360edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:51Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
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	\| [[Degrees]]		\| [[Degrees]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

ArrowHead294 at 14:47, 20 February 2025

2025-02-20T14:47:25Z

← Older revision		Revision as of 14:47, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|360~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:56, 15 January 2025

2025-01-15T18:56:59Z

← Older revision		Revision as of 18:56, 15 January 2025
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	In the 5-limit, the [[patent val]] [[support]]s the [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis {[[10976/10935]], 2097152/2083725}, which is similar to the misty temperament but has a period of 1/9- rather than 1/3-octave.		In the 5-limit, the [[patent val]] [[support]]s the [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis {[[10976/10935]], 2097152/2083725}, which is similar to the misty temperament but has a period of 1/9- rather than 1/3-octave.

	360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the 140 & 220 temperament with period 1\20. Aside from that, it provides the optimal patent val for the 41 & 360 temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis {[[390625/388962]], 67108864/66430125}.		360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the {{nowrap\|140 & 220}} temperament with period 1\20. Aside from that, it provides the optimal patent val for the {{nowrap\|41 & 360}} temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports {{nowrap\|12 & 360}} with the comma basis {[[390625/388962]], 67108864/66430125}.

	Aside from the patent val, there is a number of mappings to be considered. The 360d val, {{val\|360 571 836 '''1010'''}}, tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament.		Aside from the patent val, there is a number of mappings to be considered. The 360d val, {{val\|360 571 836 '''1010'''}}, tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament.
Line 77:		Line 77:
	\| [[Degrees]]		\| [[Degrees]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

ArrowHead294: Partial undo

2024-11-16T12:33:54Z

Partial undo

← Older revision		Revision as of 12:33, 16 November 2024
Line 26:		Line 26:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 4/3<br />(126/125)		\| 4/3<br />(126/125)
	\| [[Degrees]]		\| [[Degrees]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==

ArrowHead294 at 04:25, 16 November 2024

2024-11-16T04:25:06Z

← Older revision		Revision as of 04:25, 16 November 2024
Line 26:		Line 26:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center~~-~~all left-5"~~		{{rank-2 begin}}
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\|-		\|-
	\| 3		\| 3
	\| 149\360<br>(29\360)		\| 149\360<br />(29\360)
	\| 703.33<br>(303.33)		\| 703.33<br />(303.33)
	\| 4/3<br>(135/128)		\| 4/3<br />(135/128)
	\| [[Misty]]		\| [[Misty]]
	\|-		\|-
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	\|-		\|-
	\| 9		\| 9
	\| 149\360<br>(29\360)		\| 149\360<br />(29\360)
	\| 703.33<br>(36.67)		\| 703.33<br />(36.67)
	\| 4/3<br>(135/128)		\| 4/3<br />(135/128)
	\| [[Trimisty]]		\| [[Trimisty]]
	\|-		\|-
	\|12		\| 12
	\|73\360<br>(13\360)		\| 73\360<br />(13\360)
	\|243.333<br>(43.333)		\| 243.333<br />(43.333)
	\|3145728/2734375<br>(?)		\| 3145728/2734375<br />(?)
	\|[[Magnesium]] (360d)		\| [[Magnesium]] (360d)
	\|-		\|-
	\| 20		\| 20
	\| 149\360<br>(5\360)		\| 149\360<br />(5\360)
	\| 703.33<br>(43.33)		\| 703.33<br />(43.33)
	\| 4/3<br>(126/125)		\| 4/3<br />(126/125)
	\| [[Degrees]]		\| [[Degrees]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Music ==		== Music ==

Eliora: /* Theory */ oops

2024-02-19T18:25:46Z

Theory: oops

← Older revision		Revision as of 18:25, 19 February 2024
Line 9:		Line 9:
	360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the 140 & 220 temperament with period 1\20. Aside from that, it provides the optimal patent val for the 41 & 360 temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis {[[390625/388962]], 67108864/66430125}.		360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the 140 & 220 temperament with period 1\20. Aside from that, it provides the optimal patent val for the 41 & 360 temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis {[[390625/388962]], 67108864/66430125}.

	Aside from the patent val, there is a number of mappings to be considered. The 360d val, (360 571 836 '''1010'''), tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament.		Aside from the patent val, there is a number of mappings to be considered. The 360d val, {{val\|360 571 836 '''1010'''}}, tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 15:		Line 15:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	360 is the 13th [[highly composite edo]], with many proper divisors: {{EDOs\| 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 }}. One step of 360edo is known as '''the Dröbisch angle''', an [[interval size measure]] first proposed by Moritz Dröbisch in the 19th century at first merely by the name "angle".		360 is the 13th [[highly composite edo]], with many proper divisors: {{EDOs\| 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 }}. One step of 360edo is known as '''the Dröbisch angle''', an [[interval size measure]] first proposed by Moritz Dröbisch in the 19th century at first merely by the name "angle".

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

Eliora: cleanup

2024-02-19T18:25:28Z

cleanup

← Older revision		Revision as of 18:25, 19 February 2024
Line 7:		Line 7:
	In the 5-limit, the [[patent val]] [[support]]s the [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis {[[10976/10935]], 2097152/2083725}, which is similar to the misty temperament but has a period of 1/9- rather than 1/3-octave.		In the 5-limit, the [[patent val]] [[support]]s the [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis {[[10976/10935]], 2097152/2083725}, which is similar to the misty temperament but has a period of 1/9- rather than 1/3-octave.

	360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the 140 & 220 temperament with period 1\20. Aside from that, it provides the optimal patent val for the 41 & 360 temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis { [[390625/388962]], 67108864/66430125}.		360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the 140 & 220 temperament with period 1\20. Aside from that, it provides the optimal patent val for the 41 & 360 temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis {[[390625/388962]], 67108864/66430125}.

	Aside from the patent val, there is a number of mappings to be considered. The 360d val, (360 571 836 '''1010'''), tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament.		Aside from the patent val, there is a number of mappings to be considered. The 360d val, (360 571 836 '''1010'''), tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament.
Line 64:		Line 64:
	\|-		\|-
	\|12		\|12
	\|73\360		\|73\360<br>(13\360)
	(13\360)		\|243.333<br>(43.333)
	\|243.333		\|3145728/2734375<br>(?)
	(43.333)
	\|3145728/2734375
	(?)
	\|[[Magnesium]] (360d)		\|[[Magnesium]] (360d)
	\|-		\|-

Eliora: /* Rank-2 temperaments */

2024-02-19T18:24:57Z

Rank-2 temperaments

← Older revision		Revision as of 18:24, 19 February 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	360edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1\|3]] is about halfway between its steps. ~~Its 5-limit [[patent val]] [[support]]s the [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament~~ with ~~the comma basis [[10976/10935]], 2097152/2083725, which is similar to the misty temperament but has a period of 1/9- rather than 1/3-octave~~. In addition, 360edo provides the optimal patent val for the 41 & 360 temperament with comma basis 10976/10935, 16384000000/16209796869, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. ~~It also supports 12 & 360 with the comma basis [[390625/388962]], 67108864/66430125~~. ~~360edo tempers out the [[linus comma]], meaning 15/14 corresponds to 1/10 of the octave, 36 steps~~.		360edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1\|3]] is about halfway between its steps. It can also be used with 2.5.9.13 subgroup.

	360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the 140 & 220 temperament with period 1\20.		In the 5-limit, the [[patent val]] [[support]]s the [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis {[[10976/10935]], 2097152/2083725}, which is similar to the misty temperament but has a period of 1/9- rather than 1/3-octave.

			360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the 140 & 220 temperament with period 1\20. Aside from that, it provides the optimal patent val for the 41 & 360 temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis { [[390625/388962]], 67108864/66430125}.

			Aside from the patent val, there is a number of mappings to be considered. The 360d val, (360 571 836 '''1010'''), tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
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	\| 4/3<br>(135/128)		\| 4/3<br>(135/128)
	\| [[Trimisty]]		\| [[Trimisty]]
			\|-
			\|12
			\|73\360
			(13\360)
			\|243.333
			(43.333)
			\|3145728/2734375
			(?)
			\|[[Magnesium]] (360d)
	\|-		\|-
	\| 20		\| 20

BudjarnLambeth: /* Table of intervals */

2024-01-21T11:34:02Z

Table of intervals

← Older revision		Revision as of 11:34, 21 January 2024
Line 14:		Line 14:

	== Table of intervals ==		== Table of intervals ==
	Eliora proposes notating 360edo with calendar dates, Jan 1 being the tonic, Jan 2 being the next step, etc, and each month having even 30 days. The notation is convenient because 1 month in this scenario is equal to 1 semitone, and corresponds to [[12edo]].		[[Eliora]] proposes notating 360edo with calendar dates, Jan 1 being the tonic, Jan 2 being the next step, etc, and each month having even 30 days. The notation is convenient because 1 month in this scenario is equal to 1 semitone, and corresponds to [[12edo]].

	Any other notation system involving the number 360 can also be used.		Any other notation system involving the number 360 can also be used.

BudjarnLambeth: /* Table of intervals */

2024-01-21T11:33:37Z

Table of intervals

Show changes