3600edo - Revision history

Hotcrystal0: Odd limit

2026-06-03T20:21:31Z

Odd limit

← Older revision		Revision as of 20:21, 3 June 2026
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	== Theory ==		== Theory ==
	3600edo is consistent in the 5-limit and it is a good 2.3.5.11.17.23.31.37.41 subgroup tuning.		3600edo is consistent in the 5-odd-limit and it is a good 2.3.5.11.17.23.31.37.41 subgroup tuning.

	In the 5-limit, 3600edo [[support]]s the [[ennealimmal]] temperament, tempering out the ennealimma, {{monzo\| 1 -27 18 }}, and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. Via the 3600e [[val]] {{val\| 3600 5706 8359 10106 12453}}, 3600edo also supports the [[hemiennealimmal]] temperament in the 11-limit.		In the 5-limit, 3600edo [[support]]s the [[ennealimmal]] temperament, tempering out the ennealimma, {{monzo\| 1 -27 18 }}, and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. Via the 3600e [[val]] {{val\| 3600 5706 8359 10106 12453}}, 3600edo also supports the [[hemiennealimmal]] temperament in the 11-limit.

Overthink: /* Theory */ better linking; - redundant category

2026-04-07T19:11:57Z

Theory: better linking; - redundant category

← Older revision		Revision as of 19:11, 7 April 2026
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	== Theory ==		== Theory ==
	~~[[Category:Equal divisions of the octave\|####]]~~
	3600edo is consistent in the 5-limit and it is a good 2.3.5.11.17.23.31.37.41 subgroup tuning.		3600edo is consistent in the 5-limit and it is a good 2.3.5.11.17.23.31.37.41 subgroup tuning.

	In the 5-limit, 3600edo [[support~~\|supports~~]] the [[ennealimmal ~~temperament~~]], tempering out the ennealimma, {{monzo\| 1 -27 18 }}, and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. Via the 3600e [[val]] {{val\| 3600 5706 8359 10106 12453}}, 3600edo also supports the [[hemiennealimmal ~~temperament~~]] in the 11-limit.		In the 5-limit, 3600edo [[support]]s the [[ennealimmal]] temperament, tempering out the ennealimma, {{monzo\| 1 -27 18 }}, and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. Via the 3600e [[val]] {{val\| 3600 5706 8359 10106 12453}}, 3600edo also supports the [[hemiennealimmal]] temperament in the 11-limit.

	An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex.		An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex.

ArrowHead294 at 14:47, 20 February 2025

2025-02-20T14:47:13Z

← Older revision		Revision as of 14:47, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|3600~~}}~~, or exactly 1/3 cent each.~~		{{ED intro}}

	== Theory ==		== Theory ==

Eliora: /* Subsets and supersets */ adopt template

2023-12-13T18:50:31Z

Subsets and supersets: adopt template

← Older revision		Revision as of 18:50, 13 December 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	[[Category:Equal divisions of the octave\|####]]		[[Category:Equal divisions of the octave\|####]]
	3600edo factors as		3600edo factors as {{Factorization\|3600}}, and has subset edos {{EDOs\|1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800}}.
	~~<math>3600 = 2^~~{~~4} \cdot 3^~~{2} ~~\cdot 5^{2~~}~~</math>~~, and has subset edos {{EDOs\|1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800}}.

	A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo\|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.		A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo\|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.

Eliora: /* Subsets and supersets */

2023-08-01T19:20:11Z

Subsets and supersets

← Older revision		Revision as of 19:20, 1 August 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	[[Category:Equal divisions of the octave\|####]]		[[Category:Equal divisions of the octave\|####]]
	3600edo~~'s prime factorization is~~		3600edo factors as
	<math>3600 = 2^{4} \cdot 3^{2} \cdot 5^{2}</math>~~. Its [[Number of the divisors~~\|~~45 divisors]] are~~ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800~~, 3600~~.		<math>3600 = 2^{4} \cdot 3^{2} \cdot 5^{2}</math>, and has subset edos {{EDOs\|1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800}}.

	A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo\|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.		A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo\|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.

Eliora: cleanup

2023-07-12T15:11:24Z

cleanup

← Older revision		Revision as of 15:11, 12 July 2023
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	== Theory ==		== Theory ==
			[[Category:Equal divisions of the octave\|####]]
			3600edo is consistent in the 5-limit and it is a good 2.3.5.11.17.23.31.37.41 subgroup tuning.

			In the 5-limit, 3600edo [[support\|supports]] the [[ennealimmal temperament]], tempering out the ennealimma, {{monzo\| 1 -27 18 }}, and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. Via the 3600e [[val]] {{val\| 3600 5706 8359 10106 12453}}, 3600edo also supports the [[hemiennealimmal temperament]] in the 11-limit.

			An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex.

			One step of 3600edo is close to the [[landscape comma]].

	=== ~~Number description~~ ===		=== Prime harmonics ===
			{{Harmonics in equal\|3600}}
			=== Subsets and supersets ===
	[[Category:Equal divisions of the octave\|####]]		[[Category:Equal divisions of the octave\|####]]
	3600edo's prime factorization is		3600edo's prime factorization is
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	A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo\|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.		A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo\|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.

	~~=== Prime harmonics ===~~
	~~{{Harmonics in equal\|3600}}~~
	Aside from its relationship to cents, it is of interest as a system [[support\|supporting]] [[ennealimmal temperament]], tempering out the ennealimma, {{monzo\| 1 -27 18 }}, in the [[5-limit]] and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex. Via the [[val]] {{val\| 3600 5706 8359 10106 12453 13318 }}, 3600edo also supports [[hemiennealimmal temperament]].

	~~One step of 3600edo is close to the [[landscape comma]].~~

	[[Category:Equal divisions of the octave\|####]]<!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]]<!-- 4-digit number -->
	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]

BudjarnLambeth at 07:05, 9 July 2023

2023-07-09T07:05:32Z

← Older revision		Revision as of 07:05, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|3600}}, or exactly 1/3 cent each.		{{EDO intro\|3600}}, or exactly 1/3 cent each.

BudjarnLambeth at 04:28, 9 July 2023

2023-07-09T04:28:49Z

← Older revision		Revision as of 04:28, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|3600}}, or exactly 1/3 cent each.		{{EDO intro\|3600}}, or exactly 1/3 cent each.

Plumtree: Infobox ET added

2022-10-04T22:17:19Z

Infobox ET added

← Older revision		Revision as of 22:17, 4 October 2022
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			{{Infobox ET}}
	{{EDO intro\|3600}}, or exactly 1/3 cent each.		{{EDO intro\|3600}}, or exactly 1/3 cent each.

Eliora at 15:57, 16 September 2022

2022-09-16T15:57:42Z

← Older revision		Revision as of 15:57, 16 September 2022
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	~~The '''3600edo''' divides the octave into~~ 3600 ~~equal parts of 0.33333 (~~exactly 1/3~~) of a [[~~cent]] each~~. A cent is therefore three steps; also, the Dröbisch Angle which is 1/360 octave is ten steps~~.		{{EDO intro\|3600}}, or exactly 1/3 cent each.

	== Theory ==		== Theory ==
	It also has the advantage of expressing the steps of [[72edo]] in whole numbers. Aside from its relationship to cents, it is of interest as a system [[support\|supporting]] [[ennealimmal temperament]], tempering out the ennealimma, {{monzo\| 1 -27 18 }}, in the [[5-limit]] and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex. Via the [[val]] {{val\| 3600 5706 8359 10106 12453 13318 }}, 3600edo also supports [[hemiennealimmal temperament]].

	~~One step~~ of 3600edo is ~~also close to the~~ [[~~landscape comma~~]].		=== Number description ===
			[[Category:Equal divisions of the octave\|####]]
			3600edo's prime factorization is
			<math>3600 = 2^{4} \cdot 3^{2} \cdot 5^{2}</math>. Its [[Number of the divisors\|45 divisors]] are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600.

	~~3600edo's prime factorization~~ is		A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo\|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps.
	~~<math>3600~~ = 2^{4} ~~\cdot 3^~~{2} ~~\cdot~~ 5^{2}~~</math>~~
			=== Prime harmonics ===
			{{Harmonics in equal\|3600}}
			Aside from its relationship to cents, it is of interest as a system [[support\|supporting]] [[ennealimmal temperament]], tempering out the ennealimma, {{monzo\| 1 -27 18 }}, in the [[5-limit]] and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex. Via the [[val]] {{val\| 3600 5706 8359 10106 12453 13318 }}, 3600edo also supports [[hemiennealimmal temperament]].

	~~Its~~ [[~~Number of the divisors\|45 divisors~~]] ~~are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600~~.		One step of 3600edo is close to the [[landscape comma]].

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]]<!-- 4-digit number -->
	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]