User talk:Aura: Difference between revisions

Line 399:

::: As for 2.3.*.23, the 23rd harmonic mapping is pretty unstable in the zone of 11L 2s — it gets better mapping stability in 17L 2s, although this region has its generators sharp enough relative to 23/16 that larger EDO sizes often flip to the next flatter approximation, so the generator for that needs to be something between 23/16 and 13/9.

::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:21, 11 April 2025 (UTC)

::: The modes of 11L 2s that enable reaching 4/3 and/or 3/2 within-scale are not very many. If you want to get both, you have to use sLLLLLsLLLLLL (no other mode gets both). If you want to get 3/2 but can live without 4/3 (more common than the opposite), then you can also use LsLLLLLsLLLLL or sLLLLLLsLLLLL. If you use LLLLLLsLLLLLs or LLLLLsLLLLLLs or LLLLLsLLLLLsL you can get 4/3 but not 3/2. In EDOs with fine enough steps to distinguish 128/85(?) from 3/2, this instead gets you 128/85(?) (or 85/64(?) instead of 4/3). So if we want a MODMOS for 159edo that gets us back to 3/2 (and maybe 4/3) we need a second generator that gets tempered to be the same as 11/8 or 16/11 in the coarser EDOs supporting 11L 2s but distinguished in the finer ones. Not sure yet what that would be, and not sure yet whether 128/85 is the best slightly-inflated fifth substitute to use for this purpose. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:02, 12 April 2025 (UTC)

@@ Line 399: / Line 399: @@
 ::: As for 2.3.*.23, the 23rd harmonic mapping is pretty unstable in the zone of 11L&nbsp;2s &mdash; it gets better mapping stability in 17L&nbsp;2s, although this region has its generators sharp enough relative to 23/16 that larger EDO sizes often flip to the next flatter approximation, so the generator for that needs to be something between 23/16 and 13/9.
 ::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:21, 11 April 2025 (UTC)
+::: The modes of 11L&nbsp;2s that enable reaching 4/3 and/or 3/2 within-scale are not very many.  If you want to get both, you have to use sLLLLLsLLLLLL (no other mode gets both).  If you want to get 3/2 but can live without 4/3 (more common than the opposite), then you can also use LsLLLLLsLLLLL or sLLLLLLsLLLLL.  If you use LLLLLLsLLLLLs or LLLLLsLLLLLLs or LLLLLsLLLLLsL you can get 4/3 but not 3/2.  In EDOs with fine enough steps to distinguish 128/85(?) from 3/2, this instead gets you 128/85(?) (or 85/64(?) instead of 4/3).  So if we want a MODMOS for 159edo that gets us back to 3/2 (and maybe 4/3) we need a second generator that gets tempered to be the same as 11/8 or 16/11 in the coarser EDOs supporting 11L&nbsp;2s but distinguished in the finer ones.  Not sure yet what that would be, and not sure yet whether 128/85 is the best slightly-inflated fifth substitute to use for this purpose.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:02, 12 April 2025 (UTC)