Diaslen: Difference between revisions

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'''{{PAGENAME}}''' (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.
'''{{PAGENAME}}''' (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 sequence]]s for the three scales:
The three nicest diamech scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via [[MOS substitution]], giving [[generator sequence]]s for the three scales:

Revision as of 02:19, 8 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 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.