"The Red Planet (Miles' Mode)"

Often attributed to John Coltrane,"Miles' Mode" is probably the best known jazz composition making use of dodecaphonic technique. Vladimir Simosko and Dave Wild have made a compelling argument, however, that it was Eric Dolphy, doubtlessly well-acquainted with the work of Arnold Schoenberg, who wrote the piece and titled it "The Red Planet." 

"The Red Planet" contains a brilliant, microcosmic application of some basic tools of twelve-tone technique. (In registering the obvious semantic objection, I will also point out below that Dolphy's musical purposes are clearly non-Schoenbergian.) It is widely understood that the melody of the piece consists of a prime statement of the tone row followed by its retrograde, creating a musical palindrome:

B D E C# F# G# A G C Bb F Eb  "  Eb F Bb C G A G# F# C# E D B 

The modal arrangement of the tone row lends a distinct antecedent/consequent sound to these phrases. In miniature, the melodic contour of the antecedent suggests the statement of a basic idea (B D E C#), a repetition of the basic idea in the form of a response transposed up a fifth (F# G# A G), and a liquidation of the motive in approach of the caesura (C Bb F Eb). (This terminology is borrowed, however inappropriately, from William E. Caplin's Classical Form.) The first seven tones of the row outline B Dorian, and the remaining five comprise a C minor pentatonic collection. Thus, we hear the antecedent establish B minor, which is then destabilized by a shift to the tension-heightening C minor; the consequent phrase returns us to the initial B minor. As a member of both B Dorian and C Dorian, pitch-class (A) serves as the pivot between the two. The B minor modality is ultimately affirmed by the subsequent four-measure "coda" containing only the pitch-classes (B D E F#). The T1 transposition heard here is a device commonly referred to as "side-slipping," and it also defines the harmonic relation between the A- and B-sections of the modal jazz classics "So What" and "Impressions."

Exclusively deploying ordered interval-classes 2, 3, and 5, the tone row operative here does not pursue the typical Second Viennese School tonality-avoidant aesthetic, often characterized by the prevalence of interval-classes 1 and 6. Therefore, we can show the voice-leading of "The Red Planet" thusly:

Notice in the foreground graph how the primary tones seem to reference a chromatically altered 1-2-3 stepwise ascent (B-C-D#). Also note in the background graph how the C and Eb smoothly resolve down by half steps, in the appropriate registers, to the terminal D and B.

It is significant that the antecedent phrase "cadences" on Eb/D#: nothing subverts the minor sound more deeply than the interposition of the major third scale degree. Of course, the major third relation is integral to John Coltrane's harmonic conception generally. In his improvised bridge phrases (both in and out) on "Miles' Mode," Coltrane departs from B minor to tonicize Eb major as well as B major before returning to B minor:

Incidentally, Coltrane's sense of symmetry---even over wide swaths of time---is profound: on the in bridge he first transforms B minor to Eb major by a T4 transposition of the root; on the out bridge, complementarily, he transposes first at T8 to map root B onto G. 

The relative relationship between Eb major and C minor connects Coltrane's tonicizing improvisations to the "side-slipping" transposition of Dolphy's composition. In fact, that connection already exists in Dolphy's melody, as (G C Bb F Eb) could be heard as either an Eb major pentatonic or a C minor pentatonic collection given the absence of any harmonic corroboration. 

Interestingly, the inversion that maps Eb onto C (namely, I3, or inversion at index number 3) also functions within the tone row of "The Red Planet" to provide cohesiveness in pitch-class space. Each set of four consecutive pitch-classes in the row consists of two initial pitch-classes inverted about I3 to generate the following two. That is:

I3(B D)=(E C#); 
I3(F# G#)=(A G);
I3(C Bb)=(F Eb).

In just eight measures, then, Dolphy's composition uses basic dodecaphonic technique to create a sense of harmonic movement even within a modal context and living, soulful, well-balanced phrases as well as consistent inversional symmetry within subsets of the row. All of which provides a fertile basis for improvisational elaboration by a master like Coltrane.