60edo - Revision history

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 ===

Fitzgerald Lee: /* Notation */Added interval mappings for 60p and 60e

2026-04-25T10:58:37Z

Notation: Added interval mappings for 60p and 60e

← Older revision		Revision as of 10:58, 25 April 2026
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	default [[File:60-EDO_Revo_Sagittal.svg]]		default [[File:60-EDO_Revo_Sagittal.svg]]
	</imagemap>		</imagemap>
			== Approximation to JI ==
			=== Interval mappings ===
			{{Q-odd-limit intervals\|60}}
			{{Q-odd-limit intervals\|59.9\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 60e val mapping}}

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

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"

2026-03-13T13:32:45Z

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 13:32, 13 March 2026
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	\| [[Degrees]] (60e)		\| [[Degrees]] (60e)
	\|}		\|}
	<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

	== Diagrams ==		== Diagrams ==

Overthink: /* Intervals */ fix incorrect intervals

2026-01-09T21:27:08Z

Intervals: fix incorrect intervals

← Older revision		Revision as of 21:27, 9 January 2026
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	\| 280		\| 280
	\| [[20/17]]		\| [[20/17]]
	\| ~~''[[13/11]]'',~~ [[33/28]]		\| [[33/28]]
	\|-		\|-
	\| 15		\| 15
	\| 300		\| 300
	\| [[32/27]]		\| [[32/27]]
	\|		\| ''[[13/11]]''
	\|-		\|-
	\| 16		\| 16
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	\| 400		\| 400
	\| [[81/64]]		\| [[81/64]]
	\|		\| ''[[33/26]]''
	\|-		\|-
	\| 21		\| 21
	\| 420		\| 420
	\|		\|
	\| [[14/11]]~~, ''[[33/26]]''~~		\| [[14/11]]
	\|-		\|-
	\| 22		\| 22
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	\| 780		\| 780
	\|		\|
	\| ~~''[[52/33]]'',~~ [[11/7]]		\| [[11/7]]
	\|-		\|-
	\| 40		\| 40
	\| 800		\| 800
	\| [[128/81]]		\| [[128/81]]
	\|		\| ''[[52/33]]''
	\|-		\|-
	\| 41		\| 41
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	\| 900		\| 900
	\| [[27/16]]		\| [[27/16]]
	\|		\| ''[[22/13]]''
	\|-		\|-
	\| 46		\| 46
	\| 920		\| 920
	\| [[17/10]]		\| [[17/10]]
	\| ~~''[[22/13]]'',~~ [[56/33]]		\| [[56/33]]
	\|-		\|-
	\| 47		\| 47

Overthink: /* Theory */ note val

2026-01-09T21:25:39Z

Theory: note val

← Older revision		Revision as of 21:25, 9 January 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.		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.

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

Lucius Chiaraviglio: /* Rank-2 temperaments */ Some temperaments were missing links — fixed this, but the new links to the Decic extension won't work until the Decic page has its format updated

2025-11-25T08:50:00Z

Rank-2 temperaments: Some temperaments were missing links — fixed this, but the new links to the Decic extension won't work until the Decic page has its format updated

← Older revision		Revision as of 08:50, 25 November 2025
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	\| 340.0		\| 340.0
	\| 39/32		\| 39/32
	\| [[Houborizic]] (60) / houbor (60e)		\| [[Houborizic]] (60) / [[houbor]] (60e)
	\|-		\|-
	\| 1		\| 1
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	\| 380.0		\| 380.0
	\| 5/4		\| 5/4
	\| [[Magic]] (60) / witchcraft (60e)		\| [[Magic]] (60) / [[Magic_extensions#Witchcraft\|witchcraft]] (60e)
	\|-		\|-
	\| 1		\| 1
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	\| 580.0		\| 580.0
	\| 7/5		\| 7/5
	\| [[Tritonic]] (60e) / tritoni (60)		\| [[Tritonic]] (60e) / [[tritoni]] (60)
	\|-		\|-
	\| 2		\| 2
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	\| 500.0<br>(20.0)		\| 500.0<br>(20.0)
	\| 4/3<br>(91/90)		\| 4/3<br>(91/90)
	\| [[Decile]] (60e)<br>[[Decic]] (60) / splendecic (60e) / prodecic (60e)		\| [[Decile]] (60e)<br>[[Decic]] (60) / [[splendecic]] (60e) / [[prodecic]] (60e)
	\|-		\|-
	\| 12		\| 12
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	\| 380.0<br>(20.0)		\| 380.0<br>(20.0)
	\| 5/4<br>(81/80)		\| 5/4<br>(81/80)
	\| [[Compton]] / comptone (60e)		\| [[Compton]] / [[comptone]] (60e)
	\|-		\|-
	\| 12		\| 12
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	\| 500.0<br>(20.0)		\| 500.0<br>(20.0)
	\| 4/3<br>(126/125)		\| 4/3<br>(126/125)
	\| [[Pentadecal]] (60) / quindecal (60e)		\| [[Pentadecal]] (60) / [[Cloudy_clan#Quindeca\|quindecal]] (60e)
	\|-		\|-
	\| 20		\| 20

Lucius Chiaraviglio: /* Intervals */ `sed -E "s#[0-9]+/[0-9]+#\[\[&\]\]#g" 60EDOintervals.txt > 60EDOintervals.new.txt`

2025-11-25T08:16:36Z

Intervals: <code><nowiki>sed -E "s#[0-9]+/[0-9]+#\[\[&\]\]#g" 60EDOintervals.txt > 60EDOintervals.new.txt</nowiki></code>

Show changes

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''60edo improv'' (2025-11-22)

2025-11-22T23:26:27Z

Music: Add Bryan Deister's ''60edo improv'' (2025-11-22)

← Older revision		Revision as of 23:26, 22 November 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/nlKHUDCR3pI ''60edo improv''] (2025)		* [https://www.youtube.com/shorts/nlKHUDCR3pI ''60edo improv''] (2025-05-16)
			* [https://www.youtube.com/shorts/VA_P26_3dTk ''60edo improv''] (2025-11-22)

	; [[Robin Perry]]		; [[Robin Perry]]

BudjarnLambeth: /* Octave stretch or compression */

2025-09-23T03:51:20Z

Octave stretch or compression

@@ Line 550: / Line 550: @@
 What follows is a comparison of compressed- and stretched-octave 60edo tunings.
-edo can benefit from slightly [[stretched and compressed tuning|stretching the octave]], especially when using it as a no-11 17-limit equal temperament. With the right amount of stretch we can find better harmonics 3, 5, and 7 at the expense of somewhat less accurate approximations of 2 and 13. Tunings such as [[95edt]] or [[155ed6]] are great demonstrations of this.
+edo can benefit from slightly [[stretched and compressed tuning|stretching the octave]], especially when using it as a no-11 17-limit equal temperament. With the right amount of stretch we can find better harmonics 3, 5, and 7 at the expense of somewhat less accurate approximations of 2 and 13. Tunings such as [[155ed6]], [[95edt]] or [[zpi|301zpi]] make good options for this.
 == Scales ==