The Quartercache - Revision history

FloraC: Complete data for quartic and direct quartismic

2026-04-17T15:31:13Z

Complete data for quartic and direct quartismic

← Older revision		Revision as of 15:31, 17 April 2026
Line 12:		Line 12:
	[[Comma list]]: 117440512/117406179		[[Comma list]]: 117440512/117406179

	~~[[Sval]] [[mapping]]: [~~{{~~val~~\| 1 0 1 5 ~~}}, {{val~~\| 0 1 1 -1 ~~}}, {{val~~\| 0 0 5 1 }}]		{{Mapping\|legend=1\| 1 0 1 5 \| 0 1 1 -1 \| 0 0 5 1 }}
			: mapping generators: ~2, ~3, ~33/32

	[[~~POTE generator~~]]s: ~3/2 = 701.~~9826~~, ~33/32 = 53.~~3748~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.9875{{c}}, ~3/2 = 701.9753{{c}}, ~33/32 = 53.3743{{c}}
			: [[error map]]: {{val\| -0.012 +0.008 -0.004 +0.031 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9802{{c}}, ~33/32 = 53.3730{{c}}
			: error map: {{val\| 0.000 +0.025 +0.019 +0.075 }}

	{{Optimal ET sequence\|legend=1\| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}		{{Optimal ET sequence\|legend=1\| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}

			[[Badness]] (Sintel): 0.416

	The following rank-2 [[mos scale]]s of quartismic have been found:		The following rank-2 [[mos scale]]s of quartismic have been found:
Line 23:		Line 30:

	== Direct quartismic ==		== Direct quartismic ==
	Instead of 11-limit, defined directly in the 2.33/2.~~7/6~~ subgroup, as the quartisma itself was discovered via a representation where the generator is 33/32 and five of them stack to 7/6. [[45edo]] is an excellent tuning.		Instead of 11-limit, direct quartismic is defined directly in the 2.7/3.33 subgroup, as the quartisma itself was discovered via a representation where the generator is 33/32 and five of them stack to 7/6. [[45edo]] is an excellent tuning. It was named by [[Eliora]] in 2023.

	[[Subgroup]]: 2.33/32.~~7/6~~		[[Subgroup]]: 2.7/3.33

	[[Comma list]]: 117440512/117406179		[[Comma list]]: 117440512/117406179

	{{Mapping\|legend=2\| 1 ~~0 0~~ \| 0 1 5 }}		{{Mapping\|legend=2\| 1 1 5 \| 0 5 1 }}
	: mapping generators: ~2, ~33/32		: mapping generators: ~2, ~33/32

			[[Optimal tuning]]s:
			* [[Tp tuning\|Subgroup]] [[WE]]: ~2 = 1199.9875{{c}}, ~33/32 = 53.3743{{c}}
			: [[error map]]: {{val\| -0.012 -0.012 +0.039 }}
			* [[Tp tuning\|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~33/32 = 53.3730{{c}}
			: error map: {{val\| 0.000 -0.006 +0.100 }}

			{{Optimal ET sequence\|legend=1\| 21, 22, 45, 337, 382, 427, 472, 517, 562, 607, 652, 1911, 2563, 3215, 5778, 8993* }}

			<nowiki/>* wart for 33

	== Altierran ==		== Altierran ==

FloraC: - duplicate and misc. cleanup

2026-04-17T15:21:11Z

- duplicate and misc. cleanup

Show changes

VectorGraphics at 05:05, 12 June 2025

2025-06-12T05:05:48Z

← Older revision		Revision as of 05:05, 12 June 2025
Line 57:		Line 57:
	[[Comma list]]: 32805/32768, 161280/161051		[[Comma list]]: 32805/32768, 161280/161051

	[[Mapping]]: [{{val\| 1 0 15 1 5 }}, {{val\| 0 1 -8 1 -1 }}, {{val\| 0 0 0 5 1 }}]		[[Mapping]]: [{{val\| 1 0 15 1 5 }}, {{val\| 0 1 -8 1 -1 }}, {{val\| 0 0 0 5 1 }}]

	~~{{Multival\|legend=1\|rank=3\| -102 24 -15 75 6 -8 40 1 -5 0 }}~~

	[[POTE generator]]s: ~3/2 = 701.7299, ~33/32 = 53.3889		[[POTE generator]]s: ~3/2 = 701.7299, ~33/32 = 53.3889

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

" to "{{Technical data page}}"

2025-04-13T13:48:42Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:48, 13 April 2025
Line 1:		Line 1:
	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	'''The Quartercache''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}. Among the members of this family are quartic, Altierran, meanquarter, coin, escapismic, dietismic, kleirtismic, doublefour and quarterframe.		'''The Quartercache''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}. Among the members of this family are quartic, Altierran, meanquarter, coin, escapismic, dietismic, kleirtismic, doublefour and quarterframe.

BudjarnLambeth: {{Technical data page}}

2025-04-13T07:05:20Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 07:05, 13 April 2025
Line 1:		Line 1:
			{{Technical data page}}<br><br>
	'''The Quartercache''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}. Among the members of this family are quartic, Altierran, meanquarter, coin, escapismic, dietismic, kleirtismic, doublefour and quarterframe.		'''The Quartercache''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}. Among the members of this family are quartic, Altierran, meanquarter, coin, escapismic, dietismic, kleirtismic, doublefour and quarterframe.

Lériendil at 18:06, 8 February 2025

2025-02-08T18:06:44Z

← Older revision		Revision as of 18:06, 8 February 2025
Line 1:		Line 1:
	'''The Quartercache''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}. Among the members of this family are ~~quartismatic~~, Altierran, meanquarter, coin, escapismic, dietismic, kleirtismic, doublefour and quarterframe.		'''The Quartercache''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}. Among the members of this family are quartic, Altierran, meanquarter, coin, escapismic, dietismic, kleirtismic, doublefour and quarterframe.

	== Quartismic ==		== Quartismic ==

Lériendil: /* Quartic */

2024-11-22T03:22:32Z

Quartic

← Older revision		Revision as of 03:22, 22 November 2024
Line 20:		Line 20:
	[[Badness]]: 0.274 × 10<sup>-6</sup>		[[Badness]]: 0.274 × 10<sup>-6</sup>

	== ~~Quartismatic~~ ==		== Quartic ==
	There are some temperaments that temper out the quartisma despite having limited accuracy in their approximations of five-limit intervals. This particular temperament is the parent temperament of all such no-fives children, and is referred to as '''Saquinlu-azo temperament''' in color notation.		There are some temperaments that temper out the quartisma despite having limited accuracy in their approximations of five-limit intervals. This particular temperament is the parent temperament of all such no-fives children, and is referred to as '''Saquinlu-azo temperament''' in color notation.

ArrowHead294 at 13:54, 26 April 2024

2024-04-26T13:54:52Z

← Older revision		Revision as of 13:54, 26 April 2024
Line 21:		Line 21:

	== Quartismatic ==		== Quartismatic ==
			There are some temperaments that temper out the quartisma despite having limited accuracy in their approximations of five-limit intervals. This particular temperament is the parent temperament of all such no-fives children, and is referred to as '''Saquinlu-azo temperament''' in color notation.
	There are some temperaments in the ~~Quartercache~~ in ~~which the quartisma is tempered out, but without any sort~~ of five-limit ~~representation~~. This particular temperament is the parent temperament of all such no-fives children, and is referred to as '''Saquinlu-azo temperament''' in color notation.

	Subgroup: 2.3.7.11		Subgroup: 2.3.7.11
Line 68:		Line 67:

	=== Tenierian ===		=== Tenierian ===

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Line 80:		Line 78:

	== Meanquarter ==		== Meanquarter ==

	In meanquarter, both the meantone comma and the quartisma are tempered out.		In meanquarter, both the meantone comma and the quartisma are tempered out.

Line 96:		Line 93:

	== Coin ==		== Coin ==

	In coin, both the magic comma and the quartisma are tempered out.		In coin, both the magic comma and the quartisma are tempered out.

Line 112:		Line 108:

	== Escapismic ==		== Escapismic ==

	In escapisimic, both the escapade comma and the quartisma are tempered out, thus, it is essentially an [[Escapade family\|escapade expansion]].		In escapisimic, both the escapade comma and the quartisma are tempered out, thus, it is essentially an [[Escapade family\|escapade expansion]].

Line 128:		Line 123:

	== Dietismic ==		== Dietismic ==

	In dietismic, both the diaschisma and the quartisma are tempered out. Dietismic can easily be further tempered to [[Diaschismic family #Shrutar\|shrutar]], and in fact, it is rather unusual to find a different tempering option.		In dietismic, both the diaschisma and the quartisma are tempered out. Dietismic can easily be further tempered to [[Diaschismic family #Shrutar\|shrutar]], and in fact, it is rather unusual to find a different tempering option.

Line 150:		Line 144:

	== Kleirtismic ==		== Kleirtismic ==

	In kleirtismic, both the kleisma and the quartisma are tempered out. The "kleir-" in "kleirtismic" is pronounced the same as "Clair".		In kleirtismic, both the kleisma and the quartisma are tempered out. The "kleir-" in "kleirtismic" is pronounced the same as "Clair".

Line 166:		Line 159:

	== Doublefour ==		== Doublefour ==

	In doublefour, both the tetracot comma and the quartisma are tempered out.		In doublefour, both the tetracot comma and the quartisma are tempered out.

Eliora: /* Prequartismic */ style

2024-02-24T13:08:31Z

Prequartismic: style

← Older revision		Revision as of 13:08, 24 February 2024
Line 225:		Line 225:
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: {{monzo\|24, -6, 0, 1, -5}}, {{monzo\|-1, 4, 11, -11, 0}}, {{monzo\|-19 -25 14 13 -3}}		[[Comma list]]: {{monzo\|24 -6 0 1 -5}}, {{monzo\|-1 4 11 -11 0}}, {{monzo\|-19 -25 14 13 -3}}

	[[Mapping]]: [{{val\|1 1389 890 1395 -1383}}, {{val\|0 -1452 -929 -1457 1451}}]		[[Mapping]]: [{{val\|1 1389 890 1395 -1383}}, {{val\|0 -1452 -929 -1457 1451}}]

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T20:09:18Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 20:09, 7 May 2023
Line 231:		Line 231:
	[[Optimal tuning]] ([[CTE]]): ~64/33 = 1146.624		[[Optimal tuning]] ([[CTE]]): ~64/33 = 1146.624

	~~Vals:~~ {{~~EDOs~~\|1259e, 1866, 3125, 4384e, 4991, 6250e, 8116d, 7509ee, 9375e, 11241de}}		{{Optimal ET sequence\|legend=1\|1259e, 1866, 3125, 4384e, 4991, 6250e, 8116d, 7509ee, 9375e, 11241de}}

	=== 13-limit ===		=== 13-limit ===