Quindromeda family - Revision history

Xenllium at 22:17, 1 March 2026

2026-03-01T22:17:49Z

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Xenllium at 02:03, 1 March 2026

2026-03-01T02:03:12Z

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Xenllium at 09:32, 27 February 2026

2026-02-27T09:32:31Z

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Xenllium at 22:54, 23 January 2026

2026-01-23T22:54:55Z

← Older revision		Revision as of 22:54, 23 January 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''quindromeda family''' tempers out {{monzo\| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]]. It ~~does not split~~ the ~~octave but splits~~ the fourth in five, making it a member of [[Ploidacot/Omega-pentacot\|omega-pentacot]] temperaments.		The '''quindromeda family''' tempers out {{monzo\| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]]. It is also the temperament where the fourth ([[4/3]]) is identified by a stack of five generators, making it a member of [[Ploidacot/Omega-pentacot\|omega-pentacot]] temperaments.

	== Quindromeda ==		== Quindromeda ==

Xenllium at 22:50, 23 January 2026

2026-01-23T22:50:35Z

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FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:22:47Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:22, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Quindromeda family\| ]] <!-- main article -->		[[Category:Quindromeda family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:28:26Z

Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Quindromeda family\| ]] <!-- main article -->		[[Category:Quindromeda family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 05:17, 12 June 2025

2025-06-12T05:17:40Z

← Older revision		Revision as of 05:17, 12 June 2025
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	[[Mapping]]: [{{val\| 1 2 0 -3 }}, {{val\| 0 -5 28 70 }}]		[[Mapping]]: [{{val\| 1 2 0 -3 }}, {{val\| 0 -5 28 70 }}]

	~~{{Multival\|legend=1\| 5 -28 -70 -56 -125 -84 }}~~

	[[POTE generator]]: ~200/189 = 99.555		[[POTE generator]]: ~200/189 = 99.555
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	[[Mapping]]: [{{val\| 1 2 0 -2 }}, {{val\| 0 -5 28 58 }}]		[[Mapping]]: [{{val\| 1 2 0 -2 }}, {{val\| 0 -5 28 58 }}]

	~~{{Multival\|legend=1\| 5 -28 -58 -56 -106 -56 }}~~

	[[POTE generator]]: ~625/588 = 99.483		[[POTE generator]]: ~625/588 = 99.483
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	[[Mapping]]: [{{val\| 1 2 0 15 }}, {{val\| 0 -5 28 -147 }}]		[[Mapping]]: [{{val\| 1 2 0 15 }}, {{val\| 0 -5 28 -147 }}]

	~~{{Multival\|legend=1\| 5 -28 147 -56 219 420 }}~~

	[[POTE generator]]: ~4428675/4194304 = 99.529		[[POTE generator]]: ~4428675/4194304 = 99.529
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	[[Mapping]]: [{{val\|1 2 0 6}}, {{val\|0 -10 56 -77}}]		[[Mapping]]: [{{val\|1 2 0 6}}, {{val\|0 -10 56 -77}}]

	~~{{Multival\|legend=1\| 10 -56 77 -112 94 336 }}~~

	[[POTE generator]]: ~36/35 = 49.756		[[POTE generator]]: ~36/35 = 49.756

FloraC: Text replacement - "{{Technical data page}}

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2025-04-13T13:44:30Z

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← Older revision		Revision as of 13:44, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''quindromeda family''' tempers out {{monzo\| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]].		The '''quindromeda family''' tempers out {{monzo\| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]].

Xenllium at 11:06, 13 April 2025

2025-04-13T11:06:23Z

← Older revision		Revision as of 11:06, 13 April 2025
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	=== Subgroup temperament ===		=== Subgroup temperament ===

	The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the ~~password comma (~~[[1216/1215]]), ~~aureusma (~~[[1445/1444]]), and 6144/6137. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1\|fifth harmonic]].		The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the [[1216/1215\|password comma]] (1216/1215), [[1445/1444\|aureusma]] (1445/1444), and [[6144/6137\|langwisma]] (6144/6137). An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1\|fifth harmonic]].

	==== 2.3.5.17 ====		==== 2.3.5.17 ====
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	[[Tp tuning #T2 tuning\|RMS error]]: 0.0813 cents		[[Tp tuning #T2 tuning\|RMS error]]: 0.0813 cents

	Badness: 0.007140		[[Badness]]: 0.007140

	== Quintagar ==		== Quintagar ==
	The ''quintagar'' temperament (12&217) tempers out the hemimean comma (3136/3125) and the [[garischisma]] (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, 256/255 (the difference between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), 361/360 (between 19/18 and 20/19), and 400/399 (between 20/19 and 21/20) are equated together, and 476/475 (between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&217, tempering out 441/440), ''quinsandra'' (217&229, equating 385/384 with 400/399), and ''quinsandric'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quinsandra'' (217&229), ''quinsandric'' (12f&229), and ''quinsandro'' (12&229). The name ''quintagar'' is so named because the generator is 1/5 of the [[Schismatic family #Garibaldi\|garibaldi]] fourth (~4/3, about 497.8 cents).		The ''quintagar'' temperament (12&217) tempers out the [[3136/3125\|hemimean comma]] (3136/3125) and the [[garischisma]] (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, [[256/255]] (the difference between 16/15 and 17/16), [[289/288]] (between 17/16 and 18/17), [[324/323]] (between 18/17 and 19/18), [[361/360]] (between 19/18 and 20/19), and [[400/399]] (between 20/19 and 21/20) are equated together, and [[476/475]] (between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&217, tempering out [[441/440]]), ''quinsandra'' (217&229, equating [[385/384]] with 400/399), and ''quinsandric'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quinsandra'' (217&229), ''quinsandric'' (12f&229), and ''quinsandro'' (12&229). The name ''quintagar'' is so named because the generator is 1/5 of the [[Schismatic family #Garibaldi\|garibaldi]] fourth (~4/3, about 497.8 cents).

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7
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	== Quintakwai ==		== Quintakwai ==
	The ''quintakwai'' temperament (12&193) tempers out the hemifamity comma (5120/5103) and the compass comma (9765625/9680832~~, quinruyoyo~~) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, 225/224 (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai\|kwai]] fourth (~4/3, about 497.4 cents).		The ''quintakwai'' temperament (12&193) tempers out the [[5120/5103\|hemifamity comma]] (5120/5103) and the compass comma (9765625/9680832) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, [[225/224]] (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai\|kwai]] fourth (~4/3, about 497.4 cents).

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7
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	== Quindro ==		== Quindro ==
	The ''quindro'' temperament (205&217) is an extension of the ''quindromeda'' temperament which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079).		The ''quindro'' temperament (205&217) is an extension of the ''quindromeda'' temperament which tempers out the [[4375/4374\|ragisma]] (4375/4374), the [[5632/5625\|vishdel comma]] (5632/5625), and the [[2080/2079\|ibnsinma]] (2080/2079).

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

Quindromeda family - Revision history

Xenllium at 22:17, 1 March 2026

Xenllium at 02:03, 1 March 2026

Xenllium at 09:32, 27 February 2026

Xenllium at 22:54, 23 January 2026

Xenllium at 22:50, 23 January 2026

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

VectorGraphics at 05:17, 12 June 2025

FloraC: Text replacement - "{{Technical data page}}" to "{{Technical data page}}"

Xenllium at 11:06, 13 April 2025

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"