No-threes subgroup temperaments - Revision history

FloraC: Move mercy back here

2026-11-07T14:38:10Z

Move mercy back here

@@ Line 15: / Line 15: @@
 * Jubilic ([[50/49]]) → [[Jubilismic clan #Jubilic|Jubilismic clan]]
 * Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]]
 * Sidewalk ([[823543/800000]]) → [[2023/2000 #Sidewalk]]
@@ Line 284: / Line 283: @@
 Badness (Sintel): 0.458
 === Huntington ===

CompactStar: /* Argument */

2026-11-06T08:33:12Z

Argument

← Older revision		Revision as of 08:33, 6 November 2026
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	=== Argument ===		=== Argument ===
	Argument tempers out [[1372/1331]] in the 2.7.11 subgroup. It is the no-3 [[restriction]] of [[#Augment\|augment]].		Argument tempers out [[1372/1331]] in the 2.7.11 subgroup, equating [[14/11]] to a step of [[3edo]]. It is the no-3 [[restriction]] of [[#Augment\|augment]].

	[[Subgroup]]: 2.7.11		[[Subgroup]]: 2.7.11

FloraC: /* Llywelyn a.k.a. shoe */

2026-11-03T05:45:35Z

Llywelyn a.k.a. shoe

← Older revision		Revision as of 05:45, 3 November 2026
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	=== Llywelyn a.k.a. shoe ===		=== Llywelyn a.k.a. shoe ===
	Llywelyn a.k.a. shoe is the common [[restriction]] of [[gamelismic clan #Gorgo\|gorgo]] (16 & 21), [[breedsmic temperaments #Gorgik\|gorgik]] (21 & 37), and [[gariboh clan #Semaja\|semaja]] (16 & 37). It can be described as 16 & 21, and tempers out the [[llywelynsma]]. Its generator is a flattened [[~]][[8/7]] whole tone, seven of which give the interval class of [[5/1\|5]]. Its [[ploidacot]] is alpha-heptaseph. [[Weak extension]]s to the full 7-limit include [[marvel temperaments #Misneb\|misneb]] (21 & 32), which splits 8/7 into two for [[15/14]]~[[16/15]] each, [[archytas clan #Ultrapyth\|ultrapyth (32 & 37)]], which splits [[16/7]] into two for a [[3/2\|perfect fifth]], and [[buzzardsmic clan #Septimal buzzard\|buzzard]] (53 & 58), which splits 16/7 into three, each for [[21/16]].		Llywelyn a.k.a. shoe is the common [[restriction]] of [[gamelismic clan #Gorgo\|gorgo]] (16 & 21), [[breedsmic temperaments #Gorgik\|gorgik]] (21 & 37), and [[gariboh clan #Semaja\|semaja]] (16 & 37). It can be described as 16 & 21, and tempers out the [[llywelynsma]]. Its generator is a flattened [[~]][[8/7]] whole tone, seven of which give the interval class of [[5/1\|5]]. Its [[ploidacot]] is alpha-heptaseph. [[Weak extension]]s to the full 7-limit include [[marvel temperaments #Misneb\|misneb]] (21 & 32), which splits 8/7 into two for [[15/14]]~[[16/15]] each, [[archytas clan #Ultrapyth\|ultrapyth]] (32 & 37), which splits [[16/7]] into two for a [[3/2\|perfect fifth]], and [[buzzardsmic clan #Septimal buzzard\|buzzard]] (53 & 58), which splits 16/7 into three, each for [[21/16]].

	; Scales		; Scales

FloraC: Move llywelyn/shoe back here, as the clan is unnecessary

2026-11-03T05:16:34Z

Move llywelyn/shoe back here, as the clan is unnecessary

@@ Line 16: / Line 16: @@
 * Didacus ([[3136/3125]]) → [[Hemimean clan #Didacus|Hemimean clan]]
 * Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]]
 * Sidewalk ([[823543/800000]]) → [[2023/2000 #Sidewalk]]
@@ Line 209: / Line 208: @@
 [[Badness]] (Sintel): 0.156
 === Huntington ===

FloraC: Normalize mapping

2026-11-03T05:04:52Z

Normalize mapping

← Older revision		Revision as of 05:04, 3 November 2026
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	[[Comma list]]: 26/25		[[Comma list]]: 26/25

	{{Mapping\|legend=3\| 1 ~~2 3~~ \| 0 1 2 }}		{{Mapping\|legend=3\| 1 0 -1 \| 0 1 2 }}
	: mapping generators, ~2, ~5/4		: mapping generators, ~2, ~5

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	{{Mapping\|legend=2\| 1 0 1 3 \| 0 8 7 2 }}		{{Mapping\|legend=2\| 1 0 1 3 \| 0 8 7 2 }}

	~~Gencom mapping:~~ {{~~mapping~~\|\| 1 0 0 0 1 3 \| 0 0 0 8 7 2 }}		{{Mapping\|legend=4\| 1 0 0 0 1 3 \| 0 0 0 8 7 2 }}

	Optimal tunings:		Optimal tunings:
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	[[Comma list]]: 1352/1331		[[Comma list]]: 1352/1331

	{{Mapping\|legend=3\| 1 ~~3 3~~ \| 0 2 3 }}		{{Mapping\|legend=3\| 1 1 0 \| 0 2 3 }}

	{{Mapping\|legend=5\| 1 0 0 0 ~~3 3~~ \| 0 0 0 0 2 3 }}		{{Mapping\|legend=5\| 1 0 0 0 1 0 \| 0 0 0 0 2 3 }}
	: mapping generators, ~2, ~13/11		: mapping generators: ~2, ~26/11

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

FloraC: Sort by complexity of the subgroup formed by the first two primes, which seems more useful

2026-11-03T05:01:40Z

Sort by complexity of the subgroup formed by the first two primes, which seems more useful

Show changes

FloraC: /* Scaevola */ complete data

2026-10-27T10:00:51Z

Scaevola: complete data

← Older revision		Revision as of 10:00, 27 October 2026
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	=== Scaevola ===		=== Scaevola ===
	Scaevola is the 2.7.11-subgroup temperament tempering out 14641/14336, with a generator of [[11/8]] and mapping +4 generators is to [[7/4]]. Two strong extensions are [[score]] to 2.7.11.13 and [[joan]] to 2.9.7.11. Scaevola has a structure that is very similar to [[mavila]], but whereas ~~Mavila~~ has a "fifth" of [[3/2]], "major third" of [[5/4]], and "minor third" of [[6/5]], scaevola has a "fifth" of [[16/11]], "major third" of [[14/11]], and "minor third" of [[8/7]], substituting ~~Mavila~~'s 4:5:6 for 11:14:16. Essentially, Scaevola can be seen as a counterpart of ~~Mavila~~ for fifths even flatter than [[9edo]], such as [[11edo]]'s fifth. It was named by [[~~User:CompactStar\|~~CompactStar]] in 2026, referring to ''Scaevola'' (the genus of flowering plants), which is meant to sound reminiscent of "score" and "mavila" (the score and joan temperaments were actually named prior to this temperament).		Scaevola is the 2.7.11-subgroup temperament tempering out 14641/14336, with a generator of [[11/8]] and mapping +4 generators to [[7/4]]. Two strong extensions are [[#Score\|score]] to 2.7.11.13 and [[subgroup temperaments #Joan\|joan]] to 2.9.7.11.

			Scaevola has a structure that is very similar to [[mavila family #Mavila\|mavila]], but whereas mavila has a "fifth" of [[3/2]], "major third" of [[5/4]], and "minor third" of [[6/5]], scaevola has a "fifth" of [[16/11]], "major third" of [[14/11]], and "minor third" of [[8/7]], substituting mavila's 4:5:6 for 11:14:16. Essentially, Scaevola can be seen as a counterpart of mavila for fifths even flatter than [[9edo]], such as [[11edo]]'s fifth.

			It was named by [[CompactStar]] in 2026, referring to ''{{w\|Scaevola}}'' (the genus of flowering plants), which is meant to sound reminiscent of ''score'' and ''mavila'' (the score and joan temperaments were actually named prior to this temperament).

	[[Subgroup]]: 2.7.11		[[Subgroup]]: 2.7.11
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	{{Mapping\|legend=3\| 1 1 3 \| 0 4 1 }}		{{Mapping\|legend=3\| 1 1 3 \| 0 4 1 }}

			{{Mapping\|legend=5\| 1 0 0 1 3 \| 0 0 0 4 1 }}
	: mapping generators: ~2, ~11/8		: mapping generators: ~2, ~11/8

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1201.~~248~~{{c}}, ~11/8 = 542.~~116~~{{c}}		* [[WE]]: ~2 = 1201.2479{{c}}, ~11/8 = 542.1162{{c}}
	* [[CWE]]: ~2 = 1200.~~000~~{{c}}, ~11/8 = 541.~~940~~{{c}}		: [[error map]]: {{val\| +1.248 +0.887 -5.458 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 541.9403{{c}}
			: error map: {{val\| 0.000 -1.065 -9.378 }}

	{{Optimal ET sequence\|legend=1\| ~~TBA~~}}		{{Optimal ET sequence\|legend=1\| 2, 7d, 9, 11, 20, 31, 51, 82e, 113e, 195eee }}

	[[Badness]] (Sintel): 0.578		[[Badness]] (Sintel): 0.578
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	{{See also\| Chromatic pairs #Score }}		{{See also\| Chromatic pairs #Score }}

	Score is an extension of scaevola that ~~equates~~ [[13/8]] to +6 generators.		Score is an extension of scaevola that maps [[13/8]] to +6 generators.

	[[Subgroup]]: 2.7.11.13		Subgroup: 2.7.11.13

	[[Comma list]]: 343/338, 847/832		Comma list: 343/338, 847/832

	{{Mapping\|legend=3\| 1 1 3 1 \| 0 4 1 6 }}		{{Mapping\|legend=2\| 1 1 3 1 \| 0 4 1 6 }}

	{{Mapping\|legend=5\| 1 0 0 1 3 1 \| 0 0 0 4 1 6 }}		{{Mapping\|legend=4\| 1 0 0 1 3 1 \| 0 0 0 4 1 6 }}
	~~: mapping generators: ~2, ~11/8~~

	[[Optimal ~~tuning]]s~~:		Optimal tunings:
	* [[WE]]: ~2 = 1201.5484{{c}}, ~11/8 = 540.7963{{c}}		* WE: ~2 = 1201.5484{{c}}, ~11/8 = 540.7963{{c}}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 540.5091{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 540.5091{{c}}

	{{Optimal ET sequence\|legend=1\| 9, 11, 20 }}		{{Optimal ET sequence\|legend=0\| 9, 11, 20 }}

	[[Badness]] (Sintel): 0.368		Badness (Sintel): 0.368

	=== Bossier ===		=== Bossier ===

FloraC: /* Mabilic */ complete the listing of extensions

2026-10-27T09:46:42Z

Mabilic: complete the listing of extensions

← Older revision		Revision as of 09:46, 27 October 2026
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	{{See also\| Chromatic pairs #Mabilic }}		{{See also\| Chromatic pairs #Mabilic }}

	Mabilic is the no-3 [[restriction]] of [[mavila family #Armodue\|armodue]], [[~~mabila~~ family #~~Semabila~~\|~~semabila~~]], and [[~~magic~~ family #~~Trismegistus~~\|~~trismegistus~~]]. It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.		Mabilic is the no-3 [[restriction]] of [[mavila family #Armodue\|armodue]] (7 & 16), [[magic family #Trismegistus\|trismegistus]] (16 & 25), and [[mabila family #Semabila\|semabila]] (25 & 34). It is the 7 & 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma. [[Weak extension]]s of mabilic include [[archytas clan #Sixix\|sixix]] (7 & 25), [[vishnu family #Vishnean\|vishnean]] (16 & 34), [[marvel temperaments #Septimin\|septimin]] (9 & 41) and [[tetracot family #Monkey\|monkey]] (7 & 34).

	[[Subgroup]]: 2.5.7		[[Subgroup]]: 2.5.7

CompactStar: /* No-threes no-fives subgroup temperaments */

2026-10-22T02:37:25Z

No-threes no-fives subgroup temperaments

@@ Line 558: / Line 558: @@
 [[Badness]] (Sintel): 0.475
-=== Score ===
+=== Scaevola ===
 {{See also| Chromatic pairs #Score }}
-Score is a low-accuracy [[extension]] of the unnamed 2.7.11-subgroup temperament tempering out 14641/14336.
+Score is an extension of scaevola that equates [[13/8]] to +6 generators.
 [[Subgroup]]: 2.7.11.13

FloraC: /* Frostburn */ + redirect notice

2026-10-17T10:24:38Z

Frostburn: + redirect notice

← Older revision		Revision as of 10:24, 17 October 2026
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	=== Frostburn ===		=== Frostburn ===
			{{Redirect\|Frostburn\|the software developer\|Lumi Pakkanen}}

	Frostburn is the common [[restriction]] of [[magic family #Quadrimage\|quadrimage]] and [[subgroup temperaments #Baldy\|baldy]].		Frostburn is the common [[restriction]] of [[magic family #Quadrimage\|quadrimage]] and [[subgroup temperaments #Baldy\|baldy]].