Diaslen: Difference between revisions
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|+ | |+ Diamech scales as MOS substitution scales | ||
|- | |- | ||
!rowspan=2| | !rowspan=2| chirality | ||
!rowspan=2| filling MOS | !rowspan=2| filling MOS | ||
!rowspan=2| [[UDP]] for filling MOS | !rowspan=2| [[UDP]] for filling MOS | ||
| Line 17: | Line 17: | ||
|| 2-steps | || 2-steps | ||
|- | |- | ||
| | | 4sC || <code>mssmss</code> || 4|0(2) | ||
|colspan=2 style="text-align:right;"| <code>LmLsLsLmLss</code> | |colspan=2 style="text-align:right;"| <code>LmLsLsLmLss</code> | ||
|colspan=2| GS('''L'''+'''m''', '''L'''+'''s''', '''L'''+'''s''') | |colspan=2| GS('''L'''+'''m''', '''L'''+'''s''', '''L'''+'''s''') | ||
|- | |- | ||
| | | 4sR || <code>smssms</code> || 2|2(2) | ||
|colspan=2 style="text-align:right;"| <code>LsLmLsLsLms</code> | |colspan=2 style="text-align:right;"| <code>LsLmLsLsLms</code> | ||
|colspan=2| GS('''L'''+'''s''', '''L'''+'''m''', '''L'''+'''s''') | |colspan=2| GS('''L'''+'''s''', '''L'''+'''m''', '''L'''+'''s''') | ||
|- | |- | ||
| | | 4sL || <code>ssmssm</code> || 0|4(2) | ||
|colspan=2 style="text-align:right;"| <code>LsLsLmLsLsm</code> | |colspan=2 style="text-align:right;"| <code>LsLsLmLsLsm</code> | ||
|colspan=2| GS('''L'''+'''s''', '''L'''+'''s''', '''L'''+'''m''') | |colspan=2| GS('''L'''+'''s''', '''L'''+'''s''', '''L'''+'''m''') | ||
Revision as of 09:25, 26 February 2024
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 standard diamech scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via MOS substitution, giving generator sequences for the three scales:
| chirality | filling MOS | UDP for filling MOS | step pattern | generator sequence | ||
|---|---|---|---|---|---|---|
| template MOS: | LXLXLXLXLXX
|
intvl. class of gen.: | 2-steps | |||
| 4sC | mssmss |
4|0(2) | LmLsLsLmLss
|
GS(L+m, L+s, L+s) | ||
| 4sR | smssms |
2|2(2) | LsLmLsLsLms
|
GS(L+s, L+m, L+s) | ||
| 4sL | ssmssm |
0|4(2) | LsLsLmLsLsm
|
GS(L+s, L+s, L+m) | ||
The standard untempered 2.3.7 interpretation for diamech has L = 9/8, m = 49/48, s = 64/63.