Quintosec family - Revision history

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]]

VectorGraphics at 04:50, 12 June 2025

2025-06-12T04:50:57Z

← Older revision		Revision as of 04:50, 12 June 2025
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	{{Mapping\|legend=1\| 5 1 22 21 \| 0 2 -3 -2 }}		{{Mapping\|legend=1\| 5 1 22 21 \| 0 2 -3 -2 }}

	~~{{Multival\|legend=1\| 10 -15 -10 -47 -44 19 }}~~

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

	~~{{Multival\|legend=1\| 10 -15 0 -47 -28 42 }}~~

	[[Optimal tuning]]:		[[Optimal tuning]]:
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	: Mapping generators: ~15/14, ~8192/4725		: Mapping generators: ~15/14, ~8192/4725

	~~{{Multival\|legend=1\| 20 -30 -10 -94 -72 61 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

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

" to "{{Technical data page}}"

2025-04-13T13:44:04Z

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

← Older revision		Revision as of 13:44, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''quintosec family''' tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo\| 47 -15 -10 }}.		The '''quintosec family''' tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo\| 47 -15 -10 }}.

BudjarnLambeth: {{Technical data page}}

2025-04-13T08:39:27Z

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

← Older revision		Revision as of 08:39, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''quintosec family''' tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo\| 47 -15 -10 }}.		The '''quintosec family''' tempers out the quintosec comma, 140737488355328/140126044921875 = {{monzo\| 47 -15 -10 }}.

Xenllium at 02:41, 1 January 2025

2025-01-01T02:41:49Z

Show changes

FloraC: /* Decoid */ copypaste description from the breedsmic temperaments page.

2024-08-02T11:45:34Z

Decoid: copypaste description from the breedsmic temperaments page.

← Older revision		Revision as of 11:45, 2 August 2024
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	== Decoid ==		== Decoid ==
	{{See also\| Breedsmic temperaments #Decoid }}		{{See also\| Breedsmic temperaments #Decoid }}

			Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[linus comma]], {{monzo\| 11 -10 -10 10 }}. 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.

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

FloraC: +CTE tunings. Review optimal ET sequences.

2024-08-02T11:43:02Z

+CTE tunings. Review optimal ET sequences.

← Older revision		Revision as of 11:43, 2 August 2024
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	== Quintosec ==		== Quintosec ==
	Quintosec is naturally a 2.3.5.11 subgroup temperament. It was documented as ''qintosec'' on the 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 now restored, 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 temperament. It was documented as ''qintosec'' on the 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 now restored, and the distinctive no-''u'' form is relegated to the lower-accuracy 7-limit extension considered below.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	Mapping: {{mapping\| 5 1 22 45 \| 0 2 -3 -8 }}		Mapping: {{mapping\| 5 1 22 45 \| 0 2 -3 -8 }}

	Optimal ~~tuning (~~CTE): ~1024/891 = 1\5, ~160/99 = 831.0932 (~16/15 = 111.0932)		Optimal tunings:
			* CTE: ~1024/891 = 1\5, ~160/99 = 831.0932 (~16/15 = 111.0932)
			* CWE: ~1024/891 = 1\5, ~160/99 = 831.0743 (~16/15 = 111.0743)

	{{Optimal ET sequence~~\|legend=1~~\| 10e, 55e, 65, 205, 270, 335, 605, 940, 1545c }}		Optimal ET sequence: {{Optimal ET sequence\| 10e, 55e, 65, 205, 270, 335, 605, 940, 1545c }}

	Badness: 0.0195		Badness: 0.0195
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	{{Multival\|legend=1\| 10 -15 -10 -47 -44 19 }}		{{Multival\|legend=1\| 10 -15 -10 -47 -44 19 }}

	Optimal ~~tuning~~ (POTE): ~400/343 = 1\5, ~80/49 = 831.553 (~15/14 = 111.553)		Optimal tunings:
			* CTE: ~400/343 = 1\5, ~80/49 = 831.7095 (~15/14 = 111.7095)
			* POTE: ~400/343 = 1\5, ~80/49 = 831.553 (~15/14 = 111.553)

	{{Optimal ET sequence\|legend=1\| 10, 55d, 65d, 75, 140d~~, 215dd~~ }}		{{Optimal ET sequence\|legend=1\| 10, …, 55d, 65d, 75, 140d }}

	[[Badness]]: 0.156764		[[Badness]]: 0.156764
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	Mapping: {{mapping\| 5 1 22 21 0 \| 0 2 -3 -2 5 }}		Mapping: {{mapping\| 5 1 22 21 0 \| 0 2 -3 -2 5 }}

	Optimal ~~tuning~~ (POTE): ~55/48 = 1\5, ~80/49 = 831.311 (~15/14 = 111.311)		Optimal tunings:
			* CTE: ~55/48 = 1\5, ~80/49 = 831.1939 (~15/14 = 111.1939)
			* POTE: ~55/48 = 1\5, ~80/49 = 831.311 (~15/14 = 111.311)

	{{Optimal ET sequence~~\|legend=1~~\| 10, 55d, 65d, 140de~~, 205dde~~ }}		Optimal ET sequence: {{Optimal ET sequence\| 10, 55d, 65d, 140de }}

	Badness: 0.077907		Badness: 0.077907
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	Mapping: {{mapping\| 5 1 22 21 -7 \| 0 2 -3 -2 7 }}		Mapping: {{mapping\| 5 1 22 21 -7 \| 0 2 -3 -2 7 }}

	Optimal ~~tuning~~ (POTE): ~220/189 = 1\5, ~44/27 = 832.448 (~15/14 = 112.448)		Optimal tunings:
			* CTE: ~220/189 = 1\5, ~44/27 = 832.4051 (~15/14 = 112.4051)
			* POTE: ~220/189 = 1\5, ~44/27 = 832.448 (~15/14 = 112.448)

	{{Optimal ET sequence~~\|legend=1~~\| 10, 75~~, 160cde~~ }}		Optimal ET sequence: {{Optimal ET sequence\| 10, 75 }}

	Badness: 0.127732		Badness: 0.127732
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	{{Multival\|legend=1\| 10 -15 0 -47 -28 42 }}		{{Multival\|legend=1\| 10 -15 0 -47 -28 42 }}

	Optimal tuning (POTE): ~8/7 = 1\5, ~45/28 = 831.113 (~16/15 = 111.113)		[[Optimal tuning]]:
			* [[CTE]]: ~8/7 = 1\5, ~45/28 = 831.1061 (~16/15 = 111.1061)
			* [[POTE]]: ~8/7 = 1\5, ~45/28 = 831.113 (~16/15 = 111.113)

	{{Optimal ET sequence\|legend=1\| 10, 55, 65, 140dd~~, 205ddd, 270ddd~~ }}		{{Optimal ET sequence\|legend=1\| 10, …, 55, 65, 140dd }}

	[[Badness]]: 0.156259		[[Badness]]: 0.156259
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	Mapping: {{mapping\| 5 1 22 14 0 \| 0 2 -3 0 5 }}		Mapping: {{mapping\| 5 1 22 14 0 \| 0 2 -3 0 5 }}

	Optimal ~~tuning~~ (POTE): ~8/7 = 1\5, ~45/28 = 830.659 (~16/15 = 110.659)		Optimal tunings:
			* CTE: ~8/7 = 1\5, ~45/28 = 830.7772 (~16/15 = 110.7772)
			* POTE: ~8/7 = 1\5, ~45/28 = 830.659 (~16/15 = 110.659)

	{{Optimal ET sequence~~\|legend=1~~\| 10, 55, 65 }}		Optimal ET sequence: {{Optimal ET sequence\| 10, 55, 65 }}

	Badness: 0.081607		Badness: 0.081607
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	Mapping: {{mapping\| 5 1 22 14 0 22 \| 0 2 -3 0 5 -1 }}		Mapping: {{mapping\| 5 1 22 14 0 22 \| 0 2 -3 0 5 -1 }}

	POTE ~~generator~~: ~45/28 = 830.910 (~16/15 = 110.910)		Optimal tunings:
			* CTE: ~8/7 = 1\5, ~45/28 = 830.8942 (~16/15 = 110.8942)
			* POTE: ~8/7 = 1\5, ~45/28 = 830.910 (~16/15 = 110.910)

	{{Optimal ET sequence~~\|legend=1~~\| 10, 55, 65 }}		Optimal ET sequence: {{Optimal ET sequence\| 10, 55, 65 }}

	Badness: 0.056390		Badness: 0.056390
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	{{Multival\|legend=1\| 20 -30 -10 -94 -72 61 }}		{{Multival\|legend=1\| 20 -30 -10 -94 -72 61 }}

	[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099, or ~225/224 = 8.901)		[[Optimal tuning]]s:
			* [[CTE]]: ~15/14 = 1\10, ~8192/4725 = 951.1086 (~16/15 = 111.1086, or ~225/224 = 8.8914)
			* [[POTE]]: ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099, or ~225/224 = 8.901)

	{{Optimal ET sequence\|legend=1\| 10, ~~120~~, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}		{{Optimal ET sequence\|legend=1\| 10, …, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}

	[[Badness]]: 0.033902		[[Badness]]: 0.033902
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	Mapping: {{mapping\| 10 0 47 36 98 \| 0 2 -3 -1 -8 }}		Mapping: {{mapping\| 10 0 47 36 98 \| 0 2 -3 -1 -8 }}

	Optimal ~~tuning~~ (POTE): ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070, or ~225/224 = 8.930)		Optimal tunings:
			* CTE: ~15/14 = 1\10, ~400/231 = 951.0943 (~16/15 = 111.0943, or ~225/224 = 8.9057)
			* POTE: ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070, or ~225/224 = 8.930)

	Optimal ET sequence: {{Optimal ET sequence\| 10e, 130, 270, 670, 940, 1210, 2150c }}		Optimal ET sequence: {{Optimal ET sequence\| 10e, …, 130, 270, 670, 940, 1210, 2150c }}

	Badness: 0.018735		Badness: 0.018735
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	Mapping: {{mapping\| 10 0 47 36 98 37 \| 0 2 -3 -1 -8 0 }}		Mapping: {{mapping\| 10 0 47 36 98 37 \| 0 2 -3 -1 -8 0 }}

	Optimal ~~tuning~~ (POTE): ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083, or ~196/195 = 8.917)		Optimal tunings:
			* CTE: ~15/14 = 1\10, ~26/15 = 951.0943 (~16/15 = 111.0943, or ~196/195 = 8.9057)
			* POTE: ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083, or ~196/195 = 8.917)

	Optimal ET sequence: {{Optimal ET sequence\| 10e, 130, 270, 940, 1210f, 1480cf }}		Optimal ET sequence: {{Optimal ET sequence\| 10e, …, 130, 270, 940, 1210f, 1480cf }}

	Badness: 0.013475		Badness: 0.013475

			== Notes ==

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

FloraC: /* Decoid */ +reduced generators

2024-08-02T08:54:35Z

Decoid: +reduced generators

← Older revision		Revision as of 08:54, 2 August 2024
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	{{Multival\|legend=1\| 20 -30 -10 -94 -72 61 }}		{{Multival\|legend=1\| 20 -30 -10 -94 -72 61 }}

	Optimal tuning (POTE): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099)		[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099, or ~225/224 = 8.901)

	{{Optimal ET sequence\|legend=1\| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}		{{Optimal ET sequence\|legend=1\| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
Line 145:		Line 145:
	Mapping: {{mapping\| 10 0 47 36 98 \| 0 2 -3 -1 -8 }}		Mapping: {{mapping\| 10 0 47 36 98 \| 0 2 -3 -1 -8 }}

	Optimal tuning (POTE): ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070)		Optimal tuning (POTE): ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070, or ~225/224 = 8.930)

	{{Optimal ET sequence~~\|legend=1~~\| 10e, 130, 270, 670, 940, 1210, 2150c }}		Optimal ET sequence: {{Optimal ET sequence\| 10e, 130, 270, 670, 940, 1210, 2150c }}

	Badness: 0.018735		Badness: 0.018735
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	Mapping: {{mapping\| 10 0 47 36 98 37 \| 0 2 -3 -1 -8 0 }}		Mapping: {{mapping\| 10 0 47 36 98 37 \| 0 2 -3 -1 -8 0 }}

	Optimal tuning (POTE): ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083)		Optimal tuning (POTE): ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083, or ~196/195 = 8.917)

	{{Optimal ET sequence~~\|legend=1~~\| 10e, 130, 270, 940, 1210f, 1480cf }}		Optimal ET sequence: {{Optimal ET sequence\| 10e, 130, 270, 940, 1210f, 1480cf }}

	Badness: 0.013475		Badness: 0.013475

BudjarnLambeth: Made consistent with the formatting of other temperament pages

2024-03-19T22:30:16Z

Made consistent with the formatting of other temperament pages

← Older revision		Revision as of 22:30, 19 March 2024
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	: mapping generators: ~524288/455625, ~16384/10125		: mapping generators: ~524288/455625, ~16384/10125

	[[Optimal tuning]] ([[CTE]]): ~524288/455625 = 1\5, ~16384/10125 = 831.1061 (~16/15 = 111.1061)		[[Optimal tuning]]s:
			* [[CTE]]: ~524288/455625 = 1\5, ~16384/10125 = 831.1061 (~16/15 = 111.1061)
	~~[[Optimal tuning]] (~~[[POTE]]): ~524288/455625 = 1\5, ~16384/10125 = 831.105 (~16/15 = 111.105)		* [[POTE]]: ~524288/455625 = 1\5, ~16384/10125 = 831.105 (~16/15 = 111.105)

	{{Optimal ET sequence\|legend=1\| 10, 45c, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}		{{Optimal ET sequence\|legend=1\| 10, 45c, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc }}
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	{{Multival\|legend=1\| 10 -15 -10 -47 -44 19 }}		{{Multival\|legend=1\| 10 -15 -10 -47 -44 19 }}

	[[Optimal tuning]] ([[POTE]]): ~400/343 = 1\5, ~80/49 = 831.553 (~15/14 = 111.553)		Optimal tuning (POTE): ~400/343 = 1\5, ~80/49 = 831.553 (~15/14 = 111.553)

	{{Optimal ET sequence\|legend=1\| 10, 55d, 65d, 75, 140d, 215dd }}		{{Optimal ET sequence\|legend=1\| 10, 55d, 65d, 75, 140d, 215dd }}
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	{{Multival\|legend=1\| 10 -15 0 -47 -28 42 }}		{{Multival\|legend=1\| 10 -15 0 -47 -28 42 }}

	[[Optimal tuning]] ([[POTE]]): ~8/7 = 1\5, ~45/28 = 831.113 (~16/15 = 111.113)		Optimal tuning (POTE): ~8/7 = 1\5, ~45/28 = 831.113 (~16/15 = 111.113)

	{{Optimal ET sequence\|legend=1\| 10, 55, 65, 140dd, 205ddd, 270ddd }}		{{Optimal ET sequence\|legend=1\| 10, 55, 65, 140dd, 205ddd, 270ddd }}
Line 132:		Line 132:
	{{Multival\|legend=1\| 20 -30 -10 -94 -72 61 }}		{{Multival\|legend=1\| 20 -30 -10 -94 -72 61 }}

	[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099)		Optimal tuning (POTE): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099)

	{{Optimal ET sequence\|legend=1\| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}		{{Optimal ET sequence\|legend=1\| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}