365edo/Eliora's approach - Revision history

Lériendil: deploying new cat

2025-01-31T22:02:19Z

deploying new cat

← Older revision		Revision as of 22:02, 31 January 2025
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	[[Category:365edo]]		[[Category:365edo]]
	[[Category:Method]]		[[Category:Method]]
			[[Category:Approaches to tuning systems]]

ArrowHead294: Clean up

2024-11-25T20:32:25Z

Clean up

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Eliora: /* Using a uniform map */ better subgroup

2024-02-24T23:24:25Z

Using a uniform map: better subgroup

← Older revision		Revision as of 23:24, 24 February 2024
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	{{harmonics in equal\|365.24219}}		{{harmonics in equal\|365.24219}}

	One might take note that for harmonics 19 and 23, the uniform map features a distinct mapping from the val with the best octave stretching. Overall, the uniform map performs quite poorly in lower limits, though it provides good tunings for the 2.5.17.~~43.53~~ subgroup.		One might take note that for harmonics 19 and 23, the uniform map features a distinct mapping from the val with the best octave stretching. Overall, the uniform map performs quite poorly in lower limits, though it provides good tunings for the 2.3.5.17.23 subgroup.

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

Eliora: /* Using a uniform map */

2023-12-03T20:22:21Z

Using a uniform map

← Older revision		Revision as of 20:22, 3 December 2023
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	=== Using a uniform map ===		=== Using a uniform map ===
	~~One might~~ take interval approximations directly in 365.24219edo.		It is possible to take interval approximations directly in 365.24219edo.

	{{harmonics in equal\|365.24219}}		{{harmonics in equal\|365.24219}}

	~~The~~ uniform map performs quite poorly in lower limits~~. It~~ provides good tunings for the 5.17.43.53 subgroup.		One might take note that for harmonics 19 and 23, the uniform map features a distinct mapping from the val with the best octave stretching. Overall, the uniform map performs quite poorly in lower limits, though it provides good tunings for the 2.5.17.43.53 subgroup.

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

Eliora: /* Using a uniform map */

2023-12-03T20:20:55Z

Using a uniform map

← Older revision		Revision as of 20:20, 3 December 2023
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	=== Using a uniform map ===		=== Using a uniform map ===
	One might take interval approximations directly in 365.24219edo.		One might take interval approximations directly in 365.24219edo.

			{{harmonics in equal\|365.24219}}

			The uniform map performs quite poorly in lower limits. It provides good tunings for the 5.17.43.53 subgroup.

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

Eliora at 20:18, 3 December 2023

2023-12-03T20:18:16Z

← Older revision		Revision as of 20:18, 3 December 2023
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	{{Main\|365edo}}		{{Main\|365edo}}
	== Theory ==		== Theory ==
	As 365 is the number of days in the common year, and there is a way to implement such a fact into music. An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. ~~In 23-limit~~, ~~365eeffgghiii val's octave stretch of -0~~.~~79428~~ cents ~~is very close~~, and ~~makes 2/1 correspond to~~ 365.~~241917 days~~, ~~or 365 days 5h 48m 21~~.7s, ~~which is only about 20 seconds short~~ of ~~the tropical year in the present era~~.		As 365 is the number of days in the common year, and there is a way to implement such a fact into music. An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. Therefore, each step is equal to 3.2854936 cents, and there are ''common octaves'' consisting of 365 steps and ''leap octaves'' consisting of 366 steps. The additional step does not amount to a JI mapping on its own, but rather resets the stretched octave to match the pure octave. Given that a standard gamut of music suitable for human hearing uses 8 octaves, this means 2 of them would be leap.

	~~This approach will cover what is essentially "tropical year"~~-~~EDO~~, ~~that is 365.2422edo using the~~ 365eeffgghiii val. ~~Therefore, each step~~ is ~~equal~~ to ~~3.2854936 cents~~, and ~~there are ''common octaves'' consisting of~~ 365 ~~steps and ''leap octaves'' consisting of 366 steps~~. ~~The additional step does not amount to a JI mapping on its own~~, ~~but rather resets the stretched octave to match the pure octave~~. ~~Given that a standard gamut of music suitable for human hearing uses 8 octaves~~, ~~this means 2~~ of ~~them would be leap~~.		=== Using a val with a selected octave stretch ===
			In 23-limit, 365eeffgghiii val's octave stretch of -0.79428 cents is very close to the target value, and makes 2/1 correspond to 365.241917 days, or 365 days 5h 48m 21.7s, which is only about 20 seconds short of the tropical year in the present era.

	In the 7-limit, the val is the same as patent val for 365edo, and hence it supports the [[hemiwürschmidt]] temperament just like the unstretched pure-octave 365edo does.		In the 7-limit, the val is the same as patent val for 365edo, and hence it supports the [[hemiwürschmidt]] temperament just like the unstretched pure-octave 365edo does.
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	Mappings different from the patent val highlighted in '''bold'''.		Mappings different from the patent val highlighted in '''bold'''.

			=== Using a uniform map ===
			One might take interval approximations directly in 365.24219edo.

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

Eliora at 02:06, 25 November 2023

2023-11-25T02:06:51Z

← Older revision		Revision as of 02:06, 25 November 2023
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	Mappings different from the patent val highlighted in '''bold'''.		Mappings different from the patent val highlighted in '''bold'''.

			== Regular temperament properties ==
			365eeffgghiii val is used.

			* 11-limit commas: {896/891, 6144/6125, 6250/6237, 532400/531441}

			* 23-limit commas: {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}

	==Table of intervals==		==Table of intervals==

Eliora: /* Theory */

2023-09-17T14:00:07Z

Theory

← Older revision		Revision as of 14:00, 17 September 2023
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	As 365 is the number of days in the common year, and there is a way to implement such a fact into music. An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. In 23-limit, 365eeffgghiii val's octave stretch of -0.79428 cents is very close, and makes 2/1 correspond to 365.241917 days, or 365 days 5h 48m 21.7s, which is only about 20 seconds short of the tropical year in the present era.		As 365 is the number of days in the common year, and there is a way to implement such a fact into music. An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. In 23-limit, 365eeffgghiii val's octave stretch of -0.79428 cents is very close, and makes 2/1 correspond to 365.241917 days, or 365 days 5h 48m 21.7s, which is only about 20 seconds short of the tropical year in the present era.

	This approach will cover what is essentially "tropical year"-EDO, that is 365.2422edo using the 365eeffgghiii val. Therefore, each step is equal to 3.2854936 cents, and there are ''common octaves'' consisting of 365 steps and ''leap octaves'' consisting of 366 steps.		This approach will cover what is essentially "tropical year"-EDO, that is 365.2422edo using the 365eeffgghiii val. Therefore, each step is equal to 3.2854936 cents, and there are ''common octaves'' consisting of 365 steps and ''leap octaves'' consisting of 366 steps. The additional step does not amount to a JI mapping on its own, but rather resets the stretched octave to match the pure octave. Given that a standard gamut of music suitable for human hearing uses 8 octaves, this means 2 of them would be leap.

	In the 7-limit, the val is the same as patent val for 365edo, and hence it supports the [[hemiwürschmidt]] temperament just like the unstretched pure-octave 365edo does.		In the 7-limit, the val is the same as patent val for 365edo, and hence it supports the [[hemiwürschmidt]] temperament just like the unstretched pure-octave 365edo does.
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	=== Mapping used ===		=== Mapping used ===
	{\| class="wikitable"		{\| class="wikitable"
	!		!Prime Harmonic
	!2		!2
	!3		!3
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	!7		!7
	!11		!11
	!13		!'''13'''
	!17		!'''17'''
	!19		!'''19'''
	!23		!'''23'''
	\|-		\|-
	\|Map		\|Map
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	\|848		\|848
	\|1025		\|1025
	\|1264		\|'''1264'''
	\|1352		\|'''1352'''
	\|1493		\|'''1493'''
	\|1551		\|'''1551'''
	\|1653		\|'''1653'''
			\|-
			\|Patent val 365edo
			\|365
			\|579
			\|848
			\|1025
			\|'''1263'''
			\|'''1351'''
			\|'''1492'''
			\|'''1550'''
			\|'''1651'''
	\|-		\|-
	\|Reduced		\|Reduced
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	\|118		\|118
	\|295		\|295
	\|169		\|'''169'''
	\|257		\|'''257'''
	\|33		\|'''33'''
	\|91		\|'''91'''
	\|193		\|'''193'''
	\|}		\|}

			Mappings different from the patent val highlighted in '''bold'''.
	==Table of intervals==		==Table of intervals==

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	\|}		\|}

	~~== Rank two temperaments by generator ==~~
	~~{\| class="wikitable center-all left-5"~~
	~~!Generator~~
	~~(reduced)~~
	~~!Temperament~~
	~~!Calendar name~~
	\|-
	~~\|181\365~~
	~~\|121i & 365eeffgghiii~~
	~~\|June 30~~
	\|-
	~~\|59\365~~
	~~\|99ef & 365eeffgghiii~~
	~~\|February 28~~
	\|-
	~~\|172\365~~
	~~\|87 & 365eeffgghiii~~
	~~\|June 21~~
	\|-
	~~\|107\365~~
	~~\|58hi & 365eeffgghiii~~
	~~\|April 17~~
	\|}
	[[Category:365edo]]		[[Category:365edo]]
	[[Category:Method]]		[[Category:Method]]

Eliora at 13:55, 17 September 2023

2023-09-17T13:55:35Z

← Older revision		Revision as of 13:55, 17 September 2023
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	''Main ~~article~~: ~~[[365edo]]'~~'		{{Main\|365edo}}
			== Theory ==
			As 365 is the number of days in the common year, and there is a way to implement such a fact into music. An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. In 23-limit, 365eeffgghiii val's octave stretch of -0.79428 cents is very close, and makes 2/1 correspond to 365.241917 days, or 365 days 5h 48m 21.7s, which is only about 20 seconds short of the tropical year in the present era.

	365 is ~~the number~~ of ~~days in the common year,~~ and ~~as such this proposes some interesting intereprations~~.		This approach will cover what is essentially "tropical year"-EDO, that is 365.2422edo using the 365eeffgghiii val. Therefore, each step is equal to 3.2854936 cents, and there are ''common octaves'' consisting of 365 steps and ''leap octaves'' consisting of 366 steps.

	~~This approach will cover what is essentially "tropical year"~~-~~EDO~~, ~~that~~ is ~~365.2422edo using~~ the ~~365eeffgghiii~~ val.		In the 7-limit, the val is the same as patent val for 365edo, and hence it supports the [[hemiwürschmidt]] temperament just like the unstretched pure-octave 365edo does.

	Mapping:		=== Mapping used ===
	{\| class="wikitable"		{\| class="wikitable"
	!		!
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	\|}		\|}

	~~== Theory ==~~
	~~365eeffgghiii val shares rank two temperaments with the following vals: {{EDOs\|121i, 99ef, 68e, 27egi, 41i, 46p, 58hi, 87, 50, 94}}.~~

	~~Every note which corresponds to the first number of a month makes it's own kind of 12-tone well temperament.~~

	==Table of intervals==		==Table of intervals==

BudjarnLambeth: Moved from category "impression" to "method"

2023-04-26T09:30:56Z

Moved from category "impression" to "method"

← Older revision		Revision as of 09:30, 26 April 2023
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	\|}		\|}
	[[Category:365edo]]		[[Category:365edo]]
	[[Category:~~Impression~~]]		[[Category:Method]]