Superpyth temperament can be thought of as a mirror opposite of meantone temperament. In meantone temperament four fifths reduced an octave is equated to the 5-limit just major third 5/4, where 4 pure fifths of 3/2 reduced an octave give 81/64, larger than 5/4 by the meantone comma, 81/80. In quarter comma meantone each fifth is flattened by a quarter of this comma so that four of them reduced an octave give an exact 5/4 and the meantone comma is tempered out. In superpyth four fiths reduced an octave is instead taken to be equivalent to the septimal, supermajor third 9/7. Two fourth then give the harmonic seventh 7/4. In quarter-comma superpyth  each fifth is sharpened by a quarter of the archytas comma 64/63, the difference between two fourth of 4/3 and a harmonic seventh of 7/4 then tempered out and fourth fifths reduced an octave giving a pure 9/7. Quarter-comma meantone can be well approximated in 31edo (equal divisions of the octave), and quarter-comma superpyth in 22edo. Diatonic notes in Meantone are 5-limit (subgroup 2.3.5), where chromatic intervals may be septimal (7-limit), i.e. the augemented sixth is 7/4 and the diminished fourth is 9/7. Diatonic notes in superpyth are of the 2.3.7 subgroup, with major and minor thirds at 9/7 and 7/6 respectively. Chromatic intervals may be 5-limit, ie an augmented second of 5/4 and a diminished fourth of 6/5. Using a gamut of Ab-C# (traversed by fifths - the generator), the black notes host the octave species of the 5-limit enharmonic trichord, the 5-note scale: 1/1:5/4:4/3:3/2:15/8, our regular 5-limit M3, P4, P5 and M7. This study is a 5 chord riff that makes use of the 5-limit chromatic intervals of Superpyth[12] (12 notes of superpyth temperament generated by a continuous string of fifths), along with the diatonic intervals. The chords include the diatonic subminor seventh, subminor major seventh and included supermajor seventh, along with the chromatic major and minor seventh chords.

Superpyth[12] chromatic riff

Clarinet, sax, and keyboard player; singer, composer, and theorist.

Superpyth[12] chromatic riff

Lillian Hearne