Aura
Joined 31 August 2020
→Temperament(s) for Diatonicized Chromaticism?: Table(s) of odd harmonics in various EDOs of scales |
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:::::::::: I'll have to check them out (actually listened to 1 already, but quite a while ago, before I started thinking much about this). | :::::::::: I'll have to check them out (actually listened to 1 already, but quite a while ago, before I started thinking much about this). | ||
:::::::::: Meanwhile, I thought it would be useful to have a table of odd harmonics of the various EDOs supporting 17L 2s to make it easier to track stability of mapping, and I plan to do this for 11L 2s as well (which so far I had been doing this for by way of manual lookup of each EDO, which is time-consuming). Right now it is actually a collection of tables, because Template:Harmonics in equal doesn't have a way to string them together and doesn't have a way to set a uniform column width. Any idea how to fix this, other than manually creating a table with values copied from these? In the process of doing this, I have noticed an interesting comparison: 11L 2s has a very well-behaved 11th harmonic (it has to, since 11/8 and 16/11 is the generator pair), but doesn't seem to have well-behaved low harmonics; but in contrast, 17L 2s doesn't have a simple generator (23/16 is too flat by a few cents, and 13/9 is too sharp, and has multiple odd harmonics/subharmonics in it anyway), and the harmonics of the compound ratios that could be used as generators for it are NOT well-behaved, except that the 3rd harmonic is amazingly well-behaved, only flipping to a different mapping at 112edo and higher EDO values (and the 23rd harmonic would be well-behaved if only it wasn't flat of the actual generator — it would be an excellent generator for [[21L& | :::::::::: Meanwhile, I thought it would be useful to have a table of odd harmonics of the various EDOs supporting 17L 2s to make it easier to track stability of mapping, and I plan to do this for 11L 2s as well (which so far I had been doing this for by way of manual lookup of each EDO, which is time-consuming). Right now it is actually a collection of tables, because Template:Harmonics in equal doesn't have a way to string them together and doesn't have a way to set a uniform column width. Any idea how to fix this, other than manually creating a table with values copied from these? In the process of doing this, I have noticed an interesting comparison: 11L 2s has a very well-behaved 11th harmonic (it has to, since 11/8 and 16/11 is the generator pair), but doesn't seem to have well-behaved low harmonics; but in contrast, 17L 2s doesn't have a simple generator (23/16 is too flat by a few cents, and 13/9 is too sharp, and has multiple odd harmonics/subharmonics in it anyway), and the harmonics of the compound ratios that could be used as generators for it are NOT well-behaved, except that the 3rd harmonic is amazingly well-behaved, only flipping to a different mapping at 112edo and higher EDO values (and the 23rd harmonic would be well-behaved if only it wasn't flat of the actual generator — it would be an excellent generator for [[21L 2s]] or the soft end of [[2L 19s]]). | ||
:::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20: | :::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:12, 8 April 2025 (UTC) | ||