524edo - Revision history

ArrowHead294 at 22:59, 20 February 2025

2025-02-20T22:59:51Z

← Older revision		Revision as of 22:59, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|524~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	== Regular temperament properties ==		== Regular temperament properties ==
	Based on treating 524edo as a no-threes system:		Based on treating 524edo as a no-threes system:

	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
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	\| {{monzo\| 1217 -524 }}		\| {{monzo\| 1217 -524 }}
	\| {{mapping\| 524 1217 }}		\| {{mapping\| 524 1217 }}
	\| -0.152		\| −0.152
	\| 0.153		\| 0.153
	\| 6.67		\| 6.67
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	\| {{monzo\| 33 -13 -1 }}, {{monzo\| -4 -43 37 }}		\| {{monzo\| 33 -13 -1 }}, {{monzo\| -4 -43 37 }}
	\| {{mapping\| 524 1217 1471 }}		\| {{mapping\| 524 1217 1471 }}
	\| -0.087		\| −0.087
	\| 0.155		\| 0.155
	\| 6.79		\| 6.79
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	\| 1835008/1830125, {{monzo\| 3 7 3 -8 }}, {{monzo\| -13 -5 10 -1 }}		\| 1835008/1830125, {{monzo\| 3 7 3 -8 }}, {{monzo\| -13 -5 10 -1 }}
	\| {{mapping\| 524 1217 1471 1813 }}		\| {{mapping\| 524 1217 1471 1813 }}
	\| -0.108		\| −0.108
	\| 0.139		\| 0.139
	\| 6.09		\| 6.09
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	\| 1001/1000, 742586/741125, 2097152/2093663, 14201915/14172488		\| 1001/1000, 742586/741125, 2097152/2093663, 14201915/14172488
	\| {{mapping\| 524 1217 1471 1813 1939 }}		\| {{mapping\| 524 1217 1471 1813 1939 }}
	\| -0.082		\| −0.082
	\| 0.135		\| 0.135
	\| 5.88		\| 5.88
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	\| 1001/1000, 6664/6655, 54080/54043, 147968/147875, 285719/285610		\| 1001/1000, 6664/6655, 54080/54043, 147968/147875, 285719/285610
	\| {{mapping\| 524 1217 1471 1813 1939 2142 }}		\| {{mapping\| 524 1217 1471 1813 1939 2142 }}
	\| -0.084		\| −0.084
	\| 0.122		\| 0.122
	\| 5.37		\| 5.37
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	== Scales ==		== Scales ==
	* Ostara[7]: 62 62 62 107 62 62 107 - [[2L 5s]]		* Ostara[7]: 62 62 62 107 62 62 107 – [[2L 5s]]

FloraC: +subsets and supersets

2023-11-02T13:48:57Z

+subsets and supersets

← Older revision		Revision as of 13:48, 2 November 2023
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	== Theory ==		== Theory ==
	524edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps~~, but otherwise~~ it has a good approximation to harmonics [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[13/1\|13]], [[15/1\|15]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.15.7.11.13.17.19 [[subgroup]] interpretation. The 2.9.7.13.19 subgroup is particularly good, where it [[support]]s [[Eliora]]'s [[ostara]], the 93 & 524 temperament. The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].		524edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps. Otherwise it has a good approximation to harmonics [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[13/1\|13]], [[15/1\|15]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.15.7.11.13.17.19 [[subgroup]] interpretation. The 2.9.7.13.19 subgroup is particularly good, where it [[support]]s [[Eliora]]'s [[ostara]], the 93 & 524 temperament. The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].

	In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.		In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|524}}		{{Harmonics in equal\|524}}

			=== Subsets and supersets ===
			Since 524 factors into {{factorization\|524}}, 524edo has subset edos {{EDOs\| 2, 4, 131, and 262 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Adopt template: EDO intro; cleanup; -redundant categories; -stuff that's not directly related to this edo

2023-10-29T11:46:02Z

Adopt template: EDO intro; cleanup; -redundant categories; -stuff that's not directly related to this edo

← Older revision		Revision as of 11:46, 29 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~524 equal divisions of the octave (524edo)''', or '''524(-tone) equal temperament (524-tet, 524et)''' when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 524 [[equal]] parts of about 2.29 [[cent]]s each.		{{EDO intro\|524}}

	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|524}}~~		524edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps, but otherwise it has a good approximation to harmonics [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[13/1\|13]], [[15/1\|15]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.15.7.11.13.17.19 [[subgroup]] interpretation. The 2.9.7.13.19 subgroup is particularly good, where it [[support]]s [[Eliora]]'s [[ostara]], the 93 & 524 temperament. The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].
	524edo is ~~excellent in~~ the ~~2.7.13.19 subgroup, and good in the no~~-~~threes 19~~-limit~~. In the~~ 3~~-limit~~, it ~~is wise~~ to ~~treat 524edo as a dual-fifth system. The minor fifth~~, ~~306\524 reduces to 153\262~~, ~~as such~~, ~~on this val 524edo is contorted.~~

	~~524 years is the length of a calendar leap week cycle with 93 leap weeks~~, ~~creating a 93 out of 524 maximum evenness scale with the generator 293\524~~, ~~represented by the 93 & 524 temperament.~~

	~~In addition~~, ~~both 93~~ and ~~524 represent well the~~ 13:17:19 ~~harmonics~~. The ~~corresponding comma list in the~~ 2.7.13~~.17~~.19 subgroup is ~~16807/16796~~, ~~157339/157216, 47071232/47045881.~~ Eliora ~~proposes that this temperament be named ''~~'[[ostara]]~~'''~~, ~~after~~ the ~~feast of the spring equinox, which~~ 93\524 ~~leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231 (Dee leap week), 97 & 400 (Gregorian leap day), and 52 & 293 (Sym454) already have their identities and names~~.

	The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].

	In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.		In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.

	== ~~Scales~~ ==		=== Odd harmonics ===
			{{Harmonics in equal\|524}}
	* Ostara[7]: 62 62 62 107 62 62 107 - [[2L 5s]]

	== Regular temperament properties ==		== Regular temperament properties ==
	Based on treating 524edo as a no-threes system:		Based on treating 524edo as a no-threes system:
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \| Subgroup		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~stretch~~ (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \| Tuning ~~error~~		! colspan="2" \| Tuning Error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
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	\| 2.5		\| 2.5
	\| {{monzo\| 1217 -524 }}		\| {{monzo\| 1217 -524 }}
	\| [{{~~val~~\| 524 1217 }}]		\| {{mapping\| 524 1217 }}
	\| -0.152		\| -0.152
	\| 0.153		\| 0.153
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	\| 2.5.7		\| 2.5.7
	\| {{monzo\| 33 -13 -1 }}, {{monzo\| -4 -43 37 }}		\| {{monzo\| 33 -13 -1 }}, {{monzo\| -4 -43 37 }}
	\| [{{~~val~~\|524 1217 1471}}]		\| {{mapping\| 524 1217 1471 }}
	\| -0.087		\| -0.087
	\| 0.155		\| 0.155
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	\| 2.5.7.11		\| 2.5.7.11
	\| 1835008/1830125, {{monzo\| 3 7 3 -8 }}, {{monzo\| -13 -5 10 -1 }}		\| 1835008/1830125, {{monzo\| 3 7 3 -8 }}, {{monzo\| -13 -5 10 -1 }}
	\| [{{~~val~~\| 524 1217 1471 1813 }}]		\| {{mapping\| 524 1217 1471 1813 }}
	\| -0.108		\| -0.108
	\| 0.139		\| 0.139
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	\| 2.5.7.11.13		\| 2.5.7.11.13
	\| 1001/1000, 742586/741125, 2097152/2093663, 14201915/14172488		\| 1001/1000, 742586/741125, 2097152/2093663, 14201915/14172488
	\| [{{~~val~~\| 524 1217 1471 1813 1939 }}]		\| {{mapping\| 524 1217 1471 1813 1939 }}
	\| -0.082		\| -0.082
	\| 0.135		\| 0.135
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	\| 2.5.7.11.13.17		\| 2.5.7.11.13.17
	\| 1001/1000, 6664/6655, 54080/54043, 147968/147875, 285719/285610		\| 1001/1000, 6664/6655, 54080/54043, 147968/147875, 285719/285610
	\| [{{~~val~~\| 524 1217 1471 1813 1939 2142 }}]		\| {{mapping\| 524 1217 1471 1813 1939 2142 }}
	\| -0.084		\| -0.084
	\| 0.122		\| 0.122
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	\|}		\|}

	[[~~Category:Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~		== Scales ==
			* Ostara[7]: 62 62 62 107 62 62 107 - [[2L 5s]]

BudjarnLambeth at 06:38, 9 July 2023

2023-07-09T06:38:10Z

← Older revision		Revision as of 06:38, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	The '''524 equal divisions of the octave (524edo)''', or '''524(-tone) equal temperament (524-tet, 524et)''' when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 524 [[equal]] parts of about 2.29 [[cent]]s each.		The '''524 equal divisions of the octave (524edo)''', or '''524(-tone) equal temperament (524-tet, 524et)''' when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 524 [[equal]] parts of about 2.29 [[cent]]s each.

BudjarnLambeth at 05:43, 9 July 2023

2023-07-09T05:43:15Z

← Older revision		Revision as of 05:43, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	The '''524 equal divisions of the octave (524edo)''', or '''524(-tone) equal temperament (524-tet, 524et)''' when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 524 [[equal]] parts of about 2.29 [[cent]]s each.		The '''524 equal divisions of the octave (524edo)''', or '''524(-tone) equal temperament (524-tet, 524et)''' when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 524 [[equal]] parts of about 2.29 [[cent]]s each.

Plumtree: Infobox ET now computes most parameters automatically

2022-10-04T19:24:59Z

Infobox ET now computes most parameters automatically

← Older revision		Revision as of 19:24, 4 October 2022
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	{{Infobox ET		{{Infobox ET}}
	~~\| Prime factorization = 2<sup>2</sup> × 131~~
	~~\| Step size = 2.29008¢~~
	~~\| Fifth = 307\524 (703.0534¢)~~
	}}
	The '''524 equal divisions of the octave (524edo)''', or '''524(-tone) equal temperament (524-tet, 524et)''' when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 524 [[equal]] parts of about 2.29 [[cent]]s each.		The '''524 equal divisions of the octave (524edo)''', or '''524(-tone) equal temperament (524-tet, 524et)''' when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 524 [[equal]] parts of about 2.29 [[cent]]s each.

Eliora at 16:25, 1 September 2022

2022-09-01T16:25:09Z

← Older revision		Revision as of 16:25, 1 September 2022
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	524 years is the length of a calendar leap week cycle with 93 leap weeks, creating a 93 out of 524 maximum evenness scale with the generator 293\524, represented by the 93 & 524 temperament.		524 years is the length of a calendar leap week cycle with 93 leap weeks, creating a 93 out of 524 maximum evenness scale with the generator 293\524, represented by the 93 & 524 temperament.

	In addition, both 93 and 524 represent well the 13:17:19 harmonics. The corresponding comma list in the 2.7.13.17.19 subgroup is 16807/16796, 157339/157216, 47071232/47045881. Eliora proposes that this temperament be named '''ostara''', after the feast of the spring equinox, which 93\524 leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231 (Dee leap week), 97 & 400 (Gregorian leap day), and 52 & 293 (Sym454) already have their identities and names.		In addition, both 93 and 524 represent well the 13:17:19 harmonics. The corresponding comma list in the 2.7.13.17.19 subgroup is 16807/16796, 157339/157216, 47071232/47045881. Eliora proposes that this temperament be named '''[[ostara]]''', after the feast of the spring equinox, which 93\524 leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231 (Dee leap week), 97 & 400 (Gregorian leap day), and 52 & 293 (Sym454) already have their identities and names.

	The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].		The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].

Eliora: /* Theory */

2022-08-29T19:30:51Z

Theory

← Older revision		Revision as of 19:30, 29 August 2022
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	In addition, both 93 and 524 represent well the 13:17:19 harmonics. The corresponding comma list in the 2.7.13.17.19 subgroup is 16807/16796, 157339/157216, 47071232/47045881. Eliora proposes that this temperament be named '''ostara''', after the feast of the spring equinox, which 93\524 leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231 (Dee leap week), 97 & 400 (Gregorian leap day), and 52 & 293 (Sym454) already have their identities and names.		In addition, both 93 and 524 represent well the 13:17:19 harmonics. The corresponding comma list in the 2.7.13.17.19 subgroup is 16807/16796, 157339/157216, 47071232/47045881. Eliora proposes that this temperament be named '''ostara''', after the feast of the spring equinox, which 93\524 leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231 (Dee leap week), 97 & 400 (Gregorian leap day), and 52 & 293 (Sym454) already have their identities and names.

	The generator 293\524 represents the [[28/19]] interval in the 2.7~~.13.17~~.19 subgroup. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].		The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].

	In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.		In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.

Eliora: /* Theory */

2022-08-29T16:38:07Z

Theory

← Older revision		Revision as of 16:38, 29 August 2022
Line 14:		Line 14:
	In addition, both 93 and 524 represent well the 13:17:19 harmonics. The corresponding comma list in the 2.7.13.17.19 subgroup is 16807/16796, 157339/157216, 47071232/47045881. Eliora proposes that this temperament be named '''ostara''', after the feast of the spring equinox, which 93\524 leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231 (Dee leap week), 97 & 400 (Gregorian leap day), and 52 & 293 (Sym454) already have their identities and names.		In addition, both 93 and 524 represent well the 13:17:19 harmonics. The corresponding comma list in the 2.7.13.17.19 subgroup is 16807/16796, 157339/157216, 47071232/47045881. Eliora proposes that this temperament be named '''ostara''', after the feast of the spring equinox, which 93\524 leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231 (Dee leap week), 97 & 400 (Gregorian leap day), and 52 & 293 (Sym454) already have their identities and names.

	The generator 293\524~~, being~~ around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].		The generator 293\524 represents the [[28/19]] interval in the 2.7.13.17.19 subgroup. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].

	In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.		In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.

Fredg999 category edits: Sort key

2022-07-04T01:01:28Z

Sort key

← Older revision		Revision as of 01:01, 4 July 2022
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	\|}		\|}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->