Complex Chords Eowyn January 2007
Table of Content Complex Chords Eowyn January 2007.............................................. ........................................................ .......................................................................... .................. 1 Table of Content.............................................................................................................. 1 Introduction......................................................................................................................2 rief !ecap...................................................................................................................... 2 Triads........................................................................................................................... 2 "our note chords.............................................................................................................. # Chord Tensions........................................................... ..................................................... $ %a&7 chords................................................................................................................. $ %a&' chords................................................................................................................. ( )om7 chords................................................................................................................( 7sus$ chords.................................................................................................................( *u+7 chords.......................................................... ....................................................... ( %in7 chords............................................................ ..................................................... ( %in' chords............................................................ ..................................................... ' %in7,b(- chords...........................................................................................................' oicin+s and )rop /ositions........................................................................................... ' Inersions.....................................................................................................................' )rop positions..............................................................................................................7 "in+erin+ Chords............................................................................................................. ase tones.................................................................................................................... ubstitutions.....................................................................................................................3 )iatonic ubstitutions..................................................................................................3 Tritone ubstitution................................................................................................... 10 *ppendix 1.....................................................................................................................12 Interals......................................................................................................................12 cales and Tonal "unctions....................................................................................... 1#
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Introduction This tutorial is for those who want to go beyond simple chords and are interested in the jazz, fusion or progressive rock genres. It is an extension of the material covered in the three other music theory books available on this site. As the title implies, this tutorial focuses entirely on chords. The material presented here is not for beginners. ou need to have a basic knowledge of music theory in order to be able to fully comprehend this material. I will briefly review the basics of triad formation, and then move on to four note chords and beyond. In the appendix, you will find an additional review of intervals and other stuff discussed in detail in the three theory tutorials available on this site.
Brief Recap Triads As the name suggests, triads are three note chords. !ike all chords, triads are built by stacking up intervals of thirds. "ince a third can be major or minor, there are only four different types of triads# $%oot, &', m'( )* major triad+ e.g. $, -, ( / $%oot, &', &'( )* augmented triad+ e.g. $, -, 0( / aug $%oot, m', &'( )* minor triad+ e.g. $, -b, ( / m $%oot, m', m'( )* semi)diminished triad+ e.g. $, -b, b( / m$b1( In all these formulas, the resulting chord is said to be in root position because the root of the chord is the bass note $lowest note(. These positions can be 2inverted3 by placing one of the other constituent notes at the bass by means of cyclic permutations $see further on(. • • • •
The chord formulas above can be rewritten by expressing the constituent notes as intervals with respect to the root+ this results in the following e4uivalent formulas# &ajor chord / $5, ', 1( Augmented chord / $5, ', 01( &inor chord / $5, b', 1( "emi)diminished chord / $5, b', b1( • • • •
6ther useful chords do not consist exclusively of stacked thirds but they can usually be linked back to a $possibly degenerated( fundamental form. 7or example, the chord $, 8, 7(, consisting of a root, a second and a fourth can be considered to be the third inversion of $8, 7, (, which is 8m9 without fifth. :e will get back to this. It is possible to build a triad upon each degree of any scale and choose the constituent notes so that they all belong to the scale+ this results in the so)called
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harmonized scale. The types of chords in the harmonized scale of course depend on the type of scale being harmonized. iven the major scale#
5
;
'
<
1
=
9
>
vi
vii$b1(
The harmonization is as follows# I
ii
iii
I>
?ppercase roman numerals indicate major chords while lower case numerals indicate minor chords $please refer to Music Theory – Basic Level for a detailed explanation of the conventional %oman numeral notation(.
Four note chords 7our note chords are build the same way as triads, but they contain one more $major or minor( third, and therefore there are twice as much possible combinations as for triads. @ot all these possible combinations are really useful in practice+ in fact, some chords that do not consist exclusively of intervals of thirds are used more often than some 2pure3 thirds based chords. The most important types of four note chords are# Maj7 chord # a major triad with an additional major third. The topmost note is located a major 9 th above the root, hence the name. -xample# maj9 / $, -, , (. This is sometimes written as &9. •
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Major 6 th chord # a major triad with a major ; nd. The topmost note is located a major = th above the root, hence the name. -xample# = / $, -, , A(. Although this chord is not made of thirds only, it can be considered the first inversion of Am9 / $A, , -, (, which is made of triads only $see below for a discussion of inversions(. :hether you call this is = th or a m9 chord depends on the harmonic context. Dominant 7 th chord (7)# a major triad with an additional minor third. The topmost note is located a minor 9 th above the root. -xample# 9 / $, , 8, 7(. 7sus4 chord # a dominant 9 th chord in which the third degree is replaced by the fourth degree B as if the third was 2suspended3. -xample# 9sus< / $, , 8, 7(. Aumented 7 th chord (au7)# a dominant 9 th chord in which the 1 th has been raised by a half tone. -xample# aug9 / $, , 80, 7( Minor 7 th chord (m7)# a minor triad with an additional minor third. -xample# -m9 / $-, , , 8(
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Minor 6 th chord (m6)# a minor triad with an additional major ; nd. -xample# m= / $, -b, , A(. Min7(!") chord # a minor 9 th with a flatted fifth. -xample# m9$b1( / $, -b, b, b(. $This chord is different from the diminished 9 th chord where the minor seventh is flatted an additional half tone# dim9 / $, -b, b, bb(, although you will often find it called this way(.
It is convenient to consider <)note chords as Cspiced upC versions of their basic triad counterparts. In other words, they are functionally e4uivalent to and can be used exactly as triads. The harmonization of the major scale in < note chords is as follows# Imaj9 ii9
iii9
I>maj9
>9
vi9
vii9$b1(
Chord Tensions Although <)note chords are already more complex than triads, they are rarely played as such in jazz, progressive rock or even classic. The basic tones 5, ', 1 and 9 are often replaced by or enriched with additional tones. These notes, called harmonic tensions, make the chord progression more dynamic and the chords themselves much denser. "ometimes, these tension notes actually belong to the melody+ in that case they are called melodic tensions, but you still need to take them into consideration in the harmonic analysis $please remember# a note is a tension only if it lasts at least a 4uarter note in a
Valid Tensions E, 055, 5' 9, E, 055 E, E, 0E, 55, 055, b5', 5' E, 55 E, 55 E, 55 9, E, 55 E, 55, b5'
Maj7 chords The valid tensions are the E th, 055th and 5'th. $
7or example maj9$E( is $, -, , , 8( while maj9$055( is $, -, , , 70(. Flease note the weird 055 $70(. This note is of course not part of the key of , but we cannot use the 55th $7( on this chord, because that would transform it into a subdominant chord $please refer to #ntermediate Theory (. Fitch)wise, tensions donGt need to be such large intervals+ it is ok to use the ; nd, 0
Maj6 chords These are triads with a major sixth+ e.g. = / $, -, , A(. The valid tensions are the 9 th, Eth and 055th.
Dom7 chords The well known dom9 chord is very interesting because it supports a large number of tensions# bE, E, 0E, 55, 055, b5' and 5'. 7or example, 9$E( / E / $, , 8, 7, A(+ 9$0E( / $, , 8, 7, A0(. :hen the tension is not diatonic to the key the dom9 chord belongs to, the chord is said to be altered .
7sus4 chords These are dom9 chords in which the 'rd has been replaced by the
u!7 chords These are dom9 chords with an 01. The valid tensions are the E th and 055 th.
Min7 chords >alid tensions on these chords are the E th and the 55 th. owever, bear in mind that the E th is @6T a valid tension if the chord is iii9. Take for example -m9 $-, , , 8( in major+ this is the iii9, and the E th would be the 7 note, which would clash horribly with the root and would also transform this chord into a dominant chord since it would contain the tritone 7 ) .
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Min6 chords >alid tensions are the 9 th, Eth and 55th. -.g. Am=$55( / $A, , -, 70, 8(. This chord contains the tritone $ B 70( and is therefore functionally e4uivalent to $i.e+ re4uires the same resolution as( 89, which contains the same tritone.
Min7"#$% chords >alid tensions are the E th, 55th and b5'th. owever, the E th will only be valid if it is diatonic to the key. 7or example, suppose we are in b major, and in the progression there is a foreign chord 8m9$bE(. 7or this chord, the E th is - which is not diatonic to b so you canGt use it as a tension.
Voicings and Drop Positions Any chord can be played in a variety of ways, depending on the position of the constituent notes in the chord. In practice, chords donJt have to be played according to the theoretical formula. Take for example a 8 triad# the theoretical chord formation is $8, 70, A(. owever, the standard beginnerJs way to play that chord on the guitar is to play it close to the nut as follows# $8, A, 8, 70( if you omit the two bottom strings, or $A, 8, A, 8, 70( if you only omit the low - string, or $70, A, 8, A, 8, 70( if you fret the low - string at the ; nd fret. @one of these correspond to the theoretical formula, since the order of the notes is not the same as the canonical one, and because some notes are repeated. The specific way you decide to play a chord is called a voicin , and you already know by experience that not all voicings sound e4ually well. :hat we will discuss here is a practical techni4ue for systematically identifying all the voicings that sound well for any chord. After that we will discuss how to actually play those chords on a guitar.
&n'ersions :e have already mentioned inversions a few times. !etJs look at it now. :hen the root of the chord is the bottom note, the chord is said to be in root position. :hen the bottom note is not the root, the chord is said to be inverted. Inversions donGt change the harmonic identity and function of the chord $but they do change the way it soundsH(. !etGs look at maj9 / $, -, , (. This chord is in root position, and it has three possible inversions# $-, , , (, $, , , -( and $, , -, (. As you can see, inversions are obtained by means of cyclic permutations of the order of the constituent notes. owever, in the key of major, all these inversions remain Imaj9. "imilarly, the chord = $, -, , A( has the following inversions# $-, , A, (, $, A, , -( and $A, , -, (. '
The latter chord can also be viewed as Am9. It is the harmonic context that will decide what function the chord assumes. In any chord voicing, we call Cfirst noteC the highest note in the formation, Csecond noteC the one immediately under the first note, Cthird noteC the one under the second note, etc. 7or example, in $, -, , ( the first note is , the second note is and the third note is -.
Drop posi(ions "tarting from any inversion# ou obtain the so called 2drop ;3 position for that inversion by dropping the second note one octave, and place it at the bass. "imilarly, you obtain the so called 2drop '3 position by dropping the third note one octave and place it at the bass. •
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7or example# maj9 5# %oot position# $, -, , ( ;# 7irst inversion# $-, , , ( '# "econd inversion# $, , , -( <# Third inversion# $, , -, ( 1# %oot drop ;# $, , -, ( =# 7irst inversion drop ;# $, -, , ( 9# "econd inversion drop ;# $, , , -( K# Third inversion drop ;# $-, , , ( E# %oot drop '# $-, , , ( 5L# 7irst inversion drop '# $, -, , ( 55# "econd inversion drop '# $, , , -( 5;# Third inversion# drop '# $, , -, ( $% these t&elve 'ositions &e need to avoid those 'resentin an interval o% a m !et&een the to' t&o voices ('osition and 'osition * in this case)+ as &ell as those 'resentin an interval o% a m, !et&een any t&o voices ('osition 6 and 'osition )-
This empirical rule is valid for any voicing, and will guarantee that the voicing remains balanced. This leaves you with the following acceptable voicings for maj9# $, -, , ( $, , , -( $, , -, ( $, , -, ( $, , , -( $-, , , ( $-, , , ( $, , -, ( "imilarly, let us consider 9 / $, , 8, 7( 5# %oot position / $, , 8, 7(
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;# 7irst inversion / $, 8, 7, ( '# "econd inversion / $8, 7, , ( <# Third inversion / $7, , , 8( 1# %oot drop ; / $8, , , 7( =# 7irst inversion drop ; / $7, , 8, ( 9# "econd inversion drop ; / $, 8, 7, ( K# Third inversion drop ; / $, 7, , 8( E# %oot drop ' / $, , 8, 7( 5L# 7irst inversion drop ' / $8, , 7, ( 55# "econd inversion drop ' / $7, 8, , ( 5;# Third inversion drop ' / $, 7, , 8( "ince the 9 chord doesnGt contain any halftone interval, all these positions are acceptable ) the dominant 9th chord will always have more voicings than the Imaj9 chordH
Fingering Chords )ase (ones hords consisting of five or more notes are usually too complex to be played as such on a guitar. In those cases, you will typically have to reduce the chord to a <)note chord, which will force you to make a choice as to what notes you want to keep. -ach type of chord has a minimum set of notes called !ase tones that uni4uely distinguishes it from other types+ the table below summarizes that# &aj9 5, ', 9
= 5, ', =
& triad 5, ', 1
m triad 5, b', 1
8om9 ', b9
9sus< <, b9
m9$b1( b', b1, b9
Aug9 ', 01, b9
As you can see, the fifth is never considered a base tone $except in triads(. -ven the root of the chord can be omitted from the voicing and delegated to the bassist if there is one $or even dropped altogether if there is no bassist(. This is because the conjunction of the base tones is enough to imply the bass. Fut differently# when the listener hears that particular combination of tones in the given harmonic context, she will be able to supply the missing bass. The strategy to make a complex chord playable on a guitar can then be summarized as follows# 5. Identify the base notes for the type of chord, and include them 2. Identify the extension$s( that you want to keep, and include them '. Identify all possible voicings by identifying all the inversions and drops -xample# you want to play 5'$bE(
The full chord contains the following notes# , , 8, 7, Ab, - and is unplayable as such on a guitar. 1. "ince this chord is essentially a dom9 chord with added bE and 5', we need to keep the ' and the b9 $8 and 7(, which are the base tones of a dom9 type chord. ;. "ince we want a 5' and a bE, we need to keep the - and the Ab The chord will therefore consist of the following notes# $( ) $8( * # E The 1th $8( will certainly be omitted, and the root $( may also be omitted or delegated to the bassist. This leaves you with $, 7 Ab, -(. ou can now identify all possible inversions and drops as we did previously, and decide how to voice that chord. ood luckH
Substitutions hord substitutions are extremely important in jazz, fusion, progressive rock and even classic. As the name suggests, a chord substitution is the replacement of a given chord by another chord which has some sort o% internal relationshi' &ith the oriinal chord+ &ithout !rea.in the harmonic loic o% the chord 'roression . "ubstitutions are often frightening and they can indeed be complex to comprehend without a minimum of theoretical background. 6n the other hand, they are essential to get that jazz feeling in the music. In this section, we will look in detail at two broad categories of substitutions# 8iatonic substitutions Tritone substitutions • •
Dia(onic +u#s(i(u(ions In #ntermediate Theory we have classified the chords in three basic groups# The tonic rou', consisting of chords which contain neither the subdominant nor the subtonic The su!dominant rou', consisting of chords which contain the subdominant but not the subtonic The dominant rou', consisting of chords which contain the subdominant and the subtonic $i.e. they contain the tritone( •
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As you probably remember, chords belonging to a given group are functionally completely e4uivalent and can be freely substituted for one another. %eferring to the harmonization of the major scale, the tonic group happens to contain the chords I, iii and vi+ the subdominant group contains the chords ii and I>, and the dominant group contains the chords > and vii$b1(. :hen the harmonization is done with <)note chords, the e4uivalence between these chords becomes immediately apparent+ letJs take major as example# Tonic roup# •
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Imaj9 / maj9 / $, -, , ( contains $-, , ( which is -m which is iii+ conversely, iii / $-, , ( can be considered a Imaj9 chord without root. vi9 / Am9 / $A, , -, ( contains $, -, ( which is or I+ o moreover, the first inversion of vi9 / $A, , -, ( is $, -, , A( which is I=. "ubdominant roup# ii9 / 8m9 / $8, 7, A, ( contains $7, A, ( which is 7 or I> o o
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The e4uivalence between the >9 and the vii$b1( is more interesting and will already open up a can full of possibilities. To explain that, let us consider the A harmonic minor scale# A
8
-
7
0
A
This is the natural minor scale in which the seventh degree has been altered to provide the melodic leading tone to tonic progression, and allow for a >9 )* i harmonic progression. The >9 chord is -9 $-, 0, , 8( which is often extended in jazz with a bE to become -9$bE( / $-, 0, , 8, 7(. ecause it contains the tritone $0 ) 8(, this chord calls for the tritone resolution on the tonic chord Am through the > B i cadence. "o far, so good. @ow consider the vii9$b1( chord 0m$b1( consisting of the notes $0, , 8, 7(+ this chord is identical to the upper four notes of -9$bE( and has therefore a very strong affinity with it. "o, if you omit the tonic of the >9$bE( chord, you obtain a vii9$b1( chord and these chords can therefore be substituted to one another.
Tri(one +u#s(i(u(ion The vii9$b1( chord has one particularity# it consists only of minor thirds which means that all its constituent notes are at an e4ual intervallic distance of each other. onse4uently, inverting that chord does not in fact change it in any respectH As a result, 0m9$b1( / m9$b1( / 8m9$b1( / 7m9$b1(. In turn, as we have just discussed, each of these four $e4uivalent( chords has a strong affinity with $and can be substituted by( a >9$bE( chord, as follows# 0m9$b1( -9$bE(
m9$b1( 9$bE(
8m9$b1( b9$bE(
7m9$b1( 8b9$bE(
In the table above, the e4uivalence is both horizontal and vertical+ for example m9$b1( / 0m9$b1( / 8m9$b1( $horizontal e4uivalence(, but m9$b1( / 9$bE( $vertical e4uivalence(, and then 9$bE( / -9$bE( / b9$bE(. In other words, it is valid to play -9b$E( instead of m9$b1(H
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In fact, any of these chords can be used in place of any other chord, depending on the context and preferencesH The tritone substitution principle states that# any >9 chord can always be substituted by another >9 chord located a tritone above or below it. in addition, according to the principle of functional substitution, that >9 chord can be substituted by the vii9$b1( of the same tonality •
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"o for example, the following ii B > B I progression in major# 8m9 D 9 D maj9 will often be rewritten# 8m9 D 8b9 D maj9 In which 8b9 has been substituted to 9. A 2jazzified3 rendering of that progression might then be# 8m9$E( D 8bE D maj9$E( Another situation where tritone substitution applies is when a chord of a progression is preceded by its own >9 chord $not diatonic to the key( called extended dominant. 7or example, in major, we may have# maj9 D -9 D Am9 D The -9 chord is the >9 of Am in the A harmonic minor scale. That >9 chord is again subject to potential tritone substitution, e.g.# maj9 D 0m9$b1( D Am9
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Appendix 1 &n(er'als The following table lists the most important intervals, their e4uivalent names, and an example of each $: / whole tone, / half tone( ,ame
&inor "econd &ajor "econd &inor Third &ajor Third Ferfect 7ourth Augmented 7ourth 8iminished 7ifth Ferfect 7ifth &inor "ixth &ajor "ixth &inor "eventh &ajor "eventh 6ctave
De-ini(ion
+ym#ol
: :M ;: ;: M ':
m; &; m' &' F<
E.ui'alen( +ym#ol b; ; b' ' < 0<
Example
':
1)
b1
B b
': M <: <: M 1: 1: M =:
F1 &= &= &9 &9 K
1 b= = b9 9 K
B B Ab BA B b B B
B 8b B8 B -b BB7 B 70
%emarks# in this table, the half steps are all supposed to be diatonic $e.g. 8 B -b( as opposed to chromatic $e.g. 8 B 80(+ in a diatonic half)step interval, the names of the constituent notes change, whereas they donJt in a chromatic interval. :ith chromatic half)steps, most intervals can be augmented or diminished. An augmented interval results when an additional chromatic half tone is added $e.g. B 0 is an augmented fifth and B A0 is an augmented sixth(, while a diminished interval results when an additional chromatic half tone is subtracted from the end note of the interval $e.g. B bb is a diminished seventh(. Intervals can be ascending $as in the definitions above( or descending $e.g. B 7 is a descending fifth if the target 7 note is below the starting note(. •
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Intervals can be larger than octaves and in jazz, fusion and progressive rock some of these larger intervals are used extensively# ,ame
De-ini(ion
+ym#ol
E.ui'alen( +ym#ol
Example
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&inor @inth &ajor @inth Ferfect -leventh Augmented -leventh &inor Thirteenth &ajor Thirteenth
=: M 9: K: M
mE &E F55
bE E 55
B 8b B8 B7
E:
55M
055
B 70
5L:
m5'
b5'
B Ab
5L: M
&5'
5'
BA
+cales and Tonal *unc(ions In any scale# The first degree $first note( is called the 2tonic3 The second degree $second note( is called the 2supertonic3 The third degree $third note( is called the 2mediant3 The fourth degree $fourth note( is called the 2subdominant3 The fifth degree $fifth note( is called the 2dominant3 The sixth degree $sixth note( is called the 2superdominant3 The seventh degree $seventh note( is called the 2subtonic3 • • • • • • •
Tonal music associates a well)defined %unction to each degree, but more specifically to the5st, 'rd, 1th and 9th degrees of the scale# The tonic is the home note, around which all the other notes revolve+ the tonic indicates the tonality. The mediant is the tone that indicates whether the mode is major or minor+ if the mediant is located a major third above the tonic the mode is major, otherwise it is minor. The descending movement from the dominant towards the tonic is essential in affirming the tonality+ this movement is called a 2perfect cadence3 and is usually referred to as 2> B I3. The subdominant and the subtonic $of the major, harmonic minor and melodic minor scales( are separated by the very unstable tritone interval $i.e. an augmented fourth(, which needs to be resolved by letting the subdominant move down towards the mediant and the subtonic move up towards the tonic. This combined movement is called tritone resolution. •
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The 5st, 'rd, 1th and 9th degrees of the scale are separated by intervals of thirds, and this is why this interval plays such an important role in tonal music. In particular, the interval of a third is the essential constituent of chords# chords are build by piling up intervals of thirds.
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