57edf - Revision history

FloraC: /* Theory */ cleanup

2025-01-17T17:24:21Z

Theory: cleanup

← Older revision		Revision as of 17:24, 17 January 2025
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	== Theory ==		== Theory ==
	57edf corresponds to 97.4421[[edo]]. It is related to the [[regular temperament]] which [[tempers out]] {{monzo\| -32 33 0 -6 -1 }} and {{monzo\| 76 -8 0 -9 -11 }} in the [[11-limit]], which is supported by {{EDOs\| 877-, 3313-, 4190-, 5067-, 5944-, 6821-, 7698-, and 11011edo }}.		57edf corresponds to 97.4421[[edo]]. It is related to the [[regular temperament]] which [[tempering out\|tempers out]] {{monzo\| -32 33 0 -6 -1 }} and {{monzo\| 76 -8 0 -9 -11 }} in the [[11-limit]], which is supported by {{EDOs\| 877-, 3313-, 4190-, 5067-, 5944-, 6821-, 7698-, and 11011edo }}.

	=== Harmonics ===		=== Harmonics ===

FloraC: Cleanup

2025-01-17T17:23:49Z

Cleanup

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''57EDF''' is the [[EDF|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent|cents]] each, corresponding to 97.4421 [[edo]].
+{{ED intro}}
-It is related to the [[regular temperament]] which [[tempers out]] {{monzo| -32 33 0 -6 -1 }} and {{monzo| 76 -8 0 -9 -11 }} in the [[11-limit]], which is supported by [[877edo|877]], [[3313edo|3313]], [[4190edo|4190]], [[5067edo|5067]], [[5944edo|5944]], [[6821edo|6821]], [[7698edo|7698]], and [[11011edo|11011]] EDOs.
+== Theory ==
 == Related regular temperaments ==
@@ Line 35: / Line 40: @@
 {{Interval table}}
-== Harmonics ==
+{{Todo|cleanup}}

BudjarnLambeth: Add links

2024-12-18T04:25:32Z

Add links

← Older revision		Revision as of 04:25, 18 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''57EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent\|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out {{monzo\| -32 33 0 -6 -1 }} and {{monzo\| 76 -8 0 -9 -11 }} in the 11-limit, which is supported by [[877edo\|877]], [[3313edo\|3313]], [[4190edo\|4190]], [[5067edo\|5067]], [[5944edo\|5944]], [[6821edo\|6821]], [[7698edo\|7698]], and [[11011edo\|11011]] EDOs.		'''57EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent\|cents]] each, corresponding to 97.4421 [[edo]].

			It is related to the [[regular temperament]] which [[tempers out]] {{monzo\| -32 33 0 -6 -1 }} and {{monzo\| 76 -8 0 -9 -11 }} in the [[11-limit]], which is supported by [[877edo\|877]], [[3313edo\|3313]], [[4190edo\|4190]], [[5067edo\|5067]], [[5944edo\|5944]], [[6821edo\|6821]], [[7698edo\|7698]], and [[11011edo\|11011]] EDOs.

	== Related regular temperaments ==		== Related regular temperaments ==

ArrowHead294: Formatting

2024-10-03T14:21:21Z

Formatting

← Older revision		Revision as of 14:21, 3 October 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''57EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent\|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out \|-32 33 0 -6 -1~~>~~ and \|76 -8 0 -9 -11~~>~~ in the 11-limit, which is supported by [[877edo\|877]], [[3313edo\|3313]], [[4190edo\|4190]], [[5067edo\|5067]], [[5944edo\|5944]], [[6821edo\|6821]], [[7698edo\|7698]], and [[11011edo\|11011]] EDOs.		'''57EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent\|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out {{monzo\| -32 33 0 -6 -1 }} and {{monzo\| 76 -8 0 -9 -11 }} in the 11-limit, which is supported by [[877edo\|877]], [[3313edo\|3313]], [[4190edo\|4190]], [[5067edo\|5067]], [[5944edo\|5944]], [[6821edo\|6821]], [[7698edo\|7698]], and [[11011edo\|11011]] EDOs.

	==Related regular temperaments==		== Related regular temperaments ==
	===2.3.7 subgroup 877&5067===		=== 2.3.7 subgroup 877&5067 ===
	Commas: {{monzo\| -428 371 0 -57 }}		Commas: {{monzo\| -428 371 0 -57 }}

	POTE generator: ~1605632/1594323 = 12.3149		POTE generator: ~1605632/1594323 = 12.3149

	Mapping: [~~<~~1 1 -1\|~~, <~~0 57 371\|]		Mapping: [{{val\| 1 1 -1 }}, {{val\| 0 57 371 }}]

	EDOs: {{EDOs\|877, 4190, 5067, 5944, 6821, 7698, 8575}}		EDOs: {{EDOs\|877, 4190, 5067, 5944, 6821, 7698, 8575}}

	===2.3.7.11 subgroup 877&5067===		=== 2.3.7.11 subgroup 877&5067 ===
	Commas: \|-32 33 0 -6 -1~~>~~, \|76 -8 0 -9 -11~~>~~		Commas: {{monzo\| -32 33 0 -6 -1 }}, {{monzo\| 76 -8 0 -9 -11 }}

	POTE generator: ~1605632/1594323 = 12.3150		POTE generator: ~1605632/1594323 = 12.3150

	Mapping: [~~<~~1 1 -1 7\|~~, <~~0 57 371 -345\|]		Mapping: [{{val\| 1 1 -1 7 }}, {{val\| 0 57 371 -345 }}]

	EDOs: {{EDOs\|877, 3313, 4190, 5067, 5944, 6821, 7698, 11011}}		EDOs: {{EDOs\|877, 3313, 4190, 5067, 5944, 6821, 7698, 11011}}

	===2.3.7.11.13 subgroup 877&5067===		=== 2.3.7.11.13 subgroup 877&5067 ===
	Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663		Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663

	POTE generator: ~1605632/1594323 = 12.3150		POTE generator: ~1605632/1594323 = 12.3150

	Mapping: [~~<~~1 1 -1 7 -10\|~~, <~~0 57 371 -345 1335\|]		Mapping: [{{val\| 1 1 -1 7 -10 }}, {{val\| 0 57 371 -345 1335 }}]

	EDOs: {{EDOs\|877, 3313, 4190, 5067, 5944, 9257}}		EDOs: {{EDOs\|877, 3313, 4190, 5067, 5944, 9257}}

ArrowHead294: /* Related regular temperaments */

2024-10-03T14:19:16Z

Related regular temperaments

← Older revision		Revision as of 14:19, 3 October 2024
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	==Related regular temperaments==		==Related regular temperaments==
	===2.3.7 subgroup 877&5067===		===2.3.7 subgroup 877&5067===
	Commas: \|-428 371 0 -57~~>~~		Commas: {{monzo\| -428 371 0 -57 }}

	POTE generator: ~1605632/1594323 = 12.3149		POTE generator: ~1605632/1594323 = 12.3149

BudjarnLambeth: Intervals harmonics

2024-10-03T10:52:53Z

Intervals harmonics

@@ Line 29: / Line 29: @@
 EDOs: {{EDOs|877, 3313, 4190, 5067, 5944, 9257}}
 [[Category:Edf]]
 [[Category:Edonoi]]

Francium: Linking EDOs to their respective pages

2023-05-07T07:41:45Z

Linking EDOs to their respective pages

← Older revision		Revision as of 07:41, 7 May 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''57EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent\|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out \|-32 33 0 -6 -1> and \|76 -8 0 -9 -11> in the 11-limit, which is supported by 877, 3313, 4190, 5067, 5944, 6821, 7698, and 11011 EDOs.		'''57EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent\|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out \|-32 33 0 -6 -1> and \|76 -8 0 -9 -11> in the 11-limit, which is supported by [[877edo\|877]], [[3313edo\|3313]], [[4190edo\|4190]], [[5067edo\|5067]], [[5944edo\|5944]], [[6821edo\|6821]], [[7698edo\|7698]], and [[11011edo\|11011]] EDOs.

	==Related regular temperaments==		==Related regular temperaments==
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	Mapping: [<1 1 -1\|, <0 57 371\|]		Mapping: [<1 1 -1\|, <0 57 371\|]

	EDOs: 877, 4190, 5067, 5944, 6821, 7698, 8575		EDOs: {{EDOs\|877, 4190, 5067, 5944, 6821, 7698, 8575}}

	===2.3.7.11 subgroup 877&5067===		===2.3.7.11 subgroup 877&5067===
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	Mapping: [<1 1 -1 7\|, <0 57 371 -345\|]		Mapping: [<1 1 -1 7\|, <0 57 371 -345\|]

	EDOs: 877, 3313, 4190, 5067, 5944, 6821, 7698, 11011		EDOs: {{EDOs\|877, 3313, 4190, 5067, 5944, 6821, 7698, 11011}}

	===2.3.7.11.13 subgroup 877&5067===		===2.3.7.11.13 subgroup 877&5067===
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	Mapping: [<1 1 -1 7 -10\|, <0 57 371 -345 1335\|]		Mapping: [<1 1 -1 7 -10\|, <0 57 371 -345 1335\|]

	EDOs: 877, 3313, 4190, 5067, 5944, 9257		EDOs: {{EDOs\|877, 3313, 4190, 5067, 5944, 9257}}

	[[Category:Edf]]		[[Category:Edf]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Plumtree: Infobox ET added

2022-10-05T18:51:25Z

Infobox ET added

← Older revision		Revision as of 18:51, 5 October 2022
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			{{Infobox ET}}
	'''57EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent\|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out \|-32 33 0 -6 -1> and \|76 -8 0 -9 -11> in the 11-limit, which is supported by 877, 3313, 4190, 5067, 5944, 6821, 7698, and 11011 EDOs.		'''57EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent\|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out \|-32 33 0 -6 -1> and \|76 -8 0 -9 -11> in the 11-limit, which is supported by 877, 3313, 4190, 5067, 5944, 6821, 7698, and 11011 EDOs.

Cmloegcmluin: map → mapping

2021-11-05T19:49:21Z

map → mapping

← Older revision		Revision as of 19:49, 5 November 2021
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	POTE generator: ~1605632/1594323 = 12.3149		POTE generator: ~1605632/1594323 = 12.3149

	~~Map~~: [<1 1 -1\|, <0 57 371\|]		Mapping: [<1 1 -1\|, <0 57 371\|]

	EDOs: 877, 4190, 5067, 5944, 6821, 7698, 8575		EDOs: 877, 4190, 5067, 5944, 6821, 7698, 8575
Line 16:		Line 16:
	POTE generator: ~1605632/1594323 = 12.3150		POTE generator: ~1605632/1594323 = 12.3150

	~~Map~~: [<1 1 -1 7\|, <0 57 371 -345\|]		Mapping: [<1 1 -1 7\|, <0 57 371 -345\|]

	EDOs: 877, 3313, 4190, 5067, 5944, 6821, 7698, 11011		EDOs: 877, 3313, 4190, 5067, 5944, 6821, 7698, 11011
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	POTE generator: ~1605632/1594323 = 12.3150		POTE generator: ~1605632/1594323 = 12.3150

	~~Map~~: [<1 1 -1 7 -10\|, <0 57 371 -345 1335\|]		Mapping: [<1 1 -1 7 -10\|, <0 57 371 -345 1335\|]

	EDOs: 877, 3313, 4190, 5067, 5944, 9257		EDOs: 877, 3313, 4190, 5067, 5944, 9257

Xenllium: Created page with "'''57EDF''' is the equal division of the just perfect fifth into 57 parts of 12.3150 cents each, corresponding to 97.4421 edo. It is related to the regula..."

2019-02-14T11:26:38Z

Created page with "'''57EDF''' is the equal division of the just perfect fifth into 57 parts of 12.3150 cents each, corresponding to 97.4421 edo. It is related to the regula..."

New page

'''57EDF''' is the [[EDF|equal division of the just perfect fifth]] into 57 parts of 12.3150 [[cent|cents]] each, corresponding to 97.4421 [[edo]]. It is related to the regular temperament which tempers out |-32 33 0 -6 -1> and |76 -8 0 -9 -11> in the 11-limit, which is supported by 877, 3313, 4190, 5067, 5944, 6821, 7698, and 11011 EDOs.

==Related regular temperaments==
===2.3.7 subgroup 877&5067===
Commas: |-428 371 0 -57>

POTE generator: ~1605632/1594323 = 12.3149

Map: [<1 1 -1|, <0 57 371|]

EDOs: 877, 4190, 5067, 5944, 6821, 7698, 8575

===2.3.7.11 subgroup 877&5067===
Commas: |-32 33 0 -6 -1>, |76 -8 0 -9 -11>

POTE generator: ~1605632/1594323 = 12.3150

Map: [<1 1 -1 7|, <0 57 371 -345|]

EDOs: 877, 3313, 4190, 5067, 5944, 6821, 7698, 11011

===2.3.7.11.13 subgroup 877&5067===
Commas: 257330216/257298363, 53722307808/53710650917, 1786706395136/1786568061663

POTE generator: ~1605632/1594323 = 12.3150

Map: [<1 1 -1 7 -10|, <0 57 371 -345 1335|]

EDOs: 877, 3313, 4190, 5067, 5944, 9257

[[Category:Edf]]
[[Category:Edonoi]]