Aura
Joined 31 August 2020
m →Temperament(s) for Diatonicized Chromaticism?: Fix broken HTML symbol |
→Temperament(s) for Diatonicized Chromaticism?: Finished odd harmonics table (group) for 11L 2s. |
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:::::::::: 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]]). | :::::::::: 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]]) 20:12, 8 April 2025 (UTC) | :::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:12, 8 April 2025 (UTC) | ||
:::::::::: I finished doing the above for 11L 2s. Note that 11/8 (the dark generator, and thereby the bright generator 16/11) remains stable throughout the entire currently posted 11L 2s table &emdash; the worst relative error is -34.8%, at 127edo, so your favorite 159edo still easily fits in. Right now I strung out the odd harmonics to high values in case I need these for composite ratios, which seem likely to be needed for 17L 2s, but seem like they may not be needed for 11L 2s (but better leave them in for now until I am sure they are not needed). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:54, 9 April 2025 (UTC) | |||