User talk:Aura: Difference between revisions

Line 401:

::: 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)

:::: Well, the ~128/85 fifth of 159edo is indeed useful in its own right as an imitation of the kind of thing you see in 22edo. Perhaps we can play to the strengths of that type of system where two ~128/85 intervals octave-reduced add up to ~17/15, and two instances of ~17/15 add up to ~9/7- yes, that is how 159edo works since both 22edo and 159edo support archagall temperament. Not only that but the ~128/85 interval is 159edo's best approximation of 17edo's fifth, so we could also shoot for 11L 2s harmonies that evoke the kind of stuff found in 17edo and it's multiples. The point is that if the ~11/8 and ~16/11 intervals count as ambisonances (basically, they're both consonances and dissonances at the same time) for our intents and purposes, as I know they do for mine, then we can afford to play with some of the less accurate intervals in our 11L 2s harmonies- assuming we play our cards right. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:28, 12 April 2025 (UTC)

Revision as of 00:02, 12 April 2025 view source Lucius Chiaraviglio (talk \| contribs) 2,601 edits →Temperament(s) for Diatonicized Chromaticism?: 11L 2s modes that can reach 3/2 and/or 4/3 ← Older edit		Revision as of 04:28, 12 April 2025 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 6,010 edits →Temperament(s) for Diatonicized Chromaticism? Tags: Mobile edit Mobile web edit Newer edit →
Line 401:		Line 401:

	::: 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)		::: 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)

			:::: Well, the ~128/85 fifth of 159edo is indeed useful in its own right as an imitation of the kind of thing you see in 22edo. Perhaps we can play to the strengths of that type of system where two ~128/85 intervals octave-reduced add up to ~17/15, and two instances of ~17/15 add up to ~9/7- yes, that is how 159edo works since both 22edo and 159edo support archagall temperament. Not only that but the ~128/85 interval is 159edo's best approximation of 17edo's fifth, so we could also shoot for 11L 2s harmonies that evoke the kind of stuff found in 17edo and it's multiples. The point is that if the ~11/8 and ~16/11 intervals count as ambisonances (basically, they're both consonances and dissonances at the same time) for our intents and purposes, as I know they do for mine, then we can afford to play with some of the less accurate intervals in our 11L 2s harmonies- assuming we play our cards right. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 04:28, 12 April 2025 (UTC)