, the four-note version has been known as the nota cambiata (“changing note”), and the three-note version the incomplete cambiata. EXAMPLE 12-2

The Falling-Third Anticipation

One common melodic fragment that did not become a stereotype in later music is a three-note figure based on the falling third. In the latter half of the sixteenth century, in fact, composers such as Palestrina and Lassus took pains to avoid it (Example 12-3). The middle note, though usually a consonance, seems like an anticipation to the third note. In the Déploration it occurs prominently at the following points: m. 9 (S), m. 31 (S), m. 43 (S, imitated by Ct), m. 54 (S), and mm. 66–71 (S, B, Q, S, B, with all but the second S in augmentation). Although this figure was present occasionally in the music of Dufay and Ockeghem (see Example 9-7, m. 198, Ct), it became almost a trademark with Josquin. In Example 9-12 it appears twice in the soprano (mm. 5–6 and m. 12). In augmentation it becomes the basis for a famous passage in another lament of Josquin, a setting of David’s mourning for his son Absalom (2 Samuel 18: 33). This passage is very reminiscent of the last few measures of the Déploration. It also illustrates an unusual use of partial signatures and a range even lower than that of Ockeghem (Example 12-4). EXAMPLE 12-3

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EXAMPLE 12-4 Absalon, fili mi Josquin des Prez

But go down to the place of the dead in tears.

As we shall see, the anticipation (AN) in sixteenth-century music began to be used exclusively to emphasize the weak half of a tactus. Therefore it had to appear during the strong half as shown in Example 12-5. This fact must have had much to do with the disappearance of the motive as illustrated in Example 12-4. EXAMPLE 12-5


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12.2 The Cadential Suspension If you look back through the musical examples of Chapters 3, 6, and 9, you will see that, while cadences are almost always distinguished by the stepwise movement of two voices in contrary motion into an octave or unison, this movement is not always accomplished by means of a suspension figure. The pieces by Dunstable and Dufay, for instance, may or may not have included cadential suspensions. But starting with the generation after Dufay, the majority of authentic and Phrygian cadences are set up in such a way that the two cadential voices produce a 7–6 suspension (resolving into an octave) or a 2–3 suspension (resolving into a unison). Ockeghem employs the 7–6 suspension in Example 9-4 at mm. 5–6 (T and B) and m. 34 (S and T), and the 2–3 suspension in m. 19 (S and T) and m. 30 (S and T). He employs the 7–6 suspension elsewhere in mm. 10–11 of Example 9-8 (S and B I) and mm. 14–15 of Example 9-9 (S and B). Beginning with Josquin’s generation, the cadential suspension becomes the standard way of making an authentic or Phrygian cadence—that is, cadences in which two voices spanning a major sixth resolve outward by step to an octave, or two voices spanning a minor third resolve inward by step to a unison. Possible, but less common, is the case of two voices spanning a minor tenth resolving inward by step to an octave. We find cadential 7–6 suspensions occurring in the Déploration in m. 8 (Q and B, Phrygian cadence), mm. 27–28 (Ct and B, authentic cadence on C), m. 33 (Ct and B, suggestion of authentic cadence on D), and m. 52 (Ct and T, Phrygian cadence on A). Also, the final cadence in Example 9-7 (pages 100–101) includes a 7–6 cadential suspension between the two voices written on the top staff. Although there are other ways to end a phrase, and therefore other types of cadences, the cadence we have just been describing tends to sound more conclusive than others, probably because of the outward pull of the major sixth moving stepwise into the tonic in both voices. In Renaissance theory, and even later, it was termed the clausula vera (“true cadence”). Counting the cadential note, whatever it may be, as at least temporarily scale-degree ^1, the clausula vera consists of one voice moving from ^2 to ^1, with ^2 having the value of at least a tactus. Normally, the other voice has a suspension figure: preparation and suspension on ^1, resolution on (#)^7. Then both voices move to ^1. In the authentic version of the clausula vera, ^2–^1 is by whole-step and ^1–^7–^1 by half-step. In the Phrygian version, ^2–^1 is by half-step and ^1–^7–^1 by wholestep. In both cases the vertical interval is a major sixth moving to an octave or a minor third moving to a unison. Later, we shall see that it is also possible to have the clausula vera without the dissonant suspension. Example 12-6 shows a pre-Reformation devotional song in German, Maria zart. At least fifty years before this printing, Arnolt Schlick (c. 1450–after 1517) had made a setting of the song for voice and lute, presented as Example 12-7. In Schlick’s version, the voice sings the words to a countermelody while the lute puts the original tune in the middle voice and adds a bass line. Sing-play-sing Example 12-6 through, then examine Example 12-7. Play each line through on the piano, beginning with the middle voice, then play all three at once. Attempt to sing the top line while playing the other two. Then answer the questions in the following Self-Test.

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EXAMPLE 12-6 Maria zart (from Johann Leisentrit’s hymnal of 1567)


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EXAMPLE 12-7 Lute song: Maria zart Arnolt Schlick


Tender Mary of noble stem, a rose completely without thorns, you have restored with might what had been long lost through Adam’s fall. Saint Gabriel promised you power. Help, so that my sin and guilt may not be found out. Win grace for me, since no comfort of mercy can be gained through my own merit. At the last end, I pray, do not turn away from me at my death.

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SELF-TEST 12.1 1. Where is each clausula vera (authentic or Phrygian) located? 2. Is each clausula vera set up as a suspension figure? 3. In the modern notation used here, each tactus is a half-note. In each clausula vera, is the voice with ^ scale-degree 2 at least a full tactus long? ^ 4. How is this scale-degree 2 approached, by step or by leap? If by leap, describe. 5. What effect does the odd voice have on the clausula vera itself—that is, how would you describe the three-voice cadence?

12.3 Meter in the Single Line On page 109 we mentioned the fact that various metrical groupings and rhythmic patterns were common in Renaissance melody. The fact that a meter signature is, say, (transcribed as 2/4 or 2/2) does not necessarily mean the single melodic line is going to be perceived as a series of alternating strong and weak beats. Nor will (transcribed as 6/8 or 6/4) inevitably bring forth two beats to a measure, each divisible by three. Example 12-10 on pages 155–156 is the beginning of a four-part setting of a Flemish song, Mijn Hert altijt heft verlanghen, written sometime around 1500. The pre-existent melody is in the superius. Playing it through you will notice, first, that it begins in what became standard for chanson openings: a repeated figure with the pattern . As it continues it seems to alternate duple with triple meter, so that, for the tune alone, the following barring reflects the rhythm as sung (Example 12-8). EXAMPLE 12-8

This metrical freedom is reflected in the accompanying voices. For instance, the opening in the Ct, imitated by B and T, could be barred thus as in Example 12-9. When all voices sound together, a collective meter emerges with a regularity of beat groupings felt not so much in stressed and unstressed notes as in the placement of consonance and dissonance. We will deal extensively with this aspect of sixteenth-century music in later chapters.


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EXAMPLE 12-9

12.4 Imitation and Fore-Imitation In Mijn Hert altijt Pierre de la Rue (c. 1460–1518) has introduced the borrowed melody (S) by stating a slightly altered version of it in the lower voices. They enter successively in imitation: B imitates Ct at the octave below after three beats, tenor imitates bass at the fifth above after three beats, then S enters as if in imitation of T at the octave above after three beats. Since S is the main melody of the chanson and one that listeners of the day were likely to know already, the lower voices would be perceived as anticipating the melody to come.2 This device—very common in chorale-preludes for organ—is usually labeled Vorimitation, or “fore-imitation.” The second phrase has a bit of fore-imitation as well. It begins in mm. 9–11 in the superius with an upper neighbor motion, E5–F5–E5. This is anticipated in the tenor in mm. 8–9. More prominent is the imitation (not fore-imitation) in tenor and bass voices beginning in m. 12. Phrase 3 begins on the last quarter of m. 15 in the superius, with a descending scale in the contratenor and tenor “fore-imitating” it very subtly (m. 15, second quarter) and the bass imitating it in mm. 16–17. EXAMPLE 12-10 Mijn Hert altijt heft verlanghen Pierre de la Rue

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12.5 The Bicinium A bicinium is simply a piece for two voices, secular or sacred, vocal or instrumental. Lutheran chorales were sometimes set to music as bicinia. One of the very earliest is presented here as Example 12-11. The familiar tune, known to us today from its inclusion in practically every hymnbook as “A Mighty Fortress is Our God,” is in the tenor, the lower voice, in its original rhythm. Play one line while singing the other, then reverse parts. Take note of the cadences of each phrase. Which of the clausulae verae feature cadential suspensions? Which have something unusual about them? The perfect fourth on the last beat of m. 19 sounds as perhaps an out-of-place dissonance for this musical style (around 1525). Walter may have felt justified in that the G4 in the upper voice is a lower neighbor to the main note A4 before and after it. The parallel perfect fifths in m. 8 and m. 23 are easier to explain. Example 12-12(a) shows the basic cadence; Example 12-12(b) shows an ornamentation of the motion from G4 through F4 to E4. While this does produce parallel perfect fifths (Bb3/F4 moving to A3/E4), the E4 in the upper voice will not be heard as the real goal of the progression. It is, rather, an anticipation of the E4 in the next measure, an anticipation decorated by its own lower neighbor. EXAMPLE 12-11 Bicinium: Ein’ feste Burg Johann Walter


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Our God is a strong citadel, a sure defense; He helps us to be free from all distress that has befallen us; The old evil Enemy now thinks of combat; With great might and cunning is his dreadful preparation made; His equal is not on earth. (Martin Luther) EXAMPLE 12-12

Although many bicinia are based on imitative counterpoint, this is one which happens to be nonimitative. Another special feature of this setting of Ein’ feste Burg is that the contrapuntal addition to the original tune is more rhythmically active than the tune itself. Thus the chorale has the stately quality of a C.F., and the superius, now called the cantus, that of a lively decoration. In imitative bicinia the two voices are usually rhythmically equal.

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EXERCISE 12.1 Three pieces are given for you to analyze. Be sure to address the following in your analysis of each piece: (1) mode; (2) cadences (where? what type? cadential suspensions?); (3) imitation; (4) texture; (5) special consonance/dissonance treatment, including the nota cambiata and ornamented suspension resolutions; (6) special rhythmic or metric treatment. 1. Schlick’s three-part setting of Maria zart for organ was published in 1512. Unlike his lute song on the same melody, the tune is here placed in the top voice. Compare this with the tune as given in Example 12-6. In many ways this piece anticipates the German organ chorale-prelude of the seventeenth century. Discuss the idiomatic writing for organ as opposed to purely vocal music. Beginning with the third quarter-note of m. 10, the middle voice fore-imitates the soprano in a slightly varied version. The same device occurs beginning at m. 20. Find three further examples of fore-imitation, all in the bass voice. EXAMPLE 12-13 Organ hymn: Maria zart Arnolt Schlick


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2. Walter’s four-part setting of the chorale Komm, Gott Schöpfer (“Come, God, Creator”) was first published in 1524. It is far more elaborate than his bicinium on Ein’ feste Burg. The chorale is a German translation and musical adaptation of the plainsong hymn Veni, Creator Spiritus (see Example 1-16, pages 11–12). Although fragments or variants of the chorale appear in all voices, the clearest presentation of the first phrase is in the tenor (mm. 3–15). The three subsequent phrases are given plainly in the superius (mm. 18–26, 29–40, and 45–52). The actual final cadence is at mm. 50–51. The extension that follows may be understood as a coda. (To avoid unnecessary clutter, the text has been omitted except in the soprano.) EXAMPLE 12-14 Chorale: Komm, Gott Schöpfer Johann Walter


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3. Tallis’s If ye love me for men’s voices was probably composed between 1547 and 1550, during the reign of Edward VI. Composers for the newly instituted English service were exhorted to write in such a way as to make the text absolutely clear to the congregation. They were especially instructed to avoid melismas, writing, “as near as may be,” only one note per syllable (see page 88). Has Tallis complied with this rule? (The word “spirit” was pronounced as one syllable.) EXAMPLE 12-15 Anthem: If ye love me Thomas Tallis


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Chapter 13

Further Aspects of Species Counterpoint

13.1 Mixture of the Species In Gradus ad Parnassum Fux introduces but does not stress mixing of the species, combining, say, first, second, and third species in a single passage. Later authors have considered mixing the species a valuable exercise. The combination of second and fourth species against a C.F. in whole-notes does have the particular value of introducing an important suspension configuration that would not otherwise occur in species counterpoint, but which is common enough in real music. Example 13-1 is based on Fux’s favorite C.F. (see Example 2-1, page 18). Mark the harmonic intervals. DO NOT READ ON UNTIL YOU HAVE DONE THIS. EXAMPLE 13-1

There are three six-five chord suspensions (mm. 3, 4, and 10). Because of species mixture the third voice to these suspensions—the bass—moves at the moment the suspension resolves. This means that the sixfive chord suspension is not required to resolve to a Con4 as would happen if the bass were in whole-notes. Measures 7 and 8 have what would have been 9–8 suspensions if the bass were in whole-notes. At the moment of resolution the accompanying voice (the bass) in half-notes is free to move to another consonance. Measure 7, then, has a 9–10 suspension, while m. 8 has a 9–5. Other situations might produce a 7–3 instead of a 7–6. Instead of a 2–3 lower-voice suspension, we might find a 2–6. There are many possibilities. What matters in species counterpoint is that the resolution be a consonance. We speak of this type of configuration as a suspension with moving accompanying voice, or, in the case of the six-five chord, suspension with moving third voice. Study the illustrations in Example 13-2.


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EXAMPLE 13-2

Examples 13-2(a) and (b) are correct because the third voice—the soprano in (a), the alto in (b)—is in each case sounding a note that would result in a correct resolution even if there were no motion in the accompanying voice. We spoke earlier (page 131) of the importance in Western music of expectation on the part of the listener. Here, in order for the suspension sonority to sound right, the listener must be able to imagine that the resolution in the suspension voice will result in euphony. It is for this reason that Example 13-2(c) is good but (d), identical except for one note, is bad. In the latter case, the third voice (soprano) sounds a pitch that forms a fourth with the bass at the moment of the suspension. If the accompanying voice (bass) did not move at the moment of resolution there would be a dissonance rather than a consonance at that point. The listener would be offended, not by the resolution itself—consonant in either case—but by the expectation of a dissonant resolution. Music’s existence is not in the listener’s ear so much as in the listener’s mind.

13.2 Species Counterpoint in Four Voices Fux has Aloysius introduce four-part writing by means of his favorite C.F. He advocates placing the C.F. in each of the four parts (soprano, alto, tenor, bass) and writing all types of species counterpoint using it as a basis. The species are not mixed: three of the four voices move only in whole-notes, the remaining voice moving in half-notes, quarters, or syncopes. Example 13-3 is the version having the C.F. in the bass, all voices in whole-notes. Play through this several times, noting the spacing and register of the voices.

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EXAMPLE 13-3 Fux

The rule forbidding crossing below the bass is ignored in m. 9 in order to produce a line with a nadir. Even this maneuver does not result in a totally satisfying line as the low D3 is too isolated to make a convincing focal point. (Sing the tenor line as written, then repeat singing the D3 an octave higher. While neither may be considered excellent, which one is better?) Examples 13-4 and 13-5 demonstrate second and fourth species with the C.F. in the soprano and the alto, respectively. Play through these several times, singing the various parts. EXAMPLE 13-4 C.F. in soprano Fux

EXAMPLE 13-5 C.F. in alto Fux


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Acquaintance with Examples 13-3, 13-4, and 13-5 should make clear that species counterpoint in four voices is fundamentally the same as that in three voices. Full-triad consonances are always major or minor triads in root position or first inversion, and diminished triads in first inversion. Writing in four voices, then, means that one member of the harmony must be doubled. There is only one rule regarding doubling: Do not double a tendency note. Tendency notes, as the name implies, are notes with a pull in a particular direction. The seventh degree of the scale, when it is a member of what we would call the V chord or the vii chord, has a tendency to move up by step. These notes should not be doubled for two reasons. (1) A note with a strong pull inherent in it tends to stand out. It is already prominent and to double it is to increase this prominence unduly. (2) Doubling a tendency note increases the chances of writing parallel octaves since one is apt to let both notes follow their tendencies. Study the illustrations in Example 13-6. EXAMPLE 13-6

In Ionian and Lydian modes, the seventh degree of the scale often occurs as the fifth of a minor triad— in modern terminology as a member of the mediant chord. In this case it is not a tendency note, as it does not have the quality of a leading tone. It may be freely doubled. (See Example 13-7.) EXAMPLE 13-7

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SELF-TEST 13.1 1. Each of the following suspensions has a moving accompanying or third voice. Which are correctly done? If any are incorrect, give the reason.

2. Identify places with incorrect doubling.


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We have now completed our study of species counterpoint. If you have worked through the self-tests and the exercises diligently, making an effort to correct any mistakes that might have occurred, you should have a good understanding of the most essential principles of counterpoint as it has been practiced during the last four hundred years of European music. You are now in a position to begin to write counterpoint that emulates an actual musical style—that of the Roman school of the late sixteenth century.

13.3 Summary of Dissonance, Use in Second and Fourth Species Principle

Dissonance is dependent for its comprehension on the consonances that precede and follow it. Practice

A dissonance sounds against a note that is already sounding. Dissonances do not begin together. Dissonances on strong beats are suspensions. Dissonances on weak beats are passing tones. No other dissonances are possible in second and fourth species.

Chapter 14

The Melodic Line

14.1 Introduction to Modal Counterpoint Our study of the writing of modal counterpoint will be based on the principles of sacred music as practiced during the Counter-Reformation. The works of three composers—Palestrina, Lassus, and Victoria—are especially suitable as models because, more than other composers, they embody in a consistent way the ideals of church music as approved by the Council of Trent (1545–1563) and the subsequent Commission of Cardinals on sacred music (1564–1565). On September 10, 1562, a canon was drawn up by a committee of deputies stating in substance that at mass all things should be so ordered as to “reach tranquilly into the ears and hearts of those who hear them . . . let nothing profane be intermingled. . . . The whole plan of singing in musical modes should be constituted not to give empty pleasure to the ear, but in such a way that the words be clearly understood by all.”1 On September 17 the general session banned from church music “all seductive or impure melodies, whether instrumental or vocal, all vain and worldly texts, all outcries and uproars, that ‘the House of God may in truth be called a House of prayer.’” On November 11 two new cardinals (one of them, ironically, the Bishop of Palestrina) advocated allowing only monophonic music in church and the whole question had to be taken up again. Performances of contrapuntal masses submitted by Palestrina and Lassus, along with the lesser figures Jacob van Kerle and Giovanni Animuccia (Palestrina’s predecessor at the Vatican) persuaded the church fathers not to outlaw polyphonic music from the church. The Commission ended by making recommendations regarding the setting of Latin texts. One may well ask why we today, in studying counterpoint, should concern ourselves with what a group of mid-sixteenth-century church officials thought. The answer is that, in order to understand why Palestrina, Lassus, and later Victoria composed the way they did, we need to grasp what their attitude toward composition was. The masses of Palestrina and Lassus “persuaded” the cardinals to retain contrapuntal music in the church because Palestrina and Lassus already had the same vision of what sacred music should be as did most of the deputies to the Council: music should evoke a certain serenity, should “reach tranquilly into the ears and hearts,” and should possess the quality of objectivity. The feelings and passions of the composer, particularly his own personal reaction to the words of the liturgy, should not intrude themselves on music designed for public worship. Bach, in his B-Minor Mass, makes no secret of his personal feelings regarding the doctrine of the incarnation or his belief in the efficacy of the crucifixion and death of Christ along with his subsequent resurrection. His is a typically Baroque attitude in which music reflects and expresses strong feelings and emotions—the Dionysian aesthetic. Music of the

The Melodic Line

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Counter-Reformation, on the other hand, tends more toward the Apollonian ideal of beauty, proportion, and restraint above all else. This classical attitude sometimes surprises those who expect, say, the Crucifixus of a Palestrina mass to differ substantially in quality from the Et resurrexit. It is serenity that seems to be sought above all else, but within this general quality there are, to be sure, subtle shades of light and dark. It is of particular advantage to us as budding contrapuntists that the sacred style of Palestrina, Lassus, and Victoria is so restrained and it is for this reason that Palestrina in particular has, through the centuries, been considered the composer on which modal counterpoint should base itself. His musical texture has come to be known as strict counterpoint because the dissonance treatment, the rhythmic activity, the melodic intervals, and the registral and textural sonorities are so carefully controlled. The fact that there is less freedom in this style than in any other style, earlier or later, in the history of Western music is all to the good. Fewer options mean more thought is apt to go into the making of each decision—an optimal situation for the development of a skill. For composers there is another advantage. This is a vocal style and it can provide excellent training in effective writing for the human voice.

14.2 Notation During the first half of the sixteenth century, the sign came to be universally adopted as the standard signature for duple meter. Yet, although almost all the music of Palestrina, Lassus, and Victoria in duple meter is notated in , to perform it literally alla breve would give it an impossibly fast tempo. (The tactus—the beat—was always about the same: 50–60 beats per minute.) Clearly in the sixteenth century the sign came to mean alla semibreve.2 This is also what the sign actually means today, although we call it “alla breve.” There is a difference, though, since today we conceive a beat differently from the way it was conceived in the sixteenth century. A tactus then was executed by a down-and-up motion of the hand. For instance, in Example 14-1 each arrow pointing down represents the beginning of a tactus, the hand’s descent, and each arrow pointing up the second half of the tactus, the hand’s ascent. EXAMPLE 14-1

As should be clear from Example 14-1, a sixteenth-century tactus comprised what we would think of now as two beats, a strong beat followed by a weak beat. Strong and weak beats are shown with arrows representing the downward motion of the hand on a strong beat and the hand’s upward motion on a weak beat. Of the various modern notations offered, we will be using (c) wherein the sixteenth-century note

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values are halved. Although it will look like 4/4 time, we must remember that here both the strong beats of a measure are of equal strength: beat 3 is identical in strength to beat 1. The music can be notated in the same 1:2 ratio as 2/4 time with no difference in sound. By choosing to notate in 4/4 we can avoid writing ties about half the time and we will use only half as many barlines. This is the modern notation used by almost all contemporary musicologists and modern scholarly editions as well as practical performing editions. On the other hand, textbooks of sixteenth-century counterpoint (other than this one) regularly use notation (b) on the grounds that it looks more like the original notation. Such reasoning is beside the point. When one considers that the editions with which contemporary musicians actually come in contact have “halved” note values as in (c), it seems more worthwhile to use the same notation here. Notation (a), though used by Fux—and therefore in this study, up to this point—requires the writing of too many ties and barlines, just as a meter signature of 2/4 would do. In short, our notation of duple time will be in 4/4, each first and third beat being equally “strong” and each second and fourth being equally “weak.” Our beats 1 and 2 are the equivalent of a sixteenth-century tactus, as are our beats 3 and 4. Our notation of triple time will be in 3/4 or possibly 3/2, sticking to the 1:2 ratio in transcribing the original notation.

14.3 Melodies in Quarter-Notes and Longer Values In the sacred style of Palestrina, Lassus, and Victoria the melodic intervals employed are the same as in species counterpoint. For now, then, we must concentrate on rhythm. Example 14-2 gives three versions of a melody. The first is simply an arrhythmic series of whole-notes conforming to the acceptable melodic intervals. The second and third add durational values to the notes in a duple meter setting. Sing these at least twice each. EXAMPLE 14-2

Earlier we had occasion to point out that a Renaissance melody is apt to sound very free metrically (see page 154). Example 14-2(b), with its metrical rigidity, is not at all typical of a sixteenth-century melody. Not only are there two rhythmic patterns that are immediately repeated (mm. 3–4 and 5–6) but there is

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motion on every strong beat. The effect is a regular, almost march-like, alternation of strong and weak beats. Example 14-2(c), by making use of syncopes, puts the same pitches into a more typical Renaissance rhythmic. Discounting the last note of the phrase, which is normally required to begin on a strong beat, there are almost as many half-notes (or tied quarters) beginning on weak beats as there are on strong. Moreover, no two adjacent measures have the same rhythm. Three points need to be stressed here: 1. Until we learn to include eighth-notes, only notes of two beats ( or ) may act as syncopes. 2. A dotted half- or whole-note must begin on a strong beat. 3. When the final note of a cadence is approached from above (= scale-degree ^2), that note must be at least two beats in length. Example 14-3 presents three excerpts from the works of Palestrina, Lassus, and Victoria. They are melodic lines that use note values of quarters and larger only. The Palestrina is the uppermost voice in the overall texture of the Missa de feria, the Lassus is an inner voice of the motet Tristis est anima mea, and the Victoria is the bass of the motet O vos omnes. Play-sing-play these through several times, then answer the questions in Self-Test 14.1. EXAMPLE 14-3 (a) Missa de feria Palestrina

(b) Motet: Tristis est anima mea Lassus

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(c) Motet: O vos omnes Victoria

SELF-TEST 14.1 Fill in the blanks or choose the correct word: 1. The longest note value in the Palestrina is _______ beats long. It begins in m. ____ on a strong / weak beat. 2. The Palestrina includes three cases of syncopation. They occur in mm. ____, ____, and ____, and each one is ________ beats in length. 3. The longest notes in the Lassus are ____________-notes and occur in m. _____ and m. _____. In both cases these notes begin on the strong / weak beat. 4. The Lassus includes _________ cases of syncopation, occurring in mm. _________. Each syncopated note is _________ beats long. 5. These examples show that repeated notes are / are not acceptable. 6. The Victoria contains four occurrences of three-beat note values. The first is notated as a __________ tied to a __________. The others are notated as dotted __________. All of them begin on a strong / weak beat. 7. Of the three melodies, the one with the widest range is by ______________. This melody has a range of an octave / a sixth / a seventh. 8. These examples show that rests always begin on strong / weak beats.

EXERCISE 14.1 Using Example 14-2(c) and 14-3 as models, write four melodies in various modes and clefs. Use only note values of quarter-notes and longer. The range of each melody should be no more than a tenth at most, preferably less. If you include a rest be sure it begins on a strong beat (see Examples 14-3(a), m. 5; 14-3(b), m. 7; 14-3(c), mm. 10 and 16). Be careful to make the first note a half-note or longer. It must start on a strong beat.

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14.4 Melodies with Eighths and Sixteenths Although the correct use of eighth-note values and sixteenths is closely dependent on the Latin text to which the melody is set, we can begin to incorporate their use even at this textless stage. Sing-play-sing the melodic lines by Palestrina, Lassus, and Victoria that make up Example 14-4. When answering the questions in Self-Test 14.2, keep in mind that tied notes did not exist in sixteenth-century notation. This means that certain note values were not feasible, for the simple reason that there was no way of notating them. A note could be lengthened only by the addition of a dot, that is, half the value of the note. When a quarter-note is tied over a barline to an eighth-note on the downbeat, this is really just our way of indicating a note that is one-and-a-half beats in duration—exactly the same as a dotted quarternote. It is important to recognize the occurrences of the “single” eighth-note—that is, an eighth-note that is preceded and followed by note values longer than an eighth. In the Palestrina example below, the second note of both m. 4 and m. 5 is a single eighth, preceded by a dotted quarter and followed by a quarter, similar to the single eighth-notes in mm. 7, 9, and 13. EXAMPLE 14-4 Offertory: Ave Maria Palestrina

Motet: Tristis est anima mea Lassus

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Motet: O magnum mysterium Victoria

Benedictus Lassus

SELF-TEST 14.2 True or false 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

In m. 6 of the Palestrina, the last note is a single eighth-note. _________ In m. 9 of the Palestrina, the last note is a single eighth-note. _________ In the Lassus motet, single eighth-notes are found in mm. 2 and 5 only. _________ In none of the examples is a single eighth-note to be found at the beginning of a beat. _________ An isolated pair of eighth-notes (i.e., two eighths beamed together, preceded and followed by longer values) is found in m. 12 of the Palestrina. _________ This pair of eighths occurs on a strong beat and is followed by a syncope. _________ The fifth measure (m. 26), beat 1, of the Lassus motet shows another isolated pair of eighths. _________ The examples show that no more than three eighth-notes in a row can occur in this style. _________ Dotted quarter-notes may begin on either strong or weak beats. _________ The isolated pairs of eighth-notes on weak beats in the Lassus Benedictus are a step apart and are preceded and followed by stepwise motion. _________

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SELF-TEST 14.3 Fill in the blanks or choose the correct word or phrase. 1. The rhythm is excluded in this style because single eighth-notes that occur on the beat will inevitably emphasize the _________________. 2. The sixteenth-note pair in m. 8 of the Victoria occurs on the beat / offbeat. 3. All eighth-notes are approached and left either as repeated notes or by step. The two exceptions are in m. ______ of the Lassus motet and m. ______ of the Victoria. Both these exceptions consist of a leap of a descending / ascending third. 4. In the Palestrina, the eighth-note in m. 4 is a passing tone, that in m. 5 is another _________________. Measure 6 has a lower _________________. On the second half of beat 3 in m. 7 we find an anticipation. There is another anticipation in m. _______. 5. In the Lassus motet, m. 5, we find a single eighth-note functioning as a(n) _________________. 6. All anticipations in these examples occur on the second half of weak / strong beats.

As you go on to Exercise 14.2, remember that pitches follow the same rules as in species counterpoint: mostly stepwise motion with a few leaps and these few must be compensated for by contrary motion either preceding or following the leap. A basic principle here is that the offbeat must not be accented either by agogic accent (i.e., relatively longer duration) or by pitch accent. A concise list of rules for melodies using eighths and sixteenths would include the following: 1. Syncopes are never more than two beats long (half-notes or two tied quarters) nor are they shorter than a beat and a half ( or ). 2. Dotted quarters may begin on either strong or weak beats. 3. Anticipations are approached by step from above and occur only on the second half of a strong beat. 4. Single eighths occur only on the second half of a beat (offbeat). 5. Sixteenths appear only in pairs and on offbeats. Everything about them is stepwise. 6. Isolated pairs of eighths occur only on weak beats unless immediately followed by a syncope; each note is both approached and left by step. 7. Three eighths in a row must begin on an offbeat. 8. As many as ten eighths in a row (or possibly even a few more) may be written, but the last eighth must be on an offbeat. 9. In eighth-notes, leaps occur in a descending motion. 10. A pitch accent on the offbeat is to be avoided: thus, upper neighbors occur only on the beat. 11. All rests begin on strong beats.

EXERCISE 14.2 Considering these rules, and using the melodies of Example 14-4 as models, write four melodies in various modes. Include single eighths as passing tones and anticipations (on offbeat of strong beats only), pairs of eighths either on weak beats or on strong beats preceding syncopes, and short passages with three or more

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eighths in a row. Avoid upper neighbor notes. Keep the range of each melody within the span of an octave, or at most a ninth or tenth.

14.5 Setting Latin Words The chief principle that governs the setting of Latin words in late sixteenth-century style is this: The words must sound smooth and unhurried, and be clearly understandable. The particular rules to implement this principle are these: Rule 1. A single syllable may be carried by any one of the following note values:

Rule 2. Ordinarily an eighth-note or a smaller-value note may not carry a syllable. Rule 3. If a word is accented on the third-to-the-last syllable, then the penultimate syllable may, but need not, have the value of an eighth-note in the rhythm .

Multisyllabic words that include three similarly accented syllables may also be so treated.

Rule 4. Change from one syllable to another should occur only after a quarter or a longer-value note.

Rule 5. Do not begin a syllable on the second half of a beat, since to do so would necessarily accent the offbeat (see Chapter 14.7).

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Rule 6. A syllable is often extended over several notes. Melismas often occur in which a syllable is stretched over many notes. In such cases the syllable that is extended should be the one with the strongest accent.

Rule 7. The beginning syllables of each phrase with a new text are set syllabically.

Composers in the sixteenth century wrote the text underlay somewhat more completely than did those of the fifteenth, but still did not always specify where each syllable is to be placed. Particularly when a phrase of text is repeated it is apt to be unclear, since the music will generally have no more than a ditto mark (“ij” = twice, “iij” = three times) to indicate the number of times the words are to be sung. The seven rules given above are partly derived by scholars from examining many passages where the underlay is given. In addition, the most famous theorist of the sixteenth century, Gioseffo Zarlino (1517–1590), has given ten rules for text underlay that conform quite well with the practice of composers.3 Most of his ten rules are included in our seven. Zarlino also points out that a rest may not be inserted within a syllable—in actual practice within a word. To us today it would seem hardly necessary to point this out, but in medieval music and fifteenth-century music such things happened not infrequently, perhaps a carry-over of the hocket (see page 101, Example 9-7, mm. 192ff., and page 115, Example 9-13, mm. 22–25). One more rule of Zarlino is also important: Rule 8. The last syllable of the text must correspond with the last note of the music. The only exception to this rule is in the case of joyful words like “Alleluia” or “Hosanna,” the last syllable of which is sometimes extended over a melisma resulting in a jubilant quality. A melisma of this sort is, in fact, called a jubilus. Zarlino does not bother to say when repeated notes have to have syllables and when they don’t. However, the practice of composers makes it clear: Rule 9. All repeated notes except the anticipation carry a syllable. The anticipation, always having the value of an eighth-note, is part of what is called the portamento figure. The term itself, meaning “carried over,” implies that there will be no syllable change with either the anticipation itself or the note following. A repeated note with no syllable change is performed by a slight impulse of the voice on the repeated note. Compare the two text underlays of Example 14-5.

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EXAMPLE 14-5

This example also illustrates two rules mentioned previously: (1) m. 3 shows the extension of a syllable through a series of eighth-notes to a quarter or longer before moving to the next syllable (Rule 4); (2) m. 4 shows that unless a repeated note is part of the portamento figure (i.e., an anticipation), any repeated note must carry a syllable (Rule 9). Zarlino implies that the rules regarding the note values for syllable placement are general rules, not to be followed slavishly. The basic principle is that the composer must fit music and text together in such a way that (1) the natural accent of the word is not distorted and (2) there is no roughness due to syllable change after a short note. But common sense and practicality also play a part. When a syllable ending with a vowel is immediately followed by a syllable beginning with a vowel, the rule against changing syllables after an eighth-note may at times be relaxed. One vowel sound might merge with another without the roughness that would be heard in case of consonants so treated. Another point is this: in mass settings, the Gloria and Credo have many words. Palestrina sometimes changes syllables in these movements on or after some short notes, contrary to his practice in music with few words. A more declamatory style results and, perhaps, a slightly briefer movement than would otherwise have occurred (Example 14-6). EXAMPLE 14-6 Pope Marcellus Mass, excerpts from Gloria and Credo Palestrina

14.6 Mode While in theory there were twelve modes available to sixteenth-century composers, in actual practice these were reduced considerably. In the first place, the distinction between authentic and plagal versions disappears in polyphonic music written for various voice types. If the tenor, a high voice, is written in Dorian, the soprano, another high voice, will probably also be Dorian. But the vocal ranges of the lower voices, alto and bass, will of necessity produce Hypodorian lines. It is really not a matter of writing a piece in Mode 1 or Mode 2, but of writing a piece in Dorian mode, the ranges of the various voice types being the

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factor that determines whether each part is authentic or plagal. If a sixteenth-century composer or theorist wanted to assign a mode to a piece, the voice with the C.F., if present, usually determined the entitled mode of the piece. This was usually the tenor voice, so, when no C.F. was present, the tenor was often the voice chosen in assigning a mode. For our purposes, we do not have to consider authentic or plagal in our modal writing, and so we have six rather than twelve modes. But of these six the Lydian mode can be almost disregarded. Since the tritone between the first and fourth degrees of the scale was regularly changed to a perfect fourth by flatting the B, in effect the mode on F became a transposed version of Ionian mode. Only if a piece were to be based on a Mode 5 or Mode 6 plainsong would the composer use the pure Lydian mode. In other circumstances, with a few exceptions, Lydian was normally avoided. We have, then, five modes, each consisting of the keyboard’s “white notes”: Dorian on D, Phrygian on E, Mixolydian on G, Aeolian on A, and Ionian on C. Each of these modes might be transposed up a perfect fourth (or down a perfect fifth) by putting one flat in the signature: Dorian on G, Phrygian on A, Mixolydian on C, Aeolian on D, and Ionian on F. Normally there was no other transposition of a mode.

SELF-TEST 14.4 The following are five excerpts from Palestrina’s works. The text underlay is not necessarily as he would have had it. Sing these through, then answer the following questions: 1. Where, if anywhere, are those spots where a word is distorted by the music? 2. Where are syllables placed inappropriately? Explain. 3. In which mode is each melody?

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EXERCISE 14.3 Set the following Latin phrases as single melodies in various modes and for various voice types. Use only notes of 1, 2, 3, or 4 beats: ,

or

,

or

,

or

Try to let about as many notes of two beats begin on weak beats as on strong beats. Be mindful of the rules of text setting. Cadence by stepwise motion into the final of the mode. Use duple meter only. If you include a rest, be sure it begins on a strong beat. 1. 2. 3. 4.

Pa-ter nos-ter qui es in cae-li. (Our Father who art in heaven.) Cre-do in u-num De-um, Pa-trem om-ni-po-tén-tem. (I believe in one God, the Father almighty.) Et in ter-ra pax ho-mí-ni-bus bo-nae vo-lun-tá-tis. (And on earth peace to men of goodwill.) Quáe-ri-te pri-mum er-go re-gnum De-i. (Seek ye first, therefore, the Kingdom of God.)

14.7 The Single Eighth-Note and the Sixteenth-Note Pair We have already noticed how the single eighth-note may be used as part of the portamento figure (see page 179). It invariably appears in this connection as an anticipation on the second half of a strong beat. The preceding note must, then, be a dotted quarter or ). The single eighth-note may appear in other capacities as well, as listed on the next page. You may object that we have just stressed that only two-beat notes may act as syncopes. Yet, if the anticipation is on the second half of a strong beat, the dotted quarter must begin on a weak beat, producing a syncope. The rule above was given for Exercise 14.1 which did not include eighth-notes. Now that eighth-notes are a possibility, we may use notes of either one-anda-half beats or two beats as syncopes. The following rule, however, first given on page 173, must be stressed: Any note that begins on a weak beat may not be longer than two beats.

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Functions of the Single Eighth-Note

(All illustrations are from Palestrina’s Pope Marcellus Mass.) 1. Anticipation (AN) (portamento): on the second half of a strong beat, approached by step from above.

2. Repeated note: the second half of any beat when the word is of the type to allow a syllable on an eighthnote (Rule 3, page 178).

3. Nota cambiata (NC): a four-note figure only, starting on any beat. The most common rhythm is as illustrated here. (See Example 12-2, page 147.) The first and third notes of the nota cambiata must be consonant with any other voice present.

4. Passing tone (P): the second half of any beat.

5. Lower neighbor (N): the second half of any beat.

6. Consonant leap (CL): a leap (in a downward direction only) of a third, perfect fourth, or perfect fifth, on the second half of any beat.

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It will be noticed that the AN, NC, CL, and N occur only in descending motion. When a note is higher than its surrounding notes it tends to stand out as a pitch accent. The desire in Counter-Reformation composers for a smooth tranquility seems to be behind the reluctance to stress the second half of any beat by an upper N, an upward CL, a NC in an upward direction, or an AN approached from below. In connection with the AN, it would be well to re-emphasize here that it occurs only on the second half of a strong beat—that is, it anticipates a weak beat—and is always approached by step from above. The motive of the falling third anticipating a strong beat, so beloved of Josquin (see page 147), has no place in the style of Palestrina, Lassus, and Victoria. Occasionally composers used single eighth-notes in other ways than those listed above, but these ways happen rarely enough that they cannot be considered typical of the style. Example 14-7 shows two from the Pope Marcellus Mass. The first is a CL followed by another leap in the same direction. Two leaps in the same direction ordinarily occur only with notes at least a quarter in length. Second is an ornamentation of a cadential leading-tone by means of a syncope in diminution. This cadence became standard in the seventeenth century, but is very rarely found in the music of Palestrina, Lassus, and Victoria. EXAMPLE 14-7

Like the single eighth-note, the sixteenth-note pair—and sixteenths appear only in pairs—occurs exclusively on the second half of any beat. In sixteenths, everything must be stepwise: the approach to the sixteenth-note pair is by step, there is a step between the sixteenths themselves, and they are followed by stepwise motion. The excerpts shown in Example 14-8, again from the Pope Marcellus Mass, show sixteenth-note pairs on the second half of beats 1, 2, 3, and 4. Motion to, within, and out of the sixteenths is always by interval of a second. The sixteenth-note pair may be thought of as representing the second eighth in an eighth-note pair; therefore, all rules of rhythm for isolated eighth-note pairs apply also to the figure of eighth- plus sixteenth-note pair. EXAMPLE 14-8

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Since only lower neighbors ordinarily occur in this style, when the sixteenth-note pair is not scalewise it will invariably appear like this:

The upper neighbor is excluded:

The following figure, which gives the impression of an anticipation approached from below, is similarly atypical of the style:

EXERCISE 14.4 Using the same texts as for Exercise 14.3, write four melodies in various modes and for various voice types incorporating several single eighths and at least one sixteenth-note pair in each melody. Reminder: rests begin on strong beats only.

14.8 Isolated Eighth-Notes in Pairs Sing-play-sing the alto melody from the Pope Marcellus Mass in Example 14-9. The melody includes three isolated eighth-note pairs: two eighth-notes surrounded on either side by notes of longer value. This rhythm—short, short, long—is called an anapest. (The two eighth-notes at the start of m. 6 are not an anapest. Being preceded by an eighth, they are part of a series of three eighths.) The eighth-note pair in m. 9 on beat two is the first anapest in this melody. This is a very common figuration, recalling the sixteenthnote figure of Example 14-6(a) but in notes of double value. Just as the sixteenth-notes occur only on the weak half of a beat, so does the isolated anapestic rhythm normally begin only on weak beats. There is a natural correspondence here between shorter notes and weak beats, longer notes and strong beats. The next anapest begins on beat four of m. 10, another weak beat. (Beat one of m. 10 is, of course, a single eighthnote portamento figure since the first note of m. 10 is simply tied over from the previous measure.)

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EXAMPLE 14-9

Eighth-note pairs (anapests) occur on weak beats the great majority of the time. They are heard on strong beats only for the purpose of leading into and stressing a syncope immediately following. Such a use of an isolated eighth-note pair occurs on beat three of m. 13. Sing mm. 12–15 several times, noting how the eighth-note motion on beat three of m. 13 seems to “set up” the augmented fourth that initiates the syncope (with portamento) in mm. 13–14. The rule, then, is this: Isolated pairs of eighth-notes (anapests) normally occur on weak beats only. On strong beats they lead into a syncope. When the anapest is on a weak beat, only stepwise motion is present before, during, and after the eighth-notes. Usually this is also the case when the pair is on a strong beat, but occasionally a downward step or leap followed by a leap up to the ensuing syncope can be very effective. Consider Example 14-10, for instance, again from the Pope Marcellus Mass: EXAMPLE 14-10

SELF-TEST 14.5 Sing the given melodies through, then answer the following questions about each one: 1. Is there any incorrect or unusual use of melodic intervals? If so, where? 2. Do notes of a dotted quarter or longer begin on weak beats at least half the time? Which melody is faulty in having too few syncopes? 3. Are the single eighth-notes used correctly and is the text underlay appropriate when they occur? If not, where is an error to be found? 4. Is there any error regarding sixteenth-notes? 5. When isolated eighth-notes in pairs (anapests) occur on weak beats, is the motion into, between, and out of the pair consistently by step?

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6. Is an anapest on a strong beat invariably followed by a syncope? 7. Is there any incorrect leap involved in an anapest on a strong beat?

14.9 Eighth-Notes in Groups of Three or More The following melodies are from music by Palestrina (a) and (b), Lassus (c), (d), (f ), and (g), and Victoria (e). Sing-play-sing.

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EXAMPLE 14-11

From singing these you may quickly realize some important features of the Renaissance attitude toward melody: 1. As in species counterpoint, the second as a melodic interval far surpasses any leap in frequency of appearance. This is particularly true when motion is in eighth-notes. Of eighth-note leaps, the most common is the third, then the perfect fourth, then the perfect fifth, downward leaps being more prevalent than upward. 2. Upward leaps from an eighth-note sometimes occur. The seven melodies of Example 14-11, containing only two upward leaps involving eighth-notes, are indicative of the usual practice of these composers. Notice that upward leaps, which appear exclusively in melodies (f ) and (g)—both by Lassus—are from an eighth-note on the second half of a beat to a note of larger value.

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Ordinarily, an upward leap does not occur between two eighths. When it does, the leap is invariably from a note on the second half of a beat to a note on the beat. Thus, the offbeat is not stressed by a pitch accent. (See Example 14-12.) EXAMPLE 14-12

3. Eighth-notes appear in series of three, as in Example 14-11(b) m. 3 and m. 5, or up to as many as fifteen or sixteen, as in (d) mm. 3–5 and (f ) mm. 1–3. 4. The nota cambiata may appear with the rhythm rather than as we have seen it before. See, for instance, (b) mm. 3 and 5. 5. Upon resolving, the anticipation often appears with a decoration of sixteenths. In the portamento figure beginning at m. 4 of (b), the anticipation E4 resolves to the same pitch at beat two, then moves in sixteenths down to the B3 on beat three. In m. 5 of (d), m. 4 of (e), and m. 3 of (f ) the anticipation comes during a series of eighth-notes rather than as part of a portamento. The resolution is decorated by the same sixteenth-note figure (AN-N) used to ornament some suspension resolutions. The anticipation with sixteenth-note ornamentation is very common in this style, so common that one might even call it, along with the nota cambiata, a mannerism or cliché. 6. Occasionally Lassus writes small pitch accents on the offbeats without following them with a syncope. These notes are starred in the examples. (See melodies c, d, and f.) Nevertheless, the student should avoid such upper neighbors on the offbeat (unless followed by a syncope) as they are quite rare in the music of Palestrina. 7. Looking back over the examples in this chapter, note that the inclusion of a long melisma in eighthnotes occurs only once in a phrase. Otherwise the words are set syllabically or with only two or three notes per syllable.

SELF-TEST 14.6 Choose the word or phrase that will make the sentence true. 1. In eighth-notes, movement is by stepwise motion some of / much of / the great majority of the time. 2. When in eighth-notes, leaps are occasionally / almost always / normally by downward motion. 3. If there is a leap from an eighth-note on the second half of a beat to an eighth-note on the beat, it may be / must be / is rarely by ascending motion. 4. It is true / false that there is no special number of eighth-notes that may appear in immediate succession. 5. Of the following both are / only the first is / only the second is correct:

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EXERCISE 14.5 Write three melodies to the given texts below. Let the first be for alto in transposed Mixolydian mode, the second for tenor in transposed Phrygian, the third for bass in Dorian. Include the nota cambiata, the portamento, and single eighth-notes, as well as anapests (isolated eighth-notes in pairs) on both strong and weak beats. Also include eighth-notes in groups of from three to twelve or thirteen. Remember to include many syncopes (half-notes or dotted quarters). Some of the portamenti should have sixteenth-note ornamentation upon resolving. Do not include more than one long melisma per melody. 1. Ful-gé-bunt ju-sti si-cut lí-li-um. (The just shall flourish as the lily.) 2. Ky-ri-e e-lé-i-son (or e-léi-son). (Lord, have mercy.) 3. Ju-gum me-um su-á-ve est, et on-us me-um le-ve. (My yoke is easy and my burden light.)

14.10 Use of Accidentals Generally speaking, the sacred style of the late sixteenth century is strictly diatonic. Accidentals are used very sparingly, normally only when necessary to produce a leading tone to a cadence on D, G, or A in original modes or G, C, or D in transposed modes. In addition, one may flat the B in an original mode for the purpose of avoiding a tritone with F or for producing a Phrygian cadence on A. Similarly, in transposed modes, the E may be flatted to avoid a tritone with Bb or for making a Phrygian cadence on D. In most cases, sixteenth-century composers did not actually notate the accidentals. Instead, they relied on the good sense of the performer to include them as musica ficta (see page 90). Sing-play-sing the melodies of Example 14-13 inserting a Bb wherever necessary. (In transposed modes, use Eb.) DO NOT READ ON UNTIL YOU HAVE DONE THIS. EXAMPLE 14-13

In (a) you probably flatted the second note, for if you sang B3-natural the tritone with F3 would have been noticeable. In (b) you should have flatted the B4 in the second measure and in the fourth measure, but not the one in the penultimate measure. In (c) the E5 has to be flatted to avoid leaping by an augmented fourth.

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Naturally, when there is no danger of a tritone present in a single melody it is less obvious where one is to insert a flat on the B or the E. Often the singer must have relied on listening to the other parts, singing a flat where necessary to avoid a cross-relation (Bb immediately preceding or following a B-natural in another part, or Bb and B-natural occurring simultaneously). In Example 14-14, m. 38, Palestrina wants a Phrygian cadence on D. In the cantus, then, he writes in an Eb5 to prevent the singer from making an authentic cadence with an E5-natural and a C#5. The tenor, picking up the Eb5 from the cantus, knows to flat his first two E4s as well. In m. 40 the tenor’s second note must again be Eb4 or he would have to have leapt a tritone from the Bb3. The bass assumes his first E3 is to be flatted because he is imitating the tenor’s line (mm. 37–38). But the E3 in m. 40 cannot be entrusted to the bass singer’s instinct, because there is not sufficient evidence at this exact point one way or another. He cannot know for certain that the tenor’s note on the second half-note of the measure will be an Eb4. (Remember, there were no scores—each singer had only his own part.) Therefore Palestrina writes in the flat for him. Similarly, the composer will occasionally write in a cautionary accidental natural sign to prevent a singer from flatting a B or E that he might otherwise have presumed to be necessary. EXAMPLE 14-14 Motet: Tollite jugum meum Palestrina

In our exercises we will never rely on musica ficta. Write in every accidental you wish to be sung.

14.11 Melodic Curve A Renaissance melody customarily rises to a zenith and then descends. Often the zenith is near the beginning of the line, often it is nearer the end. Occasionally the zenith begins the line or possibly ends it. As in species counterpoint, the focal point may be a nadir rather than a zenith. Although most phrases have clear focal points, especially those of the highest voice in a composition, not every phrase is a complete unit in and of itself. Often, as phrase follows phrase, a larger curve becomes

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apparent. One of Palestrina’s most famous motets, Dies sanctificatus, in Mixolydian mode, has a cantus in which the zeniths of the various phrases combine to form a rising curve to the approximate center, then make a gradual descent to the final closing tonic. Note the scarcity of long melismas. The entire cantus of this motet is reproduced as Example 14-15(a). Example 14-15(b) is a summary that shows the zeniths of each phrase and the descent to the final in the last few measures. EXAMPLE 14-15 (a) Motet: Dies sanctificatus Palestrina

The Melodic Line

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(b) Summary

The overriding aesthetic of the sacred style of the late Renaissance is Apollonian: music should exhibit the quality of serenity. It should show restraint from emotional extremes, and its parts should show rational and well-proportioned relationships. This aesthetic, as applied to single melodic lines, can be manifested in a few basic principles. Principle: Melodic Lines are Simple and Coherent.

This is the same as the first principle we encounter in species counterpoint. Turning back to page 23 you will find this principle is put into practice by the use of the diatonic scales, by stressing stepwise motion, by compensating for leaps by means of subsequent contrary motion, and by providing a clear focal point (zenith or nadir). Principle: The Text Sounds Smooth, Unhurried, And Is Clearly Understandable.

Turning back to page 178 you will be reminded that this principle is put into practice chiefly by placing a syllable on notes at least a quarter in length and changing syllables only after a note at least a quarter in length. Melismas occur on syllables with the strongest accent. Words having an accent on the third-tolast syllable (“Ky-ri-e,” “glo-ri-a”) often allow only an eighth-note for the next-to-last syllable. Principle: Melodic Lines Flow Smoothly, Free From A Strong Metric Pulse.

The smooth flow of the line is, to a large extent, ensured by the normal absence of accents on the second half of a beat. Turning back to page 183, you will find several rules are applicable here: the avoidance of the upward leap on the second half of a beat, the avoidance of an upper neighbor note, the use of single eighth-notes only on the second half of a beat. But the upper neighbor may be used to call attention to a syncope following immediately. The undesirable effect of a strong metric pulse is avoided partly by using

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eighth-notes in pairs only on weak beats except as a means of setting off a syncope. A strong metric pulse is further avoided by being careful not to repeat rhythmic patterns in immediate succession.

EXERCISE 14.6 Using the given text, write a lengthy melody for soprano in Ionian mode consisting of four phrases. Use notes of all values as in previous exercises. Let each phrase have a clear focal point, nadir or zenith, but also contrive to form an overall rising curve climaxing somewhere in the last phrase. Try to make the melody elegant and beautiful and let it give the effect of being metrically free. Without sacrificing their general aesthetic, Renaissance composers normally let their music correspond to any ascending or descending motion implied by the text. Descending motion, for instance, would be called for in setting the words “passus et sepultus est,” while ascending motion would be appropriate for “et resurrexit” and “et ascendit in coelum.” 1. Cru-ci-fíx-us é-ti-am pro nó-bis. (“He was crucified also for us.”) 2. Sub Pón-ti-o Pi-lá-to pás-sus et se-púl-tus est. (“Under Pontius Pilate suffered and was buried.”) 3. Et re-sur-réx-it tér-ti-a dí-e se-cún-dum scrip-tú-ras. (“And rose on the third day in accordance with the scriptures.”) 4. Et a-scén-dit in cóe-lum. (“And ascended into heaven.”)

Chapter 15

Modal Counterpoint in Two Voices

Sacred music during the Counter-Reformation, as practiced by Palestrina, Lassus, and Victoria, was more strict regarding dissonance treatment than music has ever been before or since. This is one reason why it is advantageous for us to spend a fair amount of time learning to imitate it. If the style with the strictest dissonance treatment is mastered, there can be no problem in dealing with less strict styles. Our study of second- and fourth-species counterpoint has given us the opportunity to acquire some skill in the use of passing tones on weak beats and suspensions on strong beats. In fact, the most essential rule for dissonance treatment in the sacred style we are studying is this: dissonances on strong beats must be suspensions; dissonances on weak beats must be passing tones. All other dissonances occur exclusively on offbeats. In the notational system we are using, note values will be half as long as they were while we were practicing species counterpoint. In addition to passing tones and suspensions, we will be using anticipations, neighbor notes, and escape tones.

15.1 The Dissonances Passing Tones

Half-note passing tones on weak beats in second-species counterpoint become quarter-notes on weak beats (Example 15-1). EXAMPLE 15-1

Far more common is the eighth-note passing tone on the second half of any beat (Example 15-2).

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EXAMPLE 15-2

The accented passing tone occurs only as an eighth-note on the first half of a weak beat. It is called “accented” because, although it occurs on a weak beat, the passing tone is rhythmically stronger than its offbeat resolution. It occurs in descending motion only. An exceptional feature of the accented passing tone is that, contrary to normal dissonance treatment, both it and the note it is dissonant against may begin at the same time. Compare Example 15-3(a) and (b). Both are correct. It must be stressed that the accented passing tone appears only in descending motion and occurs only on a weak beat. EXAMPLE 15-3

It is possible to have an unaccented and an accented passing tone in immediate succession (Example 15-4). EXAMPLE 15-4

Suspensions

Half-note suspensions on strong beats in fourth-species counterpoint become, in our “halved” notation, quarter-note suspensions on strong beats (Example 15-5). In two-voice counterpoint only 7–6 and 4–3 occur as upper-voice suspensions. The 9–8 and 2–1 suspensions are used only when a thicker texture— three or four voices or more—permits a fuller sound on the resolution. The 7–6 is preferred to the 4–3, as the 7 is a more pronounced dissonance. The 4–3 in two-voice writing is, in fact, somewhat infrequent. In lower-voice suspensions, the 2–3 (9–10) is, of course, the only possible suspension.


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EXAMPLE 15-5

It must be remembered that in sixteenth-century notation there were neither barlines nor ties. The way to lengthen a note was to dot it, adding half its value. The following note values, then, were not feasible as there was no way of writing them:

It follows that the preparation for a suspension must be either a quarter-note or a half-note in length, but if it is a half-note the suspension cannot have an ornamented resolution since, of course, there would be no way of notating it (Example 15-6). EXAMPLE 15-6

Neighbor Notes

Neighbors occur as eighth- or sixteenth-notes exclusively and, to avoid a pitch accent on the offbeat, almost always as lower neighbors (see page 183) (Example 15-7). Occasionally one finds an upper neighbor as a way of leading into and emphasizing a syncope (Example 15-8). EXAMPLE 15-7

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EXAMPLE 15-8

Anticipations

An anticipation always has the value of an eighth-note and, as has been emphasized before, occurs only on the second half of a strong beat. Its function is to stress a weak-beat note by anticipating its pitch. Thus it makes no difference whether the anticipation is consonant or dissonant. Remember to approach it by step from above (Example 15-9). EXAMPLE 15-9

Escape Tones

There is only one context in which an escape tone appears in this style: as the second note (the eighthnote) of the nota cambiata. This eighth-note may be consonant or dissonant; it makes no difference. However, the first and third notes of the figure must both be consonant. If the fourth note of the nota cambiata is on a weak beat it may be treated as a dissonant passing tone (Example 15-10). It is very important that the first note of the nota cambiata, the dotted quarter, be consonant on each beat—that is, both the beginning of the note and the dot must be consonant in order to avoid the impression of a suspension in diminution. EXAMPLE 15-10

EXAMPLE 15-11


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As shown in Example 15-11, if the voice accompanying the nota cambiata has a dissonant note on the second beat, the effect is of a 7–6 suspension squeezed into a single quarter-note beat. A correct suspension, of course, lasts a full quarter-note beat, the resolution coming on the next weak beat. A similar situation can occur with passing tones as shown in Example 15-12. EXAMPLE 15-12

This situation occurs when one voice has a quarter-note passing tone against an eighth-note passing tone in the other voice. In this case the effect of a 4–3 suspension squeezed into a single beat results. The only time the “dot” of a dotted quarter can be dissonant is in the case of the ornamented suspension. See Example 15-13(a). In our notation dots can occur only on quarters or half-notes. In either case the dot must be consonant unless it represents a suspension. See Example 15-13(b) and (c). EXAMPLE 15-13

15.2 The True Cadence The clausula vera (“true cadence”) is the chief cadential type in the style on which we are concentrating. (As we shall shortly see, there are also other ways of ending a phrase.) The various means of producing the clausula vera all have the same basic skeleton: the standard two-voice cadence as you have learned it in previous chapters of this book, complete with suspension. In Chapter 10 you learned how to write twovoice cadences in fourth species (see page 123). Example 15-14 shows typical fourth-species cadences with their sixteenth-century-style counterparts in our “halved” notation. A version with ornamented resolution is also given.

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EXAMPLE 15-14

If you compare the fourth-species cadences with their sixteenth-century counterparts, you will find only superficial differences between them. 1. Examine 15-14(b). It will be remembered that the approach to the cadential scale-degree ^2 is not a matter of indifference (see page 21, item 5). The ^2 as a cadential note has to be approached in such a way as to make it part of a descending line. Normally the ^2 is approached by step from ^3 or by leap of a descending third from ^4. Nevertheless, at times the note immediately preceding ^2 is actually ^1 (not shown in Example 15-14), in which case the descent of the line is felt as occurring previous to this ^1. 2. Example 15-14(c) shows a Phrygian cadence. In the sixteenth-century sacred style, all cadences on E are Phrygian cadences: one voice will have E–D–E while the other has F–E. There is no D# in the style at any time. In other respects, the two-voice Phrygian cadence is similar to the two-voice cadences in other modes. In a non-transposed mode, a cadence on A may, by introducing Bbs, be of the Phrygian rather than the Aeolian type. Similarly, in a transposed mode any cadence on A will be Phrygian, with the possibility, by introducing Ebs, of a Phrygian cadence on D. No other transpositions of the Phrygian cadence are possible in the style.


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Succinct rules for creating a true cadence in two parts are as follows: 1. Choose the cadential note, which for the purposes of the cadence will be considered scale-degree ^1. This need not be the final of the mode of the piece unless you are writing the cadence for the last phrase. ^ is E, the cadence must be of the Phrygian type. In transposed modes, Phrygian If the cadential note (1) cadences are used on A. 2. The voice that moves from ^7 to ^1 must also precede the ^7 by ^1 in order for the cadential suspension to take place. One of the voices, then, will move ^1–^7–^1, the last two notes forming a suspension and its resolution. 3. The voice that moves from ^2 to ^1 must dwell on ^2 for at least two beats in order to act as the accompanying voice for the cadential suspension. The approach to 2^ must be by step or by leap of a third from above. 4. The suspension may be ornamented in one of the ways shown in Example 15-14.

15.3 The Initial Phrase in Two Voices Treatment of the various motions is the same in late sixteenth-century music as in species counterpoint: oblique and contrary motions are always good (except consecutive perfect fifths or perfect octaves by contrary motion); parallel unisons, perfect fifths, and perfect octaves are excluded; similar motion into a unison or perfect octave is excluded; similar motion into a perfect fifth is avoided except in the case of “horn fifths”—a third descending to a perfect fifth or a sixth ascending to a perfect fifth. Example 15-15 offers three illustrations of opening phrases. The first phrase of a piece invariably begins with long note values, at least a half-note, usually a dotted half or whole. One voice begins alone and the text is set syllabically. The second voice begins shortly with an imitation of the first voice’s opening motive usually at the perfect fifth above or below, though it may be at the perfect fourth, perfect octave, or even the unison. Play-sing-play the following. EXAMPLE 15-15 (a) Missa Frère Thibault Lassus

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(b) Cantiones duarum vocum, X Lassus

(c) Magnificat Palestrina

Notice first the complementary rhythm. Once motion on each beat begins (generally by the third measure at the latest) there is movement in one voice or another on each quarter-note beat. When one voice holds, the other moves. Thus the activity of the two voices is approximately equal. The excerpt by Lassus, Example 15-15(b), ends with what has come to be called a hocket cadence. The suspension voice (with the leading-tone) finishes normally, but the accompanying voice ends with the ^2. Rather than going on to ^1, the ^2 is followed by a rest. In these excerpts overhanging brackets show the opening motive and the extent of its imitation. There is no uniformity here. In Example 15-15(a) only the first four notes are imitated. In the others the imitation extends approximately three full measures. Example 15-15(c) includes two cases of voice crossing (marked “x3”). Imitation is by contrary motion.

15.4 Interior Phrases All phrases in a piece other than the first are interior phrases. Here are two examples. Play-sing-play them both before reading on.


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EXAMPLE 15-16 Missa Frère Thibault Lassus (a)

Missa Douce memoire Lassus (b)

Both of these phrases begin on weak beats. While interior phrases sometimes begin on strong beats, it is normal for them to begin on an upbeat, providing a closer connection between the end of one phrase and the beginning of the next. In addition, the weak beat beginning of an interior phrase gives it a kind of lilt, preventing it from plodding stodgily from phrase to phrase. In Example 15-16(b) the answering voice begins one beat after the initial voice. While the first voice begins on a weak beat, the second voice begins on a strong beat. This type of imitation is not so common as the type exemplified in Example 15-16(a) (weak beat answered by weak beat) but is not particularly rare. It is referred to as imitation per arsin et thesin, or “by arsis and thesis,” an arsis being an upbeat and a thesis a downbeat. Example 15-16(b) actually consists of two phrases, although the upper voice is not given a rest between them. By this maneuver the voices change function: for the penultimate phrase the alto leads, the cantus follows; for the final phrase the cantus leads and the alto follows. Generally each voice acts as leader in approximately half of the phrases.

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The final cadence of Example 15-16(b) should be examined closely. It appears to be a 2–3 suspension with the usual sixteenth-note ornamentation but in augmentation, note values doubled to eighths. This effect is of a built-in ritardando. Literally speaking, however, no rule has been changed. Example 15-17 shows the suspension with the normal sixteenth-note ornamentation as well as the same in augmentation. It can easily be seen that in the latter case the suspension may be said to resolve normally on the first C#4 (beat two), which is then followed by a lower neighbor, returning to the C#4 as a consonance. EXAMPLE 15-17

15.5 Method for Writing a Two-Voice Phrase 1. Select a text in Latin, perhaps from a mass or motet by a famous composer, or translate a text of your own choice into Latin. Be sure you know the meaning of each word as well as the stressed syllables. Let us take “Et in ter-ra pax ho-mi-ni-bus” (“And on earth peace to men”) from the Gloria of the mass. 2. Decide on a mode and whether it is to be original or transposed. (Remember, the only available transposition is up a perfect fourth with one flat in the signature.) Let us take untransposed Dorian. Decide voice types, in this case alto and soprano. 3. Starting on scale-degree ^1 or ^5 of the mode, set the opening word or words to a motive. (At the beginning of the phrase be sure to allow only one note for each syllable of the text. Only after three or four syllables is it customary to use melismas.) Let the other voice imitate this motive a perfect fourth or fifth above or below. Or it may imitate at the perfect octave above or below, or at the unison. We will begin with the alto and let the soprano imitate at the perfect fifth above (Example 15-18). EXAMPLE 15-18

4. In the leading voice, add counterpoint against the answering voice’s opening motive (Example 15-19).


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EXAMPLE 15-19

5. Complete the melodic line in the answering voice, making a suitable cadence. Add the cadence of the leading voice (Example 15-20). EXAMPLE 15-20

6. Complete the leading voice (Example 15-21). EXAMPLE 15-21

7. The result is a complete phrase in two-voice counterpoint (Example 15-22).

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EXAMPLE 15-22

SELF-TEST 15.1 Each of the following staves contains two similar fragments. Identify the incorrect ones, giving a reason for your opinion.


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EXERCISE 15.1 Write three separate phrases in two-voice counterpoint: (1) for soprano and alto in transposed Dorian, (2) for alto and tenor in Ionian, (3) for tenor and bass in Phrygian. Choose texts from among the following if you wish. Use a different text for each phrase. (Words of two syllables accent the first.) These should all be considered initial phrases of a piece. (Hence, begin syllabically.) 1. O-scu-lé-tur me o-scú-lo o-ris su-i. “O that you would kiss me with the kisses of your mouth.” (Song of Solomon 1: 2) 2. Flo-res ap-pa-ru-é-runt in ter-ra no-stra. “Flowers appear on the earth.” (Song of Solomon 2: 12) 3. Di-léc-tus me-us mi-hi, et e-go il-li. “My beloved is mine and I am his.” (Song of Solomon 2: 16) 4. Qui sé-qui-tur me, non ám-bu-lat in té-ne-bris. “He that followeth me walketh not in darkness.” (John 8: 12) 5. Ne-mo cu-rat, né-mi-ni cu-rae est; pa-thé-ti-cum, i-ta est. “Nobody minds, nobody cares; pathetic, that’s what it is.” (Eeyore in Winnie ille Pu, Chapter VI) 6. Non sem-per di-e na-tá-li mi-ser es-se de-bes. “You don’t always want to be miserable on my birthday, do you?” (ibid.)

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15.6 The Consonant Cadence Interior phrases may conclude without a true cadence simply by coming to a halt on a consonance. The last note of the phrase is usually a half-note or a whole-note, rarely a quarter although that is a possibility. Of course a phrase never ends with an eighth-note or sixteenth. Generally, each voice in the texture cadences at a slightly different time. In Example 15-23, the brackets ( ) show where each voice ends one phrase and begins the next. EXAMPLE 15-23 Cantiones duarum vocum, IV Lassus

The plagal cadence commonly occurs at the end of a composition after the final true cadence (with suspension) has finished. Normally the final is held in the upper voice and consonances beneath this final (almost inevitably scale-degrees ^4 and ^6) produce what we would call today subdominant harmony (Example 15-24). EXAMPLE 15-24 Cantiones duarum vocum, XI Lassus


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15.7 Analysis of a Bicinium The bicinium given as Example 15-25 is one of twelve Cantiones duarum vocum (“Songs for Two Voices”) composed by Lassus and published in 1577. The text is from the Scriptures (1 Corinthians 2: 9). Phrase 1: Eye has not seen, nor ear heard, Phrase 2: nor has it entered into the heart of man Phrase 3: what things God has prepared Phrase 4: for those who love him, those who love him. The division of the text into phrases follows the natural sense of the passage. Phrases that make some sense in themselves, sometimes even single words, may be repeated. Often it is the final phrase that is repeated, as in this case.1 Sing-play-sing each part of Example 15-25 then play them together, before reading on. EXAMPLE 15-25 Cantiones duarum vocum, III Lassus

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Cadences

Phrase 1 ends in m. 9 with a consonant cadence. Phrase 2 ends in m. 15 with a standard Phrygian cadence on E. Phrase 3 ends in m. 20 with a standard Aeolian hocket cadence on A. Phrase 4 ends the piece with a standard Dorian clausula vera. All cadences have a strong feeling of closure due in part to the sixteenthnote ornamented cadential suspension followed by some cessation of motion. Even Phrase 1, though literally a consonant cadence, includes this sixteenth-note ornamentation in the lower voice. However, one must not expect to find the ornamented cadential suspension consistently in other pieces. Mode

The Dorian mode of this piece is ascertained by the ending. The main body is not clear in regard to mode. True, the alto voice taken alone stresses scale-degrees ^5 and ^1 of Dorian mode and its range seems to be plagal. On the other hand, taken alone the cantus would appear to be Aeolian. This ambiguity is typical of polyphonic modal music during the late sixteenth century. Although at least one voice invariably enters with ^1 or ^5 of the mode, the other voice will imitate at the octave, perfect fourth, or perfect fifth. If the second voice to enter does so on ^5, the first voice may very well begin not on ^1 (a perfect fourth above or a perfect fifth below) but on ^2 (a perfect fifth above or a perfect fourth below). The impression, then, is that the piece is beginning in a different mode. In this case, the listener hears one voice beginning on ^2 then a second voice beginning on ^5: E followed by A. There is no way the listener can know these pitches represent ^2 and ^5 of the Dorian mode, for they could just as well (or better!) be taken as ^5 and ^1 of Aeolian or ^1 and ^4 of Phrygian. Similarly, Palestrina, in his famous Pope Marcellus Mass in Ionian


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mode, begins with D in the first two voices and continues with G, thus giving the impression of Mixolydian at the start. In the sixteenth century a composer was not necessarily bent on establishing a key or mode right away. While at least one voice will begin on ^1 or ^5 (and many times all voices do) the listener cannot be certain of the mode until the end. The interior cadences do not help either, at least not in every case. In Example 15-25 the cadences are on A, E, and A—certainly more typical of Aeolian or Phrygian than of Dorian. Yet the final cadence is on D. This is very different from Example 14-15(a) (pages 192–193), the cantus from Palestrina’s Dies sanctificatus. There the top line clearly denoted the Mixolydian mode, as shown in Example 14-15(b). Both this Palestrina piece and this Lassus piece are typical: sometimes a piece is very clear as to its mode and sometimes it is not. Later we shall see how, with the rise of tonality in the seventeenth century, composers gradually came to lay their cards on the table right away. In the eighteenth century the establishment of the key at the start of the piece was almost a requirement, having the force of an aesthetic principle. Imitation

In Example 15-25 the imitative passages are shown by overhanging brackets. It happens that this piece is highly imitative, much more so than many compositions of Lassus, Palestrina, and Victoria. Imitation may be considered the very foundation of the contrapuntal style of the late sixteenth century. (This is not to say they did not compose homophonic pieces, for they often did. But they did not usually write non-imitative counterpoint as did, for instance, Ockeghem in his Missa Mi-Mi.) Usually the imitation is not so far-reaching as in Lassus’s piece given here, but is only a matter of a measure or two at the beginning of each phrase.

15.8 Writing a Bicinium The following points should help you in writing a bicinium in the style of the second half of the sixteenth century. You should check all these with Example 15-25, with the excerpts of Example 15-15 (pages 201–202), and with the other Lassus bicinium given on pages 212–213 in connection with Exercise 15.2. 1. Begin the first voice on scale-degree ^1, ^2, or ^5 of the mode. If you choose ^1, the second voice should enter on ^1, ^4, or ^5. If you choose ^2, the second voice should enter on ^5. If you choose ^5, the second voice may enter on ^1, ^5, or ^2. But if the piece is to be in Phrygian mode, begin on ^1 or ^4, with the second voice also entering on ^1 or ^4, because it is not customary to begin on the pitch-class B. 2. The second voice should imitate the first for only a few notes. The lengthy imitations of Example 15-25 are not particularly typical. An imitative motive of only two notes is even possible. Be sure to use the same text underlay for the imitation as you did for the original motive. To ensure comprehensibility, the first few notes should have one syllable of the text each. 3. Cadence at a point in the text where there is a natural division in the sense. Any type of cadence will do, though for a continuous flow the hocket is the best technique. 4. Following the cadence, a voice should rest before beginning the next phrase. All rests begin on strong beats, beat 1 or 3. In other words, end a phrase with a long note, a whole or half, but not with a dotted half. Occasionally a phrase may end with a quarter-note, but if it is to be followed by a rest, this quarter-note must occur on a weak beat. 5. It is possible to include a rest within a phrase provided it does not do damage to the sense of the text and provided that the rest begins on a strong beat.

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6. At least one voice must be sounding at all times. To ensure this, the cadences of the two voices will usually overlap to some extent. In other words, one voice will begin the new phrase before the other voice has released its last cadential note. 7. If a portion of the text is repeated, it is customary, though not essential, to repeat its melody as well. Each portion of the text has its own motive, and each phrase will begin with a new musical idea. 8. Words that suggest motion or height are usually depicted accordingly: an upward line for ascendit (“ascended”) or surge (“arise”), a downward line for descendit (“descended”), higher pitch for coelum (“heaven”), lower for terra (“earth”) or mortuos (“dead”). Otherwise there is little attempt at word painting. “Madrigalisms” were mainly reserved for secular music during this period of music history. 9. Interior phrases, like opening ones, always begin with imitation. This imitation is usually like that of the opening phrases: at the perfect fifth, perfect fourth, or perhaps the octave or unison. However, it is possible for interior phrases to imitate at some other interval such as a second, third, sixth, or seventh. 10. When writing a hocket cadence be sure to fit the text to the music in such a way that a textual unit is finished before the rest begins. See, for instance, Example 15-25, m. 20: the last syllable of “De-us” comes on scale-degree ^2 of the cadence (upper voice) in order for the word to be completed before the rest.

EXERCISE 15.2 1. Study the bicinium Cantiones duarum vocum, No. 7 (“Justi tulerunt”). Note its mode, the location and type of internal cadences, the details of the imitative entrances of each phrase, and the dissonance treatment. In the penultimate measure, what irregularity do you find in the alto line? Cantiones duarum vocum, VII Lassus


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The just took the spoils of the wicked, And they sang, O Lord, to thy holy name And thy conquering hand they praised With one accord, O Lord our God. 2. Compose a bicinium consisting of at least three phrases. In order to keep the voices from being too far apart it is safest to choose adjacent voice types (soprano/alto, alto/tenor, tenor/bass) although it is possible to write for alto/bass or soprano/tenor by means of careful spacing. But do not write for soprano and bass. Use any text that can be construed as at least three textual phrases. You may wish to choose one from Appendix A.

Chapter 16

Modal Counterpoint in Three Voices

On the following pages are two pieces, one each by Lassus and Palestrina. Later in the chapter we will study a third piece, one by Victoria. The first two use the mass text Be-ne-díc-tus qui vé-nit in nó-mi-ne Dó-mi-ni (“Blessed is he that cometh in the name of the Lord”). These words occur at a particularly solemn moment in the Mass, where the words of consecration are pronounced over the bread and wine. Traditionally, the music for this text is given a hushed quality, and it was common during the Renaissance to use fewer voices at this moment. Thus, a mass for four or five voices will call for only three for the Benedictus, and a mass for six voices will call for only four. It is important to be familiar with the music we are focusing on. Before reading further you should get to know both settings of the Benedictus thoroughly. First, sing each line separately; then, with two classmates, perform the piece. Next, play the music several times on the piano or, if possible, the organ. If necessary you may use the two-staff reduction. Missa pro defunctis: Benedictus Lassus


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Missarum liber tertius, de feria: Benedictus Palestrina


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16.1 Texture Texture in music has to do with the relationship of the voices to each other. When all voices move together in the same rhythm, as in conductus style (see page 28), we speak of homorhythmic texture. When one voice is clearly the melody, the others accompanimental, we call the texture homophonic. Plainsong, along with other unison melody, is an example of monophonic texture. In a genuine contrapuntal texture the voices are so composed that no single voice is more prominent than any other, and yet each voice can, through attentive listening, be heard as an independent and musically satisfying entity. Throughout this book we have had occasion to point out certain factors that contribute to a genuine contrapuntal texture: (a) independence of the melodic curves (focal points of the same type occurring at various times, not

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simultaneously); and (b) complementary rhythm (a voice moves or repeats while another holds or rests). Another aspect of texture has to do with striving for richness of harmony. In practice, this means that at least two voices must be sounding at all times. In other words, rests may occur in only one voice at a time. In the two Benedictus movements these textural characteristics are plainly in evidence. In addition, other aspects of the music clearly point to particular stylistic qualities shared by these compositions and which are generally true of all sacred music of the Roman school. The first of these has to do with complementary rhythm: after the first measure or two, a composite rhythm emerges by which some event is felt to occur on or during each beat—either movement of voices or a new articulation of a given pitch. Secondly, although each voice is allotted a number of rests, these are given to only one voice at a time. In other words, except at the very beginning of the piece, the sonority is not that of a single voice, but of at least two voices, thus assuring the constant presence of harmony. In these short three-voice compositions there is less opportunity for textural variety than is afforded by longer pieces for more voices: they maintain a fairly uniform contrapuntal texture throughout. Occasionally, though, one can discern a change for brief moments. A typical example is shown in Example 16-1 from the Lassus. EXAMPLE 16-1

Here linear independence is reduced from three lines to two, since during the bracketed segments the top and bottom voices move homorhythmically in parallel thirds against the line and complementary rhythm of the middle voice. A similar situation may be noticed in the Palestrina piece beginning on beat three of m. 22 and lasting until m. 24, and again in m. 28. Such cases of three voices producing only two independent lines are common in the music of the time.

16.2 Cadences Example 16-2 (page 221) shows various ways of treating the clausula vera in three voices. The standard two-voice clausula vera is the basis of all these, the variations resulting from (1) the position of the cadential voices, (2) ornamentation of the suspension resolution, (3) various pitches and/or continued motion in the non-cadential voices, (4) hocket, and (5) production of full sonority by movement of scaledegree ^2 to scale-degree ^3 instead of to ^1. It should be kept in mind that at any given moment at least two voices are sounding—that is, in three-voice counterpoint one voice only may rest at a time. Normally, the final cadence of a piece makes its mode unmistakably clear. In all modes except Phrygian, this final cadence will position the two cadential voices in the upper parts so that the bass will inevitably move from ^5 to ^1. In other words, the final cadence coincides with what today we would call an authentic cadence, with both V and I triads in root position. The consistency with which sixteenth-century


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composers ended their compositions in this manner shows a growing awareness of the strength of the dominant to tonic bass. It may thus be considered a foreshadowing of the practice of tonal composers of the late seventeenth through the nineteenth centuries. Following this final cadence there may be a codetta-like extension. In the case of Phrygian there can, of course, be no question of a dominant to tonic bass. The standard final cadence in Phrygian has ^2 in the lowest voice and ^1–^7–^1 in an upper voice, often followed by an extension with a plagal cadence. Interior cadences, the endings of phrases within a piece, are written in many different ways. Any of the types shown in Example 16-2 are commonly found. A point mentioned before but that must be stressed again is this: it is usual for every true cadence to include the cadential suspension occurring between the voice with ^1–(#)^7–^1 and the voice with ^2–^1. This means the ^2, approached by step or descending third, has to be present for at least two beats in order for the voice with ^1–(#)^7–^1 to form a suspension against it. Thus, in Example 16-2, all cadences have the note A3 or A4 as a half-note approached by step or by leap of the third from above. EXAMPLE 16-2 Basic two-part cadence

Model three-part cadences

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Remarks: (a) ornamented resolution of the 7–6 suspension (portamento) (b) ornamented resolution of the 4–3 suspension (sixteenth-note figure); also, the third voice has continued motion through the cadence (c) deceptive cadence (third voice moves to ^6 instead of to ^1) (d) hocket cadence (cadential voice with ^ 2 drops out) (e) full-sonority cadence (cadential voice with ^2 moves to ^3 instead of to ^1). Interior phrases do not always cadence on the final of the mode as would the last phrase of a piece. Interior phrases may cadence on any note except B-natural. However, certain notes seem to be used only in connection with certain modes. For example, cadences on E are rare except in Aeolian and Phrygian while cadences on F are rare except in Dorian. Cadences on C, G, A, and D might well occur in any mode. In transposed modes, cadences on A are quite common. Because of the flat in the signature, these will be Phrygian cadences. In original modes, cadences on A may be either Aeolian-type cadences or Phrygiantype. Of course, the latter require Bb and G-natural, the former B-natural and G#. Example 16-3 shows three-voice cadences on various notes, all by Palestrina. Study these before attempting to do the exercises. The first three are in original modes, the others transposed. Lines are drawn to show the two cadential voices—those that move stepwise into the final. As you play-sing-play through the cadences, answer the following questions about each of them. DO NOT READ ON UNTIL YOU HAVE ANSWERED THESE QUESTIONS. 1. What type of suspension do the cadential voices create in themselves? 2. If there is another voice beneath the cadential voices, what type of suspension does the whole texture have? 3. Is the suspension ornamented? If so, is it with the portamento or the sixteenth-note figure? 4. In the cadences with hockets, which voice drops out? Is it ever the voice with the leading-tone? 5. Which pitch classes may carry an accidental? 6. Is there a cadence with continued motion?


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EXAMPLE 16-3

Remarks on Example 16-3 with reference to the questions above: 1. The two cadential voices always produce a 2–3 suspension in themselves if the voice with scale-degree (#)^7 is beneath the voice with ^2. A 7–6 suspension is produced if the voice with ^2 is below. 2. Since the cadential voices in all these cases are supported by a third voice beneath them on ^5, the suspensions will be labeled 54. In the case of Example 16-3(e) there is a “six-five chord” suspension (65) with portamento ornamentation before the cadence takes place. 3. In Example 16-3(b), the suspension produced by the cadential voices is ornamented with the sixteenthnote figure. 4. All except the last are hocket cadences. The voice with the leading-tone always completes the cadence. Either of the other voices may drop out. 5. Example 16-3(e) is both a hocket and a full-sonority cadence: ^5 in the lowest voice drops out and is replaced by a rest, and ^2 in the top voice moves to ^3 rather than to the expected ^1. 6. Example 16-3(c) and (e) are cadences with continued motion. That is, one or both of the cadential voices continues the line without interruption.

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SELF-TEST 16.1 Fill in the blanks or choose the correct word(s): 1. 2. 3. 4.

The Lassus Benedictus includes _________ true cadences found in mm. _________. These cadence on the notes _________. In the first of these, the standard two-voice cadence occurs in the _________ and _________ voices. The Palestrina Benedictus, discounting mm. 7 and 29–30, includes _________ true cadences. These are found in mm. _________. 5. The cadences in the Palestrina are on the notes ___________________. 6. In the Palestrina, the standard two-voice cadence appears in the two upper voices in none / all / half of / only one of the cadences.

Having completed the Self-Test, you are now in a position to summarize the cadence types to be found in the two pieces. The summary given is, with the exception of Phrygian cadences, generally true of all music in the sacred style of the Roman school. 1. Final cadence. The two upper voices have scale-degrees ^1–^7–^1 and ^2–^1, with the ^5–^1 in the lowest voice (Lassus: mm. 20–21; Palestrina: mm. 36–37). 2. Interior cadences. Any two voices may act cadentially but the ^1–^7–^1 is far more frequently an upper, rather than the lowest, voice (Lassus: mm. 9–10; Palestrina: mm. 9–10, 18–19, 23–24, 28–29). The ^2–^1 may appear as an upper voice (Palestrina: mm. 18–19) or lowest voice (Palestrina: mm. 10, 23–24). 3. Full-sonority cadences. In order to bring in the sound of an imperfect consonance, the cadential voice with ^2 moves to ^3 rather than to ^1. Full-sonority cadences are found both as interior and as final cadences. 4. Hocket cadences. Any voice except the one with ^1–^7–^1 may drop out at the last moment (Palestrina: mm. 18–19). 5. Other cadences with rests. In spite of the appearance of rests, a cadence is not considered a hocket cadence unless the rest occurs as a substitute for the last note of the cadence. For example, in the Lassus Benedictus (mm. 9–10) the bass drops out before the upper voices begin their cadence. It re-enters just as the top voice sounds the ^7. Consider also the Palestrina (mm. 9–10). Here the soprano voice drops out before the alto and bass begin the cadence. The soprano re-enters just as the cadence is completed. 6. Cadence with continued motion. At least one cadential voice completes a phrase. The other voice or voices continue for a time. There is a cadence of this type at mm. 29–30 of the Palestrina. Here the soprano and alto are the cadential voices, but the soprano moves from scale-degree ^2 to ^3, producing a full-sonority cadence. It continues the line into the next measure. 7. Consonant cadence. Neither the Lassus nor the Palestrina ends with a plagal cadence. There is, however, a consonant interior cadence at mm. 11–12 of the Lassus. 8. Pseudo-cadence. This is a “false cadence.” It can be discerned when the music has all the characteristics of a cadence except one essential: it is not the end of a phrase. Such a situation happens in the Palestrina at m. 7. In this case the initial notes of the motive in one voice are identical to part of a cadential formula, thus causing the likeness. In the Palestrina, the bass enters on the motive E3–E3–A3, the upward perfect fourth supporting the alto’s ^1–^7–^1 figure.


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EXERCISE 16.1 1. Write two-voice authentic cadences for alto and tenor, each one two measures long: (a) Ionian mode; (b) Mixolydian mode; (c) transposed Aeolian mode. 2. Add a bass to these two-voice cadences, changing them to three-voice cadences. Do not alter the basic two-voice cadence but add ornamentation. 3. Add a soprano to the two-voice cadences, changing them to three-voice cadences. Do not alter the basic two-voice cadence but add ornamentation.

EXERCISE 16.2 1. Write two-voice interior cadences for alto and bass on the notes F, D, and A using ornamentation as desired. Continue for one measure after the cadence. 2. Add a soprano to these two-voice cadences changing them to three-voice cadences. Continue the soprano into the extra measure. 3. Alter whatever is necessary to change them into hocket cadences. 4. Make at least one of the cadences a full-sonority type.

16.3 Motives and Imitation If you sang through each voice of each of the three pieces we are considering, you must have noticed the close relationship between musical motives and the text. In the Lassus, for instance, each time the word “Benedictus” appears it is sung to the motive

and “in nomine” is almost invariably either

or its close relative

The Palestrina piece goes even farther in this regard, since not only is the word “Benedictus” consistently set to the motive

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but the subsequent syllables “qui ve-”[nit] regularly have an independent motive:

The practice of establishing an inseparable connection between a text and the musical subject to which it was sung is typical of the style we are studying. A particular musical motive—especially at the beginning of a phrase—is associated with a particular set of words and, conversely, those words with that motive. In the second half of the piece by Palestrina, not only is the text “in nomine” set to its own motive

but the subsequent word “Domine” usually begins

16.4 Victoria’s Et Misericordia Ejus: Cadential Treatment The piece by Tomás Luis de Victoria has the text Et mi-se-ri-cór-di-a é-jus a pro-gé-ni-e in pro-gé-ni-es ti-mén-ti-bus é-um (“And his mercy [is on them] who fear him from generation to generation”). These words, part of the Magnificat (the canticle of Mary as found in the first chapter of the Gospel According to St. Luke) are intended not for the Mass but for the office of Vespers, held in monasteries and some churches in the late afternoon. The practice of Renaissance composers was to alternate between a unison chant formula and polyphonic settings. Thus, in a particular setting of the Magnificat only the evennumbered verses or only the odd-numbered ones might be set to music in a contrapuntal style. After becoming thoroughly acquainted with the piece in the same manner that you did for the Lassus and Palestrina, identify all the cadences and describe them to yourself. Then take the following Self-Tests, both of which refer to the Victoria.


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Et misericordia (from Magnificat Tertii Toni) Victoria

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SELF-TEST 16.2 Fill in the blanks: 1. Discounting mm. 11–12 and 29, there are _________ true cadences in the Victoria. Of these several are / one is a Phrygian cadence(s) on A and two are / one is / none is deceptive. 2. Measures 32–33 exhibit a _________ cadence. 3. The cadence at mm. _________ is a rather extreme example of the cadence with continued motion. 4. All cadences are on the note _________ except the one at mm. _________ which is on C, and another at mm. _________ which is on _________.

SELF-TEST 16.3 Choose the correct word(s): 1. In mm. 9–10 there is a Phrygian / Aeolian cadence with continued motion in the lower voices. The interval from ^ 2 to ^ 1 is in the uppermost / lowest voice and is a minor / major second. 2. The piece ends in mm. 32–33 with a true / plagal / Phrygian cadence. 3. The cadence at mm. 13–14 is / is not a hocket cadence. 4. The cadence in m. 29 may be described both as a hocket and a deceptive / plagal / true cadence. 5. At m. 11 the soprano motive for the syllables “a pro-ge-” is identical to the ^ 1–^ 7–^ 1 suspension figure of a true cadence, yet no voice completes a phrase until m. 14. At mm. 11–12, then, we have a half / deceptive / pseudo cadence.

16.5 Victoria’s Et Misericordia Ejus: Motivic Treatment Find the various motives in the Victoria and identify each of them according to the text they regularly carry. DO NOT READ ON UNTIL YOU HAVE DONE THIS. You probably discovered that at the beginning of the piece there is one long motive for the words Et misericordia ejus (“And his mercy”) and another motive, used twice only, for the repetition of the word ejus in alto and tenor. In other words, the tenor is a canonic imitation of the alto up to beat three of m. 8. The phrases a progenie (“from generation”) and in progenie (“to generation”), being so much alike, are set to the same motive—the cadence-like ^1–^7–^1 figure mentioned earlier. When we come to timentibus eum (“who fear him”) we find these words set to two contrasting motives. On the one hand, the tenor has a three-measure motive imitated by the soprano (mm. 18–24). This is characterized by repeated quarters and scalar eighths. After this they reverse roles and tenor imitates soprano after only one measure (mm. 26–28). The outer voices are thus opposed to the middle voice, the alto, who sings the same text in a staid rhythm of slow-moving notes. The alto’s motive, covering a range of no more than a minor third, is first heard in mm. 19–21, and then repeated in mm. 21–25, followed by another statement transposed up a perfect fourth (mm. 26–29), after which it returns to its original pitch level (mm. 29–32).


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Clearly we have here a situation utterly unlike the first half of the piece—and unlike the Benedictus settings of Lassus and Palestrina—since the long note values and limited pitch material of the alto are in strong contrast to the quicker movement of the outer voices. What is here sounds very much like two counterpoints against a C.F. As mentioned above, the Magnificat was customarily sung with verses in unison chant alternating with verses in a polyphonic setting. Traditionally, the Renaissance composer unified the Magnificat setting by referring to the original chant even in the verses set contrapuntally. Sometimes the reference was far-reaching indeed—the chant might serve as a C.F. basis for the entire movement, much as chorale tunes appeared in Lutheran music (see the pieces by Walter on pages 156–157 and 160–162). In this piece, Victoria has made explicit use of only the second half of the chant formula (Example 16-4). The first half of the chant is hinted at in the soprano just before the alto begins the reiterated C.F. statements (see soprano line beginning on beat four of m. 15 and going through m. 20). One might make a case for the opening motive of the piece being a variation of the first half of the chant minus its initial ascent (Example 16-5). EXAMPLE 16-4

EXAMPLE 16-5

In spite of the similarity in contour and range of the two lines, the fact that the Victoria melody is placed a third higher to a different position in the scale is enough to cast doubt on there being an intentional resemblance here. To sum up, a piece in the style of Lassus, Palestrina, and Victoria is based on the principle of imitative counterpoint. The opening word or words of each phrase of the text are set to a motive that is retained— though rarely with perfect consistency—throughout the phrase. Thus the voices imitate each other both verbally and musically. If a second phrase uses the same words, it will also use the same musical motive. New words call for new motives, which are then imitated in turn by the other voices. Cadences in one voice overlap with phrase beginnings in another voice, so that a continuous flow is produced. As in the

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bicinium, each voice begins on scale-degree ^1, ^2, or ^5, and in Phrygian ^1 or ^4. Imitation is at the unison, octave, perfect fourth, or perfect fifth (see page 211, item 1).

16.6 Part Writing Although we have had some practice in three-part writing during our survey of species counterpoint and in the first exercise of this chapter, there is still a further point to consider. This has to do with the motion of the voices with respect to each other. If a performance of our three pieces is listened to with attention, one may notice that not once do all three voices literally move in parallel or even in similar motion. In two-voice counterpoint, of course, the voices may move in the same direction, producing parallel thirds or sixths or reaching an imperfect consonance by similar motion. But in three-voice counterpoint of the late sixteenth century, parallel motion in three voices, the fauxbourdon style, is very rare indeed. Perhaps more surprising is the reluctance on the part of those composers to allow three voices to move even in similar motion. At least one voice will invariably remain on a constant pitch while the others move. Otherwise, it will move in an opposite direction to them. EXAMPLE 16-6

In Example 16-6(d) the movement of the upper voices is from perfect fifth to diminished fifth. Strangely enough, even when the motion is from perfect fifth to perfect fifth, Palestrina apparently considers that the addition of the sixteenth-notes (or a portamento) is enough to offset the effect of parallel fifths, provided they are not between outer voices. The same does not hold true of parallel octaves and unisons (Example 16-7).


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EXAMPLE 16-7

Examples of tolerable fifths between bass and middle voice, as shown in Example 16-7, may be found in mm. 21–22 and in m. 36 of Palestrina’s Benedictus (pages 216–219) as well as in Example 16-3(d) (page 223).

16.7 Consonant Harmonies There are many combinations of consonant intervals possible in three voices: Perfect consonances exclusively:

8 8 8 5 5 1 8 1 5 5 1 1

Imperfect consonances included:

8 8 6 6 5 3 3 6 3 6 3 3 3 1

Having become thoroughly familiar with our three pieces, you may be aware that all thirteen of these combinations do not appear regularly as consonant sonorities. Except at the beginning and end of a piece, there is a definite preference for those that include imperfect consonances, particularly those with a 3. By far the greatest stress is on the full sounds of 83, 63, and 53, with 33 and 31 appearing somewhat less often. As we saw at the beginning of this book, the third is a more stable consonance than the sixth (see pages 34–35). The combinations 86 and 66 as well as those without imperfect consonances tend to appear on weak beats as passing chords or in some other unstressed capacity. Consider mm. 5–10 of the Victoria. Here there are nineteen vertical sonorities of which fourteen are 83, 63, or 53. There are three 85s and two 86s. The rich sound of late sixteenth-century choral music is largely due to the high saturation of consonant harmonies that include the interval of a third above the bass: 83, 63, and 53. EXERCISE 16.3 1. Write a textless phrase of three-voice counterpoint at least six measures in length in transposed Dorian ending with a final cadence. Consonant harmonies should stress 35s and 36s. Use only note values of a quarter and larger. 2. Do the same in Mixolydian mode.

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16.8 Unaccented Dissonance As we have noted several times in this book, a dissonance on the second half of any beat may take the form of a passing tone, a lower neighbor, or—if part of the nota cambiata—an escape tone. The portamento allows for an anticipation on the second half of strong beats only. Such passing tones and lower neighbors are to be found in abundance throughout our three pieces. The nota cambiata in the Lassus at m. 8 provides an example of the dissonant escape tone. The one in the Palestrina at m. 18 is consonant. The anticipation does not occur either in the Lassus or the Victoria example, but is very prevalent in the Palestrina: mm. 6, 9, 18, 21, 27, 28, and 31. A double anticipation is in m. 36. It should be noticed that throughout these pieces the dissonant eighth on the second half of the beat occurs against other notes already sounding. Two notes dissonant with each other do not begin at the same time. This is a principle that holds true generally in all music of this style. For instance, examine Example 16-8. EXAMPLE 16-8 Missa Spem in alium: Credo Palestrina

At (a) the tenor’s portamento figure occurs against a nota cambiata in the bass. On the second half of beat one, their second notes could correctly be dissonant, but because they begin together they are rendered more harmonious by being consonant with each other. At (b) the bass’s note G3 is a passing tone consonant with the eighth-note in the alto’s nota cambiata. At (c) the tenor’s nota cambiata has a C4, consonant with the alto’s passing tone G4. Although most of the time composers followed the general rule that dissonant notes do not begin together, one comes across occasional exceptions. The most frequent are in the case of the accented passing tone, to be discussed in Section 16.9. Other exceptions occur exclusively on the second half of a beat and only when each of the two voices is acting according to normal practice. Example 16-9 will illustrate some possibilities.


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EXAMPLE 16-9 O Magnum mysterium Victoria

Missa Papae Marcelli: Benedictus Palestrina

At (a) the lower neighbor in the tenor sounds against repeated notes in the alto and bass. At (b) the soprano has a passing tone clashing against the second note of the lowest voice’s nota cambiata.

16.9 Accented Passing Tones As we learned in the previous chapter, when an eighth-note passing tone occurs in descending scalar motion, it may be dissonant even on the first half of a beat, provided that beat is weak. If you turn back to Example 15-3 (page 196) you will see that the accented passing tone and the note it is dissonant against may begin at the same time. When played on the piano this simultaneous attack of a dissonant interval may seem more of a clash than when it is sung in a correct Renaissance manner, and in any case, the obligatory descending motion of the voice with the passing tone mitigates the dissonant effect. Even such a “harshness” as occurs in the third measure of Example 16-10 sounds quite acceptable in a good performance.

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EXAMPLE 16-10 Missa Repleatur os (Credo) Palestrina

Not only is there an accented passing tone in m. 3 of Example 16-10, forming a second against the alto, but soprano and alto move in parallel seconds from beat one to beat two. This passage is clearly an orna5 mentation of the standard 65 Con4 54— —3 formula (see Example 16-11(a) and pages 136–137). EXAMPLE 16-11

The “harshness” comes about through the desire to ornament the top line. Palestrina could have accomplished this without the clash simply by using sixteenth-notes for the ornamentation rather than eighths (Example 16-11(b)). But sixteenths occur shortly before this point and immediately after. Perhaps Palestrina was reluctant to add a third set of sixteenths so close to the others. For whatever reason, he chose to use notes of more equal value despite the resulting seconds. Returning to our three pieces, we can see that the accented passing tones can be explained as a result of equalization. In m. 25 of the Victoria we find a case remarkably similar to the one written by Palestrina. Compare Example 16-12(a) with the third measure of Example 16-10. EXAMPLE 16-12


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By the simple maneuver of resolving the “six-five chord” suspension with a portamento figure, Victoria avoids the parallel seconds, but his accented passing tone produces the same dissonant second as in Palestrina. Measures 11 and 13 of the Victoria give further instances of the accented passing tone (Example 16-13). EXAMPLE 16-13

In both cases equalization, with its resulting accented passing tones, has managed to avoid the type of parallel fifths that appear in the Palestrina (mm. 21–22 and 36). One may question the validity of the argument for equalization presented above by asking why it is necessary. Can’t the accented passing tone be explained just as well simply by referring to the rule against pairs of eighth-notes on strong beats? Example 16-14 is self-explanatory. EXAMPLE 16-14

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As a justification for this passage the two arguments seem about equally useful. Nevertheless, equalization is sometimes the only plausible explanation for some accented passing tones, as in Example 16-10.

EXERCISE 16.4 Write two textless phrases of three-voice counterpoint including note values of eighths and sixteenths. Each phrase should be at least six measures in length. Use at least one accented passing tone in each phrase as well as several unaccented dissonances. Choose any mode, transposed or not, and cadence on the final of that mode.

16.10 Suspensions We begin with a short review. It will be remembered from our study of fourth species in three parts (Chapter 11, pages 130–137) that it is useful to think of the voices of a three-voice suspension in terms of their functions: the voice with the suspension is the suspension voice; the voice against which the suspension is dissonant is the accompanying voice; the remaining voice is the third voice. There are three harmonic essentials in a suspension figure: 1. The preparation, in which the voices form a consonant sonority. 2. The suspension, in which one of the upper voices becomes the suspension voice by forming a ninth, seventh, fourth, or second with the lowest (accompanying) voice; or, in which the lowest forms a second or ninth with one of the upper voices; or, in which one of the upper voices, acting as suspension voice, forms a second or seventh with the other upper voice (the “six-five chord” suspension). 3. The resolution, in which the suspension voice descends by step, forming a consonance with the other voices, which have either held their notes or moved on to other consonances. Metrically speaking, the preparation can begin on either a strong or weak beat; the suspension must occur on a strong beat and the resolution on the weak beat immediately following the suspension. The pitches chosen for the third voice in a suspension figure are very important to the tension/relaxation effect desirable in a suspension figure. Of course, for the preparation and resolution the third voice will have a pitch that is consonant with the others. Especially for the resolution, however, it is important that this consonant sonority include the full sound of an imperfect consonance. At the suspension itself, the third voice will sound a note that has the potential of providing a consonant resolution for the suspension. Thus, the usual pitch for a 9–, 7–, or 2– upper-voice suspension is a 3 (Example 16-15(a), (b), and (c)); for a 4– suspension it is a 5 (Example 16-15(d)). In case of a lower voice 2– or 9– suspension, it is 4 or 5 (Example 16-15(e), (f )). While other pitches are sometimes possible, these are by far the most common. The “six-five chord” is, of course, a special case, since the accompanying voice is an upper voice rather than the bass, and the resolution either must be a Con4 or must be accomplished by a move on the part of the third voice (bass) (see Example 16-15(g) and (h)).


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EXAMPLE 16-15

Since the interval of a perfect fourth is not a strong dissonance, the preference of Renaissance composers in a 4–3 suspension is to place the third voice on the fifth above the bass: 54—53 . The 5 and 4 together form — a second or seventh, adding pungency to the sonority. Sometimes, though, the third voice has the sixth above the bass (see Palestrina, m. 8, and Victoria, m. 17). This usage can result from matters of voice leading, motivic structure, or possibly simply the desire for a softer sound. In spite of the general rule that the preparation of a suspension must be consonant, occasionally a brief dissonant note may be allowed to appear. There are several such moments in our Victoria example (Example 16-16). The preparation, due to the soprano’s passing G4, is 75. The resolution, due to the soprano’s accented passing tone E4, begins as 54. (See also Victoria, mm. 11 and 13, and Palestrina, m. 6.) EXAMPLE 16-16

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From time to time there seem to be flagrant violations of the so-called “rules” for suspensions. Generally these do not seem so much like lapses but rather as alternative means of writing, and they rarely sound truly out of place in the style. One such occurrence is in mm. 31–32 of the Palestrina. Before reading on, examine these measures and try to ascertain in what way they break the “rules.” Also, ask yourself whether, when you performed this piece numerous times at the beginning of your study of this chapter, you felt these measures were somehow different from the rest of the piece. Did they seem especially crude, expressive, bland, pungent? Or do they blend in with the rest of the piece and so are not particularly noticeable? The problem, of course, is that while the 7–6 suspension in m. 32 is perfectly normal, the preparation is strange indeed. The alto’s E4 on beat four of m. 31 is the preparation, but in no way can it be considered consonant. (1) It forms a seventh with the bass F3. (2) If the bass F3 is taken to be an accented passing tone, the two lower voices, E3 and E4, form a fourth with the soprano. (3) The “preparation” on beat four of m. 31 is essentially the same as the suspension on beat one of m. 32. To clarify the issue we can draw up a speculative “original” for these measures—a kind of model from which Palestrina’s actual bass line deviates (see Example 16-17). EXAMPLE 16-17

It has to be admitted that the freedom Palestrina has allowed himself at this point is fairly extreme for his style. Sixteenth-century theorists sometimes spoke of certain liberties taken “for the sake of the imitation.” In this case, the word “Domine” may have demanded the motivic treatment of the three eighths in descending motion. The good effect of the whole passage, though, probably has more to do with the fact that any two voices taken alone act in a normal manner (Example 16-18). EXAMPLE 16-18


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EXERCISE 16.5 Write one phrase of textless three-voice counterpoint that includes at least three suspensions of various types not counting the final cadential suspension. Make use of all note values.

16.11 An Alternative Example Example 16-19 is a piece published by Palestrina in 1588 in a group of settings of the Lamentations of Jeremiah. The text (Lamentations 3: 24) is Pars mé-a Dó-mi-nus, dí-xi á-ni-ma mé-a, prop-tér-e-a exspec-tá-bo é-um (“The Lord is my portion,” says my soul, “therefore will I hope in Him”). It divides itself naturally into three phrases, but Palestrina combines the first two, then repeats the last. The result is still three phrases. Study this piece carefully, then note the ways in which it differs from what we have learned is the norm. DO NOT READ ON UNTIL YOU HAVE TRIED TO ANSWER THESE QUESTIONS. 1. 2. 3. 4. 5.

Is there special dissonance treatment? Explain. Is there anything unusual about the form? Explain. Is there anything novel about the texture or motivic treatment? Does the rhythmic movement conform to what is to be expected? Is there anything else especially noteworthy?

EXAMPLE 16-19 Lamentationum Hieremiae prophetae: Pars mea Dominus Palestrina

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If you considered the piece thoughtfully, your answers were probably something like these: 1. Yes, there are several spots where the dissonance treatment is unusual: (a) Measure 7, the 7 between soprano I and alto begins on beat two and continues through beat three. It is as if soprano I had a suspension figure with no corroboration from the other voices. (b) Measure 16 beat four is the preparation for the 7–6 suspension at the beginning of m. 17, but it is not a consonant sonority since the B3 in the alto is a dissonant passing tone. (c) Measure 21 has a quarter-note passing tone in soprano I against a dotted quarter followed by an eighth-note passing tone. Thus the dotted note is not


2. 3. 4.

5.

6.

7.

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consonant throughout (see Example 15-12, page 199). (d) Measure 22 beat three: since the perfect fourth above the bass is not prepared as a suspension, the six-four sonority on the strong beat is abnormal. The form is unusual in that each musical phrase comes to a complete end rather than the customary overlapping (m. 11, cadence on C; m. 17, cadence on G). The texture of this work is not consistently contrapuntal. Measures 9–10, 12–13, and 18–19 are almost “conductus style.” From m. 8 on, the texture is much less openly imitative than normal. Although the word “exspectabo” has a descending scale motive imitated in the other voices (mm. 14–16 and 19–22), this imitation is concealed within the phrase rather than initiating it. The beginning of the piece is somewhat unusual in that soprano II answers soprano I by what has later come to be called “tonal imitation”: soprano II answers soprano I at the perfect fourth below except that its first note has been lowered from B4 to A4. Thus the answer begins with a rising third rather than a rising second. We call this a tonal answer since the two versions of the opening subject clearly indicate the key of A, Aeolian mode. Also, in mm. 5–6 soprano I has a free diminution (smaller note values) of the tonal answer. The rhythmic movement is less steady than normal. Usually one can expect some kind of articulation on or during each beat once the piece is underway. But there are empty beats in mm. 7, 11, 12, 13, 17, and 18. Unusual part writing occurs in m. 13 in which all three voices move by similar motion. (But remember: events in descending motion are less prominent, and unusual happenings in descending motion are less obstrusive—think of “horn fifths” and accented passing tones. So similar motion in all voices by descending motion is less out of place than had it been a case of ascending motion.)

Palestrina’s Pars mea Dominus has been included here to illustrate the fact that, when he felt so inclined, even a composer as consistent as Palestrina was able and willing to take liberties with his compositional style. The student, on the other hand, should rarely take these liberties. We are more concerned here with becoming intimately acquainted with the regular and normal application of contrapuntal principles. The chief value of studying Pars mea Dominus, then, is to reinforce our knowledge of usual practice by pointing to that which is unusual.

EXERCISE 16.6 Write a piece (motet, mass section, or Magnificat verse) in three-voice contrapuntal style using as models the pieces by Lassus, Palestrina, and Victoria focused on in this chapter. Latin words may be of your own choosing or select a text from Appendix A. Make a fair copy and perform the work in class or with your friends. If you choose to write a Magnificat verse, consult Appendix C where you will find the entire text and the chants in the various modes.

Chapter 17

Modal Counterpoint in Four or More Voices

17.1 Texture Two pieces in four-voice counterpoint are given on the following pages. These are written in short score to enable you to play them easily on the piano or organ. The first, by Palestrina, is a section from the Credo of his famous Pope Marcellus Mass. This mass is composed in six-voice counterpoint, but, like the Benedictus, the section beginning with the words “He was crucified . . . ” is generally set for fewer voices (by tradition). The particular quality of this piece is noticeably different from the other music of the Roman school that we have so far considered. Rather than the continuous flow due to overlapping phrases, this piece is comprised of many clearly defined phrases, some as short as three measures and none longer than eight. With the exception of the last phrase, the words are not repeated—in fact, each voice is not necessarily given the complete text. In the case of the creed, owing both to its length and to its doctrinaire phraseology, the composer must seek to get through the words efficiently without extending the piece unduly. Play through this piece several times until its sound is thoroughly familiar to you. You will probably have noticed immediately that this mass section is written in non-imitative counterpoint. Another feature is its great textural and timbral variety: paired tenor (T) and bass (B) as opposed to paired alto (A) and soprano (S), the three lower voices as opposed to the three upper voices. Out of its 42 measures, only about 18 call for all four voices simultaneously, 17 are for three voices (approximately equally divided between the three upper and the three lower), and 7 are for two voices. Very striking is the predominance of homorhythmic passages: mm. 8–10 (“passus, et”), 12–14 (“Et resurrexit”), 19–21 (“Et ascendit in coelum”), 30–33 (“vivos et mortuos”), and 37–38 (“cujus regni”).


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EXAMPLE 17-1 Missa Papae Marcelli: Credo Palestrina

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He was crucified for us under Pontius Pilate Suffered, and was buried. And he rose on the third day According to the scriptures. And ascended into heaven, Sits at the right hand of the Father. And he will come again in glory To judge the living and the dead, Whose kingdom will have no end.

All these strongly declamatory areas consist of consonant sonorities, a perfect octave, perfect fifth, and a third above the bass—in more modern terms, triads in root position with the root doubled. Only twice does a passing tone turn a triad into a 63 sonority (m. 20 beat 4 and m. 38 beat 2). It is rather typical of homophonic writing in four or more voices to stress these root position triads, progressing by bass motion of perfect fifths or perfect fourths, by seconds, and sometimes by thirds. Homorhythm in three voices also appears. This takes place in the fauxbourdon passages where several parallel 63s occur in


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succession (m. 3 to m. 4 beat two; m. 14 beat 3 to m. 15, and m. 26). Three-voice fauxbourdon is not uncommon in multi-voice counterpoint as a textural contrast. Play through the motet O vos omnes by Victoria (Example 17-2) several times. Intended for the austere Holy Saturday service (the night preceding Easter), its character is rather subdued. Like the Palestrina creed section, it consists of a number of short, clearcut phrases that group themselves into four parts, Part Four being a restatement of Part Two with the addition of the final sonority (see mm. 33 and 52). This work does not show the striking textural and timbral changes of the Palestrina, although the appearance of three-voice fauxbourdon offers relief at mm. 25–26, 44–45 and 46–47. EXAMPLE 17-2 O vos omnes Victoria

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O all ye who pass this way, behold and see: If there be any sorrow like unto my sorrow. Behold, all nations (peoples) and see my sorrow.

Without being markedly imitative, O vos omnes makes some use of imitation. The opening measures illustrate a fairly common device: the pairing of imitative entries. In mm. 1–2, T ascends a third followed by the ascending third of S; A ascends a perfect fifth followed by the ascending perfect fifth of B. Thus there are essentially two opening motives, the ascending third performed by the high voices (S and T) and the ascending perfect fifth performed by the lower (A and B). A similar passage is to be heard at mm. 34–36. This time S and A begin with the rising third followed by T and B with the rising perfect fifth. Sometimes, as at mm. 11–13, one or two voices do not participate in the imitative entries. Sporadic imitation may be perceived occasionally within the phrase rather than initiating it. At mm. 20–21, for example, A seems to be echoing T on the word similis, and again at mm. 21–23, T imitates S.

17.2 Doubling in Consonant Sonorities Within a musical context certain tones, such as a leading-tone or a suspension, exhibit a strong tendency to move in a particular way, the leading tone up by half-step, the suspension down by diatonic step. These tendency notes carry a special weight or emphasis which precludes their being doubled in another voice. To double them would result in adding even more emphasis to them. Besides, the doubled note, also carrying the tendency, would have to move against this tendency or the result would be parallel octaves. Thus we may formulate a general rule: Do not double a tendency note. In the musical style we are dealing with, the practical result of this rule in 53 and 63 sonorities is to avoid doubling a leading-tone (B before a cadence on C, E before a cadence on F, or any pitch class raised a half-step by musica ficta). Any other note may be doubled. However, reference to Examples 17-1 and 17-2 confirms that in the case of a 53 sonority it is usual to double the bass, though owing to linear considerations a different note may be doubled. For instance, in the Palestrina (Example 17-1) at m. 38 beat one, the 3 above the bass is doubled in order to produce the desired smoothness of line in S and T. In the third bar of the Victoria (Example 17-2) the C#5 in S and the E4 in T are both constrained, in order to avoid augmented intervals and parallel perfect fifths, to move to D5 and D4 respectively. (See also m. 41.) With a 63 sonority any note may be doubled: in m. 20 beat four of the Palestrina it is the bass’s note; in m. 38 beat two and m. 40 beat four it is the third above the bass. In the Victoria at m. 4 beat two, the sixth above the bass is doubled. Of course when the sixth is the leading-tone, as at m. 9 of the same piece, it must not occur in another voice as well.

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Very occasionally, owing to musica ficta, one comes across a 63 consisting of a minor sixth and a major third above the bass—what today we would call an augmented triad in first inversion. In this case, the downward pull of the minor sixth against the upward pull of the major third (the interval between them being either an augmented fifth or a diminished fourth) is enough to imbue them both with tendencies. In such a case we double the bass (see Example 17-2, m. 21 beat four).

17.3 Suspensions in Four Voices Suspensions in four-voice counterpoint are a simple matter, since there is little distinct difference between most suspensions in three voices and those in four. By playing through Examples 17-1 and 17-2 again, with special regard to the four-voice suspension treatment, you will find that in most cases the addition of the fourth voice simply means a doubling of the accompanying voice. For instance, in the Palestrina at m. 11, the A3 of the accompanying voice (the bass) is doubled by the soprano, and in the other four-voice suspension (m. 41) the same doubling occurs in the alto. Similar doublings are present in the Victoria at m. 4 beat three, on the first beats of mm. 8, 9, 19, and 23, and on the third beats of mm. 29, 32, 35, 42, and 45. All these are either 4–3 or 7–6 suspensions and all the cadential suspensions are of the authentic type. When we look at the 7–6 suspension forming part of a Phrygian cadence we find a different treatment. Example 17-3 illustrates. Since in Phrygian ^2 is only a semitone above ^1, its pull toward ^1 is perhaps felt to be strong enough to preclude doubling it. And, in any case, if the ^2 were to occur in an upper voice as well, it would be difficult to find a correct subsequent motion for this upper voice. It should be pointed out that one occasionally comes across 7–6 suspensions with the third above the bass doubled even when they are not part of a Phrygian cadence.1 EXAMPLE 17-3 O vos omnes Victoria

There is another method of writing 7–6 suspension in four voices, illustrated by mm. 15 and 22 of the Victoria. In the suspensions occurring on the first beat of these measures, no voice is doubled. Instead the fourth voice sounds the fifth above the bass, subsequently moving to the third above the bass for the resolution. Example 17-4(a) shows the basic form of this suspension, while (b) and (c) show Victoria’s elaborated versions.


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EXAMPLE 17-4

5 At m. 29 of the Victoria, there is a case of a four-voice 65 Con4 54— —3 . The doubled note for the six-five chord suspension is the bass. But a six-five sonority need not double any note. Example 17-5 shows how Palestrina lets the fourth voice sound the third above the bass, making a 65 (similar to a complete seventh 3 chord in first inversion).

EXAMPLE 17-5 Motet: Alleluia tulerunt Palestrina

For the 9–8 suspension, the resolution inevitably doubles the accompanying voice (the bass). The fourth voice, then, always sounds the fifth above the bass which, along with the third sounded by the third voice, 8 give a full 5 sonority. Example 17-6 illustrates. 3

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EXAMPLE 17-6 Missa Lauda Sion: Credo Palestrina

The bass-voice suspension 2–3 (or 9–10) is rarely found in four or more voices. When it does appear, the accompanying voice is generally doubled, though there would seem to be no compelling reason against doubling the third voice. See Example 17-7. EXAMPLE 17-7 (a) Palestrina, Motet: Sicut cervus (b) Palestrina, Missa Lauda Sion: Kyrie

Double suspensions are not frequent. When they do occur they are almost always a 9–8 combined with a 4–3 (see Example 17-8(a)) or a 7–6 with a 4–3. With double suspensions, one but not both of the suspensions is usually provided with an ornamented resolution. When a double suspension consists of a 4–3 above a 7–6, parallel fifths will result. In this case either the 4–3 or the 7–6 must be ornamented to make the effect acceptable. The basic principle of three-part suspensions—that the resolution must not be anticipated by the third voice—is not strictly observed in the case of double suspensions in four or more parts (see Example 17-8(b)). Evidently the sixteenth-century composer felt that in a thick texture the effect of tension/relaxation was sufficiently expressed if just one of the suspensions received normal treatment.


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EXAMPLE 17-8 (a) Palestrina, Missa de feria: Kyrie (b) Palestrina, Missa ad fugam: Kyrie

In Example 17-8(a) the three lower voices form a consonant sonority for the preparation of the two suspensions. Simultaneously S has a dissonant passing tone. In Example 17-8(b) the double suspension results in parallel P5s since the 4–3 is above the 7–6. In addition, T anticipates the note of resolution. 8 is all but nonexistent, its rarity no doubt due to the disappointing effect of The double suspension 97— 6 — resolving on an 86 (see Example 17-9(a) and (b)). Lower-voice double suspensions, such as are illustrated in (c) and (d) of Example 17-9 are also extremely rare. Students should not ordinarily employ these unusual constructions. Still, when the double suspensions are a tenth apart, rather than as in Example 17-9(d), a good though unusual effect results (Example 17-10). In Example 17-10, T is the accompanying voice for both the S and B suspensions. Therefore, even though T sounds the resolution of the suspension in S, the rule against the third voice anticipating the note is not broken. EXAMPLE 17-9 Double suspensions to be avoided:

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EXAMPLE 17-10 Motet: O magnum mysterium Victoria

Drawn from the music of Palestrina, the musical fragments that follow are presented as a convenient way of reviewing the various suspension treatments in four voices. First are the upper-voice suspensions 9–8, 7–6, and 4–3, followed by the lower-voice suspension 2–3 (or 9–10). The “six-five chord” suspension follows, first with three different pitch classes (one doubling) and then with four different pitch classes, similar to a complete seventh chord in later music. Double suspensions, that is, simultaneous suspensions in two upper voices, are illustrated: the 7–6 with the 4–3, and the 9–8 with the 4–3. It is quite rare to find double suspensions in which one is an upper voice and the other is a bass voice, but two possibilities are shown.

Summary of Suspensions in Four Voices 7–6

4–3 and 9–8


2–3

—6 6–5 and 7 4 —3

9— 8 and 9— 8 2 —3 4 —3

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SELF-TEST 17.1 Comment on each of the following. If correct, what aspect of the foregoing discussion is being illustrated? If incorrect, why?

17.4 The Final Cadence As in three-voice final cadences, the true cadence at the end of a piece will always allow for scale-degree ^5 to move to ^1 in the lowest-sounding voice. This means, of course, placing the two cadential voices in the upper parts. Naturally this rule does not apply to Phrygian cadences. Extensions of the final cadence—forerunners of the coda—appear frequently. We have observed one in three voices already (see Victoria’s Et misericordia, pages 227–229), mm. 31–33. The usual method of writing such an extension or “coda” is to have one of the cadential voices hold its final note for two or more measures while the other voices move beneath it. Usually the voice that holds the final is the one that had had the ^1–^7–^1, though sometimes it is the voice that had had ^2–^1. For the final cadence itself the lowest voice must have scale-degree ^5, but this ^5 need not move immediately to ^1. If it moves to any note other


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than 1^ the result, of course, is a deceptive cadence into the “coda.” Since the regular consonance/dissonance treatment still holds for the voices moving during this extension, it is virtually inevitable that a plagal cadence will result. See Example 17-11. EXAMPLE 17-11 Missa Gabriel Archangelus Palestrina

The final cadence occurs at m. 40 beat 4 and resolves deceptively into the extension. There the cadential voice with ^2–^ 1 (T) holds the final for four measures while the other voices move. Potential consonances beneath the tenor’s D4 are D itself, Bb, G, and F. Thus another authentic cadence is out of the question. While the F and D may imply a tonic chord, the Bb and G produce a plagal cadence. It is doubtless for this reason that composers from the seventeenth century on have regularly associated codas with subdominant harmony. A particularly lovely effect can be produced at the end of an extension by allowing one voice on scaledegree ^1 to pass through ^2 during the plagal cadence and to reach ^3 as all voices move to the tonic chord. See the last two measures of Example 17-12.

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EXAMPLE 17-12 Missa Papae Marcelli: Agnus I Palestrina

It should be noticed that even though this example is in six voices, the leading-tone in the authentic final cadence is not doubled. It is present on beat one of m. 49 in bass I, anticipating the note of resolution on beat 2 in S, but the B4 in S moves immediately to its lower neighbor. By the time it returns to B4, the B3 in bass I has moved to G3. Unlike Example 17-11, this final cadence is not deceptive; the bass is moving as expected from ^5 to ^1. Special notice should be taken of the parallelism in A and T II—here written above T I—from m. 51 beat 3 to the end. Here is an illustration of the reduction of linear independence similar to that shown in Example 16-1 on page 220. In Example 17-12 B I moves in complementary rhythm against A and T II. Pieces in Phrygian mode end either with a standard Phrygian final cadence—2^ in lowest voice—or with a cadential extension. When the extension begins immediately with ^4 in the bass (subdominant harmony) the Phrygian cadence is often as at Example 17-13: scale-degree ^7 acts not only as the suspension resolution but also as the lowest note, bringing about a 9–8 suspension. In other words, the normal Phrygian 7–6 is in the upper voices, and scale-degree ^7 is placed beneath it. EXAMPLE 17-13 Missa de feria: Kyrie Palestrina


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Example 17-14 shows that, on the other hand, a normal Phrygian 7–6 may, by the maneuver of crossing the bass above the tenor, move directly to the subdominant. EXAMPLE 17-14 Missa Repleatur os meum Palestrina

You may have noticed in all these examples how the motion slows down when nearing the end of the piece. This reduction in rhythmic movement is by no means a rule, but it occurs with great frequency. It is also common to use the effect of the “built-in ritardando” whereby the resolution of the cadential suspension on ^7 is an eighth-note followed by a lower neighbor, returning to ^7 before the final ^1. Another illustration is in m. 49 of Example 17-12 above.

17.5 Initial Notes We have learned so far that as each voice enters it begins on scale-degree ^1 or ^5 of the mode, so that imitation is at the interval of a perfect fourth or perfect fifth, possibly at the octave. A survey of a great many pieces by Lassus, Palestrina, and Victoria will show that these are indeed the normal and usual scale degrees on which each voice begins its imitative counterpoint. (We are not speaking here of the homophonic style in which it was customary for the initial sonority to begin with an 8, 5, and 3 above the bass.) However, there are other possibilities and these are by no means infrequent. For instance, it is enough if one of the initial notes is ^1 or ^5 of the mode. The other note may be a perfect fourth or perfect fifth distant, even if this should turn out to be ^4 or ^2. For instance, the opening pitch classes of the Missa Papae Marcelli are D and G, even though the work is in Ionian mode: G is scale-degree 5^ and D is a perfect above and a perfect fourth below. In Phrygian mode there are several possibilities for opening. In one Phrygian-mode piece, the Missa Repleatur os meum, Palestrina begins each voice of the first Agnus Dei with either E or B. This would seem to be “normal,” except that in Phrygian for a voice to enter on ^5

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(pitch-class B) is less usual than for it to enter on ^4 (pitch-class A). Since the reciting tone of Mode 4 (Hypophrygian) is A in plainsong, it is easy to see that A would be chosen in preference to B. In Mode 3 (Phrygian) the reciting tone is C, and we find Palestrina occasionally using C as one of the initial pitches. In this case, since imitation has to be at the perfect fourth, perfect fifth, or perfect octave, he could choose either G or F as the other note. In the Kyrie of the Missa de feria, each of the four voices begins on F or C, even though the piece is in Phrygian mode. A second possibility occurs when a composer is making a polyphonic setting based on a chant. In singing through the chants in Chapter 10 you probably noticed that a chant may or may not begin with scale-degree 1^ or 5^ of its mode. The Renaissance composer naturally begins such a piece with the first note of the plainsong on which it is based whether it is an important scale degree in the mode or not. Finally, one occasionally comes across pieces that open with three different notes: ^1 or ^5 and the notes a perfect fourth and a perfect fifth above or below. For example, in his five-voice mass Vestiva i colli, Palestrina begins the third part of the Kyrie with three voices entering on A4, D4, and E5. To grasp the attitude behind the lack of consistency in the choice of opening notes for a piece in imitative counterpoint, we must understand that a clear establishment of the mode was not uppermost in the priorities of a sixteenth-century composer. This attitude is very different from that of the composers of the early eighteenth century who were bent on establishing the key and mode unequivocally at the beginning of a piece. In the sixteenth century the main concern was the presentation of the subject, which could be taken from an existing piece of music or newly invented, with the adaptation of the other voices to it, imitating, complementing, or in counterpoint against it, and conforming to the established practice of consonance and dissonance control. In Part Three of his famous treatise Le istitutioni harmoniche, Zarlino lists the requirements of a good composition. True, one of these requirements is that the piece must not be haphazard but should “be ordered under a prescribed and determined mode,” but he does not go on to elaborate just how this is to be accomplished.2 Instead, he lays stress on the subject and its treatment.

17.6 Types of Imitation Standard Entries

Imitative counterpoint in four or more parts may begin with one voice entering after another in fairly regular time intervals just as in our three-voice pieces in the previous chapter. Example 17-15 illustrates. EXAMPLE 17-15 Sicut cervus Palestrina


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Paired Entries

More commonly, in four-voice compositions, and often in multi-voiced pieces, the voices enter in pairs. The method is simple: write the first two voices up to the point where the third and fourth voices are to enter. Copy this two-voice contrapuntal passage at a convenient pitch level for the third and fourth voices, then compose counterpoint in the first two voices. Example 17-16 shows a typical case. EXAMPLE 17-16 Motet: Resonet in laudibus Lassus

Contrary Motion

Imitation may be by contrary motion. In Example 17-17, T and B are the inversion of S and A. EXAMPLE 17-17 Missa Sanctorum Meritis: Agnus I Palestrina

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It is possible, of course, to combine paired entries with contrary motion. In the preceding, for instance, if B had entered on the third beat of m. 3, then A and B would have been in the same relationship to each other as S and T. (Incidental note should be taken of the initial pitches of each voice in this Phrygian piece.) Double Subject

A piece may begin by presenting contrasting subjects simultaneously, as in Example 17-18, in which B imitates S and T imitates A. EXAMPLE 17-18 Missa Gabriel Archangelus: Hosanna Palestrina


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Again, double subjects presented as paired entries are an obvious possibility, as in the Hosanna from Palestrina’s Missa L’homme armé, or as shown in Example 17-19. EXAMPLE 17-19 Motet: Confortamini et jam Lassus

The double subject, marked I and II, in the Lassus example appears in T and A. When S and B enter, I and II have exchanged places: II is now beneath I. This type of voice exchange—in which an upper voice can function as a bass and vice versa—is called invertible counterpoint. When, as here, two voices are involved we speak of double counterpoint, triple counterpoint for three voices, etc.3 Invertible counterpoint is distinguished from simple voice interchange or Stimmtausch (see pages 27–28) by the fact that with the latter there is no question of a double function, since both voices remain upper voices. While the technique of invertible counterpoint was well known to sixteenth-century composers—Zarlino devotes a whole chapter to it—it occurs only sporadically and for very short spans in their music. On the other hand, it became a highly important, even essential, aspect of eighteenth-century fugue writing and for that reason we shall postpone its detailed treatment until the companion volume to this book.

17.7 Triple Time Fast Triple Meter

During the late Middle Ages and the high Renaissance, music in triple meter was very common. But by the second half of the sixteenth century, duple meter had become the norm, at least for sacred music. Fast triple meter was almost limited to homophonic textures and to those sections of otherwise duple-meter pieces in which the text called for a cheerful, dancelike atmosphere—the Hosanna of the Mass, an Alleluia, or texts such as Exultemus et laetemur (“Let us rejoice and be glad”). Not infrequently brief sections of the Gloria or Credo would be set to triple meter (e.g., In gloria Dei Patris and Et resurrexit). By “fast” triple meter, we mean music in which a whole bar is heard as a single “beat,” in modern notation either 3/2 or 3/4. Since we have been designating the quarter-note as the unit, we shall, for the sake of consistency, choose 3/4. But it is essential to keep the metrical proportions in mind: three durational units in a fast triple meter are equal to one unit in duple meter. On page 171 it was pointed out that notational practice changed during the sixteenth century so that the sign came to mean not literally “alla breve” but “alla semibreve.” Thus, in our “halved” notation, each half-note of 4/4 time has a speed of about

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50–60 beats per minute and each dotted half-note of fast triple time moves at approximately the same rate. Each quarter-note, then, has a speed of 150–180 beats per minute. In a homophonic texture there are few dissonances other than the cadential suspension. These few are rarely more than a passing note or two on the second half of a beat. The cadential suspension is regularly prepared on beat one, occurs on beat two, and resolves on beat three. Find and explain all the dissonant notes in Example 17-20. EXAMPLE 17-20 Sequence: Veni Sancte Spiritus Palestrina

Example 17-21 has a slightly more contrapuntal texture and the dissonances are still limited to unaccented passing tones and to suspensions. Examine mm. 5–6 particularly carefully. You will find a 4–3 suspension at m. 5 beat three, that resolves with portamento at m. 6 beat one. On the second beat of m. 6 there is a “six-five chord” suspension resolving on the third beat of that bar. EXAMPLE 17-21 Missa O Regem Coeli: Hosanna Palestrina

At first the placement of suspensions may seem contrary to what we have learned so far—that suspensions are correctly placed on strong beats and resolved on weak beats. The truth of the matter is better understood if we phrase the situation differently: A dissonant suspension can be one factor in our perceiving a beat as strong. When a suspension occurs, the harmony inevitably changes. A change in harmony along with the suspension’s dissonance—as opposed to a passing tone during which the harmony does not change—gives


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the sonority a kind of impact that makes us feel it to be a strong beat. Strong and weak beats are marked and respectively beneath the example. Performance of the passage will verify that what we have in mm. 5–6 is a hemiola: in contrast to mm. 1–4, consisting of two groups of three beats each, mm. 5–6 consist of three groups of two beats each—or what might be heard as a single measure of 3/2 time. This type of hemiola was much favored by sixteenth-century composers. Virtually all their fast triple meters included them, often, but by no means exclusively, near the final cadence. With the exception of hemiolas, the first beat in 3/4 time is strong and the last beat is weak. The second beat, on the other hand, seems to be neutral. When suspensions occur in the normal order of things, they are, as was pointed out above, on the second beat. In this case, of course, beat two is strong. Otherwise, it is difficult to ascertain. In Example 17-21 we have marked them as weak. Perhaps it is because of the ambiguity of strong and weak beats in triple meter that here—as opposed to duple meter—rests can begin on weak beats as well as on strong. (See Example 17-21, m. 2 and m. 7.) Moderate Triple Meter

Moderate triple meter usually has the sixteenth-century time signature which, in our notation, becomes 3/4. It can be distinguished from “fast” meter by its use of smaller note values and a more distinctly contrapuntal texture. The metrical proportions are as follows:

Thus, in “moderate” triple meter the quarter-note moves at the speed of 100–120 beats per minute, as opposed to “fast” triple meter where the quarter-note has the speed of 150–180 beats per minute (so there are 50–60 dotted half-notes per minute). Example 17-22 illustrates.

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EXAMPLE 17-22 Missa Octavi Toni: Gloria Palestrina

SELF-TEST 17.2 Choose the correct word or phrase. 1. When writing the final cadence in all modes except Phrygian, the cadential voices (^ 2–^ 1 and ^ 1–^ 7–^ 1) must be in the bass and one upper voice / upper voices. 2. In Phrygian mode in four or more voices, the bass of the final cadence is scale-degree ^ 2 unless there is a cadential extension, in which case it is ^ 2 or ^ 4 / ^2 or ^7. 3. The first bass note of the coda must be / may be scale-degree ^ 1. 4. In Phrygian mode, the initial note of each voice as it enters must be / may be E or A. 5. If a motet with no key signature begins with the imitating voices entering on D and G one cannot be / can be fairly certain that the piece is in Mixolydian mode. 6. If a piece is in transposed Dorian mode one cannot be / can be fairly certain that at least one of the entering voices will be on G or D. 7. If a piece begins with F in some voices and C in others, it is possible / impossible for its mode to be Phrygian. 8. When a piece begins with standard entries, it is always / often / never true that each voice enters after the same number of beats as did the previous voice. 9. When a piece begins with a double subject, the result is inevitably / may be paired entries. 10. In triple time, suspensions are usually on the first / second / third beat. 11. In triple time, Renaissance composers rarely / sometimes / often wrote hemiolas. 12. A hemiola is achieved by placing a suspension on beat three of a bar and beat two of the next bar / beat three of a bar and beat one of the next / beat two of a bar and beat three of the next.


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17.8 Some Notes on Writing in Five or More Voices When writing multi-voice counterpoint one must be careful not to “overload” the texture. Be sure to keep complementary rhythm by letting one or two voices hold long notes while the others move. Much of the time one or even two voices will be resting. This provides an opportunity for textural and timbral variety: the three upper voices may sing alone, then the three lower voices will contrast with them (in a five-voice work, the middle voice does double duty as the lowest of the upper “trio” and the highest of the lower “trio”). Direct octaves and fifths in outer voices occur from time to time, even in ascending motion (see asterisks in Example 17-23). EXAMPLE 17-23 Resonet in laudibus Lassus

When writing in six or more voices, the strictures against consecutive perfect fifths and perfect octaves by contrary motion are completely relaxed. Particularly in cadences one finds one low voice moving from ^ 5 up to ^1 while another moves from ^5 down to ^1. Eight-voice writing is usually a matter of two four-voice choruses in antiphonal alternation. The two choruses generally overlap for just a few beats. Only toward the end do they sing together in genuine eightpart polyphony. Twelve-voice writing occurs as three four-voice choruses. Thomas Tallis’s celebrated fortyvoice motet Spem in alium is for eight five-part choruses. Examples in standard anthologies should be studied as preparation for attempting a piece in six or more voices.4

EXERCISE 17.1 1. Write a Latin motet in imitative counterpoint in four or five voices. End with a cadential extension of at least four measures. Choose a text that will offer the opportunity for at least four overlapping phrases excluding the “coda.” 2. Write a short four-voice homophonic passage in triple time to the words “Ho-sán-na in ex-cél-sis.” Include at least one hemiola. 3. Write a short passage in eight parts for two choruses.

Chapter 18

The Rise of Tonality in the Seventeenth Century

18.1 Dissonance as Expression in the Early Seventeenth Century According to Gioseffo Zarlino, the chief theorist of the sixteenth century, dissonance in music was tolerated because it made the subsequent consonances more beautiful and sweet by contrast. He advocated treating the dissonances in very special ways so that they would lose their sting and blend smoothly with consonances. For the most part composers were already doing just this. One might say that the general trend throughout the sixteenth century was to introduce dissonant notes in spots that were metrically unstressed. Suspensions, the more noticeable dissonances, had to be carefully prepared as consonances, held as dissonances for just one and not more than one beat, and then had to resolve down by stepwise motion to a consonance on the very next beat. The sacred music of Lassus, Palestrina, Victoria, and other, less famous composers is especially consistent in the strict manner in which they treated dissonance. Near the end of the century a movement began—a movement at first centered in Florence but which soon spread to other parts of Italy—that had an enormous effect on stylistic practice. As Vincenzo Galilei (the father of the famous astronomer) explains in his counterpoint treatises written in 1589 to 1591, vocal music should express and arouse deep feelings in the listener by the manner in which the text is set. In order for music to conform to the emotional quality of the words, the rules of dissonance had to be drastically altered. Galilei and the composers he was writing about had an opposite view of dissonance from Zarlino’s: far from wanting dissonance to lose its sting and to blend with consonance, they wanted to exploit its harshness. As before, dissonances still consisted mainly of suspensions and of notes approached and left by stepwise motion, notes of adjacency, but now any type of dissonance might be placed in a metrically stressed position. Moreover, suspensions might resolve not by step but by skip, they might be ornamented by the placing of a leap between the suspension and the resolution, or they might “resolve” not on a consonance but on another dissonance. And it became acceptable to leap to a dissonant note rather than to prepare it as a consonance or to move into it by step. It must not be supposed that all the dissonances Vincenzo Galilei discussed were entirely new. He refers to and draws justification from the practice of older composers, particularly Cipriano de Rore (1516–1565). Moreover, in instrumental music written earlier in the sixteenth century one comes across some of these stressed dissonances, for instance, in the keyboard music of the Spanish composer Antonio de Cabezón (1510–1566). But the degree of stressed dissonance saturation in instrumental music of the sixteenth century is much less than in the vocal music of later composers of the seconda pratica, the “second practice,” composers such as Caccini, Peri, and Monteverdi.


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18.2 Dissonant Chords Before the Seventeenth Century It was around the beginning of the seventeenth century that a few composers and theorists began to think of harmony as a matter of chords rather than simultaneously sounding intervals. In today’s language these chords would be called major or minor triads in root position or first inversion, that is, consonant chords. But long before this, in practice though not in theory, at least two combinations of simultaneous sounding dissonant intervals had been used as chords—that is, as sonorous units comprehensible in themselves and not to be explained away as merely involving notes of adjacency or suspensions. These are the diminished triad in first inversion and the six-five chord, chords we have dealt with many times both in species counterpoint and in our study of three- and four-voice counterpoint by the composers of the Roman school. Example 18-1(a) and (b) show two diminished triads in first inversion from works by Palestrina. In (a) the triad functions as the resolution of a suspension and then moves to an implied major triad on Bb, the diminished fifth contracting normally to a third. That the first-inversion diminished triad can be treated in the same way as a consonant triad is shown by Example 18-1(b). Here Palestrina places the triad on the strong first beat as the middle in a sequence of three first-inversion chords. The suspension on beat three resolves on beat four to another diminished triad.1 EXAMPLE 18-1

Such diminished triads, then, are dissonant chords. They act as if they are consonant in that they can prepare or resolve other dissonances and can move in much the same way as consonant chords. On the other hand, containing an actual dissonance they tend to move on in a way that will provide some kind of resolution. In the eighteenth century, the famous theorist Johann Philipp Kirnberger, who was a pupil of J. S. Bach, labeled such chords essential dissonances and contrasted them with the inessential dissonances (passing tones, neighbors, suspensions, and the like).2 Rather than these terms, however, we will speak of chordal and nonchordal dissonances in order to avoid the implication that passing tones, suspensions, etc., somehow don’t matter. The other dissonant chord, the six-five chord, was first introduced in the section on species counterpoint (see Example 13-1, page 164, mm. 3 and 10). Here it is in Palestrina’s setting. In Example 18-2(a) we have a succession of two consonant sonorities, an F-major and an E-minor chord. The fact that in (b) the tenor delays its move from A to G does not alter this. But in (c), the music as Palestrina wrote it, although the top two voices are the same as in (b), the bass has, at the moment of the suspension, the note D, a perfect fifth below the suspended A in the alto. The fact that the bass D cannot be held as a half-note without an incorrect resolution of the suspension means that we do not have an ordinary suspension here. Normally a suspension occurs when two consonant sonorities are heard in succession and one voice delays (“suspends”) its motion until after the other voice or voices have moved, as we have just seen in

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Example 18-1. But in the case of the sonority on beat three of Example 18-2(c) we have a different sonority from that on beat four. Therefore in this case we have three chords, not two. EXAMPLE 18-2

Example 18-3 is a similar case in four voices, the dissonant chord being a “six-five-three” chord. It is easy to see how this passage, by applying present-day terminology, can be labeled a half-diminished seventh chord in first inversion, and even given the Roman numeral designation iiø7 in the key of A minor, followed by the dominant triad. EXAMPLE 18-3

Special notice should be taken of the fact that in all these cases the note forming the dissonance is prepared as a consonance at the same pitch level and takes on the configuration of a suspension with its 6 stepwise resolution. The resulting sonority, whether 65 or 5, is a chord in itself, and the dissonances within 3 it are essential, or chordal, dissonances. As a dissonant chord, it is both prepared and resolved: in Example 18-3(c) the dissonant second in the upper voices is prepared as a suspension on beat two, resolving to a third on beat four.

18.3 Seventh Chords in the Seventeenth Century The advocacy of the rather free use of dissonance in vocal music by Galilei and his Florentine circle, as well as its appearance in the music of Caccini, Peri, and Monteverdi, was based on the precept that music should be expressive in regard to its text. But in instrumental music, because of the lack of text, the rules of dissonance treatment were slower to be changed. When seventh chords appear, the seventh of the chord almost always takes the form of a suspension, as in the six-five chord. If not, then the seventh


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is interpretable as passing tone, as shown in Example 18-4(a). Only in the case of the major-minor seventh chord (serving as V7 or a secondary V7) was the seventh treated more freely. For instance, in the excerpt from a keyboard work shown in Example 18-4(b) the seventh simply appears without advance preparation. Although the sensitive listener may account for it as a tone that is passing from an imaginary D down to the B of the final chord, or as a neighbor that comes from an imaginary B preceding it, its origin is not explicit in the written music. EXAMPLE 18-4 (a) Toccata Pachelbel

(b) Suite in E minor: Gigue Froberger

18.4 Nonchordal Dissonance: Notes of Adjacency Nonchordal dissonance can be divided into two main categories, the first of which includes those dissonant notes that are adjacent to consonances. These are passing tones (P), neighbors (N), escape tones (E), and appoggiaturas (AP). All of these approach and/or leave the consonance by stepwise motion. EXAMPLE 18-5

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The first three in Example 18-5 are metrically weak since the dissonance is on a weaker beat or a weaker part of a beat than its resolution. In the case of the appoggiatura, the dissonance is metrically stronger than its resolution. It is this metrical stress that gives the appoggiatura its quality of “leaning” on its resolution (Italian: appoggiare, “to lean”). Thus it makes no difference whether the appoggiatura is approached by skip or by step. It is the metrical placement that determines its effect. On the other hand, most theorists recognize the possibility of accented passing tones, especially when they occur on a weak beat of the measure and the resolution is on the still weaker second half of that beat. See Example 18-6. EXAMPLE 18-6

Precise rules specifying exactly what is an accented passing tone as opposed to an appoggiatura are neither possible nor especially desirable. The effect in performance is what determines the matter and that may not always be the same for every listener. Example 18-7 shows that a passage very similar to that of Example 18-6(b) would, under the circumstances given, probably be heard as appoggiaturas rather than as accented passing tones because of the analogy between beats 1 and 2 and also because of the slurs. The student need not be troubled by differing terminology in respect to notes of adjacency. What matters is not uniformity of labels so much as an understanding that the function of the dissonant note is to relate either forward or backward to a chord tone a step away. EXAMPLE 18-7

Another common note of adjacency is illustrated in Example 18-8. This unaccented dissonance is approached by leap and resolved by step. Some would like to label this an “unaccented appoggiatura,” but to do so results in an oxymoron. By definition, an appoggiatura leans on its resolution. A better name is incomplete neighbor (IN) indicating that it is not prepared as a normal neighbor is. EXAMPLE 18-8


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Finally, there is the possibility of combining a lower and an upper neighbor into a two-note dissonant figure called a changing tone (CT). Example 18-9 shows that either the upper or the lower neighbor may appear first. If the second of the two notes in the CT is accented, the impression is of an escape tone moving to an appoggiatura (Example 18-9(c)). EXAMPLE 18-9

18.5 Nonchordal Dissonance: Time Extensions The second category of nonchord dissonance is made up of anticipations (AN) and suspensions (S). The suspension is a consonance that extends itself into the “time slot” of another note, a consonance one step below (sometimes one step above), and thus becomes dissonant for a time. The anticipation is the opposite. It occurs when a consonance moves “too soon” to its next consonance and is therefore dissonant for a time. Usually the anticipation is quite short—a beat at most, far more likely half a beat or less. The suspension, after the sixteenth century, might be as long as several beats or as short as half a beat. The tendency, though, was to continue the practice of the sixteenth century in resolving the suspension after one full beat. Example 18-10 shows a consonant progression (a), which is treated to an anticipation (b), and then a suspension (c); (d) through (f ) illustrate various means of ornamenting the suspension figure by the insertion of notes of adjacency between the suspension and its resolution; (g) inserts a leap to a consonance (CL) with a subsequent leap back to the resolution; (h) has a consonant leap with the return to the resolution filled in by a passing tone; at (i) the resolution is delayed to leave room for a consonant leap up a perfect fifth with subsequent descending passing tones. EXAMPLE 18-10

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These examples do not exhaust the possibilities for suspension ornamentation, but they should suffice to indicate the principle: Notes of adjacency, whether consonant or dissonant, may be introduced between a S and its resolution. Consonant notes introduced between a S and its resolution may be approached and left by leap. Notice that the ornamentations occur in the same voice as the suspension and its resolution. Other voices may also be ornamented simultaneously, but those would not be considered ornamention of the suspension figure.

SELF-TEST 18.1 The example below is the first section of a keyboard fantasia by Sweelinck (1562–1621). The letters (a) through (z) stand directly above a dissonant sonority. If the sonority is a chordal dissonance, indicate 6 , , or diminished 6 . If it is nonchordal, state which term (P, N, E, AP, CT, AN, S) best applies to this by 6 5 5 3 3 it.


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SELF-TEST 18.2 The passage below, taken from another keyboard piece by Sweelinck, has its top voice shorn of many of its nonchordal dissonances. Replace these with the indicated dissonances in such a way that the top line moves in steady eighth-notes. (You will have to consider whether upper or lower neighbors will be preferable in this context.)

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SELF-TEST 18.3 Ornament the following suspensions as indicated. In these examples CL indicates a jump down to a consonance.

18.6 Diminutions Composers of instrumental music in the seventeenth century tended to divide beats into smaller note values, the divisions being called diminutions. In England these diminutions were called divisions. By the use of diminutions composers were able to write vibrant active melodic lines eminently suitable for instrumental performance. 1. In Example 18-11, passing notes connect the root and third of a chord (a), or the third and fifth (b); in (c) lower neighbors and passing tones combine in an overall ascending line. EXAMPLE 18-11


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2. In Example 18-12(a) and (b), a leap between two chord tones is then filled in with a passing tone resulting in either an overall descending or ascending line. In (c) appoggiaturas ornament a line that is basically chord tones. EXAMPLE 18-12

3. In Example 18-13(a), (b), and (c), each beat is subdivided into four by means of the CT figure. On a higher level the third note of each CT acts as a P. EXAMPLE 18-13

4. In a descending scale passage, accented Ps may appear on the beat (m. 1, beat 2; m. 3 beat 2; m. 4, beat 1). If the scale is ascending, notes on the beat should normally be chordal. Compare Example 18-14(a) with the unpleasant effect of the Example 18-14(b), m. 2 beat 2. EXAMPLE 18-14

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5. Escape tones (E) in the lowest voice have a rough effect unless they anticipate a chord tone: see Example 18-15(a). In the top voice the anticipating quality is less necessary: see Example 18-15 (b), from a Toccata (in Dorian mode) by Sweelinck. EXAMPLE 18-15

6. The use of the incomplete neighbor (IN) is very effective, especially if it is approached and left in opposite directions. In the first measure of Example 18-16, the IN is approached by downward leap and left by upward step. In m. 2 beat 1, the IN is approached by upward leap and left by downward step. EXAMPLE 18-16

7. It is important for the fast-paced lines to sound natural and unforced. In Example 18-17(a) there is a “bumpy” effect from running out of notes too soon—the anticipation seems to be an awkward means of supplying another note before the next measure. The solution at (b) is much to be preferred: even though the sixteenth-note motion temporarily ceases, the stepwise move into the next measure sounds very smooth. In (c) we have an acceptable use of the anticipation.


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EXAMPLE 18-17

8. In Example 18-18 we see both bad and good continuations (g.c.). If a line in a single direction cannot move entirely by step (scalewise), the necessary leap should come within a beat rather than just before the beginning of a beat. In (a) and (b) we see questionable continuation and good continuation. On the other hand, if the direction of the line is to change, there can well be a leap into the beginning of a beat, as at (c). In (d) and (e) we see similar situations to (a) and (b) but in sixteenths instead of eighthnote triplets. And at (f ) a change of direction justifies the leap into the first beat of the second measure. EXAMPLE 18-18

EXERCISE 18.1: CONTINUOUS VARIATIONS Write a set of continuous variations (chaconne or passacaglia). These are the characteristics: 1. It should be for keyboard (harpsichord), organ with obbligato pedals, or for solo instrument(s) and continuo accompaniment (often harpsichord and a bass instrument). Choose available instruments so that it can be performed in class. 2. Compose a bass melody of from four to eight measures in triple time (3/4 or 3/2). This bass will be ^ ^ repeated at least twelve times. A short bass should begin on scale-degree 1 and end on 5, with an ^ additional 1 at the very end of the piece. The bass melody should be very simple: dotted half-notes, or half-notes and quarter-notes.

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3. Above the bass the melody instruments will play diminutions (divisions). Each variation should, for the most part, stick to a single unified type so that each variation has a character of its own. The usual procedure is to begin with larger note values and, throughout a number of variations, proceed gradually to smaller note values, giving the effect of a “rhythmic crescendo.” 4. Although some continuous variations do not vary the bass at all, it is not uncommon to find the bass also subject to some variation. Occasionally the bass is varied so consistently that it is difficult to perceive it as a series of repeated melodies—rather what holds the music together is a series of repeated harmonies that are suggested by the original bass line. 5. If the piece is to be called a chaconne, the upper voices must produce the typical chaconne rhythm much of the time. This rhythm is similar to the sarabande rhythm: in 3/4, a quarter, a dotted quarter, and an eighth. However the chaconne is unlike the sarabande in that it is faster, louder, and more vigorous. The ^ ^ typical chaconne bass is simply a descending tetrachord from scale-degree 1 down to 5, but other basses are possible. 6. If the piece is to be called a passacaglia, the bass line is likely to be eight measures long and might very well both begin and end on ^ 1. There is no particular rhythm associated with the passacaglia, but the meter is virtually always triple (3/4 or 3/2). 7. Typically, the figuration of any one variation will begin during the cadence of the previous variation. Thus the upper voice(s) will overlap the bass voice. To provide this type of dovetailing insures a continuity that is lacking in the ordinary sectional Theme and Variations so familiar from the classical era. 8. When writing for solo instrument(s) there must be a continuo part for the harpsichord. The bass line will be given to a low instrument (perhaps cello or bassoon) as well as to the left hand of the harpsichordist. The implied harmonies will be notated by figures above the bass line, as in regular figured bass. If you wish, you may write out an entire harpsichord part, but it must not be so elaborate as to detract from the solo instruments. 9. More often than not, chaconnes and passacaglie are in minor mode, but major-mode continuous variations are sometimes found. 10. The lowest note for the continuo instruments is C2 (the second ledger line below the bass clef). This is the bottom note on the organ and on the normal continuo harpsichord (there were big concert harpsichords that extended a perfect fifth lower than that). This is also the lowest note of the cello. Naturally, if you use viola as the continuo instrument, you will have to restrict the range of the bass line so that it does not extend below C3. 11. Be sure to include measure numbers and/or rehearsal letters.

Epilogue: The Nature of Counterpoint

From time to time throughout this study we have paused to express principles of counterpoint as the bases for the rules of various stylistic practices. Such principles include the following: When melodies sound together, their curves show some opposition to each other. Two or more lines in a contrapuntal texture may in reality be the same line in different temporal positions (imitative canon) or in different contours (canon by contrary or retrograde motion) or in different note values (mensuration canons, canons by augmentation or diminution) or a combination of these. Simultaneous lines produce essentially consonant harmonic intervals; dissonance is introduced as a means of passing between consonances, ornamenting a consonance, anticipating a consonance, or for a moment withholding a consonance (respectively: passing tones, neighbor and escape tones, anticipations, suspensions). Harmonic coherence is achieved through consonance. It is dissonance that imparts the quality of tension to a passage of music; because of the listener’s desired expectation as to its consonant resolution, the music is propelled forward. Thus, movement is achieved through dissonance. Coherence in a melodic line depends to a large extent on proximity of pitches: stepwise motion prevails in certain styles, gaps that do occur may be filled in or, owing to registral proximity of pitches separated in time, the listener may project a coherent shape onto a jagged line (compound melodies). These principles hold good for counterpoint in European music over a period of many centuries. It is their specific application in practice that gives rise to the various stylistic differences so obvious on the surface of music of different times and places. But these principles themselves may be said to be contained in and subordinate to one overriding principle of counterpoint. This can be simply expressed from either the composer’s standpoint or the listener’s: 1. Counterpoint occurs when the composer places two or more simultaneously sounding related lines in opposition to each other.

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Epilogue

2. Counterpoint occurs when the listener perceives that two or more simultaneously sounding lines display both a relationship and an opposition to each other. Whether one wants to approach this principle as a composer or as a listener, there are four key words to be considered: line, simultaneity, opposition, relatedness. The term “counterpoint” originates, as we know, from punctus contra punctum (“note against note”). The definition of counterpoint provided by Johannes Tinctoris in his treatise Liber de arte contrapuncti (1477) is “a moderate and rational concord made by the placing of one pitch against another . . . one note against another.” But if we are to distinguish counterpoint from harmony, a polyphonic texture from a homophonic texture, we immediately realize that it is not really a question of how we place single pitches against each other but whole lines, entire melodic units. For genuine counterpoint to take place, at least two lines must be heard simultaneously. There is a great deal of excellent music with fascinating textures involving motivic play between instruments which nevertheless cannot be termed “contrapuntal”—one case out of thousands is movement No. 3 from Beethoven’s String Quartet in C-sharp minor, Op. 131. Here there are lines, they are in opposition to each other, and they are related. Since they are not heard simultaneously we do not have counterpoint but antiphony. The matter of opposition and relatedness is less easy to dispose of. How much opposition or relatedness is required? Opposed or related in what way? Is it really necessary for lines to be related? While avoiding questions of particular musical styles is it possible to answer these questions at all? It would seem that to some extent they can be answered by considering extreme cases. If two people sing the same tune in unison no one would speak of counterpoint, since one melody is not “countered” by the other. There is no opposition. If they sing in parallel thirds or fifths there is very little opposition, since the melodic curves are identical and cannot be said to be “opposed” to anything. On the other hand, several people may sing the same tune and produce counterpoint by singing it as a round. The opposition does not come about through differences in the tune but, because of the temporal nonalignment, the curves and rhythm of the line do not match up. Relatedness may emerge in the harmonic dimension. In rounds and other imitative textures there is inevitably a strong relationship among the melodic lines. In non-imitative counterpoint, the norm is also to relate the lines but by other means—timbre, general similarities in rhythm, and above all harmony. Even lines as strikingly diverse in rhythm as those of the organum of the St. Martial school (see Example 3-2, page 25) have harmonic, melodic, and timbral relationships. While it is perfectly easy to imagine attempts at writing counterpoint with lines as unrelated to each other as possible (a siren manipulated arbitrarily against a solo cello playing a movement from a Bach suite?)1 such activities occur more as games or deliberate eccentricities than as a living part of the tradition of Western music. In the last chapter of this volume we have seen and in the second volume of this study we shall see how the same contrapuntal principles listed above were practiced from the seventeenth through the first half of the twentieth centuries. We shall trace the changes that took place in the treatment of consonance and dissonance during the time of Monteverdi, Sweelinck, and Frescobaldi along with the gradual crystallization of the modes into the major-minor system. Much of the emphasis will be on tonality—its rise during the seventeenth century, how it was understood during the late Baroque and Classic-Romantic eras—and how composers coped with the problems of writing contrapuntal textures while dealing with the harmonic organization and large-scale tonal structures that tonal music calls for. And finally, we shall seek to find which principles of counterpoint still held for composers in the twentieth century and beyond.

Answer Boxes for Self-Tests

Self-Test 1.1 1. 2. 3. 4. 5. 6. 7. 8. 9.

^5 / ^5 authentic half / whole Mixolydian; Dorian major / Ionian (reverse order also correct) ^2 / ^3 / ^5 / ^ 6 Lydian ^6 / Dorian ^7.

Self-Test 1.2 (top to bottom): 6, 4, 1, 2, 5, 8, 3, 7.

Self-Test 1.3 1. 2. 3. 4.

second / third / Aeolian / [Hypo]aeolian Phrygian / Phrygian / [Hypo]phrygian / Aeolian Dorian / Phrygian Mixolydian / Lydian.

Self-Test 2.1 (a) Good; Nos. 2, 3, 4, 5 (b) Bad; No. 8 (c) Good; Nos. 4, 8

(g) Good; Nos. 3, 4, 5 (h) Bad; Nos. 4, 8 (diminished triad) (i) Bad; No. 1

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(d) Bad; No. 6 (e) Bad; No. 3 (major sixth) (f ) Bad; No. 3 (tritone leap)

(j) Bad; No. 9 (k) Good; Nos. 3, 4, 6 (l) Bad; No. 1 (half-steps).

Self-Test 2.2 (a) (b) (c) (d)

Bad; notes 2–5 form an augmented fourth Good; notes 4–6 form a diminished fifth Bad; notes 5–6 and 6–8; also, leap in middle of line, notes 7–8 Bad; notes 3–6 form an augmented fourth.

Self-Test 3.1 1. 2. 3. 4.

above twelfth the repetition of material in a new voice canon

5. 6. 7. 8.

false conductus conductus false.

Self-Test 4.1 Dyads 1–2: oblique 2–3: parallel 3–4: contrary 4–5: similar 5–6: contrary

6–7: oblique 7–8: parallel 8–9: contrary 9–10: parallel 10–11: contrary.

Self-Test 4.2 Examples (a) and (g) are correct. In Example (b) dyad 3 is a unison, there is overlapping, and dyad 4 is a perfect fourth. In Example (c) there is overlapping between the first two dyads. Example (d) has four errors in the last two dyads alone: the upper voice leaps an ascending major sixth, the third note is a unison, there is overlapping in that the lowest voice ends on a D3, a step higher than the upper voice’s preceding note, and lastly, the approach to the final dyad, a perfect fifth, is by similar motion, causing an incorrect direct fifth. In Example (e) the alto voice outlines the tritone E4 to Bb3. In Example (f ) the first two dyads form parallel fifths. The first two dyads of Example (h) produce a direct octave.

Self-Test 4.3 There are only two errors in (a): the perfect fourth at note 3 and the direct octave at note 8. There are four errors in (b): (1) the first two notes are consecutive octaves by contrary motion (P8–P1). (2) Notes 4–7 comprise three consecutive parallel sixths, too many for independence between the melodies. (3) Notes


285

8–10: the double leap in the lower voice is not followed by movement in the opposite direction. (4) Lower voice notes 9–11 outline a tritone (B3–F3).

Self-Test 5.1 1. (a) Notes 1–2, consecutive octaves; notes 3–4 parallel perfect fifths; note 7, diminished fifth; notes 4–7, poor tenor line. (b) Note 3, alto and tenor zeniths coincide; note 6, six-four chord. Too many parallel sixths in upper voices. (c) Notes 1–2, consecutive perfect octaves; note 3, alto crosses below lowest voice; notes 2–4, more than octave between upper voices. 2. (a) (b) (c) (d)

middle voice, A3–F#3 (or A3) lowest voice, A3–F3 (or F3–F3) top voice, C5–B4 middle voice, C#4–D4.

Self-Test 6.1 1. 2. 3. 4.

round outdoor life retrograde motion hocket

5. true 6. 63s 7. sometimes.

Self-Test 7.1 1. Aeolian mode. Measures 1–2, octaves on successive downbeats; m. 5, zeniths coincide and voices cross; mm. 6–7, perfect fifths on successive downbeats. 2. (a) Ionian mode. Measure 2, C5 is an acceptable p.t. (E5 would produce direct octaves, D5 would result in a repeated note, G4 in consecutive octaves by contrary motion); m. 5, E4 is an acceptable unison (C5 or B4 would result in direct or parallel fifths, respectively); m. 6, the leading tone B4 is the only possible cadential note. (b) Phrygian mode, transposed. Measure 1, no consonance is possible (A3 or F3 would mean repetition, the upper C4 would mean crossing, a C3 a leap of a descending sixth, and a D3 would cause parallel fifths) and so the obvious p.t. G3 is the correct note here. Measure 3 could be the unison D4, providing a high zenith, or the perfect fifth G3, in which case m. 4 would provide the zenith. F3 is also possible but makes a less attractive line than either D4 or G3. In m. 7, either the consonance A3 or the passing F3 is acceptable.

286


Self-Test 8.1 1. (a) correct (b) incorrect: tritone in bass; treble and alto fifths on consecutive downbeats with similar rather than contrary motion. (c) correct (d) incorrect: soprano leaps a descending sixth; tenor and bass have perfect fifths on consecutive downbeats and intervening note is not consonant. 2. (a) (b) (c) (d)

C#4 (half-note), D4 G3, C3 E4, D4 (or F#4) D4, C#4, or E4.

Self-Test 9.1 S = superius, T = tenor (middle voice), B = bass. Measures 4–5: T and B resolve out to octave D3–D4; S enters on scale-degree ^5. Measures 14–15: T and B resolve in to unison D4; S rests. Measure 19: S and T resolve in to unison A4; B moves from scale-degree 5^ to 6^ quasi-deceptive (extension in m. 20; plagal cadence on A). Measure 23: T and B resolve out to octave F3–F4; S enters on scale-degree ^5. Measure 30: S and T act as though to resolve in to unison D4, but S drops out for one beat, then enters (“hocket cadence”); B moves ^5–^1. Measures 34–35: S and T resolve out to octave A3–A4; B moves ^5–^1 Aeolian mode. Scale degrees of cadences: ^4, ^ 4, ^1, ^6, ^4, ^1. Motive: T (m. 1); B (m. 3); B (m. 5); S and T (m. 6); T (m. 13); B (m. 15); S and B (m. 16); T (m. 16 one beat after B); T (mm. 17–18); S (m. 26); T (mm. 26–27).

Self-Test 9.2 Measure 1: 2 Measure 2: 1 (both) Measure 4: 1 Measure 5: 1 and 2 Measure 6: 1 (both) Measure 9: 1

Measure 10: 1 (both) Measure 11: 2 Measure 12: 1 Measure 13: 1 Measure 14: 2 (both) Measure 15: 1.

Self-Test 10.1 (a) incorrect: suspension metrically reversed (begins on weak beat of m. 2 and resolves on strong beat of m. 3) (b) incorrect: apparent “7–6” suspension accomplished by ascending resolution. Only 2–3 (9–10) suspensions occur in lower voice


287

(c) correct (d) incorrect: last measure suspension “resolves” in ascending direction. Also, parallel perfect octaves with previous measure (e) incorrect: parallel octaves (f ) correct.

Self-Test 10.2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

syncopes consonance consonance parallel consonant, dissonant, consonant 7–6, 4–3, 2–1, 9–8 (6–5 is available but is not a suspension) may 2–3 (9–10) 7–6 2–3 (9–10) strong.

Self-Test 10.3 (a) (b) (c) (d)

half-notes: D5 tied to D5, C#5 half-notes: G4 tied to G4, F#4 whole-notes, C4, Bb3 half-notes: C4 tied to C4, B3.

Self-Test 10.4 Measure 5, dissonance on weak beat; m. 7, 7–8 suspension.

Self-Test 11.1 1. Top to bottom: (a) sus, third, acc. (b) third, sus., acc. (c) third, acc. sus. (d) acc., third, sus. (e) sus., third, acc. (f ) third, sus., acc. In the case of (e), the middle voice forms a perfect fourth with the upper voice but it cannot be considered the accompanying voice because a perfect fourth is not dissonant when it is in the upper parts. 2. (b) (c) (d) (e) (f )

8 – 3 6 5 8 3 3 5 8 3 3 3 6 1 – 5 – 4—3

5 – 4—3 4—5 2—3 5 6 2—3 9—8 6 – 6 – 4—3

288


3. (a) (b) (c) (d) (e) (f )

A3 or B3 F4 E4 or F4 F4 B3 A3.

Self-Test 11.2 1. 2. 3. 4. 5.

preparation lowest voice must 2–3 fifth above bass

6. 7. 8. 9. 10.

Con4 V—I, viiº6—I, V6—I is suspension voice always.

Self-Test 12.1 1. Measures 4–5, 9–10, 14–15, 19–20, 24–25, 30–31, 33–34, 36–37, 41–42, 44–45, 47–48, 52–53. 2. No, the cadences at mm. 4–5, 44–45, and 52–53 are not. (At mm. 24–25 the preparation is not tied to the suspension.) 3. Yes. In mm. 19, 24, and 41, scale-degree ^2; is two tactus in length. 4. By downward leap of a third in mm. 4–5, 19–20, 33–34, and 52–53. By step in the others. 5. “Burgundian cadence” (see page 90) in mm. 4–5, 24–25, and 41–42. Plagal cadence on A in mm. 9–10, 36–37, and 52–53. Similar to modern perfect authentic cadence in mm. 14–15, 19–20, 30–31, 33–34, and 47–48. Leading-tone cadence in mm. 41–45.

Self-Test 13.1 1. Suspensions (a), (b), and (e) are correct. Suspension (f ) is also correct, but does not really have a moving accompanying voice: an octave leaves it a 7–6. In (c) the resolution is dissonant (a diminished fifth). In (d) the resolution would be dissonant if the bass did not move. This happens because the third voice is not consonant with the accompanying voice. 2. Incorrect doublings: m. 3 and m. 7. (Also, in m. 7 the tenor leaps an augmented second from m. 6 to m. 7 and anticipates the resolution of the soprano’s suspension.)

Self-Test 14.1 (1) (2) (3) (4)

three, one, strong 5, 6, 7, two whole, 4, 14, strong three, 7, 8, 12, two

(5) (6) (7) (8)

are four, half, quarter, halves, strong Victoria, octave strong.


289

Self-Test 14.2 (1) (2) (3) (4) (5)

false true true true true

(6) (7) (8) (9) (10)

true false (there are three in a row) false true true.

Self-Test 14.3 (1) single (2) offbeat (3) 4, 7, descending

(4) passing tone, neighbor, 13 (5) anticipation (6) strong.

Self-Test 14.4 1. Word distorted: (b) second “Dominum;” (d) “Exaltabo” and “Domine”. Also, the first two syllables of “Exaltabo” should be set syllabically. 2. Syllable on incorrect value: (b) tu-lé-runt. Incorrect syllable change: (b) first “Dominum” (first syllable changes after an eighth); second “Dominum” (last syllable). (c) “me-a” (changes after a sixteenth). 3. Modes: (a) Ionian (b) Mixolydian (c) transposed Ionian (d) Phrygian.

Self-Test 14.5 1. (a) mm. 3–4, four descending thirds outline a seventh. (d) mm. 2–3, F3–B tritone; last beat of m. 3 is an isolated pair of eighths not left by stepwise motion (anticipation on weak beat). 2. Melodies (a) and (b) have most longer-value notes on weak beats; (c) and (e) have approximately half on weak beats; (d), with no syncopes, is faulty. 3. In (c), the last note of m. 1 is an incorrectly used single eighth-note, since it has none of the functions listed on page 183. It seems to be a passing tone that has been aborted. At m. 3 there should be no syllable change in “Do-mi-num” after the eighth-note (but see Example 14-3(b), page 173). In (d) the last note of m. 2 should not carry a syllable. In (e) m. 2, the portamento eighth-note should not carry a syllable. 4. In (c) m. 2 beat two, the sixteenth-notes are incorrectly placed on the first half, rather than the second half, of the beat. 5. Anapests on weak beats are found in (e) m. 2 beat four, and (d) m. 2 beat two and m. 3 beat four. The eighth-note pair in m. 2 of (d) is incorrect in that it includes a leap between F3 and D3. The pair in m. 3 is incorrect in that motion out of the pair is not by step but by repeated pitch. An anticipation on the second half of the weak beat is incorrect in this style. 6. Anapests on strong beats are found in (b) m. 2 and (e) m. 1. Both are correctly followed by syncopes. 7. Measure 1 of (e) has an incorrect upward, rather than downward, leap in the isolated eighth-note pair on the strong beat.

290


Self-Test 14.6 1. the great majority 2. almost always 3. may be (for an example of a downward leap of this sort, see page 188, Example 14-11(f ), m. 2, beats 1–2) 4. true 5. only the first is (the AN can be only on the second half of a strong beat).

Self-Test 15.1 (a) (b) (c) (d) (e) (f ) (g) (h)

second: “resolution” occurs before the second beat first: rhythm not feasible (whole-note tied to a quarter) second: bad dissonance on beat 2 second: accented P on beat 2 is ascending second: bad dissonance after beat 2 first: rhythm not feasible (half-note tied to an eighth) first: “7–6” suspension in diminution both: in first a “4–3” in diminution; second has three errors: (1) a “7–6” on beat 2, (2) an AN during a weak beat, and (3) unison on beat 4 not approached by oblique motion (i) second: upper N does not lead into a syncope (k) both: eighth-note pair not approached by step.

Self-Test 16.1 1. two: mm. 9–10 and 20–21 2. F and G 3. alto, tenor

4. four: mm. 10, 18–19, 23–24, 36–37 5. A, A, C, A 6. half of.

Self-Test 16.2 (1) (2) (3) (4)

six; one is; two are (at mm. 24 and 32) plagal mm. 23–25 A, mm. 18–19 (on C), mm. 25–26, on D.

Self-Test 16.3 (1) Phrygian, lowest, minor (2) plagal (3) is


291

(4) deceptive (5) pseudo.

Self-Test 17.1 8

(a) Correct. All consonant sonorities, all 5 . 3 (b) Incorrect. Doubled tendency note on beat four. (c) Correct. 7–6 suspension on beat three with doubled accompanying voice; consonant sonority on m. 2 beat one with third above bass doubled to avoid parallel perfect fifths. (d) Incorrect. Scale-degree ^2 doubled in Phrygian cadence. (e) Correct. Phrygian cadence with third above bass doubled. (f ) Correct. 7–6 suspension with no doubling (7, 5, and 3 above bass); 5 above bass moves to 3 for the resolution; on beat three, B3 is not a leading-tone in this context so A–T doubling is correct. (g) Beat one: incorrect double suspension (9–8 with 7–6). Crossing of alto below tenor is correct. Beat three: correct “six-five chord” suspension with no doubling (fourth voice has a third above the bass). (h) Beat one: correct double suspension (7–6 and 4–3); beat three: correct “six-five chord” suspension with bass doubled. Beat four: incorrect resolution of “six-five chord” to sonority with unjustified seventh above the bass (i.e., it is not a passing tone).

Self-Test 17.2 1. 2. 3. 4. 5. 6.

upper voices ^2 or ^7 may be may be cannot be can be fairly

7. 8. 9. 10. 11. 12.

possible often may be second often beat three of a measure and beat two of the next.

Self-Test 18.1 1. (a) P

(n) N

P P

(o) N

(b)

(c) P or AP

(p) S (with IN ornament)

P P 6 5

(q) S

(f ) S

(s) S

(g) S

(t) N

6 5 3

(u) N

(d) (e)

(h)

(r) diminished 63

(i) S

(v) S (with IN ornament)

(j) S

(w) diminished 63

(k)

6 5

(x)

P P

292


(l) S

(y) P

(m) S

(z) N.

Self-Test 18.2

Self-Test 18.3

Appendix A: Some Latin Texts

1. Lux ae-tér-na lú-ce-at é-is, Light eternal shine on them, cum sánc-tis with saints

tú-is in ae-tér-num: your in eternity:

quí-a pí-us because kind

es. you are.

Dó-mi-ne: O Lord:

2. Et pas-tó-res é-rant in re-gi-ó-ne And shepherds were in region

e-á-dem the same

vi-gi-lán-tes, et cus-to-di-én-tes vi-gí-li-as nóctis watching, and guarding the watches of night sú-per gré-gem over flock 3. Dó-mi-nus The Lord

sú-um. their.

díx-it said

ad to

me: me:

Fí-li-us mé-us es tu, Son my are you. é-go hó-di-e gé-nu-i te. I today have begotten you. 4. Á-ve, Ma-rí-a, Hail, Mary,

grá-ti-a of grace

plé-na; full;

Dó-mi-nus té-cum: The Lord with you [is]: be-ne-díc-ta tu in blessed you among

mu-li-é-ri-bus women

294

et and

Appendix A

be-ne-díc-tus blessed

5. Ro-rá-te, cáe-li, Drop dew, heavens, et and

nú-bes clouds

a-pe-ri-á-tur opened be

frúc-tus vén-tris the fruit of womb

tú-i. your.

dé-su-per, from above,

plú-rant jús-tum: let rain the Just: tér-ra the earth

et and

gér-mi-net Sal-va-tó-rem. let it bud forth a Savior.

Appendix B: Pronunciation of Church Latin

When studying Latin at school, one learns “classical” pronunciation, an approximation of what is believed to have been the pronunciation in ancient Rome. During the Middle Ages, Renaissance, and even later, Latin remained the written language of scholars, but it ceased to exist, except in special circumstances, as a spoken language. It was natural, then, that pronunciation should vary. Usually it was pronounced as it was spelled, using the pronunciation of the speaker’s native language. For example, the word magnum is pronounced “mahg-noom” in Vienna and “mahn-yoom” in Rome because to a German speaker the letter g is always hard, while to an Italian g followed by n is pronounced like ny (or ni in “onion”). To this day, Latin sung by a German choir will sound different from that sung by an Italian choir, which, in turn, is different from the pronunciation of a French choir. So-called “church Latin” represents an attempt to unify the pronunciation in Catholic churches. This is what most American choirs do, in fact, use. It consists basically of pronouncing it as Italian is pronounced in Rome. This is easy to learn and sounds good in performance. It is also probably fairly close to the way Palestrina, Lassus (who spent his early life in Italy) and Victoria pronounced it.

Vowels a: e: i: o:

ah (father) eh (met) ee (machine) long o (obey) short o (bottle) u: oo (food) oe and ae (also œ and æ) = e y=i Be careful not to turn a simple vowel into a diphthong as we so often do in English. This means that e is not pronounced as e + i, as in “day” or “weigh,” and long o is not pronounced as o + u; instead, each should be pronounced as one unchanging vowel sound. Whether to use a long or short o has to be learned (“Dominus” is short).

296

Appendix B

Consonants Consonants are the same as in English except for the following: c: before a, o, or u, as in “cat”; before i or e (or oe or ae), as in “chimney” g: before a, o, or u, as in “go”; before i or e (or oe or ae), as in “George” h: silent (except between two i’s when it is pronounced as k: mihi is “mee-kee”) j = i or y r = slightly rolled, a very light d ch: pronounced as k, as in “Pinocchio” gn: pronounced as ny or ni, as in “unyouthful” or “onion” sc: before a, o, or u, as in “scat”; before i or e (or oe or ae), as in “shy” ti: if followed by a vowel, as in “bats” (so gratia is “grah-tzee-ah”) th = t (since h is silent).

Accent If a word is two syllables in length, the first syllable is accented. If more than two, the accent must be learned. In this book the accent is indicated.

Examples Kyrie eleison (although this is Greek, it is pronounced the same as church Latin): “Kée-de-eh eh-léh-eeson” (or three syllables: “eh-láy-son”) Ave, Maria, gratia plena: “Á-veh, Mah-dée-ah, gráh-tzee-ah pléh-nah” Et ascendit in caelum: “Et ah-shén-deet een chéh-loom” Agnus Dei: “Áh-nyoos Déh-ee.”

Appendix C: Tones and Text of the Magnificat: The Canticle of the Blessed Virgin Mary (Luke 1: 46–55)

English translation from the King James version. 1. Ma-gní-fi-cat á-ni-ma mé-a Dó-mi-num. My soul doth magnify the Lord. 2. Et ex-sul-tá-vit spí-ri-tus mé-us in Dé-o sa-lu-tá-ri mé-o. And my spirit hath rejoiced in God my Saviour. 3. Quí-a re-spé-xit hu-mi-li-tá-tem an-cíl-lae sú-ae: éc-ce é-nim ex hoc be- á-tam me dí-cent. For he hath regarded the lowliness of his handmaiden: for, behold, from henceforth all generations shall call me blessed. 4. Quí-a fé-cit mí-hi má-gna qui pó-tens est: et sánc-tum nó-men é-jus. For he that is mighty hath done to me great things: and holy is his name. 5. Et mi-se-ri-cór-di-a é-jus a pro-gé-ni-e in pro-gé-ni-es ti-mén-ti-bus é-um. And his mercy is on them who fear him from generation to generation. 6. Fé-cit po-tén-ti-am in brá-chi-o sú-o; dis-pér-sit su-pér-bos mén-te cór-dis sú-i. He hath showed strength with his arm; he hath scattered the proud in the imagination of their hearts. 7. De-pó-su-it po-tén-tes de sé-de, et ex-al-tá-vit hú-mi-les. He hath put down the mighty from their seats, and exalted them of low degree. 8. E-su-ri-én-tes im-plé-vit bó-nis: et dí-vi-tes di-mí-sit in-án-es. He hath filled the hungry with good things: and the rich he hath sent empty away. 9. Su-scé-pit Ís-ra-el pú-er-um sú-um, re-cor-dá-tus mi-se-ri-cór-di-ae sú-ae. He hath holpen his servant Israel, in remembrance of his mercy. 10. Sí-cut lo-cú-tus est ad pá-tres nó-stros, Á-bra-ham, et sé-mi-ni é-jus in sáe-cu-la. As he spake to our fathers, to Abraham, and to his seed forever. The following doxology is usually added: 11. Gló-ri-a Pá-tri et Fí-li-o et Spí-ri-tu-i Sánc-to: Glory to the Father and to the Son and to the Holy Ghost: 12. Sí-cut é-rat in prín-ci-pi-o et nunc et sém-per, et in sáe-cu-la sáe-cu-lo-rum. Á-men. As it was in the beginning, is now, and ever shall be, world without end. Amen.

298

Selected Tones for the Magnificat (White notes represent the reciting tone.)

Appendix C

Appendix D: Facsimile of Parts for Palestrina’s Missa Sine Nomine, Agnus II

Cantus:

Altus:

300

Tenor:

Quintus (in this case, Quintus = Tenor II):

Appendix D

Appendix D

Bassus:

Explanation of the neumes:

301

Notes

Chapter 1 1 The Acoustical Society of America identifies the eight Cs on the piano keyboard as C1–C8, and identifies all other notes with their letter names followed by the number of the C immediately below. Thus middle C is C4, the C one octave lower is C3, and the F between these two pitches if F3. 2 Perhaps it is for this reason that we have come to speak of the subdominant to tonic cadence as a plagal cadence, as opposed to the authentic or “true” cadence with the dominant chord whose root is the upper fifth. 3 Interestingly, the same “ethnic” modal names were used to refer to different modes by the ancient Greeks. A treatise entitled “Alia musica” (probably dating from the late ninth century) applied the traditional names in the configuration that has been used for the last millennium. See David E. Cohen, “Notes, Scales, and Modes in the Earlier Middle Ages,” in Thomas Christensen, ed., The Cambridge History of Western Music Theory (Cambridge: Cambridge University Press, 2002), pp. 307–363, particularly his Table 11.3. 4 Although you sometimes hear the diminished fifth referred to as a tritone, properly speaking it is only the augmented fourth that should be called a tritone, since it consists of three whole-tones between scale degrees. 5 The reason medieval theorists did not recognize Aeolian and Ionian as distinct and viable modes will be discussed in Section I-D of this chapter. 6 See Appendix C for sample tunes for reciting scriptural passages. 7 See Appendix B for Latin pronunciation. 8 Concerning this development, see chapters 12 and 13 of Thomas Christensen, ed., The Cambridge History of Western Music Theory (Cambridge: Cambridge University Press, 2002).

Chapter 2 1 You will repeatedly be asked to sing a melody, then to play it, then to sing it again. Do not neglect this triple performance. At first you will be sight-singing. The playing will correct any possible mistake. The final singing will fix the correct version in your mind. 2 David Lewin comments on and codifies this tendency in his article “An Interesting Global Rule for Species Counterpoint,” In Theory Only 6/8 (1983): 19–44. 3 The concept of “gap-fill” derives from Leonard Meyer, Emotion and Meaning in Music (Chicago: Chicago University Press, 1956) and Explaining Music (Berkeley: University of California Press, 1973). However, David Huron argues that such an expectation is really only a consequence of a principle known as “regression to the mean.” See Huron, Sweet Anticipation: Music and the Psychology of Expectation (Cambridge, MA: MIT Press, 2006).

Chapter 3 1 Our word “tenor,” from the Latin tenere (“to hold”), comes from the practice of lengthening the notes of the plainsong cantus firmus so that the other voice or voices can provide elaborate counterpoint against it. 2 This piece uses a partial signature. The chief melody, in the lower voice, makes consistent use of Bb. It is therefore

Notes

303

put into the signature. Since the upper voice uses B-natural, no accidental is placed at the beginning. Partial signatures were very common throughout the thirteenth to fifteenth centuries. 3 Such metaphors have been explored by Lawrence Zbikowski, among others; see his book Conceptualizing Music: Cognitive Structure, Theory, and Analysis (New York: Oxford University Press, 2002).

Chapter 4 1 Strictly speaking, when referring to harmonic intervals we should use the musical terms concord and discord and their adjectives concordant and discordant rather than the acoustical terms consonance (consonant) and dissonance (dissonant). The latter are matters with which physicists and physiologists have concerned themselves, using scientific approaches to the matter. Nevertheless, since the use by musicians of these terms is so widespread, we will not attempt to inflict the more accurate usage here. 2 For more on the evolution of the concepts of consonance and dissonance, see James Tenney, A History of “Consonance” and “Dissonance” (New York: Excelsior, 1988). 3 Thomas Morley, A Plain and Easy Introduction to Practical Music, ed. A. Harman (New York: W. W. Norton, 1973), p. 141. 4 To clarify, ratios as simple as these are only really accurate in “just intonation.” A great number of different tuning systems were eventually proposed that deviated from the intervallic purity indicated by these ratios; even the equal termperament of a modern piano slightly “mistunes” all of these consonances. 5 These six partials were collectively referred to as the senario by Gioseffo Zarlino in Part I of Le istitutioni harmoniche (1558). See Catherine Nolan, “Music Theory and Mathematics,” in Thomas Christensen, ed., The Cambridge History of Western Music Theory (Cambridge: Cambridge University Press, 2002), pp. 272–304 (esp. p. 277). 6 When we begin to work in three voices we will have cause to consider another odd phenomenon: the tritone or the diminished fifth, when between two upper voices, is treated as a consonance. 7 Palestrina’s complete name was Giovanni Pierluigi da Palestrina. The English equivalent would be John PeterLouis of Palestrina (the town of his birth). “Aloysius” is a Middle Latin equivalent of Louis (A-loys-ius).

Chapter 5 1 Only crossing below the bass is forbidden. 2 It is true that this diminished triad in first inversion is not literally a consonant chord since it contains a diminished fifth—or, if the upper voices are exchanged, a tritone. Nevertheless, it is treated as a consonance. Since each of the upper voices is consonant with the bass, the sonority is heard to be stable enough to function as a consonance within the phrase, but it may not begin or end a phrase. 3 In the Lydian mode, scale-degree ^ 4 must be flatted to produce the requisite viiº6.

Chapter 6 1 The motet is Je ne chant pas—Talens m’est pris—APTATUR—OMNES, to be found in the Codex Bamberg, No. 92. 2 The manuscript gives the text for the first ten measures only. To make the piece singable the remainder of the text, taken from a different version of the same piece, has been fitted to the music. 3 Quoted in Gustave Reese, Music in the Middle Ages (New York: W. W. Norton, 1940), pp. 321–322. 4 Reproduced in Manfred Bukofzer, Geschichte des englischen Diskants und des Fauxbourdons (Strasbourg: Heitz, 1936), pp. 10ff. 5 The entire piece is given as No. 33 in J. Peter Burkholder and Claude V. Palisca, eds, The Norton Anthology of Western Music, 6th ed. Vol. I (New York: W. W. Norton, 2010).

304

Notes

Chapter 9 1 Quoted by Allan W. Atlas, Renaissance Music: Music in Western Europe, 1400–1600 (New York: W. W. Norton, 1998), p. 255. 2 Atlas, ibid., suggests this mass may have been written some years earlier, perhaps in the early 1480s. 3 From a letter to Henry VIII of 1544. Quoted in Source Readings in Music History, selected and annotated by Oliver Strunk (New York: W. W. Norton, 1950), pp. 350–351. 4 This development is traced by Joel Lester in his book Between Modes and Keys: German Theory 1592–1802 (Stuyvesant, NY: Pendragon Press, 1989). 5 Reproduced in Charles Burkhart, Anthology for Musical Analysis, 6th ed. (New York: Schirmer, 2004), pp. 14–15. 6 In the solfège system of the time, both of these pitches carried the syllable Mi, hence the name of the Mass. 7 Edited by Archibald T. Davison and Willi Apel, rev. ed. (Cambridge, MA: Harvard University Press, 1949), vol. 1, p. 92. 8 You may notice a discrepancy in measure 7 of Example 9-13: the Contratenor has a half-note A4 and a wholenote G4 rather than two dotted half-notes as might be expected. Compare these to the half-notes A4 and G4 in measure 5 of the Superius. This is called alteration. See Anna Maria Busse Berger, “The Evolution of Rhythmic Notation,” in Thomas Christensen, ed., The Cambridge History of Western Music Theory (Cambridge: Cambridge University Press, 2002), pp. 628–656 (esp. pp. 633–634).

Chapter 10 1 Curiously, Aloysius also allows the 4–5 as a lower voice suspension. But this type is virtually never to be found in real music except in conjunction with the 2–3 and it is best to disallow it here. 2 There is a very good reason for forbidding crossing below the bass at this stage of the game. Especially for beginners, there is a real tendency to assume that the lowest written voice is also the lowest sounding voice. It is not uncommon, then, for a student to write, say, an A3 in the bass and an E3 in the tenor and imagine the interval to be a perfect fifth when actually, of course, it is a perfect fourth owing to the tenor’s having crossed below the bass. To exclude any crossing below the bass, then, is good discipline until further technical command of the idiom has been achieved.

Chapter 12 1 Turning back to Chapter 9, you will find it in the following places: Example 9-1, m. 1 (S); Example 9-3, m. 24 (T), m. 26 (T); Example 9-4, m. 20 (T), m. 32 (S), m. 33 (S); m. 33 (S); Example 9-6, m. 12 (S); Example 98, m. 19 (B II), m. 25 (B I); mm. 26–27 (S, in augmentation); Example 9-9, m. 12 (Ct); Example 9-13: m. 7 (S, imitated in Ct in m. 10). 2 There were at least two previous three-voice settings of this song.

Chapter 14 1 Quoted in Allan W. Atlas, Renaissance Music: Music in Western Europe, 1400–1600 (New York: W. W. Norton, 1998), p. 581. 2 See Anna Maria Busse Berger, Mensuration and Proportion Signs: Origins and Evolution (Oxford and New York: Oxford University Press, 1993), pp. 151–154. 3 These rules appear in Chapter 33 of Part Four of his Le istitutioni harmoniche (1558), published as On the Modes, trans. Vered Cohen, ed. and intro. by Claude V. Palisca (New Haven and London: Yale University Press, 1983).

Notes

305

Chapter 15 1 Repetition is a means of effecting closure, in poetry as well as music. Many madrigals and motets of the late Renaissance repeat the final section as a means of making a convincing ending.

Chapter 17 1 An example is Palestrina’s offertory Exaltabo te, m. 10 beat one. The piece is included in Soderlund and Scott, Examples of Gregorian Chant and Sacred Music of the 16th Century (Prospect Heights, IL: Waveland, 1996), pp. 202–206. 2 Part Four of the treatise deals with the modes, but mostly in a historical and theoretical way rather than a practical way. In the only chapters of Part Four in which Zarlino gives practical instructions to the composer (chapters 30–32), the modes are relegated to a position of secondary importance. 3 The particular species of double counterpoint involved in Example 17-19 is called double counterpoint at the twelfth, since the opening harmonic interval of a perfect fifth (T on G3, A on D4) becomes, when inverted, a perfect octave (B on G3, S on G4). A perfect fifth added (conjunctly) to a perfect octave results in a perfect twelfth. 4 Gustave Fredric Soderlund and Samuel H. Scott, eds, Examples of Gregorian Chant and Sacred Music of the 16th Century (Prospect Heights, IL: Waveland, 1996), pp. 247–293 passim; Archibald T. Davison and Willi Apel, eds, Historical Anthology of Music, rev. ed. (Cambridge, MA: Harvard University Press, 1949), No. 140; Kristine Forney, ed., The Norton Scores, 10th ed. (New York: W. W. Norton, 2007), Vol. I, No. 10; Carl Parrish, A Treasury of Early Music: An Anthology of Masterworks of the Middle Ages, the Renaissance, and the Baroque Era (New York: W. W. Norton, 1958), No. 28.

Chapter 18 1 It is noteworthy that in this case the augmented fourth does not expand to a sixth but moves by parallel motion to a perfect fourth at the beginning of the next measure. If the soprano and alto voices were exchanged so that the dissonant interval was a diminished fifth this parallel motion would be most unlikely. In other words, the augmented fourth often moves to a perfect fourth rather than to a sixth; the diminished fifth, on the other hand, very rarely moves by parallel motion of unequal fifths to a perfect fifth. 2 Johann Philipp Kirnberger, The Art of Strict Musical Composition [1771], trans. David Beach and Jurgen Thym, intro. and notes David Beach (New Haven and London: Yale University Press, 1982).

Epilogue 1 The human mind has a bias toward creating relationships even from unlikely sources. If a composer should make a piece from a siren and a Bach cello suite, the listener would probably infer that a statement of some kind was being made—the siren perhaps representing disaster in the real world (air raid, police, ambulance, fire) and the cello the artist in oblivious isolation, Nero fiddling while Rome burns. But this would be a counterpoint based on extramusical referents, not a genuine musical relationship between the two lines.

Select Bibliographies

Modal Counterpoint Textbooks Bassett, Leslie. Manual of Sixteenth-Century Counterpoint. New York: Appleton-Century-Crofts, 1967. Benjamin, Thomas. The Craft of Modal Counterpoint: A Practical Approach. New York: Schirmer Books, 1979. 2nd ed. (New York: Routledge), 2005. Boyden, David D. Manual of Counterpoint Based on Sixteenth-Century Practice. New York: Carl Fischer 1946. 2nd ed., 1953. Fux, Johann Joseph. The Study of Counterpoint. Translated and edited from Gradus ad Parnassum (1725) by Alfred Mann. New York: W. W. Norton, 1965. Gauldin, Robert. A Practical Approach to Sixteenth-Century Counterpoint. Englewood Cliffs, NJ: Prentice-Hall, 1985; reprinted (Prospect Heights, IL: Waveland, 1995). Heeremans, Harold. Sixteenth-Century Counterpoint. New York: H. W. Gray, 1955. Jeppesen, Knud. Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century. Translated with an introduction by Glen Haydon. Englewood Cliffs, NJ: Prentice-Hall, 1939. Krenek, Ernst. Modal Counterpoint in the Style of the Sixteenth Century. New York: Boosey & Hawkes, 1959. Mann, Alfred. The Study of Fugue. New Brunswick, NJ: Rutgers University Press, 1958. (Pages 78–138 translate a portion of Fux’s Gradus not included in The Study of Counterpoint.) Merriman, Margarita. A New Look at 16th-Century Counterpoint. Washington, DC: University Press of America, 1982. Merritt, Arthur Tillman. Sixteenth-Century Polyphony: A Basis for the Study of Counterpoint. Cambridge, MA: Harvard University Press, 1939. Morris, Reginald Owen. Contrapuntal Technique in the Sixteenth Century. London: Oxford University Press, 1922. Norden, Hugo. Fundamental Counterpoint. Boston: Crescendo, 1969. Owen, Harold. Modal and Tonal Counterpoint: From Josquin to Stravinsky. New York: Schirmer, 1992. (Part 2, Counterpoint in the Late Renaissance, extends through pages 25–120). Porter, Quincy. A Study of Sixteenth Century Counterpoint. Boston: New England Conservatory of Music, 1940. Roberts, Stella, and Irwin Fischer. A Handbook of Modal Counterpoint. New York: Schirmer, 1967. Schubert, Peter N. Modal Counterpoint, Renaissance Style. New York: Oxford University Press, 1999. 2nd ed., 2007. Smith, Charlotte. A Manual of Sixteenth-Century Contrapuntal Style. Newark: University of Delaware Press; London: Associated University Presses, 1989. Soderlund, Gustave. Direct Approach to Counterpoint in 16th-Century Style. Englewood Cliffs, NJ: Prentice-Hall, 1947. With accompanying anthology, originally published as Examples of Gregorian Chant and Works by Orlandus Lassus, Giovanni Pierluigi da Palestrina and Marc Antonio Ingegneri (New York: Appleton-Century-Crofts, 1946); revised: Soderlund, Gustave, and Samuel H. Scott, Examples of Gregorian Chant and Sacred Music of the 16th Century (Englewood Cliffs, NJ: Prentice-Hall, 1971); reprinted (Prospect Heights, IL: Waveland, 1996). Stewart, Robert. An Introduction to Sixteenth-Century Counterpoint and Palestrina’s Musical Style. New York: Ardsley House, 1994. Swindale, Owen. Polyphonic Composition: An Introduction to the Art of Composing Vocal Counterpoint in the SixteenthCentury Style. London: Oxford University Press, 1962.


307

Ultan, Lloyd. Music Theory: Problems and Practices in the Middle Ages and Renaissance. Minneapolis: University of Minnesota Press, 1977. Zarlino, Gioseffo. The Art of Counterpoint: Part Three of Le istitutioni harmoniche, 1558. Trans. Guy A. Marco and Claude V. Palisca. New York: Norton, 1968.

Sources on the History and Analysis of Modal Music Essays within edited compilations have not been cited individually, except when most of the compilation does not concern medieval or Renaissance music. Abraham, Gerald, ed. The New Oxford History of Music, vol. 4: The Age of Humanism 1540–1630. Oxford and New York: Oxford University Press, 1968. Aldrich, Putnam. “An Approach to the Analysis of Renaissance Music.” Music Review 30 (1969): 1–21. Atlas, Allan W. Renaissance Music: Music in Western Europe, 1400–1600. New York: W. W. Norton, 1998. With accompanying anthology. Bain, Jennifer. “ ‘Messy Structure’? Multiple Tonal Centers in the Music of Machaut.” Music Theory Spectrum 30/2 (2008): 195–237. Bashour, Frederick. “Towards a More Rigorous Methodology for the Analysis of the Pre-Tonal Repertory.” College Music Symposium 19/2 (1978): 140–153. Bellamy, Sister Laurette. “Some Comments on the Lais of Guillaume de Machaut.” Indiana Theory Review 2/1 (1978): 41–53. Bent, Ian. “Steps to Parnassus: Contrapuntal Theory in 1725.” In Thomas Christensen, ed., The Cambridge History of Western Music Theory. Cambridge: Cambridge University Press, 2002, pp. 554–602. Bent, Margaret. Counterpoint, Composition and Musica Ficta. New York: Routledge, 2002. Berger, Anna Maria Busse. Mensuration and Proportion Signs: Origins and Evolution. Oxford and New York: Oxford University Press, 1993. Berger, Anna Maria Busse. “The Evolution of Rhythmic Notation.” In Thomas Christensen, ed., The Cambridge History of Western Music Theory. Cambridge: Cambridge University Press, 2002, pp. 628–656. Berger, Karol. “Tonality and Atonality in the Prologue to Orlando di Lasso’s Prophetiae Sibyllarum: Some Methodological Problems in the Analysis of Sixteenth-Century Music.” Musical Quarterly 66 (1980): 484–504. Berger, Karol. “The Common and the Unusual Steps of Musica Ficta: A Background for the Gamut of Orlando di Lasso’s Prophetiae Sibyllarum.” Revue belge de musicologie 39–40 (1985–1986): 61–73. Berger, Karol. Musica Ficta: Theories of Accidental Inflections in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino. Cambridge: Cambridge University Press, 2004. Bergquist, Peter. “Mode and Polyphony around 1500: Theory and Practice.” Music Forum 1 (1967): 99–161. Blackburn, Bonnie J. “On Compositional Process in the Fifteenth Century.” Journal of the American Musicological Society 40/2 (1987): 210–284. Blackburn, Bonnie J. Composition, Printing and Performance: Studies in Renaissance Music. Aldershot, UK: Ashgate, 2000. Blackburn, Bonnie J., Edward E. Lowinsky, and Clement A. Miller, eds. A Correspondence of Renaissance Musicians. Oxford: Oxford University Press, 1991. Boyd, George. “The Development of Paraphrase Technique in the Fifteenth Century.” Indiana Theory Review 9/1 (1988): 23–62. Brown, Howard M., and Louise K. Stein. Music in the Renaissance, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1999. Bukofzer, Manfred F. Studies in Medieval and Renaissance Music. New York: W. W. Norton, 1950. Cattin, Giulio. Music of the Middle Ages I, trans. Steven Botterill. Cambridge: Cambridge University Press, 1985. Cogan, Robert, and Pozzi Escot. Sonic Design: The Nature of Sound and Music. Englewood Cliffs, NJ: Prentice-Hall,

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1976. Analysis of Josquin Benedictus from Missa L’Homme Armé on pp. 17–24, 124–130, and 254–258; analysis of Lasso “Bon jour mon coeur” on pp. 130–141. Cohen, David E. “Metaphysics, Ideology, Discipline: Consonance, Dissonance, and the Foundations of Western Polyphony.” Theoria 7 (1993): 1–86. Cohen, David E. “Notes, Scales, and Modes in the Earlier Middle Ages.” In Thomas Christensen, ed., The Cambridge History of Western Music Theory. Cambridge: Cambridge University Press, 2002, pp. 307–363. Covington, Kate. “A Theory of Dissonance in the Fourteenth Century.” Indiana Theory Review 2/1 (1978): 29–40. Crocker, Richard. “Discant, Counterpoint, Harmony.” Journal of the American Musicological Society 15 (1962): 1–21. Crocker, Richard, and David Hiley, eds. The Early Middle Ages to 1300. Oxford and New York: Oxford University Press, 1990. Cumming, Julie E. The Motet in the Age of Du Fay. Cambridge: Cambridge University Press, 1999. Davidson, Lyle. “The Structure of Lassus’ Motets a2 (1577).” Sonus 2/2 (1982): 71–90. Delone, Richard. “Machaut and the Ballade Style.” Indiana Theory Review 2/1 (1978): 15–28. Dill, Charles. “Non-Cadential Articulation of Structure in Some Motets of Josquin and Mouton.” Current Musicology 33 (1982): 37–56. Everist, Mark, ed. Music Before 1600 (Models of Musical Analysis). Oxford: Basil Blackwell, 1992. Fallows, David. Dufay. London and Melbourne: J. M. Dent, 1982. Fenlon, Iain, ed. Music in Medieval and Early Modern Europe: Patronage, Sources and Texts. Cambridge: Cambridge University Press, 1981. Fenlon, Iain. Music and Culture in Late Renaissance Italy. Oxford and New York: Oxford University Press, 2002. Forney, Kristine, ed. The Norton Scores, 10th ed. Vol. I: Gregorian Chant to Beethoven. New York: W. W. Norton, 2007. Fuller, Sarah. “Discant and the Theory of Fifthing.” Acta Musicologica 50 (1978): 241–275. Fuller, Sarah. “The Myth of ‘Saint Martial’ Polyphony.” Musica Disciplina 33 (1979): 5–26. Fuller, Sarah. “Theoretical Foundations of Early Organum Theory.” Acta Musicologica 53 (1981): 52–84. Fuller, Sarah. “On Sonority in Fourteenth-Century Polyphony: Some Preliminary Reflections.” Journal of Music Theory 30 (1986): 35–70. Fuller, Sarah. “Tendencies and Resolutions: The Directed Progression in ‘Ars Nova’ Music.” Journal of Music Theory 36/2 (1992): 229–258. Fuller, Sarah. “Modal Discourse and Fourteenth-Century French Song: A ‘Medieval’ Perspective Recovered?” Early Music History 17 (1998): 61–108. Fuller, Sarah. “Organum—Discantus—Contrapunctus in the Middle Ages.” In Thomas Christensen, ed., The Cambridge History of Western Music Theory. Cambridge: Cambridge University Press, 2002, pp. 477–502. Fuller, Sarah. The European Musical Heritage c. 800–c. 1750. New York: Random House, 1987. Rev. ed., Boston and Toronto: McGraw-Hill, 2004. Gallo, F. Alberto. Music of the Middle Ages II. Cambridge: Cambridge University Press, 1985. Gallo, F. Alberto. Music in the Castle: Troubadours, Books, and Orators in Italian Courts of the Thirteenth, Fourteenth, and Fifteenth Centuries. Chicago: University of Chicago Press, 1996. Gauldin, Robert. “The Composition of Late-Renaissance Stretto Canons.” Theory and Practice 21 (1997): 29–54. Gjerdingen, Robert. “Concrete Musical Knowledge and a Computer Program for Species Counterpoint.” In Eugene Narmour and Ruth A. Solie, eds, Explorations in Music, The Arts, and Ideas: Essays in Honor of Leonard B. Meyer. Stuyvesant: Pendragon Press, 1988, pp. 199–227. Godt, Irving. “Motivic Integration in Josquin’s Motets.” Journal of Music Theory 21/2 (1977): 264–293. Godt, Irving. “Renaissance Paraphrase Technique: A Descriptive Tool.” Music Theory Spectrum 2 (1980): 110–118. Gosman, Alan. “Stacked Canon and Renaissance Compositional Procedure.” Journal of Music Theory 41/2 (1997): 289–317. Haar, James. The Science and Art of Renaissance Music. Edited by Paul Corneilson. Princeton, NJ: Princeton University Press, 1998. Harley, John. William Byrd’s Modal Practice. Aldershot, UK: Ashgate, 2005.


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Index of Rules for Species Counterpoint

accompanying voice (in suspensions) 130–31, 136 approach to cadential ^2 21, 80 cadence three-voice first species 48–49 three-voice fourth species 137–138 three-voice second species 82–83 two-voice first species 40 two-voice fourth species 123 cadential voices 83 chromatic half-steps 21 climax in melodic line 19–20 consecutive perfect fifths and perfect octaves 38 consonance and dissonance 34–35 consonant fourth (Con4) 136–137, 139 contrary motion 36–37 cross-relations 40 crossing, voice 39, 49, 125 direct fifths 36–37, 49 dissonance 34–35, 169 double leaps 21 doubling 167 fifths, consecutive 38, 48–49 direct (hidden) 36–37, 49 unequal 48–49 final, approach to 21 first species, summary 39–40 focal point 19, 48 half steps in succession 21 harmonic intervals 33–35, 46–48 hidden (direct) fifths and octaves 36–37, 49 “horn fifth” 38–39 isolated notes 19, 22 melodic intervals 21 melodic leaps 21 melodic line 18–20 motion, types of 36–37 motions, correct 36–40

nadir 19–20 notes, isolated 19, 22 notes, repeated 21 oblique motion 36–37 octaves, direct (hidden) 36–37, 49 overlapping 36–37, 39 parallel perfect fifths and octaves, second species 76, 78 parallel intervals in succession 41, 82, 85, 118–119, 134–135 parallel motion 36–37 parallel perfect fifths, acceptable 134–135 passing tones 75–78 preferred sonorities (suspensions) 131–133 preparation (of suspension) 117–118 repeated notes 21 resolution (of suspension) 117–118, 127 similar motion 36–37 six-five chord 136–137, 139, 164 species mixture 164 suspension 117 suspension voice 130–131 suspension with moving accompanying voice 164 suspension, 7–8 121 suspensions, types of 120–121 syncope 117–118, 127 syncope, dissonant (see suspension) tendency notes 167 third voice (in suspension figures) 130–131 three-voice penultimate chord 48, 51, 83, 137–138 three-voice vertical sonorities 48, 51 tritone, melodic 22–23 unequal fifths 48–49 upward resolution 119–120 voice crossing 39, 49, 125 voice functions (in suspensions) 130–131 zenith 19–20

Index of Rules for Modal Counterpoint

accent of word 180 accent, pitch 189, 197 accidentals 190–191 accompanying voice 250 ambiguity, modal 210–211 AN (see anticipation) anapests 185–186 anticipation 179–180, 183, 198 with sixteenths 189 antiphony 282 Apollonian aesthetic 193 approach to ^2 200–201 augmentation 204 beats, strong and weak 172–173, 177 beginning of syllable 178–179 bicinium 209–212 built-in ritardando 204, 259 cadence 199–201 cadence, consonant 208, 210 cadence, deceptive 257 cadence, final in four voices 256–259 cadence, hocket 202, 210–212 cadence, plagal 208, 257–258 cadences, overlapping 212 cambiata (see nota cambiata) canon 281 change of syllable 178–180 CL (see consonant leap) clausula vera 199, 210 coda 256–257 complementary rhythm 202 consecutive perfect fifths and perfect octaves 267 consonant leap 183–184 consonant cadence 208, 210 contrary motion 202 contrary motion, imitation by 261–262 counterpoint, nature of 281–282 cross-relation 191 diminution, suspension in 198–199 diminution, syncope in 184 direct octaves and fifths 267

dissonance, function of 281 dissonance, treatment of 195–199 dotted notes 177, 182, 199 double counterpoint 263 double subject 262–263 double suspension 252–253 doubling 249–252 eighth-notes 175 eighth-note leaps 177, 183–184, 188–189 eighth-note pair 186 eighth-notes, single 175, 177, 182–184 eighth-notes, three in a row 177 escape tones 198 extensions of final cadence 256–258 fauxbourdon 246–247 final cadence, extensions 256–258 final cadence, Phrygian 258–259 five voices or more 267 focal point 191 four-voice suspensions 250–254 fourth voice of suspension 250–251 hemiola 265 hocket cadence 202, 210–212 homophonic texture 246, 259, 263–264 homorhythm 244, 246–247 imitation 201–203, 211, 260–263 imitation by contrary motion 202, 261–262 initial notes 259–260 interior phrases 202–203, 211–212 invertible counterpoint 263 jubilus 179 Latin, setting 178–180 melodic curve 191–192, 281 melodic intervals 172, 188 melodic line, coherence in 281 principle of 193–194 melody, repeated 212

Index of Rules for Modal Counterpoint

modes 180–181 modes, ambiguity in 210–211 motion, descending 184 motive 212 multisyllabic words 178 musica ficta 190–191, 250 N (see neighbor) nadir 191 NC (see nota cambiata) neighbor, lower 183–184 neighbor, upper 184 neighbor, upper and lower 197 nonimitative counterpoint 244, 282 nota cambiata 183, 189, 198–199 notes, repeated 177, 179–180, 183 notes, tied 175 offbeat 177 opening phrase 201–202 ornamented resolution 199 overlapping phrases 244 paired entries 261 pairs of eighth-notes, isolated 177 passing tone 183, 195–196, 264 per arsin et thesin 203 phrase, opening 201–202 phrases, interior 202–203, 211–12 Phrygian cadence 200–201, 210 as final cadence 258–259 pitch accents 189, 197 plagal cadence 208 portamento figure 179–180, 189 preparation for suspension 197 repeated notes 177, 179–180, 183 repeated words 212, 244 rests 211 rests begin on strong beats 177, 185, 211 rhythm, not rigid 172–173 rhythm, complementary 202 ritardando, built-in 204, 259 seventh chord 251 single eighth notes 175, 177, 182–184

single syllable 178 six-five chord 251, 254 six-five-three chord 251 sixteenth-notes 175, 177, 184 subject 260 subject, double 262–263 suspension in diminution 198–199 suspension with ornamented resolution 199, 210 suspension, preparation 197 suspensions in four voices 250–254 suspensions in two voices 196–197 suspensions, double 252–253 syllable, accent 178 syllable, beginning of 178–179 syllable, change 178, 180 syllable, extension of 179–180 syllable, last of text 179 syllable, single 178 syncope 173, 177 in diminution 184 produced by dotted quarter 182 tempo 264–265 tendency notes 249 text, last syllable 179 text, repeated 212, 244 text painting 194, 212 text setting, principle of 193 text underlay 179–180 texture, homophonic 246, 259, 263–264 tied notes 175 transposition of modes 180–181, 204 triple counterpoint 263 triple meter, fast 263–264 moderate 265 tritone 190–191 true cadence 199–201 upper neighbors leading to syncope 197 weak beat beginnings 203 word accent 180 word painting (see text painting) words, repeated 212, 244 zenith 191–192

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Index of Musical Examples

Complete pieces or movements only Adam de la Halle: Tant con je vivrai (rondeau) 31 Anon.: Alle, psallite 26–27 Anon.: Maria zart (facsimile, 1567) 150–151 Anon.: Orientis partibus 29 Anon.: Rex caeli, Domine (organum) 24 Anon.: Talent m’est pris (canon with hocket) 59–60

Lassus: Oculus non vidit (Cantiones duarum vocum, no. 3) 209–210

Dufay: Je require a tous amoureux (rondeau) 89 Dufay: Se la face ay pale (chanson) 91–93 Dufay: Missa Se la face ay pale (Kyrie) 99–100 Dunstable: textless motet 67–68 Dunstable (?): O rosa bella 72–74

Palestrina: Dies sanctificatus (cantus part only) 192–193 Palestrina: Pars mea Dominus 241–242 Palestrina: Missa de feria, third book (Benedictus) 216–219 Palestrina: Missa Papae Marcelli (from Credo) 245–246

Guillaume de Machaut: Rose, lis (rondeau) 55–56

Schlick: Maria zart (lute song) 152–153 Schlick: Maria zart (organ setting) 158–160

Josquin des Prez: Missa L’Homme armé (Agnus) 112–113 Josquin des Prez: Déploration sur le Trépas de Jean Ockeghem (“Nymphes des bois”) 141–145

Tallis: If ye love me 162–164

Landini: Gram piant’ agli ochi 70–71 Lassus: Justi tulerunt spolia (Cantiones duarum vocum, no. 7) 212–213 Lassus: Missa pro defunctis (Benedictus) 214–216

Ockeghem: Fors seulement (chanson) 94–96 Ockeghem: Missa Fors seulement (Kyrie) 102–103 Ockeghem: Missa prolationum (Osanna) 115–116

Victoria: Magnificat Tertii Toni (Et misericordia) 227–229 Victoria: O vos omnes 247–249 Walter: Ein’ feste Burg (bicinium) 156–157 Walter: Komm, Gott Schöpfer (chorale motet) 160–162

The Principles and Practice of Modal Counterpoint.pdf

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