This etude is an except from my book, The Coltrane Matrix: 40 Unique Melodic Ideas In All 12 Keys.
One of most compelling harmonic progressions in modern jazz is the Coltrane Matrix (also called the Coltrane Changes and Coltrane Cycle). Perhaps best known from John Coltrane’s iconic composition, Giant Steps, the matrix is also used as a reharmonization of many ii7-V7 based tunes and compositions. In essence, it’s the harmonic division of the octave into three equal parts, via dominant 7th chords, which returns to the starting tonality. (In the key of C, for example: CMaj7-Eb7-AbMaj7-B7-EMaj7-G7-CMaj7). It has very strong sounding tonal shifts (Giant Steps is an apt description), and is a very useful template for cultivating and expanding harmonic and melodic vocabulary in improvisation. There are many, many possibilities.
In this etude I use a triad pair combination to move through the secondary and upper partial harmony of the chords. Look at the example below:
For each major chord there is a major triad formed from the 5th degree of the scale (G Major in the first measure), and for each dominant chord there is an augmented triad formed from the 2nd degree of the scale (F Augmented in the first measure). The pattern continues, with the triads descending in whole steps, slightly “disguising” the root movement of the chords. Each augmented triad adds a raised 11th to the sound of the dominant 7th chord. And as you’ll notice, each augmented chord is simply an inversion of the same chord: F, A, C# (Db).
I’ve purposely avoided using voice leading to connect the triads in order to create a more “angular” sound (until the final dominant 7th chord through tonic). Feel free to experiment with connecting all the triads via voice leading. Again, if you are interested in exploring this chord progression further, check out my book, The Coltrane Matrix: 40 Unique Melodic Ideas In All 12 Keys.
Click the links below for a pdf copy of this etude and to hear a midi sample of it: