365edo - Revision history

ArrowHead294 at 23:00, 20 February 2025

2025-02-20T23:00:17Z

← Older revision		Revision as of 23:00, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|365~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	=== Miscellaneous properties ===		=== Miscellaneous properties ===
	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. A comma basis for the 365eeffgghiii val in the 23-limit is {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}.		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. A comma basis for the 365eeffgghiii val in the 23-limit is {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}.

	See [[365edo/Eliora's approach]].		See [[365edo/Eliora's approach]].

BudjarnLambeth: /* Interval table */

2024-01-21T11:29:47Z

Interval table

← Older revision		Revision as of 11:29, 21 January 2024
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	== Interval table ==		== Interval table ==
	~~{{Interval table}}~~		''see [[Table of 365edo intervals]]''

	== Approaches ==		== Approaches ==
	* [[365edo/Eliora's approach\|Eliora's approach]]		* [[365edo/Eliora's approach\|Eliora's approach]]

Eliora: /* Miscellaneous properties */ damn

2023-11-25T02:05:07Z

Miscellaneous properties: damn

← Older revision		Revision as of 02:05, 25 November 2023
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	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. A comma basis for the 365eeffgghiii val in the 23-limit is {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}.		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. A comma basis for the 365eeffgghiii val in the 23-limit is {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}.

	See [[365edo/Eliora's ~~Approach~~]].		See [[365edo/Eliora's approach]].

	== Interval table ==		== Interval table ==

Eliora: /* Miscellaneous properties */ oops

2023-11-25T02:04:51Z

Miscellaneous properties: oops

← Older revision		Revision as of 02:04, 25 November 2023
Line 16:		Line 16:
	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. A comma basis for the 365eeffgghiii val in the 23-limit is {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}.		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. A comma basis for the 365eeffgghiii val in the 23-limit is {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}.

	See [[365edo#Eliora's Approach]].		See [[365edo/Eliora's Approach]].

	== Interval table ==		== Interval table ==

Eliora: /* Miscellaneous properties */ cleanup

2023-11-25T01:51:09Z

Miscellaneous properties: cleanup

← Older revision		Revision as of 01:51, 25 November 2023
Line 14:		Line 14:

	=== Miscellaneous properties ===		=== Miscellaneous properties ===
	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. ~~Such a temperament eliminates~~ 300/299, ~~875~~/~~874~~, ~~1729~~/~~1725~~, ~~3060~~/~~3059~~, ~~4235~~/~~4232~~.		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. A comma basis for the 365eeffgghiii val in the 23-limit is {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}.

			See [[365edo#Eliora's Approach]].

	== Interval table ==		== Interval table ==

FloraC: Rework (2.9.15 is the correct subgroup notation; -full 23-limit as it hardly makes sense); +subsets and supersets

2023-11-09T15:08:47Z

Rework (2.9.15 is the correct subgroup notation; -full 23-limit as it hardly makes sense); +subsets and supersets

← Older revision		Revision as of 15:08, 9 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~365 equal divisions of the octave''' ('''365edo'''), or the '''365(-tone) equal temperament''' ('''365tet''', '''365et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 365 [[equal]] parts of about 3.29 [[cent]]s each.		{{EDO intro\|365}}

	== Theory ==		== Theory ==
			365edo is [[consistent]] to the [[7-odd-limit]], but both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are about halfway between its steps. As every other step of [[730edo]], it is suitable for a 2.9.15 [[subgroup]] interpretation, in which case it is identical to 730edo.

			Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the [[patent val]] in the 7-limit, with an optimal stretch of -0.52 cents, and hereby tunes the [[hemiwürschmidt]] temperament. In the 11-limit, it tempers out [[3025/3024]], [[3388/3375]], [[14641/14580]]; in the 13-limit, [[352/351]], [[1001/1000]], and [[1716/1715]].

			=== Odd harmonics ===
	{{Harmonics in equal\|365}}		{{Harmonics in equal\|365}}
	365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.5/3.9.15 subgroup, it can be regarded as every other step of [[730edo]], with one step amounting to two [[Woolhouse unit]]s.

	Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents, and hereby tunes the [[hemiwürschmidt]] temperament. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.

	=== ~~Relationship to the length of the year~~ ===		=== Subsets and supersets ===
			Since 365 factors into {{factorization\|365}}, 365edo contains [[5edo]] and [[73edo]] as subsets. A step of 365edo is exactly 2 [[Woolhouse unit]]s (2\730).

			=== Miscellaneous properties ===
	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. Such a temperament eliminates 300/299, 875/874, 1729/1725, 3060/3059, 4235/4232.		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. Such a temperament eliminates 300/299, 875/874, 1729/1725, 3060/3059, 4235/4232.

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	== Approaches ==		== Approaches ==
	* [[365edo/Eliora's approach\|Eliora's approach]]		* [[365edo/Eliora's approach\|Eliora's approach]]

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

CompactStar at 03:25, 17 September 2023

2023-09-17T03:25:34Z

← Older revision		Revision as of 03:25, 17 September 2023
Line 11:		Line 11:

	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. Such a temperament eliminates 300/299, 875/874, 1729/1725, 3060/3059, 4235/4232.		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. Such a temperament eliminates 300/299, 875/874, 1729/1725, 3060/3059, 4235/4232.

			== Interval table ==
			{{Interval table}}

	== Approaches ==		== Approaches ==

Eliora: /* Theory */

2023-05-26T14:55:00Z

Theory

← Older revision		Revision as of 14:55, 26 May 2023
Line 6:		Line 6:
	365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.5/3.9.15 subgroup, it can be regarded as every other step of [[730edo]], with one step amounting to two [[Woolhouse unit]]s.		365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.5/3.9.15 subgroup, it can be regarded as every other step of [[730edo]], with one step amounting to two [[Woolhouse unit]]s.

	Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.		Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents, and hereby tunes the [[hemiwürschmidt]] temperament. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.

	=== Relationship to the length of the year ===		=== Relationship to the length of the year ===

Eliora: /* Theory */

2023-05-26T14:31:17Z

Theory

← Older revision		Revision as of 14:31, 26 May 2023
Line 4:		Line 4:
	== Theory ==		== Theory ==
	{{Harmonics in equal\|365}}		{{Harmonics in equal\|365}}
	365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.9.15 subgroup, it can be regarded as every other step of [[730edo]], with one step amounting to two [[Woolhouse unit]]s.		365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.5/3.9.15 subgroup, it can be regarded as every other step of [[730edo]], with one step amounting to two [[Woolhouse unit]]s.

	Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.		Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.

Eliora: /* Theory */

2023-05-26T14:30:16Z

Theory

← Older revision		Revision as of 14:30, 26 May 2023
Line 4:		Line 4:
	== Theory ==		== Theory ==
	{{Harmonics in equal\|365}}		{{Harmonics in equal\|365}}
	365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching.		365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.9.15 subgroup, it can be regarded as every other step of [[730edo]], with one step amounting to two [[Woolhouse unit]]s.

	Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.		Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.

			=== Relationship to the length of the year ===

	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. Such a temperament eliminates 300/299, 875/874, 1729/1725, 3060/3059, 4235/4232.		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. Such a temperament eliminates 300/299, 875/874, 1729/1725, 3060/3059, 4235/4232.