Gamelismic family - Revision history

Squib: /* Gamel */

2026-03-02T19:54:10Z

Gamel

← Older revision		Revision as of 19:54, 2 March 2026
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	== Gamel ==		== Gamel ==
	This esoteric alternative extension tempers out [[540/539]], and sometimes comes up in temperament searches. In practice however, it is almost always desirable to further temper it to [[miracle]], which enables many more [[essentially tempered chord]]s while introducing virtually no additional error.		This esoteric alternative extension tempers out [[540/539]], and sometimes comes up in temperament searches. In practice however, it is almost always desirable to further temper it to [[miracle]], in which case is is identical to portent anyway. This enables many more [[essentially tempered chord]]s while introducing virtually no additional error.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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

2025-11-27T12:20:06Z

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

← Older revision		Revision as of 12:20, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Gamelismic family\| ]] <!-- main article -->		[[Category:Gamelismic family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: + intro to each entry

2025-11-11T13:23:18Z

+ intro to each entry

← Older revision		Revision as of 13:23, 11 November 2025
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	{{Main\| Gamelismic and portent }}		{{Main\| Gamelismic and portent }}

	Portent ~~has a~~ [[~~Normal lists #normal interval list\|normal comma list~~]] [1029/1024, 385/384~~] and also tempers out~~ 441/440.		Portent tempers out [[385/384]] and [[441/440]] and is the main extension of gamelismic. Notice the identity 1029/1024 = (385/384)⋅(441/440).

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	== Gamel ==		== Gamel ==
			This esoteric alternative extension tempers out [[540/539]], and sometimes comes up in temperament searches. In practice however, it is almost always desirable to further temper it to [[miracle]], which enables many more [[essentially tempered chord]]s while introducing virtually no additional error.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: - POTE tunings

2025-11-11T13:04:42Z

- POTE tunings

← Older revision		Revision as of 13:04, 11 November 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.7474{{c}}, ~5/4 = 385.5205{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.7474{{c}}, ~5/4 = 385.5205{{c}}
	: error map: {{val\| 0.000 -0.713 -0.793 -2.573 }}		: error map: {{val\| 0.000 -0.713 -0.793 -2.573 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.6875{{c}}, ~5/4 = 385.1853{{c}} -->~~
	~~<!-- [[TE tuning\|TE]] [[tuning map]]: {{val\| 1200.486 1901.833 2786.314 3367.676 }} -->~~

	[[Minimax tuning]]: ''c'' = 1029/1024		[[Minimax tuning]]: ''c'' = 1029/1024
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.7616{{c}}, ~5/4 = 385.3149{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.7616{{c}}, ~5/4 = 385.3149{{c}}
	: error map: {{val\| 0.000 -0.670 -0.999 -2.587 -1.586 }}		: error map: {{val\| 0.000 -0.670 -0.999 -2.587 -1.586 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.6884{{c}}, ~5/4 = 385.1618{{c}} -->~~

	[[Minimax tuning]]: ''c''<sub>1</sub> = 1029/1024, ''c''<sub>2</sub> = 385/384		[[Minimax tuning]]: ''c''<sub>1</sub> = 1029/1024, ''c''<sub>2</sub> = 385/384
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	* WE: ~2 = 1200.4540{{c}}, ~8/7 = 234.0013{{c}}, ~5/4 = 384.8733{{c}}		* WE: ~2 = 1200.4540{{c}}, ~8/7 = 234.0013{{c}}, ~5/4 = 384.8733{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.9748{{c}}, ~5/4 = 384.8812{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.9748{{c}}, ~5/4 = 384.8812{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.9128{{c}}, ~5/4 = 384.7278{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 15, 26, 31f, 41, 46, 72, 87, 159 }}		{{Optimal ET sequence\|legend=0\| 15, 26, 31f, 41, 46, 72, 87, 159 }}
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	* WE: ~2 = 1200.4888{{c}}, ~8/7 = 233.7795{{c}}, ~5/4 = 385.1398{{c}}		* WE: ~2 = 1200.4888{{c}}, ~8/7 = 233.7795{{c}}, ~5/4 = 385.1398{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.7575{{c}}, ~5/4 = 385.1447{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.7575{{c}}, ~5/4 = 385.1447{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6843{{c}}, ~5/4 = 384.9830{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 452cdef, 611cddef }}		{{Optimal ET sequence\|legend=0\| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 452cdef, 611cddef }}
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	* WE: ~2 = 1200.7019{{c}}, ~8/7 = 233.5453{{c}}, ~5/4 = 385.6079{{c}}		* WE: ~2 = 1200.7019{{c}}, ~8/7 = 233.5453{{c}}, ~5/4 = 385.6079{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4510{{c}}, ~5/4 = 385.6739{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4510{{c}}, ~5/4 = 385.6739{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4088{{c}}, ~5/4 = 385.3825{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 15f, 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}		{{Optimal ET sequence\|legend=0\| 15f, 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}
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	* WE: ~2 = 1200.6745{{c}}, ~8/7 = 233.5625{{c}}, ~5/4 = 385.5056{{c}}		* WE: ~2 = 1200.6745{{c}}, ~8/7 = 233.5625{{c}}, ~5/4 = 385.5056{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4679{{c}}, ~5/4 = 385.5892{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4679{{c}}, ~5/4 = 385.5892{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4313{{c}}, ~5/4 = 385.2890{{c}} -->~~

	Minimax tuning:		Minimax tuning:
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	* WE: ~2 = 1200.0652{{c}}, ~8/7 = 234.1856{{c}}, ~5/4 = 386.6199{{c}}		* WE: ~2 = 1200.0652{{c}}, ~8/7 = 234.1856{{c}}, ~5/4 = 386.6199{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.1748{{c}}, ~5/4 = 386.5951{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.1748{{c}}, ~5/4 = 386.5951{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4088{{c}}, ~5/4 = 385.3825{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 15f, 21e, 31, 41, 46, 72f, 77, 87, 118, 164, 205d }}		{{Optimal ET sequence\|legend=0\| 15f, 21e, 31, 41, 46, 72f, 77, 87, 118, 164, 205d }}
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	* WE: ~2 = 1200.2251{{c}}, ~8/7 = 233.4102{{c}}, ~5/4 = 382.4142{{c}}		* WE: ~2 = 1200.2251{{c}}, ~8/7 = 233.4102{{c}}, ~5/4 = 382.4142{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4017{{c}}, ~5/4 = 382.4261{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4017{{c}}, ~5/4 = 382.4261{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.3664{{c}}, ~5/4 = 382.3425{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 5, 10, 15, 25e, 26, 31, 41, 72f }}		{{Optimal ET sequence\|legend=0\| 5, 10, 15, 25e, 26, 31, 41, 72f }}
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	* WE: ~2 = 1200.5451{{c}}, ~8/7 = 233.7495{{c}}, ~14/13 = 128.4023{{c}}		* WE: ~2 = 1200.5451{{c}}, ~8/7 = 233.7495{{c}}, ~14/13 = 128.4023{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6930{{c}}, ~14/13 = 128.3684{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6930{{c}}, ~14/13 = 128.3684{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6434{{c}}, ~14/13 = 128.3440{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}		{{Optimal ET sequence\|legend=0\| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}
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	* WE: ~2 = 1200.4416{{c}}, ~8/7 = 233.7663{{c}}, ~14/13 = 128.4622{{c}}		* WE: ~2 = 1200.4416{{c}}, ~8/7 = 233.7663{{c}}, ~14/13 = 128.4622{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.7173{{c}}, ~14/13 = 128.4269{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.7173{{c}}, ~14/13 = 128.4269{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6803{{c}}, ~14/13 = 128.4149{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}		{{Optimal ET sequence\|legend=0\| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.3289{{c}}, ~5/4 = 384.5627{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.3289{{c}}, ~5/4 = 384.5627{{c}}
	: error map: {{val\| 0.000 -1.968 -1.751 -2.155 -0.137 }}		: error map: {{val\| 0.000 -1.968 -1.751 -2.155 -0.137 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.2909{{c}}, ~5/4 = 384.2120{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 5e, 10, 21e, 26e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}		{{Optimal ET sequence\|legend=1\| 5e, 10, 21e, 26e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}

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

2025-11-11T13:00:04Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

Show changes

FloraC: Units & misc. cleanup

2025-11-11T12:30:23Z

Units & misc. cleanup

← Older revision		Revision as of 12:30, 11 November 2025
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	{{Mapping\|legend=1\| 1 1 0 3 \| 0 3 0 -1 \| 0 0 1 0 }}		{{Mapping\|legend=1\| 1 1 0 3 \| 0 3 0 -1 \| 0 0 1 0 }}

	: mapping generators: ~2, ~8/7, ~5		: mapping generators: ~2, ~8/7, ~5

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	: Angle (8/7, 5/4) = 90 degrees		: Angle (8/7, 5/4) = 90 degrees

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.6875, ~5/4 = 385.1853		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~8/7 = 233.6875{{c}}, ~5/4 = 385.1853{{c}}

	[[Minimax tuning]]: c = 1029/1024		[[Minimax tuning]]: ''c'' = 1029/1024
	* [[7-odd-limit]]: 3, 5, and 7 1/4~~-comma~~ flat		* [[7-odd-limit]]: 3, 5, and 7 (1/4)''c'' flat
	: {{~~monzo~~ list\| 1 0 0 0 \| 5/2 3/4 0 -3/4 \| 5/2 -1/4 1 -3/4 \| 5/2 -1/4 0 1/4 }}		: {{Monzo list\| 1 0 0 0 \| 5/2 3/4 0 -3/4 \| 5/2 -1/4 1 -3/4 \| 5/2 -1/4 0 1/4 }}
	: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/3.5/3		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/3.5/3
	* [[9-odd-limit]]: 3 1/7-comma flat, 5 and 7 2/7-comma flat		* [[9-odd-limit]]: 3 1/7-comma flat, 5 and 7 2/7-comma flat
	: {{~~monzo~~ list\| 1 0 0 0 \| 10/7 6/7 0 -3/7 \| 10/7 -1/7 1 -3/7 \| 20/7 -2/7 0 1/7 }}		: {{Monzo list\| 1 0 0 0 \| 10/7 6/7 0 -3/7 \| 10/7 -1/7 1 -3/7 \| 20/7 -2/7 0 1/7 }}
	: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5/3.9/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5/3.9/7

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	: Angle (8/7, 12/11) = 86.657 degrees		: Angle (8/7, 12/11) = 86.657 degrees

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.6884, ~5/4 = 385.1618		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~8/7 = 233.6884{{c}}, ~5/4 = 385.1618{{c}}

	[[Minimax tuning]]: c = 1029/1024, e = 385/384		[[Minimax tuning]]: ''c''<sub>1</sub> = 1029/1024, ''c''<sub>2</sub> = 385/384
	* [[11-odd-limit]]: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat		* [[11-odd-limit]]: 3 (1/7)''c''<sub>1</sub> flat, 5 and 7 (2/7)''c''<sub>1</sub> flat, 11 (''c''<sub>2</sub> - (3/7)''c''<sub>1</sub>) flat
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 10/7 6/7 0 -3/7 0 }}, {{monzo\| 39/14 4/7 1/2 -2/7 -1/2 }}, {{monzo\| 20/7 -2/7 0 1/7 0 }}, {{monzo\| 39/14 4/7 -1/2 -2/7 1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 10/7 6/7 0 -3/7 0 }}, {{monzo\| 39/14 4/7 1/2 -2/7 -1/2 }}, {{monzo\| 20/7 -2/7 0 1/7 0 }}, {{monzo\| 39/14 4/7 -1/2 -2/7 1/2 }}]
	: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.11/5~~, 9/7~~		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11/5

	{{Optimal ET sequence\|legend=1\| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}		{{Optimal ET sequence\|legend=1\| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}
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	Mapping: {{mapping\| 1 1 0 3 5 6 \| 0 3 0 -1 4 12 \| 0 0 1 0 -1 -2 }}		Mapping: {{mapping\| 1 1 0 3 5 6 \| 0 3 0 -1 4 12 \| 0 0 1 0 -1 -2 }}

	Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.9128, ~5/4 = 384.7278		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.9128{{c}}, ~5/4 = 384.7278{{c}}

	{{Optimal ET sequence\|legend=0\| 15, 26, 41, 46, 72, 87, 159, 477cdf }}		{{Optimal ET sequence\|legend=0\| 15, 26, 41, 46, 72, 87, 159, 477cdf }}
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	Mapping: {{mapping\| 1 1 0 3 5 -5 \| 0 3 0 -1 4 -3 \| 0 0 1 0 -1 4 }}		Mapping: {{mapping\| 1 1 0 3 5 -5 \| 0 3 0 -1 4 -3 \| 0 0 1 0 -1 4 }}

	Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6843, ~5/4 = 384.9830		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.6843{{c}}, ~5/4 = 384.9830{{c}}

	{{Optimal ET sequence\|legend=0\| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }}		{{Optimal ET sequence\|legend=0\| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }}
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	Mapping: {{mapping\| 1 1 0 3 5 1 \| 0 3 0 -1 4 -10 \| 0 0 1 0 -1 2 }}		Mapping: {{mapping\| 1 1 0 3 5 1 \| 0 3 0 -1 4 -10 \| 0 0 1 0 -1 2 }}

	Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4088, ~5/4 = 385.3825		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.4088{{c}}, ~5/4 = 385.3825{{c}}

	{{Optimal ET sequence\|legend=0\| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }}		{{Optimal ET sequence\|legend=0\| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }}
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	: Angle (8/7, 6/5) = 98.6015		: Angle (8/7, 6/5) = 98.6015

	Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4313, ~5/4 = 385.2890		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.4313{{c}}, ~5/4 = 385.2890{{c}}

	Minimax tuning:		Minimax tuning:
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	Mapping: {{mapping\| 1 1 0 3 5 7 \| 0 3 0 -4 1 -5 \| 0 0 1 0 -1 -1 }}		Mapping: {{mapping\| 1 1 0 3 5 7 \| 0 3 0 -4 1 -5 \| 0 0 1 0 -1 -1 }}

	Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4088, ~5/4 = 385.3825		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.4088{{c}}, ~5/4 = 385.3825{{c}}

	{{Optimal ET sequence\|legend=0\| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }}		{{Optimal ET sequence\|legend=0\| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }}
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	Mapping: {{mapping\| 1 1 0 3 5 1 \| 0 3 0 -1 4 2 \| 0 0 1 0 -1 1 }}		Mapping: {{mapping\| 1 1 0 3 5 1 \| 0 3 0 -1 4 2 \| 0 0 1 0 -1 1 }}

	Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.3664, ~5/4 = 382.3425		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.3664{{c}}, ~5/4 = 382.3425{{c}}

	{{Optimal ET sequence\|legend=0\| 5, 10, 15, 26, 31, 41, 72f, 185cf }}		{{Optimal ET sequence\|legend=0\| 5, 10, 15, 26, 31, 41, 72f, 185cf }}
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	Mapping: {{mapping\| 1 1 2 3 3 4 \| 0 3 0 -1 4 -1 \| 0 0 3 0 -3 -1 }}		Mapping: {{mapping\| 1 1 2 3 3 4 \| 0 3 0 -1 4 -1 \| 0 0 3 0 -3 -1 }}

	Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6434, ~14/13 = 128.3440		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.6434{{c}}, ~14/13 = 128.3440{{c}}

	{{Optimal ET sequence\|legend=0\| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}		{{Optimal ET sequence\|legend=0\| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}
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	Mapping: {{mapping\| 1 1 2 3 3 4 4 \| 0 3 0 -1 4 -1 1 \| 0 0 3 0 -3 -1 -1 }}		Mapping: {{mapping\| 1 1 2 3 3 4 4 \| 0 3 0 -1 4 -1 1 \| 0 0 3 0 -3 -1 -1 }}

	Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6803, ~14/13 = 128.4149		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.6803{{c}}, ~14/13 = 128.4149{{c}}

	{{Optimal ET sequence\|legend=0\| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}		{{Optimal ET sequence\|legend=0\| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}
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	{{Mapping\|legend=1\| 1 1 0 3 -1 \| 0 3 0 -1 11 \| 0 0 1 0 1 }}		{{Mapping\|legend=1\| 1 1 0 3 -1 \| 0 3 0 -1 11 \| 0 0 1 0 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.2909, ~5/4 = 384.2120		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~8/7 = 233.2909{{c}}, ~5/4 = 384.2120{{c}}

	{{Optimal ET sequence\|legend=1\| 10, 31, 41, 72 }}		{{Optimal ET sequence\|legend=1\| 10, 31, 41, 72 }}
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	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:Gamelismic family\| ]] <!-- main article -->		[[Category:Gamelismic family\| ]] <!-- main article -->
	~~[[Category:Gamelismic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-24T00:37:08Z

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
Line 204:		Line 204:

	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Gamelismic family\| ]] <!-- main article -->		[[Category:Gamelismic family\| ]] <!-- main article -->
	[[Category:Gamelismic\| ]] <!-- key article -->		[[Category:Gamelismic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

Lériendil: Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "

2025-06-21T06:58:00Z

Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "

← Older revision		Revision as of 06:58, 21 June 2025
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	* [[7-odd-limit]]: 3, 5, and 7 1/4-comma flat		* [[7-odd-limit]]: 3, 5, and 7 1/4-comma flat
	: {{monzo list\| 1 0 0 0 \| 5/2 3/4 0 -3/4 \| 5/2 -1/4 1 -3/4 \| 5/2 -1/4 0 1/4 }}		: {{monzo list\| 1 0 0 0 \| 5/2 3/4 0 -3/4 \| 5/2 -1/4 1 -3/4 \| 5/2 -1/4 0 1/4 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/3.5/3		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/3.5/3
	* [[9-odd-limit]]: 3 1/7-comma flat, 5 and 7 2/7-comma flat		* [[9-odd-limit]]: 3 1/7-comma flat, 5 and 7 2/7-comma flat
	: {{monzo list\| 1 0 0 0 \| 10/7 6/7 0 -3/7 \| 10/7 -1/7 1 -3/7 \| 20/7 -2/7 0 1/7 }}		: {{monzo list\| 1 0 0 0 \| 10/7 6/7 0 -3/7 \| 10/7 -1/7 1 -3/7 \| 20/7 -2/7 0 1/7 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5/3.9/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5/3.9/7

	[[TE tuning\|TE]] [[tuning map]]: {{val\| 1200.486 1901.833 2786.314 3367.676 }}		[[TE tuning\|TE]] [[tuning map]]: {{val\| 1200.486 1901.833 2786.314 3367.676 }}
Line 63:		Line 63:
	* [[11-odd-limit]]: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat		* [[11-odd-limit]]: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 10/7 6/7 0 -3/7 0 }}, {{monzo\| 39/14 4/7 1/2 -2/7 -1/2 }}, {{monzo\| 20/7 -2/7 0 1/7 0 }}, {{monzo\| 39/14 4/7 -1/2 -2/7 1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 10/7 6/7 0 -3/7 0 }}, {{monzo\| 39/14 4/7 1/2 -2/7 -1/2 }}, {{monzo\| 20/7 -2/7 0 1/7 0 }}, {{monzo\| 39/14 4/7 -1/2 -2/7 1/2 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.11/5, 9/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.11/5, 9/7

	{{Optimal ET sequence\|legend=1\| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}		{{Optimal ET sequence\|legend=1\| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}
Line 132:		Line 132:
	* 17-odd-limit		* 17-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 0 }}, {{monzo\| 7/4 9/10 0 0 -3/10 -3/20 0 }}, {{monzo\| 5/2 7/5 0 0 -4/5 1/10 0 }}, {{monzo\| 11/4 -3/10 0 0 1/10 1/20 0 }}, {{monzo\| 7/2 -1/5 0 0 2/5 -3/10 0 }}, {{monzo\| 7/2 -1/5 0 0 -3/5 7/10 0 }}, {{monzo\| 4 2/5 0 0 -4/5 3/5 0 }}]		: [{{monzo\| 1 0 0 0 0 0 0 }}, {{monzo\| 7/4 9/10 0 0 -3/10 -3/20 0 }}, {{monzo\| 5/2 7/5 0 0 -4/5 1/10 0 }}, {{monzo\| 11/4 -3/10 0 0 1/10 1/20 0 }}, {{monzo\| 7/2 -1/5 0 0 2/5 -3/10 0 }}, {{monzo\| 7/2 -1/5 0 0 -3/5 7/10 0 }}, {{monzo\| 4 2/5 0 0 -4/5 3/5 0 }}]
	: ~~eigenmonzo (~~unchanged-interval) basis: 2.11/9.13/9		: unchanged-interval (eigenmonzo) basis: 2.11/9.13/9

	{{Optimal ET sequence\|legend=0\| 26, 31, 46, 72, 103, 149, 175f, 221ef }}		{{Optimal ET sequence\|legend=0\| 26, 31, 46, 72, 103, 149, 175f, 221ef }}

FloraC: Cleanup. Spell 1\1 in decimal. Note the badness metric being used

2025-05-12T10:04:18Z

Cleanup. Spell 1\1 in decimal. Note the badness metric being used