John Coltrane's landmark tune Giant Steps (1960) utilizes a harmonic plan which showcases 12-edo tuning's membership in both the aristoxenean and the augmented temperament families: the former by repetition of the dominant-7th-to-tonic functions, and the latter by the arrangement of tonics as a cycle of major-3rds. The chord progressions are as follows:
Bz Dx | Gz Bbx | Ebz | Am Dx | [G]: V | I | | II V | [Eb]: | V | I | | [B]: I | | | | Gz Bbx | Ebz F#x | Bz | Fm Bbx | [G]: I | | | | [Eb]: V | I | | II V | [B]: | V | I | | Ebz | Am Dx | Gz | C#m F#x | [G]: | II V | I | | [Eb]: I | | | | [B]: | | | II V | Bz | Fm Bbx | Ebz | C#m F#x | [G]: | | | | [Eb]: | II V | I | | [B]: I | | | II V |
Below is another version of the analysis, using more familiar abbreviations for the chord symbols: "M7" = major-7th, "m7" = minor-7th, "7" = dominant-7th:
BM7 D7 | GM7 Bb7 | EbM7 | Am7 D7 | [G]: V | I | | II V | [Eb]: | V | I | | [B]: I | | | | GM7 Bb7 | EbM7 F#7 | BM7 | Fm7 Bb7 | [G]: I | | | | [Eb]: V | I | | II V | [B]: | V | I | | EbM7 | Am7 D7 | GM7 | C#m7 F#7 | [G]: | II V | I | | [Eb]: I | | | | [B]: | | | II V | BM7 | Fm7 Bb7 | EbM7 | C#m7 F#7 | [G]: | | | | [Eb]: | II V | I | | [B]: I | | | II V |
31-edo is the first non-12-edo tuning i tried for Giant Steps. I chose 31-edo because it offers low error for prime factors 5 and 7, which are featured prominently in jazz, and its error for 3 is good enough to preserve the approximation to pythagorean root-movement. The arrangement is my own, as i play it on the piano, and the instrument timbre used is acoustic guitar. The original was done in Tonescape®, and all the other formats were generated automatically from that by Tonescape; below are the downloadable links:
Below is a screenshot of the opening chord being played in Tonescape, with the Lattice using Rectangular Geometry:
Below is the same chord, with the Lattice using Closed Curved crumpled-napkin Geometry:
The chords use the same spelling as in the analysis above, and therefore their progressions do not always follow identical pitch patterns in 31-edo as they do in 12-edo. I plan to make another 31-edo version which does preserve the same pitch patterns, but this will modulate into remote keys which in 12-edo are enharmonic equivalents but in 31-edo are not.