Talk:57edo: Difference between revisions

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::: Understandable since you caught me in the middle of the process, and I was belated in realizing that the automated interval table generator didn't fill in 3/2 and 4/3 (who would have thought?). I think tripled 19edo + highly accurate higher primes component (as was already in the description) makes a lot of sense for 57edo, which deserves more exploration. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:53, 2 January 2026 (UTC)

: I think this edo should be dual-3 dual-5, as not only should the intervals themselves be considered, but rather chords they are in. For example, a 16:19:24:28:36 chord by direct approximation of each harmonic would have only one inconsistent interval, 36/24 (not the same number of steps as 24/16), with +65.7% relative error. In contrast, by patent val, all of 36/16, 36/19, and 36/28 are inconsistent, having -68.6%, -55.4%, and -66.6% error respectively. Harmonics 9 is very common in chords, so in most cases prime 3 should be dual even if it has just about 1/3 relative error (though [[49edo]] is an exception, due to the sharpness of 5, 7, and 11). Prime 5 should also be dual, as harmonics 15 and 25 are relatively simple, and have about -70% relative error by patent val. In general, things get messy when there's inconsistencies, and EDOs don't work like JI.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 04:10, 3 January 2026 (UTC)

Revision as of 22:53, 2 January 2026 view source Lucius Chiaraviglio (talk \| contribs) 2,764 edits How to interpret 57edo ← Older edit		Revision as of 04:10, 3 January 2026 view source Overthink (talk \| contribs) autopatrolled 2,962 edits reply Newer edit →
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	::: Understandable since you caught me in the middle of the process, and I was belated in realizing that the automated interval table generator didn't fill in 3/2 and 4/3 (who would have thought?). I think tripled 19edo + highly accurate higher primes component (as was already in the description) makes a lot of sense for 57edo, which deserves more exploration. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 22:53, 2 January 2026 (UTC)		::: Understandable since you caught me in the middle of the process, and I was belated in realizing that the automated interval table generator didn't fill in 3/2 and 4/3 (who would have thought?). I think tripled 19edo + highly accurate higher primes component (as was already in the description) makes a lot of sense for 57edo, which deserves more exploration. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 22:53, 2 January 2026 (UTC)

			: I think this edo should be dual-3 dual-5, as not only should the intervals themselves be considered, but rather chords they are in. For example, a 16:19:24:28:36 chord by direct approximation of each harmonic would have only one inconsistent interval, 36/24 (not the same number of steps as 24/16), with +65.7% relative error. In contrast, by patent val, all of 36/16, 36/19, and 36/28 are inconsistent, having -68.6%, -55.4%, and -66.6% error respectively. Harmonics 9 is very common in chords, so in most cases prime 3 should be dual even if it has just about 1/3 relative error (though [[49edo]] is an exception, due to the sharpness of 5, 7, and 11). Prime 5 should also be dual, as harmonics 15 and 25 are relatively simple, and have about -70% relative error by patent val. In general, things get messy when there's inconsistencies, and EDOs don't work like JI.--[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 04:10, 3 January 2026 (UTC)