So many different harmonic relationships can be explored through the Coltrane Matrix. In this etude, I’ve superimposed a ii7-V7 chord progression as a substitution for the harmony in each measure. Take a look at the example below:
In the first measure is an F#-7b5, followed by a B7 (the Eb is the enharmonic equivalent of the D#), which is a ii7-V7 progression in the key of E minor. This “resolves” via voice-leading to the the next measure, which is the same pattern transposed down a major 3rd (D-7b5 to G7, which is the ii7-V7 for C minor), and then moves the same way into the third measure (A#-7b5 to D#7, which is the ii7-V7 of G# minor), finally resolving the #11 of C major in the last measure.
You’ll note that the superimposed progression still moves in accordance to the key shifts in the matrix (again, modulating down a major 3rd). In essence I’m replacing the key centers of each measure with E minor, C minor and G# minor, respectively. And even though there is a considerable amount of harmonic tension with these notes relative to the chords upon which they are superimposed (e.g., #11, 13, 3, 1, b13, #11, #9, 1 in the first three measures) the pattern works quite well, and adds a starkly different way to create a melodic sequence over this progression, while still maintaining the integrity of the form.
I’ve presented it here in all 12 keys for reference and practice. If you’d like to find even more unconventional ways to approach these chord changes, please take a look at my book, The Coltrane Matrix: 40 Unique Melodic Ideas In All 12 Keys. Click the links below for the .pdf version of this etude and to hear a midi sample of it: