Talk:Alphatricot family: Difference between revisions
→Other Alpha Tricot temperaments?: new section |
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What should one call temperaments that divide 3/1 into 3, but have differently constituted generators from the temperaments in the [[Alphatricot family]]? And where should one put them? | What should one call temperaments that divide 3/1 into 3, but have differently constituted generators from the temperaments in the [[Alphatricot family]]? And where should one put them? | ||
Plausible other generators (from flat to sharp) include ~[[23/16]], ~[[36/25]], and ~[[13/9]]. | Plausible other generators (from flat to sharp) include ~[[23/16]], ~[[36/25]], and ~[[13/9]]. The first two of these are too flat for microtempering, but they work for some EDO sizes supporting the same [[17L 2s]] scale that the Alphatricot family supports; likewise, the last is too sharp for microtempering, but still works for some EDO sizes supporting the same scale. | ||
Far-out other generators (from flat to sharp) include ~[[62/43 | Far-out other generators (from flat to sharp) include ~[[62/43]]. In particular, ~62/43 works without warts for the great majority of EDO values in the 17L 2s tuning spectrum table, and the few exceptions are able to benefit (according to a consistency point of view0 from a 'k' wart that makes it work for them as well. And while this has high primes, it arguably has lower overall complexity than the ~[[59049/40960]] specified on the Alphatricot family page. (In the past, I also included ~[[384/265]] even though it was sharp, due to stability of the 53rd harmonic for a pretty good subset of EDOs supporting 19L 2s, for the purpose of tempering together with one of the flat generators above; however, ~61/43 gets all of those and then some.) | ||
I've been working on building temperaments to support 17L 2s, currently in [[User:Lucius_Chiaraviglio/Musical_Mad_Science#Musical_Mad_Science_Musings_on_Diatonicized_Sixth-Tone_Sub-Chromaticism(?)|a section within the Musical Mad Science sub-page of my user page]], although I'll admit up front that this is just coming out of the initial exploration phase and currently quite badly written (and at some point in the not-too-distant future I'm going to want to archive that and make it into something more readable, possibly in its own sub-sub-page). | I've been working on building temperaments to support 17L 2s, currently in [[User:Lucius_Chiaraviglio/Musical_Mad_Science#Musical_Mad_Science_Musings_on_Diatonicized_Sixth-Tone_Sub-Chromaticism(?)|a section within the Musical Mad Science sub-page of my user page]], although I'll admit up front that this is just coming out of the initial exploration phase and currently quite badly written (and at some point in the not-too-distant future I'm going to want to archive that and make it into something more readable, possibly in its own sub-sub-page). | ||
Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:06, 29 April 2025 (UTC) | Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:06, 29 April 2025 (UTC)<br> | ||
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:16, 29 April 2025 (UTC) | |||
Latest revision as of 21:16, 29 April 2025
Other Alpha Tricot temperaments?
What should one call temperaments that divide 3/1 into 3, but have differently constituted generators from the temperaments in the Alphatricot family? And where should one put them?
Plausible other generators (from flat to sharp) include ~23/16, ~36/25, and ~13/9. The first two of these are too flat for microtempering, but they work for some EDO sizes supporting the same 17L 2s scale that the Alphatricot family supports; likewise, the last is too sharp for microtempering, but still works for some EDO sizes supporting the same scale.
Far-out other generators (from flat to sharp) include ~62/43. In particular, ~62/43 works without warts for the great majority of EDO values in the 17L 2s tuning spectrum table, and the few exceptions are able to benefit (according to a consistency point of view0 from a 'k' wart that makes it work for them as well. And while this has high primes, it arguably has lower overall complexity than the ~59049/40960 specified on the Alphatricot family page. (In the past, I also included ~384/265 even though it was sharp, due to stability of the 53rd harmonic for a pretty good subset of EDOs supporting 19L 2s, for the purpose of tempering together with one of the flat generators above; however, ~61/43 gets all of those and then some.)
I've been working on building temperaments to support 17L 2s, currently in a section within the Musical Mad Science sub-page of my user page, although I'll admit up front that this is just coming out of the initial exploration phase and currently quite badly written (and at some point in the not-too-distant future I'm going to want to archive that and make it into something more readable, possibly in its own sub-sub-page).
Added: Lucius Chiaraviglio (talk) 19:06, 29 April 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 21:16, 29 April 2025 (UTC)