Diaslen: Difference between revisions

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!colspan=2| step pattern  
!colspan=2| step pattern  
!colspan=2| [[generator sequence]]
!colspan=2| [[generator sequence]]
!rowspan=2| MOS for s = 0
|-
|-
!| template MOS:
!| template MOS:
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| 2 (4sC) || <code>mssmss</code> || 4&#124;0(2)  
| 2 (4sC) || <code>mssmss</code> || 4&#124;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''') || yes
|colspan=2| GS('''L'''+'''m''', '''L'''+'''s''', '''L'''+'''s''')  
|-
|-
| 1 (4sR) || <code>smssms</code> || 2&#124;2(2)  
| 1 (4sR) || <code>smssms</code> || 2&#124;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''') || yes
|colspan=2| GS('''L'''+'''s''', '''L'''+'''m''', '''L'''+'''s''')  
|-
|-
| 0 (4sL) || <code>ssmssm</code> || 0&#124;4(2)  
| 0 (4sL) || <code>ssmssm</code> || 0&#124;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''') || yes
|colspan=2| GS('''L'''+'''s''', '''L'''+'''s''', '''L'''+'''m''')  
|}
|}


[[Category:Rank-3 scales]]
[[Category:Rank-3 scales]]

Revision as of 03:24, 30 January 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.

The three canonical 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)