User:Moremajorthanmajor/3L 1s (perfect fifth-equivalent) - Revision history

Moremajorthanmajor: /* Notation */

2024-12-29T20:43:54Z

Notation

Moremajorthanmajor: /* Temperaments */

2024-12-29T20:04:59Z

Temperaments

← Older revision		Revision as of 20:04, 29 December 2024
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	==Temperaments==		==Temperaments==

	The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.		The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
	==='''Napoli-Meantone'''===		==='''Napoli-Meantone (Hex meantone)'''===

	[[Subgroup]]: 3/2.6/5.8/5		[[Subgroup]]: 3/2.6/5.8/5 (5.2.3)

	[[Comma]] list: [[81/80]]		[[Comma]] list: [[81/80]]
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	[[Optimal ET sequence]]: *[[28ed5]], [[44ed5]], [[72ed5]] ≈ [[7edf]], [[11edf]], [[18edf]]		[[Optimal ET sequence]]: *[[28ed5]], [[44ed5]], [[72ed5]] ≈ [[7edf]], [[11edf]], [[18edf]]
	==='''Napoli-Archy'''===		==='''Napoli-Archy (Hex Archytas)'''===

	[[Subgroup]]: 3/2.7/6.14/9		[[Subgroup]]: 3/2.7/6.14/9 (36/7.2.3)

	[[Comma]] list: [[64/63]]		[[Comma]] list: [[64/63]]

Moremajorthanmajor: /* Napoli-Meantone */

2024-12-29T19:48:55Z

Napoli-Meantone

← Older revision		Revision as of 19:48, 29 December 2024
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	[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -2 -3}}]		[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -2 -3}}]

	[[Optimal ET sequence]]: ~([[7edf]], [[11edf]], [[18edf]])		[[Optimal ET sequence]]: *[[28ed5]], [[44ed5]], [[72ed5]] ≈ [[7edf]], [[11edf]], [[18edf]]
	==='''Napoli-Archy'''===		==='''Napoli-Archy'''===

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	[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -2 -3}}]		[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -2 -3}}]

	[[Optimal ET sequence]]: ~([[~~7edf~~]], [[~~10edf~~]], [[~~13edf~~]], [[~~16edf~~]])		[[Optimal ET sequence]]: *[[28ed36/7]], [[40ed36/7]], [[52ed36/7]] ≈ [[7edf]], [[10edf]], [[13edf]]
	===Scale tree===		===Scale tree===

Moremajorthanmajor at 12:52, 8 November 2024

2024-11-08T12:52:32Z

← Older revision		Revision as of 12:52, 8 November 2024
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	\|-		\|-
	\|Minor		\|Minor
	\|~~LLsL~~		\|LsLL
	\|<nowiki>1\|2</nowiki>		\|<nowiki>1\|2</nowiki>
	\|P		\|P

Moremajorthanmajor: /* Notation */

2024-11-07T20:38:45Z

Notation

← Older revision		Revision as of 20:38, 7 November 2024
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	\|-		\|-
	\|B fab		\|B fab
	\|Yb, Ye		\|Ybb, Yee
	\|62\15, 2861.538		\|62\15, 2861.538
	\|73\18, 2825.806		\|73\18, 2825.806
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	\|50\13, 2727.273		\|50\13, 2727.273
	\|-		\|-
	\|B fa ut		\|B fa
	\| Y		\| Yb, Ye
	\|63\15, 2907.692		\|63\15, 2907.692
	\|46\11, 2905.263		\|46\11, 2905.263
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	\|-		\|-
	\|'''B si'''		\|'''B si'''
	\|'''Y#'''		\|'''Y'''
	\|'''64\15, 2953.846'''		\|'''64\15, 2953.846'''
	\|'''47\11, 2968.421'''		\|'''47\11, 2968.421'''

Moremajorthanmajor: /* Notation */

2024-11-07T15:01:17Z

Notation

Show changes

Moremajorthanmajor: /* Notation */

2024-11-07T03:11:34Z

Notation

← Older revision		Revision as of 03:11, 7 November 2024
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	\|23\11, 1452.632		\|23\11, 1452.632
	\|38\18, 1470.968		\|38\18, 1470.968
	\|15\7, 1500		\| rowspan="2" \|15\7, 1500
	\|37\17, 1531.034		\|37\17, 1531.034
	\| 22\10, 1552.941		\| 22\10, 1552.941
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	\|24\11, 1515.789		\|24\11, 1515.789
	\|39\18, 1509.677		\|39\18, 1509.677
	~~\|15\7, 1500~~
	\|36\17, 1489.655		\|36\17, 1489.655
	\|21\10, 1482.759		\|21\10, 1482.759

Moremajorthanmajor: /* See also */

2024-11-04T16:44:15Z

Moremajorthanmajor: /* See also */

2024-10-20T21:17:07Z

See also

← Older revision		Revision as of 21:17, 20 October 2024
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	[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -2 -3}}]		[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -2 -3}}]

	[[Optimal ET sequence]]: ~(7edf, 11edf, 18edf)		[[Optimal ET sequence]]: ~([[7edf]], [[11edf]], [[18edf]])
	==='''Napoli-Archy'''===		==='''Napoli-Archy'''===

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	[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -2 -3}}]		[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -2 -3}}]

	[[Optimal ET sequence]]: ~(7edf, 10edf, 13edf, 16edf)		[[Optimal ET sequence]]: ~([[7edf]], [[10edf]], [[13edf]], [[16edf]])
	===Scale tree===		===Scale tree===

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	[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone		[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone

	[[6L 2s (52/23-equivalent)]] - Neapolitan gentle temperament		[[6L 2s (88/39-equivalent)]] - Neapolitan gentle temperament

	[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy		[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy
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	[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone		[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone

	[[9L 3s (22/13-equivalent]]) - Bijou gentle temperament		[[9L 3s (44/13-equivalent)]] - Bijou gentle temperament

	[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy		[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy
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	[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning		[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning

	[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal tuning		[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal meantone tuning

	[[18L 6s (80/7-equivalent)]] - Subdozenal high septimal tuning		[[18L 6s (80/7-equivalent)]] - Subdozenal high septimal meantone tuning

	[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning<references />		[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning<references />

Moremajorthanmajor: /* Notation */

2024-10-15T18:52:14Z

Notation

Show changes

← Older revision		Revision as of 16:44, 4 November 2024
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	\|}		\|}
	{\| class="wikitable"		{\| class="wikitable"
	\|+Cents~~<ref name=":04">Fractions repeating more than 4 digits written as continued fractions</ref>~~		\|+Cents
	! colspan="2" \|Notation		! colspan="2" \|Notation
	!Supersoft		!Supersoft
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	[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning		[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning

	[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal meantone tuning		[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal (meantone) tuning

	[[18L 6s (80/7-equivalent)]] - Subdozenal ~~high septimal~~ meantone ~~tuning~~		[[18L 6s (512/45-equivalent)]] - Subdozenal 1/6-comma meantone

	[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning~~<references~~ />		[[18L 6s (80/7-equivalent)]] - Subdozenal high septimal tuning

			[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning

			[[18L 6s (11/1-equivalent)\|18L 6s (12/1-equivalent)]] - Warped Pythagorean tuning