Quartismic family - Revision history

FloraC: Redirected page to Catalog of rank-4 temperaments#Quartismic (117440512/117406179)

2026-04-17T15:02:05Z

Redirected page to Catalog of rank-4 temperaments#Quartismic (117440512/117406179)

← Older revision		Revision as of 15:02, 17 April 2026
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	~~{{Technical data page}}~~		#redirect [[Catalog of rank-4 temperaments #Quartismic (117440512/117406179)]]
	~~The '''quartismic family''' is a family of~~ [[rank-4]] temperaments tempers out the [[quartisma]] – the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].

	== Quartismic ==

	~~The 11-limit parent comma for the quartismic family is the the quartisma with a ratio of~~ 117440512/117406179 ~~and a monzo of {{monzo\| 24 -6 0 1 -5 }}. As the quartisma is an unnoticeable comma, this rank-4 temperament is a [[microtemperament]].~~

	~~[[Subgroup]]: 2.3.5.7.11~~

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

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

	~~Mapping generators: ~2, ~3, ~5, ~33/32~~

	~~[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683~~

	{{Optimal ET sequence\|legend=1\| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}

	~~[[Badness]]: 0.274 × 10<sup>-6</sup>~~

	~~== Tridecimal quartismic ==~~
	~~[[Subgroup]]: 2.3.5.7.11.13~~

	~~[[Comma list]]: 6656/6655, 123201/123200~~

	~~[[Mapping]]: [{{val\| 1 0 0 1 5 6 }}, {{val\| 0 1 0 1 -1 -3 }}, {{val\| 0 0 1 0 0 1 }}, {{val\| 0 0 0 5 1 3 }}]~~

	~~[[Optimal tuning]] ([[CTE]]~~)~~: ~2 = 1\1, ~3/2 = 701.9695, ~5/4 = 386.3174, ~33/32 = 53.3698~~

	~~{{Optimal ET sequence\|legend=1\| 22, 43f, 46, 65d, 89f, 111, 159, 224, 270, 494, 764, 1012, 1236, 1506, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816dee }}~~

	~~[[Badness]]: 1.739 × 10<sup>-6</sup>~~

	~~[[Category:Temperament families]]~~
	~~[[Category:Microtemperaments]]~~
	~~[[Category:Quartismic]]~~
	~~[[Category:Rank 4~~]]

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

2025-11-27T12:32:02Z

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

← Older revision		Revision as of 12:32, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Microtemperaments]]		[[Category:Microtemperaments]]
	[[Category:Quartismic]]		[[Category:Quartismic]]
	[[Category:Rank 4]]		[[Category:Rank 4]]

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

2025-06-24T00:26:34Z

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

← Older revision		Revision as of 00:26, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Microtemperaments]]		[[Category:Microtemperaments]]
	[[Category:Quartismic]]		[[Category:Quartismic]]
	[[Category:Rank 4]]		[[Category:Rank 4]]

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

" to "{{Technical data page}}"

2025-04-13T13:46:27Z

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

← Older revision		Revision as of 13:46, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''quartismic family''' is a family of [[rank-4]] temperaments tempers out the [[quartisma]] – the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].		The '''quartismic family''' is a family of [[rank-4]] temperaments tempers out the [[quartisma]] – the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:51:20Z

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

← Older revision		Revision as of 11:51, 13 April 2025
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	The '''quartismic family''' is a family of rank-4 temperaments tempers out the [[quartisma]] – the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].		{{Technical data page}}<br><br>
			The '''quartismic family''' is a family of [[rank-4]] temperaments tempers out the [[quartisma]] – the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].

	== Quartismic ==		== Quartismic ==

Francium: typo

2024-01-09T13:17:08Z

typo

← Older revision		Revision as of 13:17, 9 January 2024
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	The '''quartismic family''' is a family of rank-4 temperaments tempers out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].		The '''quartismic family''' is a family of rank-4 temperaments tempers out the [[quartisma]] – the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo\|24 -6 0 1 -5}}, however, most of the members of this rank-4 family currently have yet to be explored. For other families that are defined by the tempering of this comma, see [[the Quartercache]].

	== Quartismic ==		== Quartismic ==

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

2023-05-07T18:28:12Z

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

← Older revision		Revision as of 18:28, 7 May 2023
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	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683

	{{~~Val list~~\|legend=1\| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}		{{Optimal ET sequence\|legend=1\| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}

	[[Badness]]: 0.274 × 10<sup>-6</sup>		[[Badness]]: 0.274 × 10<sup>-6</sup>
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	[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9695, ~5/4 = 386.3174, ~33/32 = 53.3698		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9695, ~5/4 = 386.3174, ~33/32 = 53.3698

	{{~~Val list~~\|legend=1\| 22, 43f, 46, 65d, 89f, 111, 159, 224, 270, 494, 764, 1012, 1236, 1506, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816dee }}		{{Optimal ET sequence\|legend=1\| 22, 43f, 46, 65d, 89f, 111, 159, 224, 270, 494, 764, 1012, 1236, 1506, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816dee }}

	[[Badness]]: 1.739 × 10<sup>-6</sup>		[[Badness]]: 1.739 × 10<sup>-6</sup>

FloraC: /* Quartismic */ +obvious extension

2023-01-31T10:42:54Z

Quartismic: +obvious extension

← Older revision		Revision as of 10:42, 31 January 2023
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	The 11-limit parent comma for the quartismic family is the the quartisma with a ratio of 117440512/117406179 and a monzo of {{monzo\| 24 -6 0 1 -5 }}. As the quartisma is an unnoticeable comma, this rank-4 temperament is a [[microtemperament]].		The 11-limit parent comma for the quartismic family is the the quartisma with a ratio of 117440512/117406179 and a monzo of {{monzo\| 24 -6 0 1 -5 }}. As the quartisma is an unnoticeable comma, this rank-4 temperament is a [[microtemperament]].

	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 117440512/117406179		[[Comma list]]: 117440512/117406179
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	[[Mapping]]: [{{val\| 1 0 0 1 5 }}, {{val\| 0 1 0 1 -1 }}, {{val\| 0 0 1 0 0 }}, {{val\| 0 0 0 5 1 }}]		[[Mapping]]: [{{val\| 1 0 0 1 5 }}, {{val\| 0 1 0 1 -1 }}, {{val\| 0 0 1 0 0 }}, {{val\| 0 0 0 5 1 }}]

	~~{{Multival\|legend=1\|rank=4\|~~ 5 ~~1 0 -6 -24 }}~~		Mapping generators: ~2, ~3, ~5, ~33/32

	[[~~POTE generator~~]]s: ~3/2 = 701.~~9826~~, ~5/4 = 386.~~3427~~, ~33/32 = 53.~~3748~~		[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9742, ~5/4 = 386.3137, ~33/32 = 53.3683

	{{Val list\|legend=1\| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}		{{Val list\|legend=1\| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}

	[[Badness]]: 0.274 × 10<sup>-6</sup>		[[Badness]]: 0.274 × 10<sup>-6</sup>

			== Tridecimal quartismic ==
			[[Subgroup]]: 2.3.5.7.11.13

			[[Comma list]]: 6656/6655, 123201/123200

			[[Mapping]]: [{{val\| 1 0 0 1 5 6 }}, {{val\| 0 1 0 1 -1 -3 }}, {{val\| 0 0 1 0 0 1 }}, {{val\| 0 0 0 5 1 3 }}]

			[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9695, ~5/4 = 386.3174, ~33/32 = 53.3698

			{{Val list\|legend=1\| 22, 43f, 46, 65d, 89f, 111, 159, 224, 270, 494, 764, 1012, 1236, 1506, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816dee }}

			[[Badness]]: 1.739 × 10<sup>-6</sup>

	[[Category:Temperament families]]		[[Category:Temperament families]]

Fredg999 category edits: Removing from Category:Regular temperament theory using Cat-a-lot

2022-03-02T22:11:18Z

Removing from Category:Regular temperament theory using Cat-a-lot

← Older revision		Revision as of 22:11, 2 March 2022
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	[[Badness]]: 0.274 × 10<sup>-6</sup>		[[Badness]]: 0.274 × 10<sup>-6</sup>

	~~[[Category:Regular temperament theory]]~~
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Microtemperaments]]		[[Category:Microtemperaments]]
	[[Category:Quartismic]]		[[Category:Quartismic]]
	[[Category:Rank 4]]		[[Category:Rank 4]]

Fredg999 category edits: Moving from Category:Microtemperament to Category:Microtemperaments using Cat-a-lot

2022-02-28T20:14:06Z

Moving from Category:Microtemperament to Category:Microtemperaments using Cat-a-lot

← Older revision		Revision as of 20:14, 28 February 2022
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	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:~~Microtemperament~~]]		[[Category:Microtemperaments]]
	[[Category:Quartismic]]		[[Category:Quartismic]]
	[[Category:Rank 4]]		[[Category:Rank 4]]