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:
| 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.