MICHAEL BARKL
ANALYSING HARMONY
Published by Michael Barkl 7/4 Pleasant Avenue, North Wollongong NSW 2500, Australia Copyright © Michael Barkl, 2009
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CONTENTS
Preface
3
Chapter One:
Chords and Extensions
5
Chapter Two:
Chord Progression
10
Chapter Three:
Principles of Modulation
15
Chapter Four:
Diminished Chords and Patterns
20
Chapter Five:
Seven Analytical Examples
23
Chapter Six:
Substitute Chords
26
Chapter Seven: Cadences
33
Chapter Eight:
Passing Diminished Chords and the Death of Chord ii
38
Chapter Nine:
Blues
42
Chapter Ten:
Analysing Excerpts from Standards
45
Chapter Eleven: Analysing Standards
49
Chapter Eleven: Analysing The Beatles
58
Chapter Thirteen:The ‘Tristan Chord’
60
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PREFACE ‘To define something is to begin to lie about it’, as they say. This booklet is therefore not about truth but expediency. Its purpose is to make some kind of sense or order from tonal harmony as used in the popular music of the mid20th century; the kind of music that is known as the ‘great American songbook’ and has been used as ‘standards’ by jazz musicians. The benefit of using this kind of repertoire is that, because it is highly ‘refined’, in the sense of being systematised and predictable, other musics, such as classical and pop, may be usefully compared with it to highlight similarities and differences of tonal use. The purpose of the booklet is twofold. Firstly, it may assist songwriters suffering from the ‘lost chord’ of songwriter’s block. The patterns and substitute chords analysed here can provide a range of chords that have the ‘correct’ harmonic function: it’s then a matter of choosing one according to taste. Secondly, an analytical understanding can greatly assist the improvising musician to develop broader and more complex melodic ideas over longer time-frames, rather than responding to each individual chord as it comes along. This is not an academic work and does not intend to provide an accurate historical basis for its observations. Instead, it reflects the response of the modern musician that has grown up with American music.
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CHAPTER ONE:
Chords and Extensions
Just because classical, pop and jazz music are ubiquitous, this doesn’t mean that that is what ‘real music’ is, just as Coca Cola is not necessarily ‘the real thing’. It seems the triumph of Western civilisation, and now more particularly American ‘culture’, is its success as an export.1 A glance at the work of ethnomusicologists will confirm that today’s popular music, though played in one form or another around the world, is just one of the many musics humankind have invented; and it’s just as well to remember here that there’s no suggestion that it’s the ‘best’. Perhaps the greatest thing African music has to offer the world is rhythm; for Indian music it may be melody; for Australian Aboriginal music it may be social cohesion. For European music it might just be harmony. Received wisdom is that European music, derived from middle-eastern Arabic music, was once monodic, melodic, highly decorated, modal, and accompanied by percussion and drones. Formalised phrase endings, or cadences, fell to and settled on their target pitch. The development of polyphony maintained this ‘horizontal’ orientation by combining melodies. Two melodies, both settling to a final cadence through formalised approaches, began to be heard ‘vertically’, since the formula was repeated and lost its focus on linearity. With the addition of parts, the vertical cadential formulas came to be heard as ‘chords’. When we study these chords, it’s just as well to remember that there may be no such thing: chords are slices cut from polyphony. So, if a classical musician shows little orientation towards or understanding of chords, it’s not necessarily because he or she is dim. On the contrary, this musician may have a more refined or complex understanding. To define these calibrations [chords] we begin to disassociate them from their context; we begin to lie about them by simplifying them and focussing on limited aspects of them. In other words, just because something is useful, it does not mean it’s correct. Understanding chords and chord progressions is very useful for the contemporary performing or songwriting musician, and it is hoped that this booklet may be useful too, if not correct. To understand this booklet, the reader is expected to already understand two things: chords and their conventional extensions [or ‘tensions’ as the Americans would say]. That is, firstly, the so-called ‘scale-tone 7ths’ for both the major and minor scale. 1
See Jared Diamond, Guns, Germs and Steel, London: Vintage, 2005.
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For the major scale these are [in the key of C]: Cmaj7 Dmin7 Emin7 Fmaj7 G7 Amin7 Bmin7b5 Chords with a major 3rd between the root and the 3rd are given in uppercase Roman numerals, while chords with a minor third are given in lowercase. Therefore, the chords of the major scale are I, ii, iii, IV, V, vi, vii. Chords for the minor scale are conventionally derived from the harmonic minor scale, viz [in the key of c minor]:2 Cmin/maj7 Dmin7b5 Ebmaj7+ Fmin7 G7 Abmaj7 Bdim Minor scale-tone 7ths are therefore i, ii, III, iv, V, VI, vii. The second prerequisite, understanding extensions, includes the knowledge that there is a difference between ‘added-note’ chords, such as C6, and extensions, such as Cmaj13. A 13th [or an 11th or a 9th] implies the inclusion of the 7th.3 Moreover, a 13th may also include an 11th and/or a 9th as per the musician’s performance practice. The inclusion of a 9th, 11th or 13th makes no comment on the voicing of the chord. An important aspect of chord extensions is that, when used within the key, they do not change the function of the chord. That is, chord I in C major is always chord I, and chord IV in C major is always chord IV. Hypothetically, 9ths, 11ths and 13ths [or their chromatic alterations] may be added as extensions to any chord. In practice, however, only some are what we may regard as ‘conventional’; that is, used by performing musicians on a regular basis without overtaxing the sensibilities of the common listener.
2
It must be acknowledged that the minor scale is a slippery concept, and composers regularly use chords derived from the melodic minor form. This changes not only the root and colour of the chord, but also the available extensions. Consideration of the melodic minor as a generator of chords is addressed below. 3 6+7=13; 4+7=11.
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There is a simple rule: if the extension is a full tone above a lower degree chord note [the root, 3rd or 5th], then it is conventional. If it is only a semitone above a lower degree chord note then it is not [but for a couple of exceptions which I will clarify later].4 However, the addition of the 9th is generally heard to be significantly less of a ‘tension’ than the 11th or the 13th. Cmaj7 will therefore extend to Cmaj9, Cmaj7#11 and Cmaj13, but not Cmaj11. If Cmaj11 is written, the musician will play Cmaj7sus [that is, replacing the E with the F]. However, in the key of C major, chord I will never be Cmaj7#11, because the F# is out of key. One sharp implies the key of G major, and Cmaj7#11 therefore implies chord IV in G major. Chord I in C major may extend to Cmaj9 or Cmaj13. Chord ii may extend to Dmin9, Dmin11 or Dmin13.5 Chord iii may extend to Emin11 only.6 Chord IV may extend to Fmaj9, Fmaj7#11 and Fmaj13. Chord V may extend to G9 and G13.7 Chord vi may extend to Amin9 and Amin11.8 Chord vii may extend to Bmin11b5, or even Bmin7b5b13.9 In the minor key: Chord i may extend to Cmin/maj9 and Cmin/maj11.10 Chord ii may be extended to Dmin11b5 and Dmin7b5b13. Chord III may be extended to Ebmaj9+ only. Chord iv may be extended to Fmin9 and Fmin13.11 Chord V may be extended to G7b9 and G7b13. Chord VI may be extended to Abmaj7#11 and Abmaj13.12 Chord vii may be extended to include the note G.13
4
Why might this be the case? The western musical sensibility holds that a tone is much less discordant than a semitone when played harmonically [vertically]. 5 The minor 13th chord is somewhat rarer than the minor 9th and minor 11th no doubt because of the discord and functional implications of the tritone between the 3rd and the 13th. 6 Emin9 includes the out-of-key note F# and Emin13 includes C#. 7 G11 will be played as G7sus [or G9sus] and G7#11 is out of key. 8 But not Amin13, since F# is out of key. 9 Bmin9b5 includes C#, so is out of key. The b13 is G, one tone above the b5. 10 As with chord ii in the major key, the min/maj11 is rare because of the tritone between the 7th and the 11th. 11 The 11th would be Bb, implying the melodic minor descending form, whereas B is the note in the harmonic minor scale. 12 The 9th would be Bb, implying the melodic minor descending form, whereas B is the note in the harmonic minor scale 13 Although one could say G was the b13th, diminished chords do not carry this nomenclature due to their association with the octatonic [or ‘diminished’] scale. That is, with 9 notes to the octave instead of 8, 9ths, 11ths and 13ths become misnomers. The resultant name for the chord is the clumsy Bdim(addG).
7
Chord V, extended to G7b9 and G7b13, appears to ‘break’ the ‘toneabove’ extension rule, and indeed it does for good reason. The ear hears an alternative powerful structure that overrides the ‘tone-above’ extension rule. G7b9 is chord vii, Bdim, with a G-bass, and G7b13 is chord III, Ebmaj9+, with a G-bass. Diminished chords are symmetrically constructed from three minor 3rds; Eb+ is an augmented chord: two major 3rds. It is well known and understood that the melodic minor scale modifies the harmonic minor scale for a smoother melodic effect; that is, to avoid the augmented second between the 6th and 7th degrees. The ‘ascending’ form preserves the raised 7th degree leading note and, additionally, raises the 6th degree. The ‘descending’ form, which doesn’t require the leading note to be raised, follows the key signature, and is known as the ‘natural minor’ or the Aeolian mode. In practice, the ‘ascending’ form may descend and the ‘descending’ form may be used ascending. The actual scale form used is more likely to be determined by the harmony. All things being equal, chord i accompanies melodic movement between the 5th degree and the upper tonic in the normal ‘scalar’ manner: that is, raising the 6th and 7th degrees ascending and following the key signature descending. Chord iv, having the flattened submediant as its 3rd, accompanies the ‘descending’ form, whether the melodic movement is descending or ascending. Chord V, having the raised leading note as its 3rd, accompanies the ‘ascending’ form, whether the melodic movement is ascending or descending.14 One of the significant outcomes of the interaction of the melodic minor scale with minor harmony is that, in jazz music at least, the minor 6th chord [an ‘added note’ chord, not an extension], is normally used as the 4-note version of chord i rather than the minor/major 7th. Jazz musicians associate the ascending form of the melodic minor with the minor 6th chord and call the scale the ‘jazz melodic minor’.15 Despite the traditional association of the harmonic minor scale with ‘chords in the minor key’, some composers and songwriters use chords derived from the jazz melodic minor scale and the Aeolian mode within the minor key context. The scale tone 7ths on each degree in the c jazz melodic minor are: Cmin6 Dmin7 Ebmaj7+ F7 14
In the same way, chords ii and VI accompany the ‘descending’ form and chord III accompanies the ‘ascending’ form. 15 That is, the ‘jazz melodic minor’ scale is the same ascending and descending.
8
G7 Amin7b5 Bmin7b5 Note the two ‘dominant’ 7th chords and two min7b5 [half-diminished] chords. For the c Aeolian mode [the natural minor], the scale tone 7ths are: Cmin7 Dmin7b5 Ebmaj7 Fmin7 Gmin7 Abmaj7 Bb7
The point of the discussion so far has been to clarify chord functional type within a key. That is, when we begin to analyse harmony and we say ‘chord IV of C major‘, it is understood that it makes no difference whether the chord is Fmaj7, Fmaj9, Fmaj7#11 or Fmaj13. The next section will discuss modal chord progression and chord progression within a key.
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CHAPTER TWO:
Chord Progression
While this booklet is specifically about analysing tonal harmony, a brief acknowledgement must be given to modal practice, if only to differentiate the two. ‘Modal music’ in this context refers to 20th century jazz or pop music, not to, say, European music in the 14th century or to non western practices. To simplify, modal music accentuates the melodic over the harmonic, and tonal music accentuates the harmonic over the melodic. This is not to assert that, say, Indian classical musicians do not feel the harmonic [vertical] relationships of their melodies in relation to the drone any more or less than western musicians feel the importance and musicality of melodic movement. Indeed, modal music and tonal music often intersect in such a way as to be impossible to determine when one becomes the other. American ‘jazz improvisation theory’ typically teaches mode association: Maj7 chord = Ionian [or Lydian] Min7 chord = Dorian [or Aeolian or Phrygian] Dominant 7 chord = Mixolydian [or a range of altered scales] Min7b5 chord = Locrian Diminished = Octatonic [diminished] Augmented = Whole-tone Some songs have only one chord, such as Herbie Hancock’s Memphis Underground [C7 throughout] and Curtis Amy’s Native Land [Gmin7 throughout]. Others don’t change the root, only the chord colour, such as La Nevada Blues by Gil Evans: Gmin9 x 2 bars Gmaj7 x 2 bars Gmin9 x 2 bars Gmaj7 x 2 bars Gmin9 x 2 bars Gmaj7 x 2 bars Often, modal songs may change chord by step while maintaining chord colour. Impressions by John Coltrane gives one of the simplest of examples: Dmin7 x 16 bars Ebmin7 x 8 bars Dmin7 x 8 bars
10
The skill of the professional improvising performer is to layer different sounds [scales and chords] over what is essentially a d-eb-d drone. Beginning jazz students, however, will be instructed to use D Dorian, Eb Dorian and D Dorian, at least as a starting point. So, while non European modal music, such as Indian classical music, typically has drones that do not move, the harmony, or drone, of Impressions is a slow three-note melody d-eb-d. Moreover, it’s heard melodically because the chord colour does not change and therefore the chord function does not change. The basic movement of simple melodies is step-wise movement, and other pieces from the ‘modal jazz’ repertoire show the melodic component of the harmony. Milestones by Miles Davis, for example: Gmin7 x 16 bars Amin7 x 16 bars Gmin7 x 8 bars Again, the harmonic colour is the same for each chord [thereby focusing attention on the melodic component] and the movement is step-wise: home-away-home. Bob Brookmeyer’s Hum moves the harmony in a single direction while maintaining chord colour: Gmin7/C x 8 bars Abmin7/Db x 8 bars Amin7/D x 8 bars Bbmin7/Eb x 8 bars16 Other songs move by a small leap of a 3rd, often known as a ‘skip’, while maintaining chord colour, such as Herbie Hancock’s Maiden Voyage: D7sus x 4 bars F7sus x 4 bars D7sus x 4 bars F7sus x 4 bars Eb7sus x 4 bars Db7sus x 4 bars D7sus x 4 bars F7sus x 4 bars Here the melodic component is d-f-d-f-eb-db-d-f. Other songs move by step or skip, changing chord colour but maintaining a connection through a common chord note. Sakara by Francy Boland: Dmin7 x 16 bars Gmin7b5/C x 8 bars17 16
These chords are identical to C9sus, Db9sus, D9sus, Eb9sus.
11
Dmin7 x 8 bars Here the change of chord colour implies a more ‘harmonic’ relationship, though some connection is maintained by the common chord note f. The other notes change by step: c bb ag ff d db More complex songs include Herbie Hancock’s Cantaloupe Island, where the note ‘f’ is common throughout: Fmin7 x 4 bars Db7 x 4 bars Dmin11 x 4 bars Fmin7 x 4 bars Even more subtle is John Coltrane’s Like Sonny, which begins each eightbar phrase modally and ends each phrase tonally. The progression ascends by minor 3rd, the 3rd of each min7 chord in the first and third phrases providing the link to the next min7 chord.18 In the second phrase the progression descends by major 3rd, each 3rd of the chord becoming the 5th of the subsequent chord. Dmin7 x 2 bars Fmin7 x 2 bars Abmin7 Bb7b13 Ebmaj7 x 2 bars Amin7 x 2 bars Fmin7 x 2 bars C#min7 F#7 Bmaj7 x 2 bars Dmin7 x 2 bars Fmin7 x 2 bars Abmin7 Bb7b13 Ebmaj7 x 2 bars For modal chord succession we can make the following summary:
17 18
Gmin7b5/C is effectively the same as C7b9sus. Moreover, their roots outline the dominant of the new key. That is, d-f-ab = 3-5-7 of Bb7.
12
1. Simple modal chord successions typically use minor 7th and dominant 7th chords; these are associated with Dorian and Mixolydian modes respectively. 2. Connection between chords is established melodically through movement by step or skip while maintaining chord colour [see Impressions, Hum, Maiden Voyage], or movement by step or skip while maintaining a common chord note [see Sakara, Cantaloupe Island, Like Sonny], or maintenance of the root and a change of chord colour only [see La Nevada Blues], or simply no chord change at all [see Memphis Underground, Native Land]. Non-modulating tonal music19 uses chords within a key to provide movement, contrast, and, most importantly, forward moving direction based on the notion of ‘harmonic resolution’. And this is where tonal music differs from modal: in modal music we speak of ‘chord succession’; in tonal music we speak of ‘chord progression’. In tonal music, any chord may be followed by any other chord in the same key in order to ‘connect’. Convention dictates that there are ‘strong’ progressions and ‘weak’ progressions.20 In triadic harmony, strong progressions [within a key] are where less than half the notes are in common [that is, root movement by 4ths or 2nds]; a weak progression is where more than half the notes of the triad are in common [root movement by 3rds]. However, movement by 2nds may become weak after two or more chords are heard in succession because the melodic component is heard more strongly than the harmonic. Extension of triads to the 7th and beyond does not significantly change the relative strength or weakness of a particular progression. A preponderance of strong progressions is typically used in rousing music; weak progressions are typically used in ambient and gentle music. Most conventional music is a combination of strong and weak progressions. In the average, conventional, piece of music, strong or weak progressions are used within the bar where there are two chords per bar [or the equivalent durational unit of change where there is one chord per bar or less]. Strong progressions are used across the bar line, especially at the end of a phrase where a cadence needs to be articulated. The common chord progression I-vi-ii-V shows some of these characteristics. In C Major it is:
C:
Cmaj7 I
Am7 vi
Dm7 ii
19
G7 V
That is, tonal music that does not change key. The words ‘strong’ and ‘weak’ are not intended to convey any positive or negative connotation. Strong means ‘a significant harmonic change’ and weak means ‘an insignificant harmonic change’. 20
13
With regard to the triadic component of the progression above, from C to Am the common notes are c-e and the progression is weak. From Am to Dm the different notes are d-f and the progression is strong. From Dm to G the different notes are g-b and the progression is strong. The same principles apply if the key is minor: Cmin/maj7 Cm: i
Abmaj7 VI
Dm7b5 ii
G7b9 V
Chord progressions may be part tonal and part modal [see Like Sonny]. Additionally, they can be part major and part minor. Convention has allowed that equivalent degree chords from the minor can be inserted into major progressions [and vice versa]. For example: Cmaj7 C: I Cm:
Abmaj7
Dm7 ii
VI
G7b9 V
Or: Cmin/maj7 C: Cm: i
Am7 vi
Dm7b5
G9 V
ii
The following chapter begins to address the purpose of this booklet; that is, the principles of modulating harmony.21
21
The descriptive method of analysis shown above, with the key identified on the left and the degree of the chord shown under the chord symbol on the relevant line, is an extension of the system used by Walter Piston. See Walter Piston, Principles of Harmonic Analysis, Boston: Schirmer, 1933. This is the system that will be used in this booklet.
14
CHAPTER THREE: Principles of Modulation The following chapter introduces the basics of tonal harmony within the modulatory context; that is, the simplified 20th century system of chord progression and modulation.22 Of fundamental importance is the ability to identify the key at any point in the music. Key is defined by chord V. There is only one dominant 7th chord in a key, so it provides a convenient marker. Moreover, the same dominant 7th chord is chord V in both the major and the parallel minor key: G7 is chord V for both C major and c minor.23 The only way to indisputably identify whether the key is major or minor [without looking at the context] is if the dominant chord is extended to the 9th. G9 specifies C major [since it includes an a-natural] and G7b9 specifies c minor [since it includes an a-flat]. However, in the absence of a specified 9th, the context of Dm7b5-G7 would suggest the minor key for G7. That is, musicians would normally expect to extend the chord to G7b9 in performance in this context. Key is not defined by chord I since the same chord colour is present for both chord I and chord IV. Cmaj7 could be chord I in C, but it may also be chord IV in G and chord VI in e minor: only context can clarify. However, chord V has evolved a compelling relationship with chord I, which serves to articulate time by implying a forward moving development through time.24 The relationship is one of ‘resolution’ of the ‘dissonance’. In the key of C, G7 holds the characteristic dissonance of the ‘tritone’25 from b-f. The traditional resolution of this dissonance is to move both notes by step in contrary motion: b c; f e. The resultant chord c-e is C, chord I.26 The principles of modulatory harmony [that is, establishing a range of contrasting keys throughout a piece of music] therefore revolve around the use of chord V.
22
This chapter and subsequent chapters are based on, and are an amplification of, the material contained in lessons 16, 17 and 18 of The Berklee Correspondence Course, Boston: Berklee Press, 1971. This material was not published separately and was withdrawn from circulation in 1984. 23 There is only one minor7b5 in a key too, but its changing function, chord vii in the major and chord ii in the minor, make it much less useful as a marker. Moreover, chord vii is rarely used in the major key. 24 By contrast, a feature of modal music is to ‘suspend’ time by experiencing the moment rather than the context of the moment in time. This is typical of meditative music, trance music, and some sacred music and dance music. 25 The tritone is an interval of three tones. 26 This applies equally to the minor chord c-eb.
15
Principle 1: Any chord I may be preceded by chord V in the same key.27 This usually occurs over the bar line. In the key of C:
C:
G7 V
C I
Principle 2: Any chord V may be preceded by the V of V. [This may or may not be across the bar line.] In the key of C: D7
G7 V
C: G: V
C I
Principle 2 is the result of an ‘ellipsis’.28 That is, the ‘complete’ chord progression may be seen originally to be D7-G-G7-C. Over time, the arrival to chord I in the new key of G was assumed before the chord colour change to G7, and was therefore able to be left out without compromising the listener’s sense of connection. To acknowledge the achievement of the ‘target’ key I will figure the analysis as below: D7
G7 V [I]
C: G: V
C I
The acknowledgement of chord I in G is in brackets because G7 is not really chord I in the key of G. However, the target, and incidentally the 1st principle above, has been achieved by G7 acting in place of G. The principle may be extended further [see the song Sweet Georgia Brown by Ben Bennie and Maceo Pinkard]. E7
A7
C: G: D: A: V
D7 V [I]
V [I]
G7 V [I]
Principle 3: Any V may be preceded by chord ii in the same key. This usually occurs within the bar. In the key of C:
C:
Dm7 ii
G7 V
C I
27
These principles apply equally to major and minor keys. An ‘ellipsis’ is where there is an omission that would complete or clarify the construction. In language, an ellipsis is where a clarificatory word may be omitted when it would be tedious to include it. In music, the exact target chord is often omitted for the same reason. 28
16
Also: Am7 C: G: ii
D7 V
G7 V [I]
C I
A ‘delayed resolution’ is also common: Am7 C: G: ii
D7
Dm7 ii
V
G7 V [I]
C I
A7
Am7
D7
ii
V [I]
Therefore we may have: Bm7 C: G: D: A: ii
E7
Em7
ii
V [I]
V
Dm7 ii
G7 V [I]
Principle 4: Any chord ii may be preceded by chord V of ii. This usually occurs across the bar line. In the key of C: A7 C: Dm: V
Dm7 ii [i]
G7 V
C I
Here V of ii may be usefully defined as being in a minor key [since ii is a minor chord and the most natural chord extension of chord V for the performing musician would be A7b9]. This principle may be extended as follows: G#m7 C#7 C: Dm: D: Em: E: F#m: V F#: ii
F#m7 B7
Em7
A7 V
Dm7 ii [i]
G7 V
ii [i]
V ii [i]
Because chord ii, as a minor 7th, is in a major key, and the dominant 7th is looking forward to a resolution to the minor key, the key of the first half of each bar above is major and the key of the second half of each bar is minor, which accounts for the extra key lines.
17
Principle 5 is the final principle: Anything may follow chord I. This principle, in a sense, is similar to the modal harmony principles. Once we’re ‘home’, we can go off in any direction. The following eight examples show the above principles in action.
Example 3.1: Bm7 C: G: D: A: ii
E7
Em7
ii
A7
Am7
D7
ii
V [I]
V [I]
V
Dm7 ii
G7 V [I]
C I
Example 3.2: Abm7 Db7 C: Dm: D: Em: E: Gbm: Gb: ii
F#m7 B7
Em7
A7 V
V
V
ii [i]
E7
Em7
Dm7 ii [i]
G7 V
C I
Dm7 ii [i]
G7 V
C I
Dm7 ii
G7 V [I]
C I
ii [i]
Example 3.3: F#m7 B7 C: Dm: D: A: E:
Bm7
A7 V
ii ii
ii
V [I]
Bm7
E7
Am7
D7 V
V
ii [i]
V
[I]
Example 3.4: F#m7 B7 C: G: Am: A: E:
ii ii
V
[I]
18
Example 3.5: F#m7 B7 C: G: D: Em: E:
V
Em7
A7
Am7
D7
ii [i]
V
ii
V [I]
Bm7
E7
Am7
D7
ii [i]
V
V
E7
Em7
A7
Dm7 ii
G7 V [I]
C I
Dm7 ii
G7 V [I]
C I
Dm7 ii [i]
G7 V
C I
Dm7 ii [i]
G7 V
C I
ii
Example 3.6: C#m7 F#7 C: G: Am: A: Bm: B
V
ii [i]
ii
Example 3.7: C#m7 F#7 C: Dm: D: A: Bm: B:
Bm7
V ii V
ii [i]
V
[I]
ii
Example 3.8: C#m7 F#7 C: Dm: D: Em: E: B
F#m7 B7
Em7
A7 V
ii [i]
V ii ii
V
[I]
19
CHAPTER FOUR: Diminished Chords and Patterns The following chapter applies the basic principles from the previous chapter to typical progressions found in numerous popular songs. To do so, we need to understand the application of the diminished chord in popular music. The diminished chord has a dominant function, just like chord V, or, to be exact, V7b9. From chapter 1, we know that the diminished chord is chord vii in the minor key. In the key of c minor, chord vii would be Bdim: b-d-f-ab. It will be noticed that this chord has the characteristic tritone of the dominant 7th chord, b-f, which is why it is heard as a version [or ‘substitute’] of chord V. Indeed, if the note ‘g’ is played under Bdim we have G7b9: g-b-d-f-ab. In terms of the principles discussed in the previous chapter, chord vii in the minor key behaves in the same way as chord V. There is, however, a problem: Bdim = Ddim = Fdim = Abdim.29 That is, the notes of all these chords are identical [because the diminished chord is a stack of minor 3rds] and the chord symbol used is normally chosen with reference to the desired bass note rather than with reference to the root. Additionally, because the 7th of the scale [the ‘leading note’] is normally an undesirable bass note, the name of the diminished chord often is not the root of the diminished chord. Thus, principle 1 from the previous chapter may appear as: Bdim C: Cm: vii
C I
Or: Ddim C: Cm: vii
C I
29
Note that, because of their ambiguity, diminished chords are the only chords that may be ‘spelt’ any way.
20
Or: Fdim C: Cm: vii
C I
Or: Abdim C: Cm: vii
C I
Note, however, that the analysis is always the same, because each diminished chord is acting as Bdim [a substitute of G7b9], chord vii of c minor. Some of the following chord patterns use diminished chords in the manner shown above.
Pattern 1 we have seen before in chapter 2, and is found in innumerable songs:
C:
Cmaj7 I
Am7 vi
Dm7 ii
G7 V
Pattern 2 is based on principle 2, the ‘V of V’ principle: D7 C: G: V
Dm7 ii
G7 V [I]
C I
Pattern 3 is similar to pattern 2 but uses the diminished chord instead: Ebdim C: Gm: vii
Dm7 ii
G7 V [i]
C I
Ebdim [eb-f#-a-c] is identical to F#dim [f#-a-c-eb], which is vii of g minor and a substitute for chord V of g minor, D7b9: d-f#-a-c-eb. . Ebdim is chosen as the chord symbol to facilitate the bass movement by step: ebd.
21
Pattern 4 is based on principle 4, the ‘V of ii’ principle: A7b9
Dm7 ii [i]
C: Dm: V
G7 V
C I
Pattern 5 is similar to pattern 4 but uses the diminished chord instead:
C: Dm:
C I
C#dim vii
Dm7 ii [i]
G7 V
C I
In this case bass note of the diminished chord and the root note are the same. C#dim [c#-e-g-bb] is a substitute for A7b9: a-c#-e-g-bb.
Pattern 6 is unique in that the final key of C is established by context and not by chord V:
C: Cm: F:
C I
C7
F IV
Fm6
C I
iv V
I
The pattern is a decoration of C-F-C [I-IV-I] in the key of C. IV-I is decorated by the insertion of iv borrowed from the parallel minor key. These kinds of borrowings are easy to understand. If one was singing, for example, an ‘a’ from the F chord and resolving it to a ‘g’ from the C chord, the ‘ab’ [forming the Fm chord] would simply become a chromatic approach note to ‘g’. C7-F is a modulation to the key of F, and the chord of F is in two keys at once—called a ‘pivot’ chord. C7 may follow C because of principle 5: anything may follow chord I.
22
CHAPTER FIVE:
Seven Analytical Examples
The following chapter applies the basic patterns from the previous chapter to simple song chord progressions and provides analyses for them.30 Each example is eight bars long.
Example 5.1: C C: I Cm: F:
C: Cm: Dm:
C I
C7
F IV
Fm6 iv
V
A7
Dm7 ii
I
G7 V
C I
Fm6
C I
iv V
[i]
The first four bars are pattern 6; bars 5 and 6 are pattern 4, and bars 7 and 8 are derived from pattern 6.
Example 5.2:
F: Gm:
Gm7 ii
Am7 F: Fm: Gm: G: ii
C7 V
D7b9
F I
Gm7 ii
D7b9
C7 V
F I
V
Gm7 ii [i]
C7 V
F I
Bbm6
F I
iv V
[i]
Bars 1-2 are a ii-V-I in F; bars 2-4 are pattern 4, as are bars 5-7; bars 7-8 are derived from pattern 6.
30
The chord progressions are taken directly from Berklee lesson 17, which are left un-analysed in the original text. The list of keys down the left hand side of each analysis does not follow a prescribed order: I have simply attempted to group things together.
23
Example 5.3: G G: I Gm: C: Am:
G G: I Dm:
Abdim
Am7 ii
D7 V
G I
G7
C IV
Cm6 iv
vii
[i]
Bbdim
Am7 ii
vii
D7 V [i]
G I
V
I
C IV
G I
Bars 1-3 are pattern 5 [Abdim = G#dim]; bars 3-5 are pattern 6; bars 5-7 are pattern 3 [Bbdim = C#dim]; bars 7-8 are simply a I-IV-I decoration in the key of G.
Example 5.4: Fm7 Ab: Ebm: Eb: ii
Ab: Ebm:
Bb7
Bbm7 Eb7 ii V
Ab I
Bdim vii
V
Bbm7 ii
[I]
Eb7 V [i]
Ab I
Db IV
Ab I
Bars 1-3 are pattern 2; bars 4-7 are pattern 3 [Bdim = Ddim].
Example 5.5:
Bb: Fm:
Bb I
Bb Bb: I Bbm: Eb:
Gm7 vi
Cm7 ii
F7 V
Bb I
Dbdim
Cm7 ii
vii
Bb7
Eb IV
V
I
Ebm6
Bb I
iv
Ebm6
F7 V [i]
Bb I
iv
Bars 1-3 are pattern 1; bars 3-4 are pattern 3; bars 5-7 are pattern 6 and bars 7-8 are derived from pattern 6.
24
Example 5.6: D D: I G: Em: E:
G D: IV Dm: G: I A: Em:
F#m7 B7
Em7 ii
A7 V
D I
D7 V
V
[i]
B7b9
E7
A7 V
V [i]
[I]
V
ii
Gm6
D I
D I
iv
Bars 2-4 are pattern 4; bars 4-6 are pattern 6; bars 6-7 are a variation of pattern 4; bars 7-8 are pattern 2.
Example 5.7: Eb Eb: I F: G:
F Eb: F: I
Am7
ii
Fm7 ii
D7
G
V
Gm7
C7
ii
V
I
Bb7 V
Eb I
Ab IV
Eb I
Example 7 is a series of ii-V-I progressions in the keys of G-F-Eb.
25
CHAPTER SIX:
Substitute Chords
The following chapter introduces basic substitute chords. These substitutes do not change the principles of chord progression established in chapter 3. Instead, different chords are given the same harmonic function. The first substitute we may call the ‘iii for I substitute’. That is, chord iii may substitute for chord I. In the key of C, Em7 may substitute for Cmaj7. Chapter 1 in this booklet confirmed that chord I may extend to the major 9th. Cmaj9 has, therefore, the notes c-e-g-b-d. Emin7 has the notes e-gb-d. The overlap is so substantial, and not surprising since chords are built in 3rds, that the listener will easily allow the upper part of Cma9 [that is, Emin7] to stand for Cmaj9 itself. Chord iii is never used for chord I at the end of a piece of music. Typically, it is used as a pivot chord to move the progression into another key.
C: Dm: D:
Dm7 ii
G7 V
Em7 A7b9 iii [I] V ii
Dm7 ii [i]
G7 V
C I
Here, Emin7 is simultaneously chord iii in C and chord ii in D. I have included an acknowledgement of Emin7 as a substitute of chord I in C [in brackets] in order to fulfil principle 1 in chapter 3. Here is another example: Ab Ab: I Bbm: Bb:
Adim vii
Bbm7 Eb7 ii V [i]
Cm7 F7b9 iii [I] V ii
Bbm7 Eb7 ii V [i]
Ab I
With time and familiarity chord iii has also altered to include the minor form. Thus: Dm7 C: ii Dm:
G7 V
Em7b5 A7b9 [iii][I] ii V
Dm7 ii [i]
26
G7 V
C I
With further familiarity an ellipsis [from Em7-E7] has become common, where chord iii has become chromatically altered to a dominant form: Dm7 C: ii Am: G:
G7 V
E7b9 [iii][I] V
Am7
D7
[i] ii
V
Dm7 ii
G7 V
C I
[I]
The second common substitute may be called the ‘bVII7 for iv substitute’; that is, in the key of C, Bb7 for Fm6. We are familiar with chord iv as the second last chord from pattern 6. The notes in Fm6 are f-ab-c-d. The notes in Bb9 [extended from Bb7] are bb-d-f-ab-c. Like the ‘iii for I substitute’, these chords are close enough for the listener to accept. Here is pattern 6 [from chapter 4] with the substitute:
C: Cm: F: Eb:
C I
C7
F IV
Bb7
C I
[iv] V
I V
While Bb7 is ‘literally’ in the key of Eb, it does not require resolution to a target because it is functioning as chord iv, which, in the analysis, is identified in brackets.31 The third common substitute is known as the ‘tritone substitute’. This is where, in the key of C, Db7 substitutes for G7. It will be observed that G7 [g-b-d-f] and Db7 [db-f-ab-cb] have, enharmonically, the same tritone ‘b-f’. Since the tritone is the ‘operative’ part of the dominant chord, one chord may substitute for the other. Indeed, superimposing Db7 on G7 would give the chord G7b9#11, a colourful, but not unusual, chord.32 Changing G7 to Db7 in Pattern 2 [chapter 4] gives the following analysis: D7 C: Cm: Gb G: V Dbm: [V]
Dm7 ii
Db7
C I
[V] V [i]
31
It should be acknowledged that the Bb7 tritone can resolve by step in contrary motion to part of the C chord, or, more properly, because it is a substitute for iv, the c minor chord: d eb; ab g. Classical musicians will recognise this as being the ‘interrupted cadence’, something I will discuss later. Note also that Bb7 occurs as chord VII in the Aeolian mode [see chapter 1]. 32 An extension of Db7 to Db9 with G7 would give G7b9#11b13; an extension of Db7 to Db13 with G7 would give G7b9#9#11b13.
27
Db7 is literally, though not functionally, in Gb: hence V of Gb without the ‘target’ resolution specified on that line. Db7 is identified as substituting for V of c minor rather than C major, since Db7 includes the note ‘ab’ [the b9 in G7] and also a ‘db’, which is a chromatic approach note to ‘c’: Db7/G = G7b9b5. This also gives the chord a more minor colour, being associated with the Phrygian mode.33 D7 loses its target of G major, instead becoming a substitute for Ab7, V of db minor. To summarise, D7 is literally V of G; it is also a substitute for V of db minor, which is why [V] is in brackets. Db7 is literally V of Gb major; it is also a substitute for V of c minor, which is why [V] is in brackets, and the target for V of db minor, which is why [i] is in brackets. If both dominant chords are substituted, the analysis becomes a little simpler: Ab7 C: Cm: Gb Db: V
Dm7 ii
Db7
C I
[V] V [I]
With a tritone substitute for G7, pattern 4 [from chapter 4] would appear: A7b9 C: Cm: Gb Dm: V
Dm7 ii
Db7
C I
[V] V [i]
When both dominant 7ths are substituted, the result is: Eb7 C: Cm: Gb Dm: [V] Ab: V
Dm7 ii
Db7
C I
[V] V [i]
33
Tritone substitutes are essentially altered dominants and are not really in a minor key at all, though the net effect is ‘minor-ish’. Instead, they are the product of an ellipsis of the voice-leading of the dominant 9th resolving to the tonic though chromatic appoggiature. In the progression G9 C, the voice-leading may be as follows: d-d#-e [to account for the b13 or #5]; d-db-c [to account for the #11 or b5]; a#-b-c [#9]; a-ab-g [b9].
28
However, when the dominant 7th chords change, application of the ‘ii-V principle’ [principle 3 from chapter 3] can result in further variation. Pattern 2 may look like this: D7 C: Cm: Gb G: V Dbm: [V]
Abm7 Db7
ii
C I
[V] V [i]
Note that Abm7 is not a substitute for Dm7. It is an alternative ii-V progression. At first sight pattern 4 may also begin to look different: A7b9
Abm7 Db7
C: Cm: Gb Abm: [V] Dm: V
ii [i]
C I
[V] V
While A7b9 changes to being a substitute for Eb7, the functional analysis is essentially the same. Here are the seven analytical examples from chapter 5 with some of the above substitutions added. Example 6.1:
C: Cm: Eb: F: Fm: Cb:
C: Cm: Gb: Eb: Dm: Ab:
C I
Gb7
F IV
Bb7 [iv] V
I [V] V
C I
Eb7
Dm7 ii
Db7
C I
[V] V
Bb7 [iv] V
[V] V
[i]
29
C I
Example 6.2:
F: Fm: Cb: Gm: G: Db:
Gm7 ii
C7 V
Am7 Ab7 iii [I]
Gm7 ii
Gb7
F I
[V] V [V]
[i]
ii V
Am7 F: Fm: Cb: Fm: Ab: Gm: Db: G: ii
Ab7
Gm7 ii
Gb7
F I
Eb7
F I
[V] V [iv] V [V] V
[i]
Example 6.3: G G: I Gm: Bb: Db: C: Cm: Gb: Am:
G G: I Gm: Db: Abm:
Abdim
Am7 ii
Ab7
G I
Db7
C IV
[V]
F7 [iv] V
V I [V] V vii
Bbdim
vii
[i]
Am7 ii
Ab7
G I
C IV
G I
[V] V [i]
Note that the Bbdim, which was acting as a C#dim [vii of d minor], is now acting as a Gdim [vii of ab minor].
30
Example 6.4: Fm7 Ab: Abm: D: Ebm: Eb: ii A: Am:
E7
Bbm7 A7 ii [V] V
Ab I
Bdim
[V] V
[I] vii
Bbm7 Ab: ii Abm: D: Am:
A7
Ab I
Db IV
Ab I
[V] V [i]
Bdim, which was acting as a Ddim [vii of eb minor], is now acting as a G#dim [vii of a minor].
Example 6.5: Bb Bb: I Bbm: E: Bm:
Bb: Bbm: Db: Eb: Ebm: B:
Bb I
Gm7 vi
Cm7 ii
F7 V
Dm7 Dbdim iii [I]
Cm7 ii
[V] V [i]
vii
E7
Eb IV
Ab7
Bb I
[iv] V
Ab7
B7
Bb I
[iv] V
I [V] V
Dbdim, which was acting as Edim [vii of f minor], is now acting as an A#dim [vii of b minor].
31
Example 6.6:
D: Dm: Ab: Gm: Em: E: Bb:
D I
F#m7 F7
Em7 ii
Eb7
D I
Ab7
[V] V [V] [V]
[i]
ii V
G D: IV Dm: F: Ab: G: I Ebm: A: Em: Bb:
C7
D I
F7
E7
[iv] V
Eb7
D I
[V] V [V] V [i]
[V] V
[i]
Example 6.7: Eb Eb: I F: Fm: Cb: G: Gm: Db:
F Eb: Ebm: A: F: I
Am7
Ab7
G
Gm7
Gb7
ii [V] V ii
I [V] V
Fm7 ii
E7
Eb I
[V] V
32
Ab IV
Eb I
CHAPTER SEVEN: Cadences The following chapter discusses cadences, and typical substitute chords used at cadence points. Cadences are the formulaic chord progressions used to end harmonic phrases. Classical musicians recognise four basic cadences: Perfect: Plagal: Interrupted: Imperfect:
VI IV I V vi anything V
Contemporary popular music employs the same cadences, incorporating substitute chords as well. Additionally, because cadences are formulaic, and therefore more predictable, more distant substitutes are often used, which would not necessarily be common within normal harmonic progressions. Perfect cadences take the two forms already discussed:
C:
G7 V
C I
And: Db7
C I
C: Cm: [V] Gb: V
Extension of the ‘iii for I substitute’ would allow the following, though it is not common:
C:
Bm7b5 vii
C I
Bm7b5 [b-d-f-a] and G9 [g-b-d-f-a] have the same tritone and are close enough to have the same function. Plagal cadences are IV-I:
C:
F IV
C I
33
They can also be a substitute of IV-I. Therefore:
C:
Dm7 ii
C I
Dm7 [d-f-a-c] has the same notes as F6 [f-a-c-d]. Indeed, this relationship is the same as the ‘iii for I substitute’. A much less obvious substitute for the plagal cadence is:
C: E:
B7 [IV] V
C I
There are a few reasons why this seems to work. Firstly, B7 is the tritone substitute for F7, which is chord IV in the blues. Secondly, it’s a kind of interrupted cadence in e minor [V-VI]: it’s familiar, but can’t be an interrupted cadence because it ends on chord I. Thirdly and finally, the B7 contains the note ‘a’, which is a fundamental component of the plagal cadence. The plagal minor cadence is the one familiar from pattern 6: Fm6 C: Cm: iv
C I
It generates an interesting number of substitute versions, including the one already discussed: Bb7 C: Cm: [iv] Eb: V
C I
The operative note in the plagal minor cadence is ‘ab’, so the following becomes possible: Abmaj7 C: Cm: VI [iv]
C I
Abmaj7 [ab-c-eb-g] may be heard as the upper part of Fm9 [f-ab-c-eb-g].
34
The following is also seen as a variation on the above especially in a bluesy context:34 Ab7 C: Cm: [iv] Db: V
C I
Also: Dbmaj7 C: Cm: [iv] Ab: IV
C I
Here, Dbmaj7 works because Cmin [c-eb-g] is the upper part of Abmaj7 [ab-c-eb-g], which would be chord I. Additionally, Fm7 is the upper part of Dbmaj9. The interrupted cadence [or ‘deceptive’ as some say] may be interpreted in the contemporary context as V ‘substitute for I’. That is, V vi [G7 Am7, or G7 Abmaj7 in the minor key], or V iii [G7 Em7]. The first example typically ends phrases, and the second example is often used to modulate as shown in chapter 6. The imperfect cadence is likewise interpreted in the contemporary context as ‘anything’ ‘V or substitute for V’. Further extension of the ‘iii for I’ substitute to other degrees of the scale may also be seen. In the major key, these are: iii for I: Em7 for C, as previously discussed; note, however, that Em7 may not extend to Em9 in this context and stay in key: Em9/C = Cmaj7#11. IV for ii: F for Dm7 as previously discussed. Fmaj7/D = Dm9; Fmaj9/D = Dm11; Fmaj7#11/D = Dm13. And ii is also a substitute for IV: Dm7/F = F6; Dm9/F = Fmaj13. V for iii is not a substitute: G7/E does not equal Em9, nor is Em7b9 a conventional extension. vi for IV: Am7/F = Fmaj9; Am9/F = Fmaj7#11; Am11 = Fmaj13 vii for V: Bm7b5/G = G9; Bm11b5/G = G13. I for vi: Cmaj7/A = Am9; Cmaj9 = Am11.
34
Blues will be discussed in more detail later.
35
ii for vii is not a substitute: Dm7/B includes the note ‘c’, an unconventional extension for Bmin7b5. In the minor key the ‘III for i’ substitutes are as follows. III for i: Ebmaj7+/C = Cmin/maj9; Ebmaj9+/C = Cmin/maj11; Ebmaj7#11+/C = Cmin/maj13. iv for ii is not a substitute in the minor key: Fm7/D includes the note ‘eb’, an unconventional extension for Dm7b5. However, ii may be substituted for iv: Dm7b5/F = Fm6. V for III, unlike the major key, is a substitute in the minor: G7/Eb = Ebmaj9+; G9/Eb = Ebmaj9#11+. III may also be substituted for V: Ebmaj7+/G = G7b13 VI for iv: Abmaj7/F = Gm9; Abmaj9/F = Fm11; Abmaj7#11 = Fm13. iv may also be substituted for VI: Fm7/Ab = Ab6. vii for V is the diminished chord with the dominant function, as discussed in chapter 4: Bdim/G = G7b9. i for VI is not a substitute, unlike the major key: Cmin/maj7/Ab includes the note ‘b’, an unconventional extension for Abmaj7. ii for vii is not a substitute: Dm7b5/B includes the note ‘c’, an unconventional extension for Bdim.
Extended cadential patterns normally proceed in the order: subdominant subdominant-minor dominant tonic.35 Thus: F C: IV Cm:
Fm6
G7 V
C I
iv
35
That is, any number or combination of chords may be used as long as the functions proceed in this order. The possibilities are therefore: subdominant tonic; subdominant-minor tonic; dominant tonic; subdominant subdominant-minor tonic; subdominant dominant tonic; subdominant-minor dominant tonic; subdominant subdominant-minor dominant tonic. The classic ii-V-I is therefore subdominant dominant tonic.
36
The substitutes presented in this chapter may be inserted in the appropriate places for interesting effects. Even the following is possible: B7 C: [IV] Cm: Gb: Eb: E: V
Bb7
Db7
[iv]
[V] V
C I
V
And therefore: D#m7b5 [IV]
C: Cm: Gb: Eb: E: vii
Dm7b5
Fm7b5
[iv]
[V] vii
vii
37
C I
CHAPTER EIGHT: Passing Diminished Chords and the Death of Chord ii The following chapter discusses problems with ‘passing’ diminished chords, and presents the ‘death of chord ii’. There are a number of common ‘passing diminished patterns’. The first is familiar: Example 8.1 C C: I Dm:
C#dim
Dm7 ii [i]
vii
The second is similar: Example 8.2
C: Em:
Dm ii
D#dim
Em7 iii [i]
vii
As is the next Example 8.3 F C: IV Gm:
F#dim
G7 V [i]
vii
Example 8.2 may also appear as: Example 8.4
C: Em:
Dm ii
D#dim
C/E I [iii] [i]
vii
And Example 8.3 may appear as: Example 8.5 F C: IV Gm:
F#dim
C/G I [V] [i]
vii
38
C/G, while literally chord I, is generally heard as V with a double appoggiatura.36 That is, the chord after C/G would normally be G or G7:37 ed cb gg The following two examples are probably heard as decorations of the first chord, whatever the ‘analysis’ may be. Example 8.6
C: Em:
C I
Cdim
C I [iii] [i] VI
vii
Cdim = D#dim.38
Example 8.7 G7 C: V Bm:
Gdim
G7 V [vii] [i] [VI]
vii
Gdim = A#dim. The next two examples are Example 8.4 and 8.5 backwards, with an extra resolution: Example 8.8 C/E C: I Gm:
Ebdim
Dm7 ii
G7 V [i]
F IV
G7 V [i]
vii
Example 8.9 C/G C: I Gm:
Gbdim vii
36
This 2nd inversion chord is familiar for its functional use as an upbeat to the cadenza in a concerto. A cadenza is essentially a decorated resolution of the appoggiature. 37 An exception to this is where the bass moves through the chord as an arpeggio, such as C-C/E-C/GC. Here C/G is heard as C. 38 Note that B7b9 C would be interpreted as a plagal cadence in the key of C, and an interrupted cadence in the key of e minor.
39
Sometimes the resolution is not given: Example 8.10 C/E C: I Gm:
Ebdim vii
Dm7 ii [V] [i]
C I
F IV [V] [i]
C I
Example 8.11
C: Gm:
C/G I [V]
Gbdim vii
How can this be? How can ii be V, and how can IV be V? In contemporary popular and jazz music chord ii is customarily linked to chord V [see principle 3 in chapter 3] as the ii-V pattern. Chord ii has, therefore, lost its individual characteristics and is heard as a double appoggiatura into chord V: ff dd cb ag Indeed, the chord Dm7/G is G9sus. Through association, chord ii has become a version of chord V. This is also why the ‘till ready’ vamp of ii-Vii-V-ii-V, etc., is used. Functionally, the harmony hovers on the dominant. Chord IV has the same function as chord ii. Fmaj7/G is G13sus and, when resolved to G7, is heard as a triple appoggiatura.39 ff ed cb ag It should be noted that it is relatively rare for chord ii [or chord IV] to act as chord V. Typically, it occurs in standard patterns like those above, where the familiarity of the pattern is a factor. At this stage in this booklet our analyses have been simplified down to a basic level: chord-I, or not-chord-I.40
39
Fmaj7/G is famous as the ‘LA chord’ of smooth west coast music.
40
The ‘chord-I group’ includes I, iii, and vi. The ‘not-chord-I group’ includes V, ii, IV, and vii. In tonal music, ‘not-I’ moves to I, its target. This type of analysis is concerned with finding the targets, which are the real or implied keys. Pattern 1 from chapter 4 was given as
C:
Cmaj7 I
Am7 vi
Dm7 ii
G7 V
We can now see that this is functionally the same as two bars of chord I, followed by two bars of chord V.
40
This is not a new idea. See, for example, Heinrich Schenker, “Vom Organischen der Sonatenform,” in Das Meisterwerk in der Musik, Vol.II, Musich: Drei Masken, 1926; trans. W.Drabkin as “On Organicism in Sonata Form,” in The Masterwork in Music, Vol.II, Cambridge University Press, 1996.
41
CHAPTER NINE:
Blues
The following chapter briefly discusses the influence of the blues on tonal chord progressions. While the first blues records were made in the 1920s when the form was already developed, the first time the word actually appeared on a piece of sheet music was in 1912, when Memphis Blues and Dallas Blues were published. As far as can be ascertained, the term ‘blues’ was never used in any 19th century writings on black music, though some people speculate that the term may be derived from the phrase ‘the blue devils’, which dates from Elizabethan times.41 There have been, and continue to be, many original, ‘authentic’ and important characteristics of blues, such as call-and-answer or the slow ground beat influence from work songs. Over the years blues has been incorporated into boogie-woogie and rock ‘n’ roll and has been appropriated to make ‘white blues’ and jazz.42 Along the way much of the original character has been lost [for example, blues does not ‘have’ to have a slow ground beat] whilst still being identified as ‘blues’. One of the important identifiers is that the form has three phrases; nowadays these phrases have been regularised into four bars each [’12bar blues’]. Traditionally, the first phrase made a declamation. The second phrase was more or less a repeat of the first phrase, but with a flattened melodic inflection, at least at the beginning of the phrase—a so-called ‘blue note’. The third phrase was an answering or ‘commenting’ phrase: ‘My man, my man, he treats me awful mean You know, my man, my man, he treats me awful mean Oh yeah, he’s the meanest man I’ve ever seen.’ The second important contemporary identifier is the choice of chord for the beginning of the second, inflected, phrase. When attempting to accompany, with chords, what would have been nonwestern, modal music, one can imagine that the early performers just played simple chords that seemed to fit. For example, if the first phrase centred around the pitch ‘e’, the chord could be C; and if the second phrase inflected the pitch to ‘eb’, the second chord could be F [to make 41
James Lincoln Collier, The Making of Jazz, NY: Delta, 1979. This may not be as surprising as it first sounds. It’s well known that ‘removed’ societies often maintain words or customs for longer than the ‘original’ culture. 42 See, for example, White Blues (1983) by Michael Graillier, title track of Chet Baker’s compilation album, Camden CD 74321 451892.
42
F7], or indeed Ab or Ab7 [or even Eb7], which are also used to begin the second phrase in a number of blues songs. While it seems that the important blues characteristic is the flattened melody note in the second phrase, and not the particular chord that is used to harmonise with it, the choice of harmony here has become strongly associated with a ‘bluesy’ feel in the harmonic context. The last phrase is a turnaround, so the dominant chord would have been the clear choice. This means the whole form could be harmonised by the primary triads I-IV-I-V-I. The addition of 7ths to every chord reduces their harmonic function and makes the result more ‘modal’. Blues is not, therefore, fully tonal and to attempt to fit it in to a tonal analysis means one has to ignore the functionality of the dominant 7th chords, particularly in the second phrase.43
C: F:
C7 [I] V
F7 C: [IV] F: [I] Bb: V
C: F:
G7 V
C7
C7
C7
F7
C7 [I] V
C7
G7
C7 [I] V
C7
The result is that the dominant 7th as chord IV has come to be a particularly strong blues ‘identifier’. Indeed, one only has to use it to make the song immediately sound more ‘bluesy’. Contemporary popular music and jazz regularly ‘borrow’ this chord [or the dominant 7th on the flattened submediant—Ab7 in the key of C] in the same way as chords from the parallel minor key are ‘borrowed’. Even the most tonal of ‘white blues’ progressions include the ‘blue note’ in this vital position. Note the passing diminished pattern in the second phrase [from example 8.5 in chapter 8]: C7 C: [I] F: V Bb:
F7 [IV]
C7 [I] V
Gm7
C7
ii
V
V
43
Note that F7 as chord IV is present in the jazz melodic minor [see chapter 1] and to analyse it as chord IV in c minor [rather than a variant of IV in C major] would therefore be possible.
43
F7 [IV] [I]
C: F: Gm: D: Bb: V
D7 C: F: Bb: D: [I] G: V
F#dim
C7 [I]
vii
[i]
A7
V
G7 V
C7 [I] V
F7 [IV] V
[I]
44
C7 [I] V
G7 V
CHAPTER TEN:
Analysing Excerpts from Standards
The following chapter analyses some excerpts from the ‘great American songbook’.44 Talk of the Town F F: I Fm: Ab: Bbm: Cm:
F: C: G: Dm: Ab: Ebm: A:
F I
Abdim
Gm7 ii
C7 V
F I
F7+
Bb IV
[iv] V V vii
E7
[V] V
[i]
[i]
Eb7
[V] V [i]
D7
G7
Gm7 ii
V [I]
V [i]
But Beautiful
G: Bm: Am:
G I
44
Abdim
Am7 ii
Bbdim
vii
[i]
Bm7b5 E7
A7
A7
V [i]
V
ii
vii
G/B G: I [iii] D: Am: Bm: [i]
Am7 G: ii Dm: D:
Eb7
D7 V
V
Bm7 Bbdim iii [I] vii
Am7 ii
D7 V [i]
[I]
These excerpts are taken from the Berklee, lesson 18 assignments.
45
G I
C7 V [I]
Em7 G: vi D: ii
A7
Am7 ii
D7 V [I]
V
Cynthia’s in Love Fm7: Eb: ii Ebm: Bbm:
Bb7b9
Fm7 ii
Gm7 iii
Gbdim
V vii
Fm7 ii
Eb: F: Cm: Gb: Bbm:
Eb I
Bb7 V
Eb I
Db7
[V] V
C7 V [i]
[i]
Blue Room
F: Gm: Cm:
F: C: Fm: Ab: Bb:
F I
Abdim
Gm7 ii
C7 V
F I
D7b9 V
vii
F I
F7
Gm7 ii [i]
C7 V
Gm7 ii
C7 V [I]
[i]
Bb IV
Eb7
F I
G7 V
[iv] V V
I
There’s No You F F: I Fm: Cb:
Bbm6
F I
Dbm7 Gb7
iv ii
46
[V] V
F F: I Cm: Fm: [i]
Am7 iii
Abdim
Gm7 ii
C7 V [i]
Bb I
C7
vii
Moonglow Eb IV
Bb: Bbm: F:
Ebm6 iv
V
Cm7 Bb: ii F: Fm: Dm:
F7 V [I]
Bb/D Dbdim I [iii] vii
Cm7 Dbdim Bb/D ii [V] I [iii] [i] vii
[i]
Cm7 [bar 8] = F9sus [see chapter 8]. I Understand F#m7 F7 E7 G: D: A: Em: E: ii Bb:
V [V] [i]
A7
Am7 ii
V [I]
D7 V [I]
G I
V
G/B E7 G: I [iii] Am: V A: [ii]
Am7 ii [i]
D7 V
47
G I
Am7 ii
Gone with the Wind
Eb: Fm:
Fm7 ii
Am7 Eb: G: ii Am:
Eb: Bbm:
Eb: Ebm: Gb: Fm: Gm:
Bb7 V
Eb I
D7
G
V
I
Ebmaj9 I
C7b9
Bb7 V
Eb I
V
Fm7 ii [i]
E7b9
Am7
D7
G
V
I
V
ii [i]
Gbdim
Fm7 ii
Bb7 V [i]
Fm7 ii
Db7
vii
Eb I
Bb7+
Gm7b5 C7 [I] [iii]
V
[V]
[iv] V ii [i]
V
[i]
Bb7+ [bar 13] is also functioning as D7b5#5.
48
Bb7 V
CHAPTER ELEVEN:
Analysing Standards
The following chapter analyses some standards from the ‘great American songbook’.45 Some of them have tricky sections.
All of Me
C: A:
C6 I
A7
C6 I
E7
E7
V
V
A7
Dm7
Dm7
V
[i] iv
[i] iv
E7 C: Am: V G:
E7
Am7
Am7
V
[i] ii
[i] ii
D13
D13
Dm7 ii
G7 V [I]
Dm i
D7
C: A: [I] Dm: V Am:
C: G: V
V
Beautiful Love Em7b5 Dm: ii Gm:
A7#5 V
Gm7 Dm: Gm: [i] F: ii
C7
Fmaj7
V
I
V
45
Em7b5 A7 ii V
These standards are taken from Chuck Sher [ed.], The New Real Book, Petaluma: Sher Music Co, 1988.
49
Dm Dm: i Am: Eb:
Gm7 iv
A7 V [i]
[V] V
1st time Dm Dm: i Em: 2nd time Dm Dm: i Bbm: Em: Am: Eb:
Bb7
B7b5
Em7b5 ii [i]
V
B7#9
Bb7
[V] V
[i] [V] V
A7 V
A7 V
Dm i
Dm i
[i]
Blame it on My Youth Ebmaj7 Fm7 Eb: I ii Fm:
Eb: Fm: Ab:
Fm7 ii
Edim vii
Gm7 iii
Cm7 vi
Fm7 ii
Edim vii
Fm7 ii [i]
Bb7 V
Gm7 Fm7 Bb7 iii [I] ii V
Fm7 ii [i]
Bb7 V
Ebmaj7 Eb7sus Eb7
I V
Abmaj7 Bb7 Eb: IV V Ab: I
Gm7 Cm7 iii [I] vi
Fm7 ii
Bb7 V
Dm7b5 G7 Eb: Cm: ii V F: Bb:
Cm
Abmaj7 C7
i
VI [i] V
V
Ebmaj7 I
F7 Bb7sus Bb7 V V [I] V
[I]
But Beautiful Gmaj7 G: I Am: Bm:
Bm7b5 E7b9 ii
Am9 ii [i]
V
C#m7b5 F#7b9
ii
50
V
Gmaj7 G: I [iii] Bm: [i] Am: D: 1st time D13 G: V D: [I] Gm: Em:
A9
A9
ii
[i] V
V
Am7 D9sus D7 ii V V
Gmaj7 B7 [I]
V
Cdim
Bm7 Em7 iii [I] vi
vii
[i]
V
V
Em7
A9
G: Em: [i] D: ii 2nd time D7 G: V Em: Gm: Bb:
Bm7b5 E7sus E7
Am7 ii
V
D7/C V
Gmaj7/D E7 G: I Bb: [I] [iii] Am: V
D7 V [I]
Bm7 Em7 iii [I] vi
Am7 F#m7b5 B7 Em ii vi iv ii V i
F9
[iv] V
Am7 ii
D7 V
G6 I
G6 I
[i]
Notes: Bars 1-5 decorate a slow I-ii-iii progression. The F9 in the 5th last bar has two functions: firstly it is part of a iv-I in G [see chapter 6]; secondly, it is V-I in Bb, where the G second inversion chord functions as a D chord [see chapter 4].
51
Darn That Dream
G: Gm: Ab: F: Fm: Em: Am:
G6 I
Bbm7 Eb7 Am7
ii
B7b5
Em7 vi
V
[i]
D7 Cm6 V iv
Bm7b5 E7 [I] [iii]
V iii [I] [iv] iv
ii
V
1st time Am7 G: ii Am: [i] Bb: Gm: Ab: Dm: Eb:
F9
Bm7 Bbm7 iii [I]
V [iv]
Am7 ii
Bm7 Bb7 Am7 D7
D7 V
iii [I] ii [V] [i]
V
[i] ii [V] [V]
[i] V 2nd time G6 Fm7 Bb7 G: I Eb: ii V
Ebmaj7 Cm7 G: Eb: I E: Bbm:
vi
Ebmaj7 Cm7 G: Eb: I vi Dbm: Ab: Dm: Repeat [A] section
Fm7
Bb7
Gm7
ii
V
iii [I]
F#m7 B7
ii
Gm
Am7 ii
V [V]
Fm7
Bb7
ii
V [i]
D7 V
Bbm7 Eb7 Am9 D13
[V]
[i] ii [IV] V [V]
ii
V
iii [I]
[i]
Notes: In bar 2, Am7 functions as chord I in F, allowing Eb7 to function as chord iv in f minor [see chapter 6]. Cm6 in bar 3 has been given as chord iv and so may move to a substitute for chord I in bar 4. However, it may also be heard as F9, the substitute dominant of E7 in the next bar [see chapter 6]. The passing Bbm7 in bar 6 is given as Eb11 [see chapter 8]. The D7-Bbm7 progression in the last two bars requires explanation: Bbm7=Db6, allowing D7 to be the dominant substitute of Ab7.
52
Gee Baby, Ain’t I Good to You C7 Eb: C: [I] Fm: V Db: Gm: F: Bb:
C7 Eb: C: [I] Fm: V Db: Gm: F: Bb: Ab:
Ab6 Eb: Ab: I Bbm: Gm: Cm:
C7 Eb: C: [I] Fm: V Db: Gm: F: Bb: Cm: [i]
Ab7
[i] V [V]
G7
C7
V
[I]
F7
[i] V [V]
Eb6 I
G7 V
[i] V
Ab7
Bb7 V
G7
C7
V
[I]
[I] V
F7
[I]
Bb7 V
Eb6 I
Eb7
[i] V
[I] V
[I] V
Adim
vii
Eb6/Bb Eb7 I V [i]
Ab6
Adim
Dm7b5 G7
I vii ii
Ab7
[i] V [V]
G7
C7
V
[I]
F7
Bb7 V
[i] V
Eb6 I
[i] V
[I] V
[I]
Notes: Even though C7 in the first bar is intended to invoke a bluesy sound, there is a clear resolution to a substitute for Fmin [see chapter 7].
53
I’m Old Fashioned
F:
F6 I
Dm7 vi
Bb6/F F: IV [I] Dm:
C7 V
F6 I
Fmaj7 I
Dm7 F: C: ii Dm: [i]
Gm7 F: ii C: Cm:
F6 F: I A:
Gm7 ii
A7
ii
V
G13
Dm7
G13
V
ii
V
Gm7 ii
C7 V [I] [i]
Abdim
vii
Dm7 vi
Gm7 ii
C7 V
F6 I
Dm7 vi [I]
C#m7 D7
E7
F#dim
iii [I]
V
[vi] [I]
V
Dm7 vi
Gm7 ii
C7 V
F6 I
Cm7 F: Fm: Bb: ii Dm: C:
F7 [I]
Bbmaj7 Eb9#11
V
I
Bm7
E7
ii
V
Gm7 ii
C7 V
Dm7 vi
Gm7 ii
Am7 Dm7 Dm7/C
C7 V
Bm7b5 Bbm6
iii [I] iv
Am7 Dm7 iii [I] vi vi [I]
C7 V
[I] [i]
vii
F6 I
F: C:
Gm7 ii
Em7b5
Gm7 ii
Amaj7 Bm7 F: A: I ii G: Gm:
F:
Dm7 vi
iv
[V]
[i] ii
Gm7 ii
C7 V
54
ii
vii [V]
F6 I
Notes: Unusually, the G13 in bar 12 waits four bars for its resolution in bar 16. In bar 23, E7-F#m7 would not be unusual as the progression V-vi; in this case E7-F#dim is much less usual, but since it is an ellipsis of V-vi, F#dim is acceptable in place of I.
Jersey Bounce F6 I
F: C:
Gm7 F: ii C: Cm:
F6 I
F:
F: Fm: C: Gb:
Gm7 ii
F13 F: Bb: V Ab:
Db13 F: Fm: Ab: [I] Gb: [ii] V Cm: Repeat [A2] section
F6 I
C7 V [I]
G7
G7
V
V
F6 I
Abdim
Gm7 ii
vii
F6 I
C7 V
[i]
G7
G7
V
V
F6 I
Db9
C13 V
F6 I
[iv] [I] V
F13
Eb13
Eb13
V
[I] [ii] V
V
Db13
C7 V
C7#5 V
V [V]
[i]
Notes: In bars 15-16, Db9-F6 is a plagal minor cadence [see chapter 7]. In bar 19, Eb13 is taken as an ellipsis of Bbm7-Eb13 [see chapter 8], thus
55
F13 finds its target. Likewise, Db13 in bar 21 is taken to be an ellipsis of Abm7-Db13, allowing Eb13 to ‘resolve’.
Killing Me Softly with His Song Bbm7 Ab: ii
Eb9 V
Ab I
Db IV
Bbm7 Ab: ii
Eb9 V
Fm vi
Fm vi
Bbm7 Ab: ii Fm:
Eb7 V
Ab I
C7
Fm Ab: Fm: i
Bbm7 ii iv
Eb V
Ab I
Fm Ab: Eb: ii
Bb/D
Eb V I
Db IV
Ab: F: Fm: Db:
Ab I
V
V
Db IV
Gbmaj7
Gbmaj7
F
F
I I
[iv] IV
IV
Notes: This song is potentially difficult because of the lack of chord extensions that ‘pin’ down the chord function. Modulations are made via pivot chords rather than through resolution of the dominant 7th. Gbma7-F is a plagal minor cadence [see chapter7].
Lady Bird Cmaj7 C: I Cm: Eb:
Cmaj7 I
56
Fm7
Bb7
iv ii
[iv] V
C: Ab:
Cmaj7 I
Abmaj7 C: Ab: I G:
C: Cm: G: Ab:
Dm7 ii
Cmaj7 I
Abmaj7
Bbm7
Eb7
ii
V
Am7
D7
ii
V
Cmaj7 Eb7 I
Abmaj7 G7#5
I
G7 V
VI [I] V
57
I
V
CHAPTER TWELVE:
Analysing The Beatles
The following chapter analyses a couple of interesting excerpts from The Beatles songs. The song Yesterday contains a dominant 7th that apparently does not resolve: it accompanies the line, ‘I believe in yesterday’:
F: C:
Dm7
G7
ii
V
Bb F IV [V] I [I]
In this case, chord IV, Bb, is acting as a dominant, C9sus [see chapter 8].
The introductory chord of A Hard Day’s Night is notated with the chord symbol Gsus4/D before moving into the first chord of the song, G. Gsus4=g-c-d. However D7sus=d-g-a-c. Since the note ‘a’ is not necessarily required, Gsus4=D7sus. Thus: Gsus4/D G: I [V]
G I
The first four bars include tonal and modal aspects: G G: I Gm: Bb:
C IV
G I
F
G I
[iv] V
Although the progression G-F-G is modal, it recalls the chord iv substitution [see chapter 6] even without the extension to the dominant 7th. Sgt. Pepper’s Lonely Hearts Club Band is strongly influenced by the blues, and so is not ‘tonal’. Every chord is a dominant 7th so the progression is heard melodically as a kind of riff: I-II-IV-I. Assigning the dominant chords as chord V in a particular key, while perhaps being literally correct, completely misses the point. C7 might be heard as a target [D9b13sus] for A7 [see Yesterday and chapter 8]. G7 G: [I] C: V D: F:
A7 [ii] V
C7 [IV] [I] [I] V
G7 [I] V
58
Come Together is interesting because almost all the major chords extend to the dominant 7th except chord V. Here is the second verse: D7#9 D: [I] Gm: V
D7#9
D7#9
D7#9
A D: V Gm: C:
A
G7 [IV] [i] V
G7
D7#9 [I] V
D7#9
Bm D: vi Gm:
A V
G IV
A V
D7#9 as chord I and G7 as chord IV are imported from the blues.
59
CHAPTER THIRTEEN: The ‘Tristan Chord’ Wagner’s ‘Tristan Chord’ is notorious as a subject for analysis.46 The one given below is how Paul Cooper heard it: a French 6th resolving to the dominant of a minor [E7], followed by another to G7, and then [what amounts to] another to B7.47
Cooper’s interpretation is the same as how the jazz musician would hear it.48 Bar 3 is clearly E7 with an appoggiatura in the first voice from a#-b. Similarly, bar 2 is F7b5, with a long appoggiatura in the first voice from g#a. Confusion may come from naming the chord on the downbeat of bar 2 as its own chord Db9 or G7b9#5, by focussing on the f-b tritone for example, or as Fm7b5. Instead, if heard as a tritone substitute for B7, the first beat of bar 2 may be named F7b5#9, though this is missing the point somewhat. Bars 6-7 are identical, but transposed. Bars 10-11 are slightly different. The final chord in bar 10, though, is C+, which may still function as a tritone substitute for the dominant of B7.
46
Richard Wagner’s opera Tristan und Isolde was composed from 1857 to 1859 and was widely regarded as a departure from the ‘classical’ harmonic system. The following excerpt is a piano reduction of the first eleven bars of the ‘Prelude’. 47 Paul Cooper, Perspectives in Music Theory, NY: Dodd, Mead & Co, 1975, p.219. 48 A French 6th is enharmonically the same as the tritone substitute for V of V.
60
What is not happening is a clear resolution of each imperfect cadence: E7 is followed by G7, followed by B7. Why is there no resolution? Perhaps the answer is this is art music, where expected resolutions are delayed and larger patterns are articulated thematically over longer time scales; additionally, in this highly dissonant context, even resolutions to the dominant 7th, followed by a rest, may be heard as ‘final’ enough to move the tonality elsewhere.49 However, if compelled to retrospectively force this sophisticated music into the mindset of American jazz harmony, the following will have to do: G7 followed by E7 is not unusual in jazz harmony [see chapter 7], but E7 followed by G7 is. However, if the general key is taken to be a minor/C major, the first phrase is an imperfect cadence in the relative minor and the second phrase an imperfect cadence in the relative major. This key relationship is so close that we should find logical progression at the chord-to chord level, despite the chromaticism. If E7 was followed by Am, the interpretation would be V-i; or V-of-vi to vi in C major. If E7 were followed by Ab, the interpretation would be V-of-vi [C major] to VI in c minor, with the Am being replaced by Ab as a chord ‘borrowed’ from c minor. The extension of Ab to Ab7 may be understood as an ellipsis [see chapter 3]. With the second phrase ending on G7, the first chord of the third phrase being C+ is uncontroversial. Omitting the melody-only bars,50 the chordal analysis would look like this: F7b5 Am: C: Em: [V] Bbm: V Cm: Gm: Dbm: Bm: Fm:
E7 V
Ab7b5 [i]
G7 V
C+ iii [I]
[i]
B7
V [VI] [V] V
V [i] [V] V
49
[i]
Note that the tonalities articulated are not radical: the music moves from the minor key, to the relative major, to the dominant of the minor. 50 I hear the melody-only bars as moving from 5-to-3 of the chord [not from 3-to-1]. Thus, the anacrusis and bar 1 are Dm [iv of a minor], bars 4-5 are E [V of a minor], and bars 8-9 are G [V of C major]. These last two are uncontroversial as they merely prolong the previous chord. Hearing Dm as the first chord is a back-formation.
61
