Coltrane Cycles and the Blues

Jazz is a syncretistic music, and I therefore believe that it requires a heterogeneous approach to analysis. 

In a previous post, I discussed Coltrane's chromatic major third cycles in terms of harmonic implications derived from the principles of tonality. Scholars like William Rothstein, Matthew Bribitzer-Stull, and David Kopp have traced the history of the chromatic major third full cycle (I-bVI-III#-I) back to examples in Schubert and Rossini, and they demonstrate how such chromatic mediant relationships abounded throughout nineteenth-century music. It is apparent that Coltrane's application of the major third cycle belongs in this lineage, perhaps as mediated by Slonimsky. 

It would be an obvious mistake, however, to neglect to have an ear to the blues when analyzing jazz music, especially the music of an artist like John Coltrane. 

In his book Origins of the Popular Style, Peter van der Merwe persuasively describes the melodic practice of the blues as consisting partly of a "process of piling up thirds" (124):

"In short, the blues mode takes the form of a ladder of thirds, but it is a flexible ladder that can be extended up or down at will." (125)

Listening to any of his improvisations on "Impressions" reveals that what is typically misconstrued as "Dorian modality" is instead Coltrane's version of just such a blues-derived, "ladder-of-thirds" melodicism. The so-called "mode" is most often a six-note scale abstracted from the stacks of thirds on top of and below the tonic: i.e., D-F-A-C and D-B-G. 

There is, then, a sense in which it might be appropriate to think of Coltrane's emphasis on chromatic (major and minor) third relations and cycles as a translation into harmonic terms of the "ladder of thirds" melodic concept that Van der Merwe finds central to blues practice. When Coltrane prolongs a harmony with digressions through third-related keys, I suggest that he is "composing-out" the pendular or stacked thirds of a higher-level blues melody.

Another element of blues melody comes to the fore in conjunction with Coltrane's mediant-based harmony: the variable third. According to Van der Merwe, 

"...[in] genuine blues tunes there will be no question of a clear-cut contrast such as we find between the classical major and minor... major and minor or neutral thirds may be juxtaposed throughout." (120).

When Coltrane moves from a minor tonic to the major mediant, for example, or from a major tonic to the major submediant, the major third and minor third of the tonic key will be intermixed. As just one example from Coltrane's playing, this excerpt from the eleventh and twelfth bars of "Countdown" illustrates: 

Here Coltrane is in the act of traversing from D major to B-flat major via F7, but in these five beats one hears only the collection (D E F F# G A). These are simply scale steps 1-2-3-4-5 in D, where scale step 3 includes both the major and minor variants. 

When taken all together, the pitch classes of the three triads contained in a chromatic major third cycle (I-bVI-III#-I) yield the hexatonic collection, set class (014589). This collection consists of two augmented triads a semitone apart. Coltrane used two hexatonic scales as a basis for his composition "One Down, One Up," for instance.

Notably, the hexatonic collection contains major and minor triads built on shared roots. Thus a possible non-discrete tetrachordal subset of the hexatonic collection is set class (0347), shown in the example above. Bearing the intervals of a minor third, major third, and fifth, an example of this set class is (D F F# A). This is a "triad" with the variable third that Van der Merwe describes as a hallmark of blues melody.

It appears therefore that the hexatonic collection and the blues have a certain affinity, which John Coltrane succeeded in making audible.