Coltrane changes
Encyclopedia
In jazz harmony
Jazz harmony
Jazz harmony is the theory and practice of how chords are used in jazz music. Jazz bears certain similarities to other practices in the tradition of Western harmony, such as many chord progressions, and the incorporation of the major and minor scales as a basis for chordal construction, but...

, the Coltrane changes (Coltrane Matrix or cycle, also known as chromatic third relations and multi-tonic changes) are a harmonic progression
Chord progression
A chord progression is a series of musical chords, or chord changes that "aims for a definite goal" of establishing a tonality founded on a key, root or tonic chord. In other words, the succession of root relationships...

 variation using substitute chords over common jazz chord progressions. These substitution patterns were first demonstrated by jazz musician John Coltrane
John Coltrane
John William Coltrane was an American jazz saxophonist and composer. Working in the bebop and hard bop idioms early in his career, Coltrane helped pioneer the use of modes in jazz and later was at the forefront of free jazz...

 on the album Blue Train
Blue Train (album)
Blue Train is a hard bop jazz album by John Coltrane, released in 1957 on Blue Note Records, catalogue BLP 1577. Recorded at the Van Gelder Studio in Hackensack, New Jersey, it is Coltrane's second solo album, the only one he recorded for Blue Note as a leader, and the only one he conceived...

on the tunes "Lazy Bird
Lazy Bird
Lazy Bird is a musical composition by John Coltrane, first appearing on his 1957 album Blue Train.Its name is most likely a play on the title of the Tadd Dameron composition "Lady Bird": Coltrane biographer Lewis Porter has proposed a harmonic relationship between "Lady Bird" and the A section of...

" and "Moment's Notice". Coltrane continued his explorations on the 1960 album Giant Steps
Giant Steps
-Personnel:* John Coltrane — tenor saxophone* Tommy Flanagan — piano* Wynton Kelly — piano on "Naima"* Paul Chambers — bass* Art Taylor — drums* Jimmy Cobb — drums on "Naima"* Cedar Walton — piano on "Giant Steps' and Naima" alternate versions...

, and expanded upon the substitution cycle in his compositions "Giant Steps
Giant Steps (composition)
"Giant Steps" is a jazz composition by John Coltrane, first appearing as the first track on the album of the same name . The composition contains a rapid and improvised progression of chord changes through three keys shifted by major thirds, creating an augmented triad.-Title:The song title comes...

" and "Countdown", the latter of which is a reharmonized version of Miles Davis
Miles Davis
Miles Dewey Davis III was an American jazz musician, trumpeter, bandleader, and composer. Widely considered one of the most influential musicians of the 20th century, Miles Davis was, with his musical groups, at the forefront of several major developments in jazz music, including bebop, cool jazz,...

's "Tune Up." The ability to solo over the Giant Steps/Coltrane cycle remains one of the standards by which a jazz musician's improvising ability is measured.

The changes serve as a pattern of chord substitution
Chord substitution
In music theory, chord substitution is the use of a chord in the place of another related chord in a chord progression. 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...

s for the ii-V-I progression
II-V-I
The ii-V-I turnaround, ii-V-I progression, or ii V I even ii V VIII, also known as the dominant cadence, is a common cadential chord progression used in a wide variety of music genres, especially jazz harmony...

 (supertonic
Supertonic
In music or music theory, the supertonic is the second degree or note of a diatonic scale, one step above the tonic. In music theory, the supertonic chord is symbolized by the Roman numeral ii in a major scale, indicating that the chord is a minor chord , or ii in a natural minor scale, indicating...

-dominant
Dominant (music)
In music, the dominant is the fifth scale degree of the diatonic scale, called "dominant" because it is next in importance to the tonic,and a dominant chord is any chord built upon that pitch, using the notes of the same diatonic scale...

-tonic
Tonic (music)
In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

) and are noted for the tonally
Tonality
Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...

 unusual root
Root (chord)
In music theory, the root of a chord is the note or pitch upon which a triadic chord is built. For example, the root of the major triad C-E-G is C....

 movement down by major third
Major third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...

s (as opposed to the usual minor or major second
Major second
In Western music theory, a major second is a musical interval spanning two semitones, and encompassing two adjacent staff positions . For example, the interval from C to D is a major second, as the note D lies two semitones above C, and the two notes are notated on adjacent staff postions...

s, see steps and skips
Steps and skips
In music, a step, or conjunct motion, is a linear or successive interval between two pitches which are consecutive scale degrees. Any larger interval is called a skip , or disjunct motion...

, thus the "giant steps"), creating an augmented triad
Augmented triad
In music, an augmented triad is a triad, or chord, consisting of two major thirds . The term augmented triad arises from an augmented triad being a three note chord, or triad, whose top note is raised, or augmented...

.

Influences

David Demsey, saxophonist and Coordinator of Jazz Studies at William Paterson University, cites a number of influences leading toward's 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
Numerology
Numerology is any study of the purported mystical relationship between a count or measurement and life. It has many systems and traditions and beliefs...

 significance representing a "'magic triangle
Trimurti
The Trimurti is a concept in Hinduism "in which the cosmic functions of creation, maintenance, and destruction are personified by the forms of Brahmā the creator, Vishnu the maintainer or preserver, and Śhiva the destroyer or transformer," These three deities have been called "the Hindu triad" or...

,'" or, "the trinity
Trinity
The Christian doctrine of the Trinity defines God as three divine persons : the Father, the Son , and the Holy Spirit. The three persons are distinct yet coexist in unity, and are co-equal, co-eternal and consubstantial . Put another way, the three persons of the Trinity are of one being...

, God, or unity." However, as seen above, 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 et al.

Miles Davis
Miles Davis
Miles Dewey Davis III was an American jazz musician, trumpeter, bandleader, and composer. Widely considered one of the most influential musicians of the 20th century, Miles Davis was, with his musical groups, at the forefront of several major developments in jazz music, including bebop, cool jazz,...

, who mentored Coltrane in many ways, was in the late 1950s moving toward the modal
Modal jazz
Modal jazz is jazz that uses musical modes rather than chord progressions as a harmonic framework. Originating in the late 1950s and 1960s, modal jazz is characterized by Miles Davis's "Milestones" Kind of Blue and John Coltrane's classic quartet from 1960–64. Other important performers include...

 style demonstrated on Kind of Blue
Kind of Blue
Kind of Blue is a studio album by American jazz musician Miles Davis, released August 17, 1959, on Columbia Records in the United States. Recording sessions for the album took place at Columbia's 30th Street Studio in New York City on March 2 and April 22, 1959...

. 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
Sheets of sound
Sheets of sound was a term coined in 1958 by Down Beat magazine jazz critic Ira Gitler to describe the new, unique improvisational style of John Coltrane...

 style while playing with Davis and with pianist Thelonious Monk
Thelonious Monk
Thelonious Sphere Monk was an American jazz pianist and composer considered "one of the giants of American music". Monk had a unique improvisational style and made numerous contributions to the standard jazz repertoire, including "Epistrophy", "'Round Midnight", "Blue Monk", "Straight, No Chaser"...

 during this period.

Coltrane studied harmony
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...

 at the Granoff School of Music
Granoff School of Music
The Granoff School of Music is a music school in Philadelphia, Pennsylvania, USA, founded by Isadore Granoff , a Ukrainian immigrant.Alumni of Granoff include Dizzy Gillespie, Sonny Fortune and John Coltrane...

 in Philadelphia, exploring contemporary techniques and theory. He also spent much time studying the Thesaurus of Scale and Melodic Patterns by Nicolas Slonimsky
Nicolas Slonimsky
Nicolas Slonimsky was a Russian born American composer, conductor, musician, music critic, lexicographer and author. He described himself as a "diaskeuast" ; "a reviser or interpolator."- Life :...

 (1947), which additionally served as practice material. The first half of Giant Steps (melody and harmony) is contained in the Preface of Slonimsky's book.
The bridge of the Rodgers and Hart
Rodgers and Hart
Rodgers and Hart were an American songwriting partnership of composer Richard Rodgers and the lyricist Lorenz Hart...

 song and jazz standard
Jazz standard
Jazz standards are musical compositions which are an important part of the musical repertoire of jazz musicians, in that they are widely known, performed, and recorded by jazz musicians, and widely known by listeners. There is no definitive list of jazz standards, and the list of songs deemed to be...

 "Have You Met Miss Jones?
Have You Met Miss Jones?
"Have You Met Miss Jones?" is a popular song that was written for the musical comedy, I'd Rather Be Right. The music was written by Richard Rodgers and the lyrics by Lorenz Hart. The song was published in 1937....

" (1937) predated Tadd Dameron
Tadd Dameron
Tadley Ewing Peake "Tadd" Dameron was an American jazz composer, arranger and pianist. Saxophonist Dexter Gordon called Dameron the "romanticist" of the bop movement, while reviewer Scott Yanow writes that Dameron was the "definitive arranger/composer of the bop era".-Biography:Born in Cleveland,...

's "Lady Bird", after which Coltrane named his "Lazy Bird
Lazy Bird
Lazy Bird is a musical composition by John Coltrane, first appearing on his 1957 album Blue Train.Its name is most likely a play on the title of the Tadd Dameron composition "Lady Bird": Coltrane biographer Lewis Porter has proposed a harmonic relationship between "Lady Bird" and the A section of...

", by incorporating modulation by major third
Major third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...

(s). (shown by the * 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):


| * | | * | | * | | * | ||
| BbM7 | Abm7 Db7 | GbM7 | Em7 A7 | DM7 | Abm7 Db7 | GbM7 | Gm7 C7 ||

Coltrane substitution

The Coltrane substitution, Coltrane changes, or "'Countdown' formula" is as follows. Given the 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:
ii7 | | V7 | I ||
dm7 Eb7 | Ab B7 | E G7 | C ||
m2 P4 m3 P4 m3 P4

Notice a dominant seventh chord
Dominant seventh chord
In music theory, a dominant seventh chord, or major minor seventh chord,is a chord composed of a root, major third, perfect fifth, and minor seventh. It can be also viewed as a major triad with an additional minor seventh...

 preceding and thus tonicizing
Tonicization
In music, tonicization is the treatment of a pitch other than the overall tonic as a temporary tonic in a composition. Tonicization is achieved through the use of the scale and harmonies of the tonicized key. The most common method of tonicization uses leading tones, dominant-tonic chord...

 a major chord on C and also E and Ab, both a major third from C.
(V7 | I)(V7 | I)(V7 | I)
Eb7 | Ab B7 | E G7 | C
This also may begin on C, as on "Giant Steps
Giant Steps (composition)
"Giant Steps" is a jazz composition by John Coltrane, first appearing as the first track on the album of the same name . The composition contains a rapid and improvised progression of chord changes through three keys shifted by major thirds, creating an augmented triad.-Title:The song title comes...

", giving:
C Eb7 | Ab B7 | E G7 | C ||
m3 P4 m3 P4 m3 P4

The 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
Modulation (music)
In music, modulation is most commonly the act or process of changing from one key 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...

. The standard Western chromatic scale
Chromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...

 has twelve equidistant semitones. When arranged according to the circle of fifths
Circle of fifths
In music theory, the circle of fifths shows the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys...

, it looks like this:


Looking above at the marked chords from "Have You Met Miss Jones?", B-G-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 cycle
Interval cycle
In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class. In other words a collection of pitches by starting with a certain note and going up by a certain interval until the original note is reached In music, an interval cycle is a collection...

s will appear as different polygons on the diagram.

"Tune Up"

These are the first eight bars of the Miles Davis composition "Tune Up." The chord changes are relatively simple, a straightforward application of the ii-V-I progression
II-V-I
The ii-V-I turnaround, ii-V-I progression, or ii V I even ii V VIII, also known as the dominant cadence, is a common cadential chord progression used in a wide variety of music genres, especially jazz harmony...

, which is extremely common in jazz.

| ii | V | I | ii | V | I ||
| Em7 | A7 | DM7 - | Dm7 | G7 | CM7 - ||

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 chord gets 4 beats.

"Countdown"

The Changes below show Coltrane's substitution of chord changes over "Tune Up". When writing jazz tunes that substitute chords, it is very common to title the tune with a play on words of the name of the original composition, hence "Tune Up" became "Countdown". 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 | BbM7 Db7 | GbM7 A7 | DM7 | Dm7 Eb7 | AbM7 B7 | EM7 G7 | CM7 ||
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 2 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", 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(*) 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
Lazy Bird
Lazy Bird is a musical composition by John Coltrane, first appearing on his 1957 album Blue Train.Its name is most likely a play on the title of the Tadd Dameron composition "Lady Bird": Coltrane biographer Lewis Porter has proposed a harmonic relationship between "Lady Bird" and the A section of...

", also features two tonal centers a major third apart in its A section.

"Giant Steps"

The Giant Steps cycle is the culmination of Coltrane's theories applied to a completely new chord progression:
Coltrane uses the Coltrane cycle in ascending Major 3rd tonal transpositions in the opening bars and then ascending ii V I progressions separated by a major 3rd 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|
| BM7* D7 | GM7* Bb7 | EbM7* | Am7 D7 | GM7* Bb7 | EbM7* F#7 | BM7* |
Ascending/Descending ii V I progression separated by a Major 3rd (Tonal centers E - G - B - E - B)
| ii V | I | ii V | I | ii V | I | ii V | I | ii V :||
| Fm7 Bb7 | EbM7* | Am7 D7 | GM7* | C#m7 F#7 | BM7* | Fm7 Bb7 | EbM7* | C#m7 F#7 :||
This diagram shows what scales are used for the different chords:
BMaj7
B Maj scale
D7 to GMaj7
G Maj scale
B7 to EMaj7
Eb Maj scale
Am7 to D7 to Gmaj7
G Maj scale
B7 to EMaj7
Eb Maj scale
F7 to BMaj7
B Maj scale
Fm7 to B7 to EMaj7
Eb Maj scale
Am7 to D7 to GMaj7
G Maj scale
Cm7 to F7 to BMaj7
B Maj scale
Fm7 to Bb7 to EMaj7
Eb Maj scale
Cm7 to F7
B Maj scale

Solo Formula

Coltrane's Solo Improvisation on the Giant Steps changes uses several patterns that he derived, practiced and employed while he played with Miles Davis and during his solo career. The Coltrane solo scale and chord choices have been analyzed by Jazz Theorist David Baker (and many others). On 4/4 tunes 'Trane breaks down the 4 beats into eight eighth notes. Most bebop jazz standards typically have two quarter beats per chord change. Individual two beat patterns have four eight notes. Coltrane uses these four note groups
Four note group
Four note group patterns are one of many ways used to formulate improvised solos in jazz. "Four-Note Grouping [sic] is an improvisation technique that uses major and minor triads along with specific passing notes as a means of generating lines...

 to play either a scale fragment in the key of the chord change, an arpeggio of the chord change or a bebop pattern. Although the chord changes are typically for either 2 beats or a whole measure, Trane would often stretch or shorten the duration he played on a particular chord to really use tension and release in a more artistic way.

Sample

These variations were used to compose other Coltrane tunes based on other jazz standards:

The 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 doesn't return to the "I" chord, and in "Countdown" the progression begins on the IIm7 each time.). The standard substitution can be found in several Coltrane compositions and arrangements all recorded around this time. These include: "26-2" (a re-harmonization of Charlie Parker's "Confirmation"), "Satellite" (based on the standard "How High the Moon"), the original tune "Exotica," Coltrane's arrangement of the standard "But Not for Me," and on the bridge of his arrangement of the famous ballad "Body and Soul."

In addition, Coltrane's tune "Fifth House" (based on "What is This Thing Called Love") is particularly notable because the standard substitution is implied over an ostinato
Ostinato
In music, an ostinato is a motif or phrase, which is persistently repeated in the same musical voice. An ostinato is always a succession of equal sounds, wherein each note always has the same weight or stress. The repeating idea may be a rhythmic pattern, part of a tune, or a complete melody in...

 bass pattern, with nobody actually playing 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.

Further reading

  • Yamaguchi, Masaya (2002). "A Creative Approach to Multi-Tonic Changes: Beyond Coltrane's Harmonic Formula", Annual Review of Jazz Studies 12. ISBN 0810850052.

External links

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