Talk:Alphatricot family: Difference between revisions

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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?

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~~]] and ~[[384/265~~]]. 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 ~~both of these have~~ high primes, ~~they~~ arguably ~~have~~ lower overall complexity than the ~[[59049/40960]] specified on the Alphatricot family page.

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)

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)

== Alphatrident and the two 2.3.5.13-subgroup extensions ==

Alphatrident has an alternative extension 53 & 282 that uses the same mapping for prime 13 as alphatrillium. The currently canonical 11-limit extension should be decanonicalized.

As such, 2.3.5.13-subgroup "alphatricot" is the same mapping used in alphatrimot and our current "alphatrident", whereas 2.3.5.13-subgroup "alphatrillium" is the same mapping used in alphatrillium and the alternative "alphatrident". It follows that 2.3.5.13-subgroup "alphatricot" should be called 2.3.5.13-subgroup ''alphatrimot'' for the same reason that 2.3.5.13-subgroup ''alphatrillium'' is called so.

[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:47, 9 September 2025 (UTC)

@@ Line 3: / Line 3: @@
 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&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]] and ~[[384/265]].  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 both of these have high primes, they arguably have lower overall complexity than the ~[[59049/40960]] specified on the Alphatricot family page.
+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)
+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)
+== Alphatrident and the two 2.3.5.13-subgroup extensions ==
+Alphatrident has an alternative extension 53 & 282 that uses the same mapping for prime 13 as alphatrillium. The currently canonical 11-limit extension should be decanonicalized.
+As such, 2.3.5.13-subgroup "alphatricot" is the same mapping used in alphatrimot and our current "alphatrident", whereas 2.3.5.13-subgroup "alphatrillium" is the same mapping used in alphatrillium and the alternative "alphatrident". It follows that 2.3.5.13-subgroup "alphatricot" should be called 2.3.5.13-subgroup ''alphatrimot'' for the same reason that 2.3.5.13-subgroup ''alphatrillium'' is called so.
+[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:47, 9 September 2025 (UTC)