Rajko Maksimovic Maksimovic
MORE ON MODES A Step towards a General Theory of Modes
Belgrade, 1995
© by Rajko Maksimovic Makenzijeva 35 11000 Belgrade Serbia e-mail:
[email protected] http://www.rajko-maksimovic.net http://www.myspace.com/rajkomaksimovic
2
INTRODUCTION
There is no doubt that a serious crisis of tonal (major-minor) system began with Wagner's chromaticity in Tristane and Ysolde, and later with Debussy's usage of whole-tone scale as well as of the pentatonic scale. Atonal music - in the beginning of the XX century - denied all basic principles of the traditional (tonal) music, and all consequences of those principles - the shape of melody, vertical (harmonic) structure, building of musical forms. Looking from our standpoint now, it was almost chaos. Soon afterwards Schönberg declared principles of twelve tone music trying to make order and a new system in organizing his music of that time. One of his basic principles was absolute equality among tones, i.e. negation of any possible hierarchy. Indeed, such a "democracy" not only cancelled the supremacy of the tonic and dominant, but also prevented any possible advantage of any tone in general. Serial music and its last instance integral serialism elaborated Schönberg's principles further, to their maximum. Aleatory music applied certain features of serial music but in much freer form - at least the absolute equality of tones was not under the strict control. Certain inequality of tones might have happened, if not willingly - then by chance. Many composers tried to make make certain order in musical musical thought in somehow different way. Olivier Messiaen, one of the leading figures of French music in last few decades, was one of them. In his book "Technique de mon Language Musicale" he proclaimed and explained his modal system and 1 showed how it worked. He had "invented" 7 modes of limited transposition and from them he derived very complex harmonic structures, harmonic progressions 2 and melody shaping. Probably the second mode was the most attractive and popular one (thanks to its great richness and vitality) and many composers throughout the world had had certain experience with it. As a matter of fact Messiaen did not invent it, but merely systemized and systematically used it. used it. That mode can be found sporadically in Ravel, Bartok, Stravinsky and even Scriabine and Korsakow. By the way Scriabine mode means exactly that. The 3 same pattern of intervals (121212) can be found in the Istrian scale, but in the range of only a diminished di minished sixth. 1
See more about Messiaen's modes in Chapter I 2nd mode divides an octave in four identical segments (minor thirds), each one o ne consisting of one minor minor and one major major second. (8 different tones in an octave) 3 In this paper I'll use the widely accepted convention for numeric presentat ion of intervals, as follows: 1 = minor minor second; 2 = major second; 3 = minor third; 4 = major third; 5 = perfect fourth; 6 = tritone; 7 = perfect fifth; 8 = minor minor sixth; 9 = major sixth; 10 = minor seventh; 11 = major seventh; 12 = perfect octave. 2
3
CHAPTER I STARTING KNOWLEDGE
In my practice as a composer I had used some of the Messiaen's modes (2nd & 3rd), but also the Mediaeval modes – Dorian, Phrygean, Lydian, Mixolydian, Aeolian, as well as the (anhemitonic) pentatonic scale (d-e-g-a-c). During the practice I encountered with modal or scale structures which were not in any theory known to me. That forced me to think about the problem and to find out the way to embrace all possible cases (known to me) – such as mediaeval modes, Messiaen's modes, pentatonic and some others, – in one single theory of modes, where all a ll mentioned ones would be only particular types or cases. Naturally, to achieve this goal (General Theory of Modes) I had to start from already known principles, combine them, make further conclusions and, finally – make a larger, all-including system s ystem.. 4
a) Principles of mediaeval theory of modes ....... (See sheet 1) Four (diatonic) tones make a tetrachord, which is considered as the basic unit in constructing modes. There were four different tetrachords, here listed by sharpness, depending on the position of a se mitone: mitone: lydian L 2-2-2 -(1) semitone outside tetrachord. mixolydian 2-2-1 M (also known as major ) dorian D 2-1-2 (also known as minor ) phrygean 1-2-2 P
Lydian is the "sharpest", phrygean is the "mildest". [We can include here (as an option) the harmonic tetrachord, known as the upper tetrachord in the harmonic minor. It is also known as the oriental O 1-3-1 since it is found in many folk scales of the oriental area, like Phrygean minor-major, Gipsy minor and alike].
Two tetrachords standing a whole step apart (called diazeuxis) make an authentic mode, with the first tone of the lower tetrachord as the finalis (tonic). Thus: L–M = Lydian mode Lyd M + D = Mixolydian mode Mix D+D = Dorian mode Dor P+P = Phrygean mode Phr
4
In fact fact these names are from the Ancient Greeks which were (wrongly) (wrongly) used later later in Middle Ages 4
Here the sign "+" stands for a whole-step diazeuxis, except the Lydian mode where the sign "–" stands for a semiton se mitone. e. When the upper tetrachord becomes the lower one (by the octave transposition) it links with the other one (former lower, now upper) on the synaphe, thus making a plagal mode: ML = DM = DD = PP =
Hypolydian mode Hypomixolydian mode Hypodorian Hypophrygean
Hypolyd Hypomix Hypodor Hypophryg
keeping the same finalis as in the authentic mode and differing from it only in melodic range. It should be noted that the Lydian and Mixolydian modes have a major triad on the finalis and form the major type, while the Dorian and Phrygean modes have a minor triad on the finalis and form the minor type. Each one of the modes is featuring one particular interval as its representative, or characteristic or characteristic one (counting from the finalis): lydian fourth mixolydian seventh dorian sixth phrygean second
(augm. 4) (minor 7) (major 6) (minor 2)
lyd.4 for Lydian mode mix.7 for Mixolydian mode dor.6 for Dorian mode phr.2 for Phrygean mode
We may call lyd. 4 and phr. 2 as primarily characteristic since these intervals show up uniquely, only in "their modes". Mix.7 and dor.6 are secondarily characteristic, though, since these intervals as such can be found in other modes (minor 7 in Phrygean and Dorian; major 6 in Lydian and Mixolydian), but they are considered characteristic in respect to the corresponding tonic triad, i.e. minor 7 in spite of the major triad in Mixolydian and major 6 in spite of the minor triad in Dorian mode. Later practice of post-renascence period brought up two modes more: Ionian and Aeolian. As a matter of fact they were the result of chromatic alterations of real modes. Flattening of augm. 4 in Lydian mode to avoid the tritone jump, or sharpening of min. 7 in Mixolydian mode to obtain the leading tone in cadences and elsewhere – produced the Ionian mode (later called: major scale); flattening of maj. 6 in Dorian mode (what was considered as normal since early times) – created Aeolian mode (later called: natural minor scale). Some theorists claim that these modes have characteristic intervals, too, – aeolian sixth (min.6) and ionian seventh (maj. 7), respectively, but we think opposite: both of them are middle solutions, the result of a compromise, since both of them became by truncation (or negation) of real characteristics of real 5
modes – therefore, they are uncharacteristic modes having no characteristic interval! Nevertheless Nevertheless we can include include them in our list list arranged by sharpness: by sharpness: mode tetrachords interval characteristic Lydian Ionian Mixolydian
L–M M+M M+D
lyd 4 – mix 7
** (strong) – (none) * (medium)
Dorian Aeolian Phrygean
D+D D+P P+P
dor 6 – phr 2
* – **
It should be noted that these modes are made either of identical or similar or similar (adjacent in our list) tetrachords. So called Locrian mode is out of this discussion since it has no consonant triad on the tonic (it has a diminished triad) and besides it is structurally unbalanced (it unbalanced (it links two extreme tetrachords). Nevertheless it may be of our particular interest: Locrian
loc 5 (dim.5th)
P–L
*** (strongest)
b) Principles of Messiaen's M essiaen's modal theory............. (See sheet 2)
An octave is divided on 2, 3, 4 or 6 identical segments (tritones, maj. 3rds, min. 3rds, maj. 2nds). All the segments of a mode have the identical internal structure. The segments are linked by a common tone - (the synaphe). In respect to the size of the constitutional segments, corresponding mode has limited number of possible transpositions, as follows: mode
pattern
num. of segm.
1st mode 2nd mode 3rd mode 4th mode 5th mode 6th mode 7th mode
2-2-2-2-2-2 12-12-12-12 211-211-211 1131-1131 141-141 2211-2211 11121-11121
6 4 3 2 2 2 2
range of segm. 2 3 4 6 6 6 6
num. of transp. 1 1 1 1 1 1 1
+ + + + + + +
1 2 3 5 5 5 5
It is never said in the book, but it is obvious, that the (perfect) octave is considered as the measure of periodicity. of periodicity. That means that all modes repeat 6
themselves in upper or lower octaves, i.e. after the completion of an octave they proceed the same pattern out of it. All these modes generate very specific harmonic structures and progressions. It is possible to make chords of 3, 4, 5 or more tones either by skipping one tone and take every other or to skip two tones and take every third. It is possible to combine both these ways. c) Principles of the pentatonic pe ntatonic mode................ mode................ (See sheet 3)
The semitone is avoided. The maj.2 and min.3 alternate until the octave is reached. Then the tones repeat themselves. Two consecutive maj.2 may happen There are three types of pentatonic rows (using here only white piano keys): c-d -e-g-a-c-d-e...; -e-g-a-c-d-e...;
-g -a-c-d-f...; c-d-f -g -a-c-d-f...;
e-g-a-h-d-e-g-a...;
Thanks to the absence of a semitone and tritone, tonal feeling is very doubtful. Any of the tones may act as a tonic, so: no one is a real tonic. It is true that among five tones, only one of them (marked bold) has major seconds on both sides, but this is not enough to promote that tone as a real tonic. In the harmonic elaboration this mode eliminates chords by thirds. Instead, chords (of no matter matter how many many tones) consist of the combination(s) of perfect fourths and fifths, major seconds and minor thirds.
7
CHAPTER II EXPANDING OF BASIC PRINCIPLES OF EARLIER THEORIES
First of all we have to see what is our goal, i.e. what is the meaning of this paper? Brief answer might be in following few statements: a) Looking throughout the (European) history of music we notice that in all times some kind of a tonal feeling was more or less present; from Gregorian or Byzantine monophonic singing up to Stravinsky's polytonality – we could recognize the gravitational force of one (or two or even more) tone(s). b) We can conclude that some kind of a tonal feeling helps both in organizing musical form (time) by the composer and to its comprehensiveness by the listener. c) Among many problems of our time, one might be how to establish the sense of tonic and yet to avoid worn out traditional solutions (especially of majorminor system). d) I think that the variety of modes I am going to present in this paper may be a good base to start off. Naturally, I always underline that any method or system or knowledge are just tools. Without the the real talent of the user they remain an an empty shell without the living body. On the contrary: a talented person without knowledge (tools) remains – the poor talent. Therefore, only the talented and earnest person equipped with the broad knowledge, up-to-date information and good taste may be one to create something really new and of good quality. * At the very beginning I took the Messiaen's modal system and asked two basic questions: – Why all the segments of a mode must be identical?
8
– Why the range of a mode must be an octave? What to do with the tone-rows which – following certain logic or pattern – quite normally and smoothly skip the tone of the first octave above? When I began thinking this way I realized that the octave – though the first natural transposition – as a mode frame is too cramped. To answer the first question I was helped by the Mediaeval modes. Three of them (Ionian, Dorian and Phrygean) are made of two identical tetrachords, but the others (Lydian, Mixolydian, Aeolian and Locrian) have different ones. That encouraged me to dig up even the Messiaen's modes! I took the third one 211-211-211, and made another pattern: 211-121-112. (See figure on sheet 4). That's different. That's the new mode! Then, I tried some unusual combinations of tetrachords and also got the result (See sheet 4). Then I "attacked" the octave range. I began from a scale (mode) known in – which links several major (Mixolydian) theory as the Antique Major – which tetrachords on the synaphe, synaphe, like a chain. chain. (See figure on sheet 3). Though most of the tones have their octave transpositions, it is obvious that octave is not the interval of periodicity of the mode as a whole. We We may notice notice that "b natural" and "e natural" in upper octaves have flats! For that reason the mixolydian segment transforms into aeolian one in the upper octave. If, for instance, we want the first tetrachord (g-a-b-c) to find transposed somewhere else in the mode but in exactly the same sequence of tones (g-a-b-c), we have to wait not less than 5 octaves! The interval of its periodicity is 5 octaves! So the next thing I had realized was that: – similarly to the interval of one octave which is reachable either in 6 wholetone steps, or in jumps of 4 minor-thirds, minor-thirds, 3 major-thirds, 2 tritones tritones (Messiaen's modes) – interval of two octaves may be reached in 3 minor-sixth jumps, – three octaves may be reached in 4 major-sixth jumps, – five octaves may be reached in 12 perfect-fourth jumps, – seven octaves may be reached in 12 perfect-fifth jumps.
These jumps which evenly divide ranges of 1 octave, 2 octaves, 3 octaves, 5 octaves and 7 octaves – I named modules. And modules happen to be the basic units in mode construction. co nstruction. 9
• Module is a unit similar and analogous to tetrachords in mediaeval theory and to segments to segments in Messiaen's, but it has specific features, too. Each module has three essential (and variable) features: – number of tones included in it – internal disposition (spacing) of tones (interval pattern) – occupied interval (range) • Modules of one particular particular mode are made of a constant number of tones (3, 4, 5, i.e. trichords, tetrachords, pentachords etc.) – exactly like in the Messiaen's theory – while the • internal spacing of tones within modules modules of the same mode mode as well as • their occupied intervals may vary, depending on type of the the particular mode; mode; these two features are very unlike the Messiaen's system. There are two types of mode construction: I.– linear II.– centrally oriented, with two subtypes – –symmetrical –gravitational and all of them may be good base for creating unusual, interesting (and logical!) – melodic shapes, contrapuntal tissues, complex and compound harmonic structures and progressions – naturally depending on the individual taste and craft.
I.
LINEAR TYPE
This type is built by the superposition of two, three, or more modules, linked on the synaphe or with w ith a diazeuxis in between. • An octave may and (preferably) may not be the interval of periodical repetition (transposition). 1.1.
If it is, then we have the variety of modes mentioned earlier in this text, such as: mediaeval modes, Messiaen's modes, pentatonic and many other modes and scales of folk folk tradition or "synthetically" "synthetically" made; we can still do something new, e.g. we can divide an octave on equal segments (like Messiaen did), but to fill them (unlike Messiaen) with differently organized (spaced) trichords, tetrachords etc. (see an example on Sheet 4); I call all of them closed modes.
1.2/3 If the octave is not the interval of periodical repetition, then we have several categories of basically different modes:
10
1.1. –(By periodical repetition after 1.2.1 – By periodical repetition after 1.2.2 – By periodical repetition after 1.3.1 – By periodical repetition after 1.3.2 – By periodical repetition after 1.4 – Non periodical (irregular)
1 octave - see above) closed 2 octaves semi-closed 3 octaves semi-closed 5 octaves open 7 octaves open
1.1. The modes of the first category – octave modes modes – I call closed or finished since everything happens within an octave (tones and their relations show their qualities and potentials) and the octave as an interval is reachable by any voice or instrument. 1.2. For that very very reason, 2-octave-, and especially 3-octave-modes, I call semi-closed since a voice or an instrument may not reach the (upper or lower) end of the mode (which exists theoretically) and thus the mode may not show all its characteristics and potentials in that voice. 1.3. Third category – 5-octave- and 7-octave-modes – in most cases will stay "unfinished"; points of repetition (periodicity) will hardly be reached and the awareness of both the beginning and the end of the mode will be missing. Usually they are open on both sides. In extreme (though possible) cases, if a work is scored for for an orchestra, piano or organ, the the whole range of five five and even seven octaves may be reached, either in succession or simultaneously. In those cases, particularly, particularly, the following fact comes into force: •
The key consequence of periodicity of modes after two or more octaves is that the situation changes from octave to octave, from register to register. (See sheets from from 5 to 11 as examples of the upper statement, especially in multi-voice harmonic movements). All modules of a linear mode occupy the same interval (min. 3rd, maj. 3rd, perf. 4th, tritone, perf. 5th, min. 6th, maj. 6th, or: 3, 4, 5, 6, 7, 8, 9 semitones).
modes), but it may • They may may have an identical identical internal spacing (homogeneous (homogeneous modes), modes). vary as well (heterogeneous (heterogeneous modes).
11
II. CENTRALLY ORIENTED MODES
linear concept of mode construction (up-and-down), modes Instead of the linear concept may be organized centrally oriented, from the center, in both directions. Two types are possible: Symmetrical (with mirrored "wings") Asymmetrical
• A special sub-type sub-type of the symmetrical symmetrical type are gravitational modes, where expand their ranges modules, moving from the center away, progressively expand their (e.g.: dim.4, perf.4, aug.4, perf.5, min.6, etc.), whilst keeping the constant number of tones within them. • Consequently, internal dispositions also change. • Looking the opposite way, from the ends towards the center, modules decrease their range and consequently increase density and gravitation of the center – tonic. • Particularly interesting and illustrative cases of symmetrical of symmetrical and gravitational modes are with the center on keys d or g# at the piano, since piano keyboard is symmetrical to these two points. po ints. Unusual (but possible) type is a symmetrical, gravitational mode with double tonic! Its construction goes similarly to the previous one, but instead of one second is treated as the center. Now from its point (tone) as a center, a minor second is upper tone starts the right wing of the mode, while from the lower tone starts the left wing. Tones of both wings belong to the same mode and, when played in multi-voice texture, they produce very interesting, or at least unexpected, combinations combinations of tones. tones. (See sheets 12 12 & 13) Of course, I am aware that all this is not The General Theory of Modes, as I mentioned. Yet it gives the idea what the modes are and how they might be. I may never finish this task but I think that this paper throws a new light on the problem. Each composer may now dig on his (her) own. For the moment it is enough.
12
WARNING!
All what is shown here ought to be understood only as an attempt to establish a kind of order among tones, potential relations among them and especially the gravitational power of tonic. The worst thing would be is to understand this as a recipe for successful composing! It should never be forgotten that great masters from the past are great, among other merits, because they used to outrun the system they had inherited! Remember multiple appogiaturas in Bach's organ and piano works (which are out of chord ), ), also his chromatic alterations of a given scale; or take Beethoven and his frequent changes of tonality; and many, many other cases. And now we come to the crucial question: what is the the relation (if any) between the rational element in music (knowledge, theories, systems etc.) and irrational one – commonly called inspiration (or intuition)? We state that both elements have always been present in compositional practice – more or less, and in best examples they show beautiful and harmonic interdependence. On the other hand extreme cases, from our point of view, are clear: strongly predominant rational element kills musical being, while the absolute lack of it gives an illiterate product. Therefore, I think that both elements are essential essential with light predominance of intuition. This opinion is based on experience: it is much easier to "civilize" a "savage" musical idea than to add some kind of spontaneity to a piece rigidly written according to a certain ce rtain system. It’s the time to quote Anatole France here: “The art is being threatened by two monsters: the Artist who is not master and the Master who is not artist”. IN SHORT: Theoretical knowledge and in general rational experience gives the music its body whilst inspiration is the soul of music. [This paper was prepared for a group of Greek graduate students of composition who – in 1995 – attended my course in Karditza, Greece]
13
