Pinedye

Pinedye (also denoted 1s in groundfault's aberrismic theory) is a quasi-diatonic scale pattern with step signature 5L 2M 1s. The name pinedye is a blend of pine (7L1s) and diatonic. 20edo is the first edo with 5L 2M 1s and hence the first edo with a quasi-diatonic ternary scale.

The standard untempered 2.3.5 interpretation for pinedye has L = 10/9, M = 27/25, s = 81/80. Pental pinedye has generator sequence GS(4/3, 4/3, 5/4) or GS(5/4, 4/3, 4/3), or in step vector form GS(2L+M, 2L+M, 2L+s) or GS(2L+s, 2L+M, 2L+M).