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"). [1] Coltrane continued his explorations on the 1960 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.
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.[ citation needed ]
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." [2] 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. [2] 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." [3] He developed his sheets of sound style while playing with Miles Davis and with pianist Thelonious Monk during this period. [4] 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. [5]
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). [6]
A series of similar-sounding chord changes occurs in "Ondine", the first movement of Maurice Ravel's 1908 piano suite, "Gaspard de la nuit."
Other early appearances include the verse to the standard "Till the Clouds Roll By" (1917) by Jerome Kern. [7] 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). [8] (highlighted yellow below) "Giant Steps" and "Countdown" may both have taken the inspiration for their augmented tonal cycles from "Have You Met Miss Jones?". [9]
│ | B♭Maj7 | │ | A♭m7 | D♭7 | │ | G♭Maj7 | │ | Em7 | A7 | │ | DMaj7 | │ | A♭m7 | D♭7 | │ | G♭Maj7 | │ | Gm7 | C7 | │ |
The Coltrane substitution, Coltrane changes, or Countdown formula, is as follows. Start with a ii–V–I turnaround lasting four measures:
ii7 | V7 | I | I | |||||
│ | Dm7 | │ | G7 | │ | C | │ | C | │ |
with the dominant chord (V7) preceding the tonic (I).
One substitutes two chords for each of the first three: [10]
Notice a dominant seventh chord preceding and thus tonicizing a major chord on C and also E and A♭, both a major third from C.
V7 | I | V7 | I | V7 | I | |||
E♭7 | │ | A♭ | B7 | │ | E | G7 | │ | C |
This also may begin on C, as on "Giant Steps", giving:
│ | C | E♭7 | │ | A♭ | B7 | │ | E | G7 | │ | C | │ | ||||
╲╱ m3 | ╲╱ P4 | ╲╱ m3 | ╲╱ P4 | ╲╱ m3 | ╲╱ P4 |
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. [11] The standard Western chromatic scale has twelve equidistant semitones. [12] When arranged according to the circle of fifths, it looks like this:
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) [11]
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.
These are the first eight bars of the Miles Davis composition "Tune Up".[ citation needed ] The chord changes are relatively simple, a straightforward application of the ii–V–I progression, which is extremely common in jazz.
ii | V | I | ii | V | I | |||||||||||
│ | Em7 | │ | A7 | │ | DMaj7 | │ | DMaj7 | │ | Dm7 | │ | G7 | │ | CMaj7 | │ | CMaj7 | │ |
The chord progression is a standard ii7–V7–I progression in D major and then in C major. Assume that the time signature is 4
4 and that each ii and V chord gets four beats and the I chord gets eight beats.
The changes below show Coltrane's substitution of chord changes over "Tune Up". The ii–V–I progression from "Tune Up" still appears but is enhanced with several transition chords that lead to a more complex harmonic progression.
ii | V | I | ii | V | I | |||||||||||||||||||
│ | Em7 | F7 | │ | B♭Maj7 | D♭7 | │ | G♭Maj7 | A7 | │ | DMaj7 | │ | Dm7 | E♭7 | │ | A♭Maj7 | B7 | │ | EMaj7 | G7 | │ | CMaj7 | │[ citation needed ] |
In the standard Coltrane change cycle the ii–V–I is substituted with a progression of chords that cycle back to the V–I at the end. In a 4
4 piece, each chord gets two beats per change.
Coltrane developed this modified chord progression for "Countdown", which is much more complex. At its core, "Countdown" is a variation of "Tune Up", [13] but the harmonic substitutions occur rapidly and trick the listener into thinking that they are listening to a completely unrelated tune. The ii, V and I remain, but in between are other chords (highlighted in yellow and blue) from the major thirds cycle centered around each I. Preceding the first chord of each major thirds cycle is its V chord.
An earlier Coltrane piece, "Lazy Bird", also features two tonal centers a major third apart in its A section.
The "Giant Steps" cycle is the culmination of Coltrane's theories applied to a completely new chord progression. Coltrane uses the cycle in descending major third tonal transpositions in the opening bars and then ascending ii–V–I progressions separated by a major third in the second section of "Giant Steps". The second section is basically the inverse of the bridge section described in "Have You Met Miss Jones" above.
I | Coltrane substitution cycle | ii | V | I | Coltrane substitution cycle | ||||||||||||||||
│ | BMaj7 | D7 | │ | GMaj7 | B♭7 | │ | E♭Maj7 | │ | Am7 | D7 | │ | GMaj7 | B♭7 | │ | E♭Maj7 | F♯7 | │ | BMaj7 | │[ citation needed ] |
Ascending/descending ii–V–I progression separated by a major third (tonal centers E♭, G, B, E♭, B)
ii | V | I | ii | V | I | ii | V | I | ii | V | I | ii | V | ||||||||||||||
│ | Fm7 | B♭7 | │ | E♭Maj7 | │ | Am7 | D7 | │ | GMaj7 | │ | C♯m7 | F♯7 | │ | BMaj7 | │ | Fm7 | B♭7 | │ | E♭Maj7 | │ | C♯m7 | F♯7 | │[ citation needed ] |
This table shows which scales are used for the different chords:
Chords | Scale | Change in scale |
---|---|---|
BMaj7 | B major | I |
D7 → GMaj7 | G major | V-I |
B♭7 → E♭Maj7 | E♭ major | V-I |
Am7 → D7 → GMaj7 | G major | ii-V-I |
B♭7 → E♭Maj7 | E♭ major | V-I |
F♯7 → BMaj7 | B major | V-I |
Fm7 → B♭7 → E♭Maj7 | E♭ major | ii-V-I |
Am7 → D7 → GMaj7 | G major | ii-V-I |
C♯m7 → F♯7 → BMaj7 | B major | ii-V-I |
Fm7 → B♭7 → E♭Maj7 | E♭ major | ii-V-I |
C♯m7 → F♯7 | B major | ii-V |
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".[ citation needed ]
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.
In music, harmony is the concept of combining different sounds together in order to create new, distinct musical ideas. Theories of harmony seek to describe or explain the effects created by distinct pitches or tones coinciding with one another; harmonic objects such as chords, textures and tonalities are identified, defined, and categorized in the development of these theories. Harmony is broadly understood to involve both a "vertical" dimension (frequency-space) and a "horizontal" dimension (time-space), and often overlaps with related musical concepts such as melody, timbre, and form.
In a musical composition, a chord progression or harmonic progression is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice era of Classical music to the 21st century. Chord progressions are the foundation of popular music styles, traditional music, as well as genres such as blues and jazz. In these genres, chord progressions are the defining feature on which melody and rhythm are built.
In music, modulation is the change from one tonality to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization.
Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.
In music theory, the circle of fifths is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music, the sequence is: C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯, E♯ (F), C. This order places the most closely related key signatures adjacent to one another. It is usually illustrated in the form of a circle.
A secondary chord is an analytical label for a specific harmonic device that is prevalent in the tonal idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization.
An augmented triad is a chord, made up of two major thirds. The term augmented triad arises from an augmented triad being considered a major chord whose top note (fifth) is raised. When using popular-music symbols, it is indicated by the symbol "+" or "aug". For example, the augmented triad built on A♭, written as A♭+, has pitches A♭-C-E:
In music, function is a term used to denote the relationship of a chord or a scale degree to a tonal centre. Two main theories of tonal functions exist today:
Chromaticism is a compositional technique interspersing the primary diatonic pitches and chords with other pitches of the chromatic scale. In simple terms, within each octave, diatonic music uses only seven different notes, rather than the twelve available on a standard piano keyboard. Music is chromatic when it uses more than just these seven notes.
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."
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.
"Giant Steps" is a jazz composition by American saxophonist John Coltrane. It was first recorded in 1959 and released on the 1960 album Giant Steps. The composition features a cyclic chord pattern that has come to be known as Coltrane changes. The composition has become a jazz standard, covered by many artists. Due to its speed and rapid transition through the three keys of B major, G major and E♭ major, Vox described the piece as "the most feared song in jazz" and "one of the most challenging chord progressions to improvise over" in the jazz repertoire.
The Andalusian cadence is a term adopted from flamenco music for a chord progression comprising four chords descending stepwise – a iv–III–II–I progression with respect to the Phrygian mode or i–VII–VI–V progression with respect to the Aeolian mode (minor). It is otherwise known as the minor descending tetrachord. Traceable back to the Renaissance, its effective sonorities made it one of the most popular progressions in classical music.
In music, the axis system is a system of analysis originating in the work of Ernő Lendvai, which he developed in his analysis of the music of Béla Bartók.
In jazz, a turnaround is a passage at the end of a section which leads to the next section. This next section is most often the repetition of the previous section or the entire piece or song.
The ii–V–I progression is a common cadential chord progression used in a wide variety of music genres, including jazz harmony. It is a succession of chords whose roots descend in fifths from the second degree (supertonic) to the fifth degree (dominant), and finally to the tonic. In a major key, the supertonic triad (ii) is minor, and in a minor key it is diminished. The dominant is, in its normal form, a major triad and commonly a dominant seventh chord. With the addition of chord alterations, substitutions, and extensions, limitless variations exist on this simple formula.
Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.
In music, harmonization is the chordal accompaniment to a line or melody: "Using chords and melodies together, making harmony by stacking scale tones as triads".
The Lydian Chromatic Concept of Tonal Organization is a 1953 jazz music theory book written by George Russell. The book is the founding text of the Lydian Chromatic Concept (LCC), or Lydian Chromatic Theory (LCT). Russell's work postulates that all music is based on the tonal gravity of the Lydian mode.
"26-2" is a musical composition written by American jazz musician John Coltrane. The song was recorded by Coltrane in 1960, but it released ten years later by Atlantic Records on an album entitled The Coltrane Legacy with a rhythm section composed of McCoy Tyner on piano, Steve Davis on bass, and Elvin Jones on drums. The composition itself is a contrafact of Charlie Parker's tune "Confirmation", with harmonic alterations to the original chord changes used by Coltrane in a number of his compositions. This harmonic modification is commonly known as Coltrane Changes, which have been most notably used in Coltrane's "Giant Steps". "26-2" is one of several contrafacts by Coltrane, others including "Countdown", a contrafact of Miles Davis's "Tune Up"; and "Satellite" from the album Coltrane's Sound, which is based upon the chord progression of "How High the Moon". Coltrane plays the first statement of the melody on tenor saxophone and switches to soprano saxophone for the last statement of the melody on the recorded version.
"Countdown" is a hardbop jazz standard composed by American jazz saxophonist John Coltrane that was first featured on his fifth studio album, Giant Steps, in 1960. The song is a contrafact of Miles Davis's "Tune Up", which is reharmonized to the Coltrane changes. The original recording has been described as having "resolute intensity. .. [that] does more to modernize jazz in 141 seconds than many artists do in their entire careers".