60edo - Revision history

BudjarnLambeth: /* Scales */

2026-10-03T13:39:39Z

Scales

← Older revision		Revision as of 13:39, 3 October 2026
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	** 5-tone slendro: 12 12 12 12 12		** 5-tone slendro: 12 12 12 12 12
	* Harmonics 8-16: 10 9 9 7 7 6 6 6		* Harmonics 8-16: 10 9 9 7 7 6 6 6
			* Harmonics 6-12: 13 12 10 9 8 8
	* [[Magic]][13]: 3 3 10 3 3 3 10 3 3 3 10 3 3		* [[Magic]][13]: 3 3 10 3 3 3 10 3 3 3 10 3 3
	* Magic[22]: 3 3 3 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 1 3 3 3		* Magic[22]: 3 3 3 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 1 3 3 3

BudjarnLambeth: /* Scales */

2026-10-03T13:29:03Z

Scales

← Older revision		Revision as of 13:29, 3 October 2026
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	** 7-tone pelog: 6 8 12 8 5 14 7		** 7-tone pelog: 6 8 12 8 5 14 7
	** 5-tone slendro: 12 12 12 12 12		** 5-tone slendro: 12 12 12 12 12
			* Harmonics 8-16: 10 9 9 7 7 6 6 6
	* [[Magic]][13]: 3 3 10 3 3 3 10 3 3 3 10 3 3		* [[Magic]][13]: 3 3 10 3 3 3 10 3 3 3 10 3 3
	* Magic[22]: 3 3 3 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 1 3 3 3		* Magic[22]: 3 3 3 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 1 3 3 3

BudjarnLambeth: /* Scales */

2026-10-03T13:04:14Z

Scales

← Older revision		Revision as of 13:04, 3 October 2026
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	* Baobab{{idio}} (approximated from [[30afdo]]): 16 9 10 9 8 8		* Baobab{{idio}} (approximated from [[30afdo]]): 16 9 10 9 8 8
	* [[Catnip]][24]: 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2		* [[Catnip]][24]: 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2
			* [[Compton]][36]: 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1
			* [[Compton]][48]: 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1
	* Approximations of [[gamelan]] scales:		* Approximations of [[gamelan]] scales:
	** 5-tone pelog: 6 8 20 5 21		** 5-tone pelog: 6 8 20 5 21

BudjarnLambeth: /* Scales */

2026-10-03T13:00:24Z

Scales

← Older revision		Revision as of 13:00, 3 October 2026
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	* Amulet{{idio}} (approximated from [[25edo]], subset of [[magic]]): 5 2 5 5 2 5 7 5 5 2 5 7 5		* Amulet{{idio}} (approximated from [[25edo]], subset of [[magic]]): 5 2 5 5 2 5 7 5 5 2 5 7 5
	* Baobab{{idio}} (approximated from [[30afdo]]): 16 9 10 9 8 8		* Baobab{{idio}} (approximated from [[30afdo]]): 16 9 10 9 8 8
			* [[Catnip]][24]: 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2
	* Approximations of [[gamelan]] scales:		* Approximations of [[gamelan]] scales:
	** 5-tone pelog: 6 8 20 5 21		** 5-tone pelog: 6 8 20 5 21

BudjarnLambeth: /* Scales */

2026-10-03T12:53:04Z

Scales

← Older revision		Revision as of 12:53, 3 October 2026
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	== Scales ==		== Scales ==
	* [[5- to 10-tone scales in 60edo]]
	* Amulet{{idio}} (approximated from [[25edo]], subset of [[magic]]): 5 2 5 5 2 5 7 5 5 2 5 7 5		* Amulet{{idio}} (approximated from [[25edo]], subset of [[magic]]): 5 2 5 5 2 5 7 5 5 2 5 7 5
	* Baobab{{idio}} (approximated from [[30afdo]]): 16 9 10 9 8 8		* Baobab{{idio}} (approximated from [[30afdo]]): 16 9 10 9 8 8
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	** 7-tone pelog: 6 8 12 8 5 14 7		** 7-tone pelog: 6 8 12 8 5 14 7
	** 5-tone slendro: 12 12 12 12 12		** 5-tone slendro: 12 12 12 12 12
			* [[Magic]][13]: 3 3 10 3 3 3 10 3 3 3 10 3 3
			* Magic[22]: 3 3 3 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 1 3 3 3
			* ''[[5- to 10-tone scales in 60edo]]''
	{{todo\|expand section}}		{{todo\|expand section}}

BudjarnLambeth: /* Scales */

2026-09-09T06:18:50Z

Scales

← Older revision		Revision as of 06:18, 9 September 2026
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	== Scales ==		== Scales ==
	* [[5- to 10-tone scales in 60edo]]		* [[5- to 10-tone scales in 60edo]]
	* Amulet{{~~idiosyncratic~~}} (approximated from [[25edo]], subset of [[magic]]): 5 2 5 5 2 5 7 5 5 2 5 7 5		* Amulet{{idio}} (approximated from [[25edo]], subset of [[magic]]): 5 2 5 5 2 5 7 5 5 2 5 7 5
			* Baobab{{idio}} (approximated from [[30afdo]]): 16 9 10 9 8 8
	* Approximations of [[gamelan]] scales:		* Approximations of [[gamelan]] scales:
	** 5-tone pelog: 6 8 20 5 21		** 5-tone pelog: 6 8 20 5 21
	** 7-tone pelog: 6 8 12 8 5 14 7		** 7-tone pelog: 6 8 12 8 5 14 7
	** 5-tone slendro: 12 12 12 12 12		** 5-tone slendro: 12 12 12 12 12
			{{todo\|expand section}}

	== Instruments ==		== Instruments ==

Lucius Chiaraviglio: /* Rank-2 temperaments */ Insert Uniform maps before this

2026-07-07T18:18:37Z

Rank-2 temperaments: Insert Uniform maps before this

← Older revision		Revision as of 18:18, 7 July 2026
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	\| 9.44		\| 9.44
	\|}		\|}

			=== Uniform maps ===
			{{Uniform map\|edo=60}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

FloraC: /* Rank-2 temperaments */ update and convert to minimal-generator form

2026-07-07T11:10:16Z

Rank-2 temperaments: update and convert to minimal-generator form

← Older revision		Revision as of 11:10, 7 July 2026
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	\| 380.0		\| 380.0
	\| 5/4		\| 5/4
	\| [[Magic]] (60) / [[~~Magic_extensions#Witchcraft\|~~witchcraft]] (60e)		\| [[Magic]] (60) / [[witchcraft]] (60e)
	\|-		\|-
	\| 1		\| 1
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	\|-		\|-
	\| 2		\| 2
	\| ~~19\60<br>(~~11\60)		\| 11\60
	\| ~~380.0<br>(~~220.0)		\| 220.0
	\| ~~5/4<br>(~~25/22)		\| 25/22
	\| [[Astrology]] (60de) / [[divination]] (60e)		\| [[Astrology]] (60de) / [[divination]] (60e)
	\|-		\|-
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	\|-		\|-
	\| 5		\| 5
	\| 19\60~~<br>(5\60)~~		\| 1\60
	\| ~~380.0<br>(100~~.0)		\| 20.0
	\| ~~5/4<br>(256~~/~~245)~~		\| 81/80
	\| [[~~Warlock~~]]		\| [[Quintile]] (60)
	\|-		\|-
	\| 5		\| 5
	\| 25\60~~<br>(1\60)~~		\| 5\60
	\| ~~500.0<br>(20~~.0)		\| 100.0
	\| 4/~~3<br>(81/80)~~		\| 256/245
	\| [[~~Quintile~~]] ~~(60)~~		\| [[Warlock]]
	\|-		\|-
	\| 6		\| 6
	\| ~~17\60<br>(~~3\60)		\| 3\60
	\| ~~340.0<br>(~~60.0)		\| 60.0
	\| ~~375/308<br>(~~1760/1701)		\| 1760/1701
	\| [[Semiseptichrome]] (11-limit, 60e)		\| [[Semiseptichrome]] (11-limit, 60e)
	\|-		\|-
	\| 10		\| 10
	\| ~~25\60<br>(~~1\60)		\| 1\60
	\| ~~500.0<br>(~~20.0)		\| 20.0
	\| ~~4/3<br>(~~91/90)		\| 91/90
	\| [[Decile]] (60e)<br>[[Decic]] (60) / [[splendecic]] (60e) / [[prodecic]] (60e)		\| [[Decile]] (60e)<br>[[Decic]] (60) / [[splendecic]] (60e) / [[prodecic]] (60e)
	\|-		\|-
	\| 12		\| 12
	\| ~~19\60<br>(~~1\60)		\| 1\60
	\| ~~380.0<br>(~~20.0)		\| 20.0
	\| ~~5/4<br>(~~81/80)		\| 81/80
	\| [[Compton]] / [[comptone]] (60e)		\| [[Compton]] / [[comptone]] (60e)
	\|-		\|-
	\| 12		\| 12
	\| ~~12\60<br>(~~2\60)		\| 2\60
	\| ~~240.0<br>(~~40.0)		\| 40.0
	\| ~~8/7<br>(~~40/39)		\| 40/39
	\| [[Catnip]] (60cf)		\| [[Catnip]] (60cf)
	\|-		\|-
	\| 15		\| 15
	\| ~~25\60<br>(~~3\60)		\| 3\60
	\| ~~500.0<br>(~~20.0)		\| 20.0
	\| ~~4/3<br>(126~~/~~125)~~		\| 91/90
	\| [[Pentadecal]] ~~(60)~~ / [[~~Cloudy_clan#Quindeca\|~~quindecal]] (60e)		\| [[Pentadecal]] / [[quindecal]] (60e)
	\|-		\|-
	\| 20		\| 20
	\| ~~25\60<br>(~~2\60)		\| 2\60
	\| ~~500.0<br>(~~20.0)		\| 20.0
	\| ~~4/3<br>(~~99/98)		\| 99/98
	\| [[Degrees]] (60e)		\| [[Degrees]] (60e)
	\|}		\|}
	<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~~		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

	== Diagrams ==		== Diagrams ==

FloraC: /* Notation */ SZG notation

2026-05-12T13:51:24Z

Notation: SZG notation

← Older revision		Revision as of 13:51, 12 May 2026
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	== Notation ==		== Notation ==
	===~~Ups~~ and downs notation===		=== Stein–Zimmermann–Gould notation ===
	60edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).		[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
			{{Sharpness-sharp5-szg\|60}}

			=== Kite's ups and downs notation ===
			60edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
	{{Sharpness-sharp5a}}		{{Sharpness-sharp5a}}
	Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5\|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:{{Sharpness-sharp5\|60}}

	=== Sagittal notation ===		=== Sagittal notation ===
	This notation is a superset of the notations for ~~EDOs~~ [[12edo#Sagittal notation\|12]] and [[6edo#Sagittal notation\|6]].		This notation is a superset of the notations for edos [[12edo #Sagittal notation\|12]] and [[6edo #Sagittal notation\|6]].

	==== Evo flavor ====		==== Evo flavor ====
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	default [[File:60-EDO_Revo_Sagittal.svg]]		default [[File:60-EDO_Revo_Sagittal.svg]]
	</imagemap>		</imagemap>

	== Approximation to JI ==		== Approximation to JI ==
	=== Interval mappings ===		=== Interval mappings ===

MisterShafXen: - redundant words

2026-05-06T20:44:48Z

- redundant words

← Older revision		Revision as of 20:44, 6 May 2026
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	== Theory ==		== Theory ==
	Since {{nowrap\| 60 {{=}} 5 × 12 }}, 60edo belongs to the family of edos which contain [[12edo]], and like the other small edos of this kind, it [[tempering out\|tempers out]] the [[Pythagorean comma]], 531441/524288 ({{monzo\| -19 12 }}). In the [[5-limit]], it tempers out both the [[magic comma]], 3125/3072, and the [[amity comma]], 1600000/1594323, and supplies the [[optimal patent val]] for 5-limit [[magic]]~~, tempering out 3125/3072~~. In the [[7-limit]] it tempers out [[225/224]], [[245/243]], [[875/864]], and [[10976/10935]], and [[support]]s [[magic]], [[compton]] and [[tritonic]] temperaments. In the [[11-limit]], the 60e [[val]] {{val\| 60 95 139 168 '''207''' }} scores lower in [[badness]] than the [[patent val]] {{val\| 60 95 139 168 '''208''' }} and makes for an excellent tritonic tuning. It tempers out [[121/120]] and [[441/440]], whereas the patent val tempers out [[100/99]], [[385/384]] and [[540/539]]. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for [[13-limit]] tritonic. As a no-fives [[subgroup temperament]], it is also excellent for the 2.3.7.11.13-subgroup [[bleu]] temperament, using the 60d val.		Since {{nowrap\| 60 {{=}} 5 × 12 }}, 60edo belongs to the family of edos which contain [[12edo]], and like the other small edos of this kind, it [[tempering out\|tempers out]] the [[Pythagorean comma]], 531441/524288 ({{monzo\| -19 12 }}). In the [[5-limit]], it tempers out both the [[magic comma]], 3125/3072, and the [[amity comma]], 1600000/1594323, and supplies the [[optimal patent val]] for 5-limit [[magic]]. In the [[7-limit]] it tempers out [[225/224]], [[245/243]], [[875/864]], and [[10976/10935]], and [[support]]s [[magic]], [[compton]] and [[tritonic]] temperaments. In the [[11-limit]], the 60e [[val]] {{val\| 60 95 139 168 '''207''' }} scores lower in [[badness]] than the [[patent val]] {{val\| 60 95 139 168 '''208''' }} and makes for an excellent tritonic tuning. It tempers out [[121/120]] and [[441/440]], whereas the patent val tempers out [[100/99]], [[385/384]] and [[540/539]]. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for [[13-limit]] tritonic. As a no-fives [[subgroup temperament]], it is also excellent for the 2.3.7.11.13-subgroup [[bleu]] temperament, using the 60d val.

	=== Odd harmonics ===		=== Odd harmonics ===