Talk:Alphatricot family: Difference between revisions

(3 intermediate revisions by 3 users not shown)

Line 1:

~~So di~~/~~tetra~~/~~octacot~~ are all 2/~~4/8edf~~, ~~why~~ is ~~tricot 3edt?~~ [[User:~~Bootmii~~|~~Bootmii~~]] ([[User talk:~~Bootmii~~|talk]]) 06:47, ~~17 March 2022~~ (UTC)

== 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 [[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)<br>

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:16, 29 April 2025 (UTC)

@@ Line 1: / Line 1: @@
-So di/tetra/octacot are all 2/4/8edf, why is tricot 3edt? [[User:Bootmii|Bootmii]] ([[User talk:Bootmii|talk]]) 06:47, 17 March 2022 (UTC)
+== 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&nbsp;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&nbsp;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&nbsp;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&nbsp;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)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:16, 29 April 2025 (UTC)