Harmonic movements
Ways to move chords

Chord substitution

In music theory, chord substitution is the technique of using a chord in place of another in a progression of chords, or a chord progression. Much of the European classical repertoire and the vast majority of blues, jazz and rock music songs are based on chord progressions. "A chord substitution occurs when a chord is replaced by another that is made to function like the original. Usually substituted chords possess two pitches in common with the triad that they are replacing."

A chord progression may be repeated to form a song or tune. Composers, songwriters and arrangers have developed a number of ways to add variety to a repeated chord progression. There are many ways to add variety to music, including changing the dynamics (loudness and softness).

The diminished triad can be used to substitute for the dominant seventh chord. In major scales, a diminished triad occurs only on the seventh scale degree. For instance, in the key of C, this is a B diminished triad (B, D, F). Since the triad is built on the seventh scale degree, it is also called the leading-tone triad. This chord has a dominant function. Unlike the dominant triad or dominant seventh, the leading-tone triad functions as a prolongational chord rather than a structural chord since the strong root motion by fifth is absent.

Use in blues, jazz and rock music

Jazz musicians often substitute chords in the original progression to create variety and add interest to a piece.

The substitute chord must have some harmonic quality and degree of function in common with the original chord, and often only differs by one or two notes. Scott DeVeaux describes a "penchant in modern jazz for harmonic substitution."

One simple type of chord substitution is to replace a given chord with a chord that has the same function. Thus, in the simple chord progression I–ii–V–I, which in the key of C major would be the chords C–DM–G–C, a musician could replace the I chords with "tonic substitutes". The most widely used substitutes are iii and vi (in a Major key), which in this case would be the chords "e minor" and "a minor".

This simple chord progression with tonic substitutes could become iii–ii–V–vi or, with chord names, "e minor–d minor–G Major–a minor". Given the overlap in notes between the original tonic chords and the chord substitutes (for example, C major is the notes "C, E, and G", and "e minor" is the notes "E, G and B"), the melody is likely to be supported by the new chords. The musician typically uses her/his "ear" (sense of the musical style and harmonic suitability) to determine if the chord substitution works with the melody.

There are also subdominant substitutes and dominant substitutes. For subdominant chords, in the key of C major, in the chord progression C major/F major/G7/C major (a simple I /IV/V7/I progression), the notes of the subdominant chord, F major, are "F, A, and C". As such, a performer or arranger who wished to add variety to the song could try using a chord substitution for a repetition of this progression. One simple chord substitute for IV is the "ii" chord, a minor chord built on the second scale degree. In the key of C major, the "ii" chord is "d minor", which is the notes "D, F, and A". As there are two shared notes between the IV and "ii" chords, a melody that works well over IV is likely to be supported by the "ii" chord.

Types

The ii–V substitution is when a chord or each chord in a progression is preceded by its supertonic (ii7) and dominant (V7), or simply its dominant. For example, a C major chord would be preceded by Dm7 and G7. Since secondary dominant chords are often inserted between the chords of a progression rather than replacing one, this may be considered as 'addition' rather than 'substitution'.

Chord quality alteration is when the quality of a chord is changed, and the new chord of similar root and construction, but with one pitch different, is substituted for the original chord, for example the minor sixth for the major seventh, or the major seventh for the minor.

The diminished seventh chord is often used in place of a dominant 7th chord. In the key of A Major the V chord, E dominant 7th (which is made up the notes E, G♯, B, and D) can be replaced with a G♯ diminished seventh chord (G♯, B, D, F). If the diminished seventh chord (G♯) is followed by the I chord (A), this creates chromatic (stepwise semitonal) root movement, which can add musical interest in a song mainly constructed around the interval of the fourth or fifth. The diminished seventh chord on the sharpened second scale degree, ♯IIo7, may be used as a substitute dominant, for example in C: ♯IIo7 = D♯–F♯–A–C♮ ↔ B–D♯–F♯–A = VII7, which creates the chromatic root movement D – D♭ – C. Contrast with the original ii–V–I progression in C, which creates the leading-tone B – C.

In a tritone substitution, the substitute chord only differs slightly from the original chord. If the original chord in a song is G7 (G, B, D, F), the tritone substitution would be D♭7 (D♭, F, A♭, C♭). Note that the 3rd and 7th notes of the G7 chord are found in the D♭7 chord (albeit with a change of role). The tritone substitution is widely used for V7 chords in the popular jazz chord progression "ii-V-I". In the key of C, this progression is "d minor, G7, C Major". With tritone substitution, this progression would become "d minor, D♭7, C Major," which contains chromatic root movement. When performed by the bass player, this chromatic root movement creates a smooth-sounding progression. "Tritone substitutions and altered dominants are nearly identical...Good improvisers will liberally sprinkle their solos with both devices. A simple comparison of the notes generally used with the given chord [notation] and the notes used in tri-tone substitution or altered dominants will reveal a rather stunning contrast, and could cause the unknowledgeable analyzer to suspect errors. ...(the distinction between the two [tri-tone substitution and altered dominant] is usually a moot point)."

Tonic substitution is the use of chords that sound similar to the tonic chord (or I chord) in place of the tonic. In major keys, the chords iii and vi are often substituted for the I chord, to add interest. In the key of C major, the I major 7 chord is "C, E, G, B," the iii chord ("III–7") is E minor 7 ("E, G, B, D") and the vi minor 7 chord is A minor 7 ("A, C, E, G"). Both of the tonic substitute chords use notes from the tonic chord, which means that they usually support a melody originally designed for the tonic (I) chord.

The relative major/minor substitution shares two common tones and is so called because it involves the relation between major and minor keys with the same key signatures, such as C major and A minor.

The augmented triad on the fifth scale degree may be used as a substitute dominant, and may also be considered as ♭III+, for example in C: V+ = G–B–D♯, ♭III+ = E♭–G–B♮, and since in every key: D♯ = E♭. "Backdoor ii–V" in C: IV7–♭VII7–I. Chord symbols for the conventional ii–V progression are above the staff, with the chord symbols for the substitution in parentheses.

The chord a minor third above, ♭VII7, may be substituted for the dominant, and may be preceded by its ii: iv7. Due to common use the two chords of the backdoor progression (IV7-♭VII7) may be substituted for the dominant chord. In C major the dominant would be G7: GBDF, sharing two common tones with B♭7: B♭DFA♭. A♭ and F serve as upper leading-tones back to G and E, respectively, rather than B♮ and F serving as the lower and upper leading-tones to C and E.

Application

In jazz, chord substitutions can be applied by composers, arrangers, or performers. Composers may use chord substitutions when they are basing a new jazz tune on an existing chord progression from an old jazz standard or a song from a musical; arrangers for a big band or jazz orchestra may use chord substitutions in their arrangement of a tune, to add harmonic interest or give a different "feel" to a song; and instrumentalists may use chord substitutions in their performance of a song. Given that many jazz songs have repetition of internal sections, such as with a 32-bar AABA song form, performers or arrangers may use chord substitution within the A sections to add variety to the song.

Jazz "comping" instruments (piano, guitar, organ, vibes) often use chord substitution to add harmonic interest to a jazz tune with slow harmonic change. For example, the jazz standard chord progression of "rhythm changes" uses a simple eight bar chord progression in the bridge with the chords III7, VI7, II7, V7; in the key of B♭, these chords are D7, G7, C7, and F7 (each for two bars). A jazz guitarist might add a "ii–V7" aspect to each chord, which would make the progression: "a minor, D7, d minor, G7, g minor, C7, c minor, F7. Alternatively, tritone substitutions could be applied to the progression.

Note that both the back door progression and ♯IIo7, when substituted for V7, introduces notes that seem wrong or anachronistic to the V7 chord (such as the fourth and the major seventh). They work only because the given instances of those chords are familiar to the ear; hence when an improviser uses them against the V7, the listener's ear hears the given precedents for the event, instead of the conflict with the V7. — Coker (1997), p. 82

Theoretically, any chord can substitute for any other chord, as long as the new chord supports the melody. In practice, though, only a few options sound musically and stylistically appropriate to a given melody. This technique is used in music such as bebop or fusion to provide more sophisticated harmony, or to create a new-sounding re-harmonization of an old jazz standard.

Jazz soloists and improvisers also use chord substitutions to help them add interest to their improvised solos. Jazz soloing instruments that can play chords, such as jazz guitar, piano, and organ players may use substitute chords to develop a chord solo over an existing jazz tune with slow-moving harmonies. Also, jazz improvisers may use chord substitution as a mental framework to help them create more interesting-sounding solos. For example, a saxophonist playing an improvised solo over the basic "rhythm changes" bridge (in B♭, this is "D7, G7, C7, and F7", each for two bars) might think of a more complex progression that uses substitute chords (e.g., "a minor, D7, d minor, G7, g minor, C7, c minor, F7). In doing so, this implies the substitute chords over the original progression, which adds interest for listeners.

Tritone substitution

The tritone substitution is a common chord substitution found in both jazz and classical music. Where jazz is concerned, it was the precursor to more complex substitution patterns like Coltrane changes. Tritone substitutions are sometimes used in improvisation—often to create tension during a solo. Though examples of the tritone substitution, known in the classical world as an augmented sixth chord, can be found extensively in classical music since the Renaissance period, they were not heard until much later in jazz by musicians such as Dizzy Gillespie and Charlie Parker in the 1940s, as well as Duke Ellington, Art Tatum, Coleman Hawkins, Roy Eldridge and Benny Goodman.

The tritone substitution can be performed by exchanging a dominant seventh chord for another dominant seven chord which is a tritone away from it. For example, in the key of C major one can use D♭7 instead of G7. (D♭ is a tritone away from G).

In tonal music, a conventional perfect cadence consists of a dominant seventh chord followed by a tonic chord. For example, in the key of C major, the chord of G7 is followed by a chord of C. In order to execute a tritone substitution, common variant of this progression, one would replace the dominant seventh chord with a dominant chord that has its root a tritone away from the original.

Franz Schubert's String Quintet in C major concludes with a dramatic final cadence that uses the third of the above progressions. The conventional G7 chord is replaced in bars 3 and 4 of the following example with a D♭7 chord, with a diminished fifth (G♮ as the enharmonic equivalent of Adouble flat); a chord otherwise known as a 'French sixth'.

Coltrane changes

Coltrane changes (Coltrane Matrix or cycle, also known as chromatic third relations and multi-tonic changes) are a harmonic progression variation using substitute chords over common jazz chord progressions. These substitution patterns were first demonstrated by jazz musician John Coltrane on the albums Bags & Trane (on the track "Three Little Words") and Cannonball Adderley Quintet in Chicago (on "Limehouse Blues"). Coltrane continued his explorations on the 1959 album Giant Steps and expanded on the substitution cycle in his compositions "Giant Steps" and "Countdown", the latter of which is a reharmonized version of Eddie Vinson's "Tune Up". The Coltrane changes are a standard advanced harmonic substitution used in jazz improvisation.

Function

The changes serve as a pattern of chord substitutions for the ii–V–I progression (supertonic–dominant–tonic) and are noted for the tonally unusual root movement by major thirds (either up or down by a major third interval), creating an augmented triad. Root movement by thirds is unusual in jazz, as the norm is circle of fifths root movement, such as ii-V-I, which in the key of C is D dorian, G7 and C major.

Influences

David Demsey, saxophonist and coordinator of jazz studies at William Paterson University, cites a number of influences leading to Coltrane's development of these changes. After Coltrane's death it was proposed that his "preoccupation with... chromatic third-relations" was inspired by religion or spirituality, with three equal key areas having numerological significance representing a "magic triangle", or, "the trinity, God, or unity." However, Demsey shows that though this meaning was of some importance, third relationships were much more "earthly", or rather historical, in origin. Mention should be made of his interests in Indian ragas during the early 1960s, the Trimurti of Vishnu, Brahma and Shiva may well have been an inherent reference in his chromatic third relations, tritone substitutes, and so on. In playing that style, Coltrane found it "easy to apply the harmonic ideas I had... I started experimenting because I was striving for more individual development." He developed his sheets of sound style while playing with Miles Davis and with pianist Thelonious Monk during this period. In terms of the origin of this “sheets of sound” technique, saxophonist Odean Pope considers pianist Hasaan Ibn Ali a major influence on Coltrane and his development of this signature style.

Coltrane studied harmony with Dennis Sandole and at the Granoff School of Music in Philadelphia. He explored contemporary techniques and theory. He also studied the Thesaurus of Scales and Melodic Patterns by Nicolas Slonimsky (1947).

The first appearance of the "Coltrane changes" appear in the verse to the standard "Till the Clouds Roll By" by Jerome Kern. The bridge of the Richard Rodgers song and jazz standard "Have You Met Miss Jones?" (1937) predated Tadd Dameron's "Lady Bird", after which Coltrane named his "Lazy Bird", by incorporating modulation by major third(s). (highlighted yellow below) "Giant Steps" and "Countdown" may both have taken the inspiration for their augmented tonal cycles from "Have You Met Miss Jones?".

"Have You Met Miss Jones?" B section chord progression (bridge):

│ B♭Maj7 │ A♭m7 D♭7 │ G♭Maj7 │ Em7 A7 | │ DMaj7 │ A♭m7 D♭7 │ G♭Maj7 │ Gm7 C7 │

Major thirds cycle

The harmonic use of the chromatic third relation originated in the Romantic era and may occur on any structural level, for example in chord progressions or through key changes. The standard Western chromatic scale has twelve equidistant semitones. When arranged according to the circle of fifths, it looks like this.

svg

Precisely because of this equidistancy, the roots of these three chords can produce a destabilizing effect; if C, A♭ and E appear as the tonic pitches of three key areas on a larger level, the identity of the composition's tonal center can only be determined by the closure of the composition. — Demsey (1991)

Looking above at the marked chords from "Have You Met Miss Jones?", B♭, G♭ and D are spaced a major third apart. On the circle of fifths it appears as an equilateral triangle.

By rotating the triangle, all of the thirds cycles can be shown. Note that there are only four unique thirds cycles. This approach can be generalized; different interval cycles will appear as different polygons on the diagram.

Standard substitution

Although "Giant Steps" and "Countdown" are perhaps the most famous examples, both of these compositions use slight variants of the standard Coltrane changes (The first eight bars of "Giant Steps" uses a shortened version that does not return to the I chord, and in "Countdown" the progression begins on ii7 each time.) The standard substitution can be found in several Coltrane compositions and arrangements recorded around this time. These include: "26-2" (a reharmonization of Charlie Parker's "Confirmation"), "Satellite" (based on the standard "How High the Moon"), "Exotica" (loosely based on the harmonic form of "I Can't Get Started"), Coltrane's arrangement of "But Not for Me", and on the bridge of his arrangement of "Body and Soul".

In "Fifth House" (based on "Hot House", i.e. "What Is This Thing Called Love") the standard substitution is implied over an ostinato bass pattern with no chordal instrument instructed to play the chord changes. When Coltrane's improvisation superimposes this progression over the ostinato bass, it is easy to hear how he used this concept for his more free playing in later years.