No-fives subgroup temperaments - Revision history

FloraC: Recategorize

2026-10-16T13:51:53Z

Recategorize

← Older revision		Revision as of 13:51, 16 October 2026
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	[[Badness]] (Sintel): 0.0841		[[Badness]] (Sintel): 0.0841

	[[Category:~~Temperament collections]]~~		[[Category:Catalogs of subgroup temperaments]]
	~~[[Category:Subgroup~~ temperaments]]		[[Category:Catalogs of rank-2 temperaments]]
	[[Category:~~Rank~~ 2]]

CompactStar: /* Betaxenean */

2026-10-15T03:49:12Z

Betaxenean

← Older revision		Revision as of 03:49, 15 October 2026
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	=== Betaxenean ===		=== Betaxenean ===
	Betaxenean tempers out the [[Betarabian comma]]. It splits a [[3/1\|perfect twelfth]] into two halves of [[512/297]].		Betaxenean tempers out the [[Betarabian comma]]. It splits a [[3/1\|perfect twelfth]] into two halves of [[512/297]]. [[Baragon]] is a full 11-limit extension that combines this temperament with [[godzilla]], albeit not as accurate as normal betaxenean.

	[[Subgroup]]: 2.3.11		[[Subgroup]]: 2.3.11

FloraC: /* Hemif */ add lots of stuff from parahemif

2026-10-03T11:02:36Z

Hemif: add lots of stuff from parahemif

← Older revision		Revision as of 11:02, 3 October 2026
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	=== Hemif ===		=== Hemif ===
	Hemif is the no-5 [[restriction]] of [[hemififths]], and the add-7 [[extension]] of [[namo]].		Hemif tempers out the [[parahemif comma]], equating a [[Pythagorean apotome]] with a stack of two septimal third-tones of [[28/27]], and splits the fifth in two. In this temperament, the interval class of [[7/1\|7]] is found at +13 steps, as a semi-augmented sixth (C–A{{demisharp2}}). It also equates the large septimal diesis of [[49/48]] with the [[Pythagorean comma]]. This means the fifth should be tuned sharp and the septimal third-tone should be flattened to a somewhat large quartertone which can be used as the undecimal quartertone of [[33/32]], leading to a natural 11-limit extension where [[243/242]] and [[896/891]] are tempered out.

			Hemif is the common [[restriction]] of [[hemififths]] (41 & 58) and [[salsa]] (24 & 41), and the add-7 [[extension]] of [[namo]]. A [[weak extension]] of it is [[sruti]] (24 & 34d).

	[[Subgroup]]: 2.3.7		[[Subgroup]]: 2.3.7

FloraC: Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

2026-09-30T17:44:30Z

Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

Show changes

FloraC: Text replacement - "Gencom mapping: {{mapping| " to "{{Mapping|legend=4| "

2026-09-30T17:43:30Z

Text replacement - "Gencom mapping: {{mapping| " to "{{Mapping|legend=4| "

← Older revision		Revision as of 17:43, 30 September 2026
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	Subgroup-val mapping: {{mapping\| 1 1 -1 2 \| 0 2 13 5 }}		Subgroup-val mapping: {{mapping\| 1 1 -1 2 \| 0 2 13 5 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 1 0 -1 2 \| 0 2 0 13 5 }}		{{Mapping\|legend=4\| 1 1 0 -1 2 \| 0 2 0 13 5 }}

	Optimal tunings:		Optimal tunings:
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	Sval mapping: {{mapping\| 1 1 -1 2 4 \| 0 2 13 5 -1 }}		Sval mapping: {{mapping\| 1 1 -1 2 4 \| 0 2 13 5 -1 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 1 0 -1 2 4 \| 0 2 0 13 5 -1 }}		{{Mapping\|legend=4\| 1 1 0 -1 2 4 \| 0 2 0 13 5 -1 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 -1 -3 -3 \| 0 4 9 10 }}		Subgroup-val mapping: {{mapping\| 1 -1 -3 -3 \| 0 4 9 10 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 -1 0 -3 -3 \| 0 4 0 9 10 }}		{{Mapping\|legend=4\| 1 -1 0 -3 -3 \| 0 4 0 9 10 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 -1 -3 -3 -6 \| 0 4 9 10 15 }}		Subgroup-val mapping: {{mapping\| 1 -1 -3 -3 -6 \| 0 4 9 10 15 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 -1 0 -3 -3 -6 \| 0 4 0 9 10 15}}		{{Mapping\|legend=4\| 1 -1 0 -3 -3 -6 \| 0 4 0 9 10 15}}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 -1 -3 -3 5 \| 0 4 9 10 -2 }}		Subgroup-val mapping: {{mapping\| 1 -1 -3 -3 5 \| 0 4 9 10 -2 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 -1 0 -3 -3 5 \| 0 4 0 9 10 -2 }}		{{Mapping\|legend=4\| 1 -1 0 -3 -3 5 \| 0 4 0 9 10 -2 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 1 2 3 \| 0 5 7 4 }}		Subgroup-val mapping: {{mapping\| 1 1 2 3 \| 0 5 7 4 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 1 0 2 3 \| 0 5 0 7 4 }}		{{Mapping\|legend=4\| 1 1 0 2 3 \| 0 5 0 7 4 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 1 2 3 3 \| 0 5 7 4 6 }}		Subgroup-val mapping: {{mapping\| 1 1 2 3 3 \| 0 5 7 4 6 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 1 0 2 3 3 \| 0 5 0 7 4 6 }}		{{Mapping\|legend=4\| 1 1 0 2 3 3 \| 0 5 0 7 4 6 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 0 -21 -14 \| 0 1 15 11 }}		Subgroup-val mapping: {{mapping\| 1 0 -21 -14 \| 0 1 15 11 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 0 0 -21 -14 \| 0 1 0 15 11 }}		{{Mapping\|legend=4\| 1 0 0 -21 -14 \| 0 1 0 15 11 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 0 -21 -14 -9 \| 0 1 15 11 8 }}		Subgroup-val mapping: {{mapping\| 1 0 -21 -14 -9 \| 0 1 15 11 8 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 0 0 -21 -14 -9 \| 0 1 0 15 11 8 }}		{{Mapping\|legend=4\| 1 0 0 -21 -14 -9 \| 0 1 0 15 11 8 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 0 -21 -14 -9 -5 \| 0 1 15 11 8 6 }}		Subgroup-val mapping: {{mapping\| 1 0 -21 -14 -9 -5 \| 0 1 15 11 8 6 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 0 0 -21 -14 -9 0 0 -5 \| 0 1 0 15 11 8 0 0 6 }}		{{Mapping\|legend=4\| 1 0 0 -21 -14 -9 0 0 -5 \| 0 1 0 15 11 8 0 0 6 }}

	Optimal tunings:		Optimal tunings:
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	Subgroup-val mapping: {{mapping\| 1 0 -21 -14 -9 -5 -38 \| 0 1 15 11 8 6 27 }}		Subgroup-val mapping: {{mapping\| 1 0 -21 -14 -9 -5 -38 \| 0 1 15 11 8 6 27 }}

	~~Gencom mapping:~~ {{~~mapping~~\| 1 0 0 -21 -14 -9 -5 0 0 -38 \| 0 1 0 15 11 8 0 0 6 27 }}		{{Mapping\|legend=4\| 1 0 0 -21 -14 -9 -5 0 0 -38 \| 0 1 0 15 11 8 0 0 6 27 }}

	Optimal tunings:		Optimal tunings:

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:38:47Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

Show changes

FloraC: Text replacement - "{{Mapping|legend=3| " to "{{Mapping|legend=5| "

2026-09-30T17:34:09Z

Text replacement - "{{Mapping|legend=3| " to "{{Mapping|legend=5| "

← Older revision		Revision as of 17:34, 30 September 2026
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	{{Mapping\|legend=2\| 1 0 -3 \| 0 3 11 }}		{{Mapping\|legend=2\| 1 0 -3 \| 0 3 11 }}

	{{Mapping\|legend=3\| 1 0 0 -3 \| 0 3 0 11 }}		{{Mapping\|legend=5\| 1 0 0 -3 \| 0 3 0 11 }}
	: mapping generators: ~2, ~81/56		: mapping generators: ~2, ~81/56

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	{{Mapping\|legend=2\| 1 1 -1 \| 0 2 13 }}		{{Mapping\|legend=2\| 1 1 -1 \| 0 2 13 }}

	{{Mapping\|legend=3\| 1 1 0 -1 \| 0 2 0 13 }}		{{Mapping\|legend=5\| 1 1 0 -1 \| 0 2 0 13 }}
	: mapping generators: ~2, ~2187/1792		: mapping generators: ~2, ~2187/1792

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	{{Mapping\|legend=2\| 1 -1 -3 \| 0 4 9 }}		{{Mapping\|legend=2\| 1 -1 -3 \| 0 4 9 }}

	{{Mapping\|legend=3\| 1 -1 0 -3 \| 0 4 0 9 }}		{{Mapping\|legend=5\| 1 -1 0 -3 \| 0 4 0 9 }}
	: mapping generators: ~2, ~14/9		: mapping generators: ~2, ~14/9

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	{{Mapping\|legend=2\| 1 0 -13 \| 0 1 10 }}		{{Mapping\|legend=2\| 1 0 -13 \| 0 1 10 }}

	{{Mapping\|legend=3\| 1 0 0 -13 \| 0 1 0 10 }}		{{Mapping\|legend=5\| 1 0 0 -13 \| 0 1 0 10 }}
	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

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	{{Mapping\|legend=2\| 1 1 2 \| 0 5 7 }}		{{Mapping\|legend=2\| 1 1 2 \| 0 5 7 }}

	{{Mapping\|legend=3\| 1 1 0 2 \| 0 5 0 7 }}		{{Mapping\|legend=5\| 1 1 0 2 \| 0 5 0 7 }}
	: mapping generators: ~2, ~54/49		: mapping generators: ~2, ~54/49

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	{{Mapping\|legend=2\| 1 0 -21 \| 0 1 15 }}		{{Mapping\|legend=2\| 1 0 -21 \| 0 1 15 }}

	{{Mapping\|legend=3\| 1 0 0 -21 \| 0 1 0 15 }}		{{Mapping\|legend=5\| 1 0 0 -21 \| 0 1 0 15 }}
	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

Godtone: /* Semitonic */ detail

2026-09-28T13:07:14Z

Semitonic: detail

← Older revision		Revision as of 13:07, 28 September 2026
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	== Temperaments with a higher-limit gene ==		== Temperaments with a higher-limit gene ==
	=== Semitonic ===		=== Semitonic ===
	Note that [[34edo]] and [[46edo]] also support this temperament but do not appear in the optimal ET sequence due to their sharp fifths, but they are on opposite sides of the just-17's tuning such that 34 + 46 = [[80edo]] is effectively a pure [[consistent circle]] of 80 [[17/16]]'s; all of these are good tunings for the related temperament [[srutal]].		Note that [[34edo]] and [[46edo]] also support this temperament but do not appear in the optimal ET sequence due to their sharp fifths, but they are on opposite sides of the just-17's tuning such that 34 + 46 = [[80edo]] is effectively a pure [[consistent circle]] of 80 [[17/16]]'s; all of these are good tunings for the related temperament [[srutal]] in 2.3.5.17 (sometimes called [[srutal archagall]] to distinguish it from diaschismic, which prefers tunings with a more just fifth), but the accuracy of primes 7, 11 and 13 varies depending on the tuning; especially, 34edo's 7 is extremely sharp and its 11 not much better.

	[[Subgroup]]: 2.3.17		[[Subgroup]]: 2.3.17

Godtone: /* Temperaments with a higher-limit gene */ introduce technical term

2026-09-28T13:00:04Z

Temperaments with a higher-limit gene: introduce technical term

← Older revision		Revision as of 13:00, 28 September 2026
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	== Temperaments with a higher-limit gene ==		== Temperaments with a higher-limit gene ==
	=== Semitonic ===		=== Semitonic ===
	Note that [[34edo]] and [[46edo]] also support this temperament but do not appear in the optimal ET sequence due to their sharp fifths, but they are on opposite sides of the just-17's tuning such that 34 + 46 = [[80edo]] is effectively a pure circle of 80 [[17/16]]'s; all of these are good tunings for the related temperament [[srutal]].		Note that [[34edo]] and [[46edo]] also support this temperament but do not appear in the optimal ET sequence due to their sharp fifths, but they are on opposite sides of the just-17's tuning such that 34 + 46 = [[80edo]] is effectively a pure [[consistent circle]] of 80 [[17/16]]'s; all of these are good tunings for the related temperament [[srutal]].

	[[Subgroup]]: 2.3.17		[[Subgroup]]: 2.3.17

Godtone: /* Temperaments with a higher-limit gene */ note tunings 34, 46, 80 as being very close to just-17's tuning

2026-09-28T12:59:14Z

Temperaments with a higher-limit gene: note tunings 34, 46, 80 as being very close to just-17's tuning

← Older revision		Revision as of 12:59, 28 September 2026
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	== Temperaments with a higher-limit gene ==		== Temperaments with a higher-limit gene ==
	=== Semitonic ===		=== Semitonic ===
			Note that [[34edo]] and [[46edo]] also support this temperament but do not appear in the optimal ET sequence due to their sharp fifths, but they are on opposite sides of the just-17's tuning such that 34 + 46 = [[80edo]] is effectively a pure circle of 80 [[17/16]]'s; all of these are good tunings for the related temperament [[srutal]].

	[[Subgroup]]: 2.3.17		[[Subgroup]]: 2.3.17