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; it also sounds a little like 5L 3s. 20edo is the first edo with 5L 2m 1s and hence the first edo with a quasi-diatonic ternary scale.

The step pattern of pinedye is LLmLLmLs (chiral, 1sR), LLmLLsLm (chiral, 1sL), or LLsLLmLm (achiral, 1sC).

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) (for 1sR), GS(4/3, 5/4, 4/3) (for 1sL), or GS(5/4, 4/3, 4/3) (for 1sC), or in step vector form GS(2L+m, 2L+m, 2L+s), GS(2L+,, 2L+s, 2L+m), resp. GS(2L+s, 2L+m, 2L+m).