User:FloraC/Temperament extension issues - Revision history

FloraC: Renewed opinion on hemiwürschmidt

2026-09-29T08:42:17Z

Renewed opinion on hemiwürschmidt

← Older revision		Revision as of 08:42, 29 September 2026
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	; Hemiwürschmidt		; Hemiwürschmidt
	: 7-limit → 11-limit		: 11-limit → 13-limit
	: 11-limit hemiwürschmidt should be decanonicalized. ~~The 7~~-limit optimum is between 99 and 130~~. The 11-limit extension shifts it~~ to somewhere ~~between~~ 130 ~~and~~ 161, and ~~is a significant drop in accuracy. Hemiwürschmidt is also described~~ as a 2.3.5.~~7.23~~-subgroup ~~temperament~~, which is ~~more natural~~.		: 13-limit hemiwürschmidt should be decanonicalized. While the 11-limit extension is a significant drop in accuracy, it doesn't shift the optimum too much (from between 99 and 130 to somewhere near 130, as 291 (= 130 + 161) isn't more accurate), and it can be reasoned based on it using the same mapping as the 2.3.5.11-subgroup version of würschmidt, the latter of which is supported by the "core" equal temps, 31, 34 and 65. The 13-limit version is where the shift of optimum becomes qualitative difference and the 31 and 99e vals are both questionable anyway.
	: Proposed solution:		: Proposed solution:

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	; Würschmidt		; Würschmidt
	: 5-limit → 7-limit		: 5-limit → 7-limit
	: 7-limit würschmidt should be decanonicalized. Almost all the notable supporting equal temperaments are dual-7: 34, 65, 96, and 127, and that speaks something about it. Würschmidt is also described as a 2.3.5.23-subgroup temperament, which is more natural.		: 7-limit würschmidt should be decanonicalized. Almost all the notable supporting equal temperaments are dual-7: 34, 65, 96, and 127, and that speaks something about it. Würschmidt is also described as a 2.3.5.11.(23)-subgroup temperament, which is more natural.
	: Proposed solution:		: Proposed solution:

FloraC at 09:07, 21 September 2026

2026-09-21T09:07:59Z

← Older revision		Revision as of 09:07, 21 September 2026
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	: 7-limit → 11-limit		: 7-limit → 11-limit
	: 11-limit lunatic should be decanonicalized. Lunatic has at least three extensions: 205 & 323, 323 & 441, and 441 & 559. Perhaps, the canonicity of 441 & 559 could be argued on the basis that the 7-limit optimum is very close to 441; however, compared to the good efficiency and portability of the 7-limit temperament, this 11-limit extension is pretty mid.		: 11-limit lunatic should be decanonicalized. Lunatic has at least three extensions: 205 & 323, 323 & 441, and 441 & 559. Perhaps, the canonicity of 441 & 559 could be argued on the basis that the 7-limit optimum is very close to 441; however, compared to the good efficiency and portability of the 7-limit temperament, this 11-limit extension is pretty mid.
			: Proposed solution:

			; Maquila
			: 5-limit → 7-limit
			: 7-limit maquila should be decanonicalized, or alternatively the 5-limit restriction should. In either case, it's a low-accuracy, high-badness extension that uses the dual-7 65edo.
	: Proposed solution:		: Proposed solution:

FloraC at 09:05, 21 September 2026

2026-09-21T09:05:46Z

← Older revision		Revision as of 09:05, 21 September 2026
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	: Paradigmic has two notable 13-limit extensions: 80 & 99e and 80 & 99ef, and like above, 80 & 99e is the simpler 19-form whereas 80 & 99ef is more accurate. 80 & 99ef also supports 13-limit parapyth, which is an extra point. It follows that 13-limit paradigmic needs a distinct name too.		: Paradigmic has two notable 13-limit extensions: 80 & 99e and 80 & 99ef, and like above, 80 & 99e is the simpler 19-form whereas 80 & 99ef is more accurate. 80 & 99ef also supports 13-limit parapyth, which is an extra point. It follows that 13-limit paradigmic needs a distinct name too.
	: Proposed solution:		: Proposed solution:

	~~; Secund~~
	~~: 11-limit → 13-limit~~
	~~: 13-limit secund should be decanonicalized, for the other extension is obviously way better.~~
	~~: Proposed solution: delete 13-limit secund. Secundly → 13-limit secund. Status: pending community reactions.~~

	; Tertiaseptal		; Tertiaseptal
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	=== Rank-3 temperaments ===		=== Rank-3 temperaments ===
	~~; Agni~~
	~~: 11-limit → 13-limit~~
	: 13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72, even tho the latter has a little higher badness. Proposing to rename it to pavaka, after another name of Agni.
	~~: Proposed solution: 13-limit agni → pavaka. Status: pending community reactions.~~

	; Artemis		; Artemis
	: 11-limit → 13-limit		: 11-limit → 13-limit
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	: 11-limit nessafof should be decanonicalized. Extending nessafof to the 11-limit is complicated since both 84edo and 99edo have ambiguous interpretations (see the case with parakleismic). Currently we have catalogued the two low-complexity 15-form extensions, which makes sense. One is being called ''nessa'' so the other may simply be ''fof''.		: 11-limit nessafof should be decanonicalized. Extending nessafof to the 11-limit is complicated since both 84edo and 99edo have ambiguous interpretations (see the case with parakleismic). Currently we have catalogued the two low-complexity 15-form extensions, which makes sense. One is being called ''nessa'' so the other may simply be ''fof''.
	: Proposed solution: 11-limit nessafof → fof. Status: changed.		: Proposed solution: 11-limit nessafof → fof. Status: changed.

			; Secund
			: 11-limit → 13-limit
			: 13-limit secund should be decanonicalized, for the other extension is obviously way better.
			: Proposed solution: delete 13-limit secund. Secundly → 13-limit secund. Status: changed.

	=== Rank-3 temperaments ===		=== Rank-3 temperaments ===
			; Agni
			: 11-limit → 13-limit
			: 13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72, even tho the latter has a little higher badness. Proposing to rename it to pavaka, after another name of Agni.
			: Proposed solution: 13-limit agni → pavaka. Status: changed.

	; Aphrodite		; Aphrodite
	: 11-limit → 13-limit		: 11-limit → 13-limit

FloraC at 07:39, 18 September 2026

2026-09-18T07:39:23Z

← Older revision		Revision as of 07:39, 18 September 2026
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	== Preliminaries ==		== Preliminaries ==
			=== Objectives ===
			"It's just labeling mathematical objects." I hear you say.

			The goal is to make the scope of a temp name more coherent so that you need less modification and explanation to the names you use, ultimately to facilitate exploring the space of useful ideas and to reduce the friction in the communication of these ideas.

	=== Terms ===		=== Terms ===
	; Segment		; Segment

FloraC: Seems like necessary clarification

2026-08-28T13:33:45Z

Seems like necessary clarification

← Older revision		Revision as of 13:33, 28 August 2026
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	{{Editable user page\|Please add ~~ideas and~~ name proposals. }}		{{Editable user page\|Please add name proposals. Discussion goes to the talk page. }}

	A list of issues with temperament extensions.		A list of issues with temperament extensions.

			== Preliminaries ==
			=== Terms ===
			; Segment
			: For rank-2 temps, refers to a tuning range of an extension, often bounded by equal temps. Segments often zigzag, i.e., the tuning of the added element changes direction as the tuning of the generator crosses a boundary, entering the range of another extension. A ''central segment'' is a range, among many, that takes the middle part of the original tuning range, and thus is most fit for a canonical extension.

			=== Other notes ===
			* The edo joins used here imply tuning ranges.

	== Open issues ==		== Open issues ==

FloraC at 13:02, 17 August 2026

2026-08-17T13:02:41Z

← Older revision		Revision as of 13:02, 17 August 2026
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	: 7-limit → 11-limit		: 7-limit → 11-limit
	: 11-limit alphatrident should be decanonicalized. The tuning is not very representative of 7-limit alphatrident. Specifically, alphatrident has three 11-limit extensions: 176 & 229, 229 & 282, and 282 & 335d. The first and last are supported by 53 which means they are simpler, but they are not representative of the 7-limit optimum. The middle one is representative of the 7-limit optimum, but is very complex. Therefore, the situation is similar to slendric, where none of the extensions should be canon.		: 11-limit alphatrident should be decanonicalized. The tuning is not very representative of 7-limit alphatrident. Specifically, alphatrident has three 11-limit extensions: 176 & 229, 229 & 282, and 282 & 335d. The first and last are supported by 53 which means they are simpler, but they are not representative of the 7-limit optimum. The middle one is representative of the 7-limit optimum, but is very complex. Therefore, the situation is similar to slendric, where none of the extensions should be canon.
			: Proposed solution:

			; Chlorine
			: 7-limit → 11-limit
			: 11-limit chlorine should be decanonicalized. The 612 & 935 extension isn't more complex (with the same Graham complexity in the 11-odd-limit) but is way more accurate.
	: Proposed solution:		: Proposed solution:

FloraC at 05:01, 3 August 2026

2026-08-03T05:01:54Z

← Older revision		Revision as of 05:01, 3 August 2026
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	: 7-limit → 11-limit		: 7-limit → 11-limit
	: 11-limit tertiaseptal should be decanonicalized. Tertiaseptal has three 11-limit extensions: 109 & 140, 140 & 171, and 171 & 202. Perhaps, the canonicity of 171 & 202 could be argued on the basis that the 7-limit optimum is very close to 171; however, compared to the absolute supremacy of the 7-limit temperament, this 11-limit extension is plain bad. ''Tertia'' and ''tertiaseptia'' are bad-tasted names so we might wanna reconsider these names too.		: 11-limit tertiaseptal should be decanonicalized. Tertiaseptal has three 11-limit extensions: 109 & 140, 140 & 171, and 171 & 202. Perhaps, the canonicity of 171 & 202 could be argued on the basis that the 7-limit optimum is very close to 171; however, compared to the absolute supremacy of the 7-limit temperament, this 11-limit extension is plain bad. ''Tertia'' and ''tertiaseptia'' are bad-tasted names so we might wanna reconsider these names too.
			: Proposed solution:

			; Wesley
			: 5-limit → 7-limit
			: 7-limit wesley should be decanonicalized. The tuning is not very representative of 5-limit wesley. Roman (26 & 29) is most representative, even tho it's a little more complex.
	: Proposed solution:		: Proposed solution:

FloraC: /* Rank-3 temperaments */

2026-07-26T14:06:32Z

Rank-3 temperaments

← Older revision		Revision as of 14:06, 26 July 2026
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	; Agni		; Agni
	: 11-limit → 13-limit		: 11-limit → 13-limit
	: 13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72.		: 13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72, even tho the latter has a little higher badness. Proposing to rename it to pavaka, after another name of Agni.
	: Proposed solution:		: Proposed solution: 13-limit agni → pavaka. Status: pending community reactions.

	; Artemis		; Artemis
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	: 11-limit → 13-limit		: 11-limit → 13-limit
	: 13-limit big brother should be decanonicalized. See the case with artemis.		: 13-limit big brother should be decanonicalized. See the case with artemis.
	: Proposed solution:		: Proposed solution:

			; Freya
			: 11-limit → 13-limit
			: 13-limit freya should be decanonicalized. 11-limit freya has three extensions: 31 & 41 & 270, 31 & 72 & 270, and 41 & 72 & 270. 31 & 41 & 270 is a pretty neutral choice, but is also the least efficient out of all three.
			: Proposed solution:

	== Closed issues ==		== Closed issues ==

Overthink: /* Rank-2 temperaments */ add details

2026-07-13T20:31:28Z

Rank-2 temperaments: add details

← Older revision		Revision as of 20:31, 13 July 2026
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	; Keemun		; Keemun
	: 11-limit → 13-limit		: 11-limit → 13-limit
	: 13-limit keemun should be decanonicalized. Kema, which maps prime 13 to +14 steps, is the right extension to use, as in all kleismic temperaments.		: 13-limit keemun should be decanonicalized. Kema, which maps prime 13 to +14 steps, is the right extension to use, as in all kleismic temperaments. Its edo join is 15 & 19, while the current canonical 13-limit extension is 15f & 19, and 15 is better than 15f. Kema is additionally supported by patent 34, while the current canonical extension uses the much less accurate 34f. The mapping of prime 13 to -5 generators is inaccurate and in the opposite direction compared to primes 3, 5, and 7, making other intervals of 13 more complex.
	: Proposed solution:		: Proposed solution:

FloraC at 10:27, 8 July 2026

2026-07-08T10:27:27Z

← Older revision		Revision as of 10:27, 8 July 2026
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	; Schismatic family		; Schismatic family
	: Various dubious extensions. ~~Will eventually collect them and add to the talk page~~.		: Various dubious extensions. See [[Talk: Schismatic family #Extensions]]. Pending public reactions.

	; Tetracot family		; Tetracot family