User:Moremajorthanmajor/7L 3s (perfect eleventh-equivalent) - Revision history

Moremajorthanmajor: /* And Scale tree */

2024-11-26T17:05:46Z

And Scale tree

← Older revision		Revision as of 17:05, 26 November 2024
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	\|4L+4s, 11L+7s		\|4L+4s, 11L+7s
	\|}		\|}
	==~~And~~ Scale tree==		==Scale tree==
	The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible ~ed8/3s, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between ~ed8/3 would be (3+2)\(10+7) = 5\17 – five degrees of [[17edXI]]:		The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible ~ed8/3s, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between ~ed8/3 would be (3+2)\(10+7) = 5\17 – five degrees of [[17edXI]]:
	{\| class="wikitable center-all"		{\| class="wikitable center-all"

2024-11-07T20:34:29Z

Intervals

2024-11-07T06:16:56Z

Intervals

2024-10-28T00:08:22Z

Bolivar-Meantone

← Older revision		Revision as of 00:08, 28 October 2024
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	[[Mapping]]: [{{val\|1 0 -3}}, {{val\|0 1 6}}]		[[Mapping]]: [{{val\|1 0 -3}}, {{val\|0 1 6}}]

	[[Optimal ET sequence]]: ~[[17ed8/3]], ~[[27ed8/3]], ~[[44ed8/3]]		[[Optimal ET sequence]]: [[17ed8/3]], [[27ed8/3]], [[44ed8/3]]
	==='''Bolivar-Superpyth'''===		==='''Bolivar-Superpyth'''===
	[[Subgroup]]: 8/3.2.7/6		[[Subgroup]]: 8/3.2.7/6
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	[[Mapping]]: [{{val\|1 0 2}}, {{val\|0 1 -4}}]		[[Mapping]]: [{{val\|1 0 2}}, {{val\|0 1 -4}}]

	[[Optimal ET sequence]]: ~[[17ed8/3]], ~[[24ed8/3]], ~[[31ed8/3]], ~[[38ed8/3]]		[[Optimal ET sequence]]: [[17ed8/3]], [[24ed8/3]], [[31ed8/3]], [[38ed8/3]]
	==7-note subsets==		==7-note subsets==
	If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L 4s (eleventh equivalent)\|3L 4s]]:		If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L 4s (eleventh equivalent)\|3L 4s]]:

2024-10-28T00:06:36Z

Scale tree

← Older revision		Revision as of 00:06, 28 October 2024
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	\|-		\|-
	\| 45\64		\| 45\64
	\|506.~~{{Overline\|6}}~~\|\|7\|\|5\|\|1.400\|\|		\|506.667\|\|7\|\|5\|\|1.400\|\|
	\|-		\|-
	\| 19\27		\| 19\27
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	[[Mapping]]: [{{val\|1 0 -3}}, {{val\|0 1 6}}]		[[Mapping]]: [{{val\|1 0 -3}}, {{val\|0 1 6}}]

	[[Optimal ET sequence]]: [[17ed8/3]], [[27ed8/3]], [[44ed8/3]]		[[Optimal ET sequence]]: ~[[17ed8/3]], ~[[27ed8/3]], ~[[44ed8/3]]
	==='''Bolivar-Superpyth'''===		==='''Bolivar-Superpyth'''===
	[[Subgroup]]: 8/3.2.7/6		[[Subgroup]]: 8/3.2.7/6
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	[[Mapping]]: [{{val\|1 0 2}}, {{val\|0 1 -4}}]		[[Mapping]]: [{{val\|1 0 2}}, {{val\|0 1 -4}}]

	[[Optimal ET sequence]]: [[17ed8/3]], [[24ed8/3]], [[31ed8/3]], [[38ed8/3]]		[[Optimal ET sequence]]: ~[[17ed8/3]], ~[[24ed8/3]], ~[[31ed8/3]], ~[[38ed8/3]]
	==7-note subsets==		==7-note subsets==
	If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L 4s (eleventh equivalent)\|3L 4s]]:		If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L 4s (eleventh equivalent)\|3L 4s]]:

2024-05-26T02:31:07Z

Scale tree

2023-07-26T02:20:15Z

2023-07-18T22:26:28Z

Scale tree

← Older revision		Revision as of 22:26, 18 July 2023
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	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	! colspan="10" \|Generator		! colspan="10" \|Generator
	!Cents~~<ref name=":0">Fractions with repeat period 2 or longer in minutes and seconds</ref>~~		!Cents
	!L		!L
	!s		!s

2023-07-11T23:21:16Z

← Older revision		Revision as of 23:21, 11 July 2023
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	[[Mapping]]: [{{val\|1 0 -3}}, {{val\|0 1 6}}]		[[Mapping]]: [{{val\|1 0 -3}}, {{val\|0 1 6}}]

	[[Optimal ET sequence]]: 17ed8/3, 27ed8/3, 44ed8/3		[[Optimal ET sequence]]: [[17ed8/3]], [[27ed8/3]], [[44ed8/3]]
	==='''Bolivar-Superpyth'''===		==='''Bolivar-Superpyth'''===
	[[Subgroup]]: 8/3.2.7/6		[[Subgroup]]: 8/3.2.7/6
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	[[Mapping]]: [{{val\|1 0 2}}, {{val\|0 1 -4}}]		[[Mapping]]: [{{val\|1 0 2}}, {{val\|0 1 -4}}]

	[[Optimal ET sequence]]: 17ed8/3, 24ed8/3, 31ed8/3, 38ed8/3		[[Optimal ET sequence]]: [[17ed8/3]], [[24ed8/3]], [[31ed8/3]], [[38ed8/3]]
	==7-note subsets==		==7-note subsets==
	If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L 4s (eleventh equivalent)\|3L 4s]]:		If you stop the chain at 7 tones, you have a heptatonic scale of the form [[3L 4s (eleventh equivalent)\|3L 4s]]:
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	== See also ==		== See also ==
	[[7L 3s (8/3-equivalent)]]<references />		[[7L 3s (8/3-equivalent)]] - idealized tuning

			[[14L 6s (7/1-equivalent)]] - Guidotonic dominant Archytas tuning

			[[14L 6s (78/11-equivalent)]] - Guidotonic dominant Neogothic tuning

			[[14L 6s (36/5-equivalent)]] - Guidotonic dominant Meantone tuning<references />

2023-07-11T23:09:22Z

Scale tree