Diaslen

Diaslen (also denoted 4s in groundfault's aberrismic theory) is a family of quasi-diatonic ternary scale patterns with scale signature 5L2m4s, so named by groundfault who considers 33edo's L:m:s = 5:2:1 a good tuning for it. The name diamech is a blend of dia- and the TAMNAMS prefix mech- for machinoid. 23edo is the only edo without a diatonic fifth that has a 5L2mks ternary scale pattern, namely 5L2m4s with L:m:s = 3:2:1.

The three nicest diamech scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via MOS substitution, giving generator sequences for the three scales:

5L2m4s as MOS_subst(5, 2, 4; m, s; k)

k	filling MOS	UDP for filling MOS	step pattern		generator sequence
			template MOS:	LXLXLXLXLXX	intvl. class of gen.:	2-steps
2 (4sC)	mssmss	4|0(2)	LmLsLsLmLss		GS(L+m, L+s, L+s)
1 (4sR)	smssms	2|2(2)	LsLmLsLsLms		GS(L+s, L+m, L+s)
0 (4sL)	ssmssm	0|4(2)	LsLsLmLsLsm		GS(L+s, L+s, L+m)

The canonical untempered 2.3.7 interpretation for diamech has L = 9/8, m = 49/48, s = 64/63.