Quintosec family - Revision history

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:36Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:32, 24 September 2026
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	Comma list: 5632/5625, 26214400/26198073		Comma list: 5632/5625, 26214400/26198073

	~~Mapping:~~ {{~~mapping~~\| 5 1 22 45 \| 0 2 -3 -8 }}		{{Mapping\|legend=0\| 5 1 22 45 \| 0 2 -3 -8 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 225/224, 243/242, 3840/3773		Comma list: 225/224, 243/242, 3840/3773

	~~Mapping:~~ {{~~mapping~~\| 5 1 22 21 0 \| 0 2 -3 -2 5 }}		{{Mapping\|legend=0\| 5 1 22 21 0 \| 0 2 -3 -2 5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 225/224, 385/384, 332750/321489		Comma list: 225/224, 385/384, 332750/321489

	~~Mapping:~~ {{~~mapping~~\| 5 1 22 21 -7 \| 0 2 -3 -2 7 }}		{{Mapping\|legend=0\| 5 1 22 21 -7 \| 0 2 -3 -2 7 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 243/242, 385/384, 686/675		Comma list: 243/242, 385/384, 686/675

	~~Mapping:~~ {{~~mapping~~\| 5 1 22 14 0 \| 0 2 -3 0 5 }}		{{Mapping\|legend=0\| 5 1 22 14 0 \| 0 2 -3 0 5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 91/90, 169/168, 243/242, 385/384		Comma list: 91/90, 169/168, 243/242, 385/384

	~~Mapping:~~ {{~~mapping~~\| 5 1 22 14 0 15 \| 0 2 -3 0 5 1 }}		{{Mapping\|legend=0\| 5 1 22 14 0 15 \| 0 2 -3 0 5 1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 2401/2400, 5632/5625, 9801/9800		Comma list: 2401/2400, 5632/5625, 9801/9800

	~~Mapping:~~ {{~~mapping~~\| 10 0 47 36 98 \| 0 2 -3 -1 -8 }}		{{Mapping\|legend=0\| 10 0 47 36 98 \| 0 2 -3 -1 -8 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095		Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095

	~~Mapping:~~ {{~~mapping~~\| 10 0 47 36 98 37 \| 0 2 -3 -1 -8 0 }}		{{Mapping\|legend=0\| 10 0 47 36 98 37 \| 0 2 -3 -1 -8 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 2401/2400, 42592/42525, 1771561/1769472		Comma list: 2401/2400, 42592/42525, 1771561/1769472

	~~Mapping:~~ {{~~mapping~~\| 30 0 141 108 80 \| 0 2 -3 -1 1 }}		{{Mapping\|legend=0\| 30 0 141 108 80 \| 0 2 -3 -1 1 }}
	: mapping generators: ~45/44, ~8192/4725		: mapping generators: ~45/44, ~8192/4725

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	Comma list: 676/675, 2401/2400, 4096/4095, 6656/6655		Comma list: 676/675, 2401/2400, 4096/4095, 6656/6655

	~~Mapping:~~ {{~~mapping~~\| 30 0 141 108 80 111 \| 0 2 -3 -1 1 0 }}		{{Mapping\|legend=0\| 30 0 141 108 80 111 \| 0 2 -3 -1 1 0 }}

	Optimal tunings:		Optimal tunings:

FloraC: Note what qinto might be useful for

2026-09-07T07:54:32Z

Note what qinto might be useful for

← Older revision		Revision as of 07:54, 7 September 2026
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	=== Qinto ===		=== Qinto ===
			This alternative extension can be tuned to [[75edo]] and [[85edo]], both in [[patent val]]s.

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

FloraC: Change 13-limit sengasec (see talk)

2026-09-07T07:54:05Z

Change 13-limit sengasec (see talk)

← Older revision		Revision as of 07:54, 7 September 2026
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	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: ~~105~~/~~104~~, ~~144~~/~~143~~, 243/242, ~~686~~/~~675~~		Comma list: 91/90, 169/168, 243/242, 385/384

	Mapping: {{mapping\| 5 1 22 14 0 22 \| 0 2 -3 0 5 -1 }}		Mapping: {{mapping\| 5 1 22 14 0 15 \| 0 2 -3 0 5 1 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~8/7 = ~~239~~.~~9825~~{{c}}, ~45/28 = ~~830~~.~~8492~~{{c}} (~16/15 = 110.~~9018~~{{c}})		* WE: ~8/7 = 240.1611{{c}}, ~13/8 = 831.2123{{c}} (~16/15 = 110.7289{{c}})
	* CWE: ~8/7 = 240.0000{{c}}, ~45/28 = 830.~~9071~~{{c}} (~16/15 = 110.~~9071~~{{c}})		* CWE: ~8/7 = 240.0000{{c}}, ~13/8 = 830.6933{{c}} (~16/15 = 110.6933{{c}})

	{{Optimal ET sequence\|legend=0\| 10, 55, 65 }}		{{Optimal ET sequence\|legend=0\| 10, 55f, 65f }}

	Badness (Sintel): 2.33		Badness (Sintel): 2.08

	== Decoid ==		== Decoid ==

FloraC: + history of the naming of sengasec

2026-09-04T08:18:27Z

+ history of the naming of sengasec

← Older revision		Revision as of 08:18, 4 September 2026
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	== Sengasec ==		== Sengasec ==
	Sengasec can be described as the 10 & 65 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.		Sengasec can be described as the 10 & 65 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit. It was named by [[Xenllium]] in 2021.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Expand

2026-09-04T08:00:23Z

Expand

← Older revision		Revision as of 08:00, 4 September 2026
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	== Quintosec ==		== Quintosec ==
			Quintosec has a 1/5-octave period and a generator of around 831 [[cent]]s such that two of them plus a period make the [[3/1\|3rd harmonic]]. However, an equivalent generator is the neutral third, in addition to the minimal generator, [[~]][[16/15]]. The [[ploidacot]] of this temperament is pentaploid dicot.

	Quintosec is naturally a [[2.3.5.11 subgroup\|2.3.5.11-subgroup]] temperament. It was documented as ''qintosec'' on the [https://x31eq.com/temper/ Temperament Finder], which was probably due to a typo<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo Tuning Group \| ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>. The original, intended spelling is restored here, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.		Quintosec is naturally a [[2.3.5.11 subgroup\|2.3.5.11-subgroup]] temperament. It was documented as ''qintosec'' on the [https://x31eq.com/temper/ Temperament Finder], which was probably due to a typo<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo Tuning Group \| ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>. The original, intended spelling is restored here, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.

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	Optimal tunings:		Optimal tunings:
	* WE: ~55/48 = 239.8038{{c}}, ~80/49 = 830.6313{{c}} (~15~~/14~~ = 111.2200{{c}})		* WE: ~55/48 = 239.8038{{c}}, ~80/49 = 830.6313{{c}} (~16/15 = 111.2200{{c}})
	* CWE: ~55/48 = 240.0000{{c}}, ~80/49 = 831.2911{{c}} (~15~~/14~~ = 111.2911{{c}})		* CWE: ~55/48 = 240.0000{{c}}, ~80/49 = 831.2911{{c}} (~16/15 = 111.2911{{c}})

	{{Optimal ET sequence\|legend=0\| 10, 55d, 65d, 140de }}		{{Optimal ET sequence\|legend=0\| 10, 55d, 65d, 140de }}
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	Optimal tunings:		Optimal tunings:
	* WE: ~220/189 = 239.9453{{c}}, ~44/27 = 832.2583{{c}} (~15~~/14~~ = 112.4224{{c}})		* WE: ~220/189 = 239.9453{{c}}, ~44/27 = 832.2583{{c}} (~16/15 = 112.4224{{c}})
	* CWE: ~220/189 = 240.0000{{c}}, ~44/27 = 832.4403{{c}} (~15~~/14~~ = 112.4403{{c}})		* CWE: ~220/189 = 240.0000{{c}}, ~44/27 = 832.4403{{c}} (~16/15 = 112.4403{{c}})

	{{Optimal ET sequence\|legend=0\| 10, 75 }}		{{Optimal ET sequence\|legend=0\| 10, 75 }}
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	== Sengasec ==		== Sengasec ==
	Sengasec can be described as the 10 & 55 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.		Sengasec can be described as the 10 & 65 temperament, tempering out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Decoid ==		== Decoid ==
	Decoid tempers out 2401/2400, the [[breedsma]], and 67108864/66976875, the [[decovulture comma]], as well as {{monzo\| 11 -10 -10 10 }}, the [[linus comma]]. ~~Either~~ ~[[8/7]] or ~[[16/15]] ~~can be used as its generator~~. ~~It may be described as the 130 & 270 temperament, and as one might expect,~~ 181\940 or 233\1210 makes for an excellent tuning choice.		Decoid tempers out 2401/2400, the [[breedsma]], and 67108864/66976875, the [[decovulture comma]], as well as {{monzo\| 11 -10 -10 10 }}, the [[linus comma]]. It may be described as the 130 & 270 temperament, and its [[ploidacot]] is decaploid dicot. The hemitwelfth or neutral third can be used as a generator, but also ~[[8/7]], ~[[16/15]], or the [[marvel comma]]. 181\940 or 233\1210 makes for an excellent tuning choice.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-09-04T07:38:10Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Units & misc. cleanup

2026-09-04T06:50:36Z

Units & misc. cleanup

Show changes

FloraC: Notes -> references; recategorize

2026-08-14T12:18:15Z

Notes -> references; recategorize

← Older revision		Revision as of 12:18, 14 August 2026
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	Badness: 0.040873		Badness: 0.040873

	== ~~Notes~~ ==		== References ==

	~~[[Category:Temperament families]]~~
	[[Category:Quintosec family\| ]] <!-- main article -->		[[Category:Quintosec family\| ]] <!-- main article -->
	[[Category:Quintosec\| ]] <!-- key article -->		[[Category:Quintosec\| ]] <!-- key article -->
	[[Category:~~Rank~~ 2]]		[[Category:Temperament families]]
			[[Category:Catalogs of rank-2 temperaments]]

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

2025-11-27T12:27:11Z

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

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

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

2025-06-24T00:37:37Z

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

← Older revision		Revision as of 00:37, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Quintosec family\| ]] <!-- main article -->		[[Category:Quintosec family\| ]] <!-- main article -->
	[[Category:Quintosec\| ]] <!-- key article -->		[[Category:Quintosec\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]