F G D Ab Db C D Eb Ab Db A F D Ab B E B Db Eb Bb C G D E Gb G Ab F (the modulations beginning at 4:54) #ALoveSupreme50
— Miles Okazaki (@milesokazaki) December 9, 2014
Ethan Iverson replied to point out that this sequence exhibits full chromatic saturation. Okazaki responded with a quote from Ravi Coltrane, and a photo from John Coltrane's score indicating that the inclusion of transpositions through all twelve keys was intentional.
@milesokazaki As you know, this has all 12 keys. Any other mathematical reason for this particular sequence? cc: @dan__voss
— Ethan Iverson (@ethan_iverson) December 9, 2014
@ethan_iverson I've heard differing opinions. In Kahn's book, Ravi says "deliberately random." Coltrane's score says: pic.twitter.com/FDDwvDSi3Z
— Miles Okazaki (@milesokazaki) December 9, 2014
I answered by listing the transpositions in terms of interval class, which highlights how transpositions by whole-steps and fourths (ic2 and ic5) predominate. As Lewis Porter showed, these intervals—which also comprise the set-class (025)—underlie the composition of the entire suite.
.@ethan_iverson @milesokazaki Transpositions by interval class: 256512155443635522525522113 Steps &fourths prevail as elsewhere in the suite
— dan voss (@dan__voss) December 9, 2014
We could certainly speculate about why Coltrane found it necessary to "move freely" "in all 12 keys." But perhaps the indication in his score to "start & end in E♭ concert minor" is more suggestive. Indeed, I find myself inclined to hear the sequence of transpositions—despite the chromaticism—as fairly tonal in its higher-level voice-leading.
Coltrane's transpositions of the (025) motif initially outline an F minor triad. There is a step-wise ascent to the third, with the second scale-step G expanded by its lower dominant, and the fifth, displaced to the lower octave, is approached by its upper neighbor D♭. Next the seventh is reached by step, extending the tonic F minor triad to a seventh chord.
The transpositions then proceed through two clicks on the circle of fifths to the submediant, D♭. To my hearing, this previously-foreshadowed upper neighbor (indicated by the flags above) to the fifth degree of the tonic F minor is prolonged and transferred to the lower register. The rising fourth of A♭ to D♭ is repeated as a transposition up a semitone and expanded by arpeggiation from the lower third. I have spelled this "D minor triad" enharmonically as E♭♭ to indicate that it can be heard to function as a Phrygian II to the prolonged D♭, and because the preceding D♭ does not sound merely like a chromatic neighbor but is additionally reinterpreted as a leading tone. Subsequently, Coltrane returns to the A♭/D♭ pole and inverts it to prolong a descending D♭ minor triad, embellished by leaps up to the seventh.
At this point the initial ascent through the F minor seventh chord is roughly reversed. The original register is reinstated and E♭ falls back to C, which is immediately preceded by the only instance of the subdominant, B♭. Then, as earlier, the second scale degree is expanded, this time as a prolongation of the dominant of the dominant through a step-wise ascent from the lower fifth. Finally, A♭ falls to tonic F to complete the structure in appropriate blues fashion.
While Coltrane's sequence does not by any means possess a typical Schenkerian structure, its voice-leading nonetheless evokes a tonal outline. Rather than construct a step-wise Urlinie, Coltrane stacks thirds in a manner common both in his music and to blues music generally; a central elaboration follows, then a very roughly symmetrical return. (In the graph below, parentheses indicate that the register has been idealized.)
Coltrane may have been "moving freely" through these transpositions, but the resulting music is hardly "random." The higher-level voice-leading reveals an emergent tonal structure which shows Coltrane's improvisation on A Love Supreme to be as ordered and coherent as his composing.
