Talk:Alphatricot family - Revision history

FloraC at 08:47, 9 September 2025

2025-09-09T08:47:50Z

← Older revision		Revision as of 08:47, 9 September 2025
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	Added: [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 19:06, 29 April 2025 (UTC)<br>		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)		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)

Lucius Chiaraviglio: Improve the writing of my post, and fix a typo in the scale link

2025-04-29T21:16:17Z

Improve the writing of my post, and fix a typo in the scale link

← Older revision		Revision as of 21:16, 29 April 2025
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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~~]] 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).		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)

Lucius Chiaraviglio: /* Other Alpha Tricot temperaments? */ new section

2025-04-29T19:06:34Z

Other Alpha Tricot temperaments?: new section

← Older revision	Revision as of 19:06, 29 April 2025
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		== 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]].

		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.

		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)

FloraC: FloraC moved page Talk:Tricot family to Talk:Alphatricot family: Follow the specifications of ploidacot

2025-03-16T13:29:57Z

FloraC moved page Talk:Tricot family to Talk:Alphatricot family: Follow the specifications of ploidacot

← Older revision	Revision as of 13:29, 16 March 2025
(No difference)

Bootmii: oops I think I understand

2022-03-17T08:24:21Z

oops I think I understand

← Older revision		Revision as of 08:24, 17 March 2022
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	~~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)~~

Bootmii: Created page with "So di/tetra/octacot are all 2/4/8edf, why is tricot 3edt? ~~~~"

2022-03-17T06:47:39Z

Created page with "So di/tetra/octacot are all 2/4/8edf, why is tricot 3edt? ~~~~"

New page

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)