220edo - Revision history

FloraC: Update link

2026-04-05T12:19:46Z

Update link

← Older revision		Revision as of 12:19, 5 April 2026
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	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
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	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 349 -220 }}		\| {{Monzo\| 349 -220 }}
	\| {{~~mapping~~\| 220 349 }}		\| {{Mapping\| 220 349 }}
	\| −0.5304		\| −0.5304
	\| 0.5302		\| 0.5302
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 20 -17 3 }}, {{monzo\| 23 6 -14 }}		\| {{Monzo\| 20 -17 3 }}, {{monzo\| 23 6 -14 }}
	\| {{~~mapping~~\| 220 349 511 }}		\| {{Mapping\| 220 349 511 }}
	\| −0.4912		\| −0.4912
	\| 0.4364		\| 0.4364
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	\| 2.3.5.7		\| 2.3.5.7
	\| 6144/6125, 10976/10935, 390625/388962		\| 6144/6125, 10976/10935, 390625/388962
	\| {{~~mapping~~\| 220 349 511 618 }}		\| {{Mapping\| 220 349 511 618 }}
	\| −0.5538		\| −0.5538
	\| 0.3932		\| 0.3932
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	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\|-		\|-
	\| 11		\| 11
	\| 91\220<br />(9\220)		\| 91\220<br>(9\220)
	\| 496.36<br />(49.09)		\| 496.36<br>(49.09)
	\| 4/3<br />(36/35)		\| 4/3<br>(36/35)
	\| [[Hendecatonic]]		\| [[Hendecatonic (temperament)\|Hendecatonic]]
	\|-		\|-
	\| 20		\| 20
	\| 91\220<br />(3\220)		\| 91\220<br>(3\220)
	\| 496.36<br />(16.36)		\| 496.36<br>(16.36)
	\| 4/3<br />(126/125)		\| 4/3<br>(126/125)
	\| [[Degrees]]		\| [[Degrees]]
	\|}		\|}
	<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/>* [[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

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"

2026-03-13T13:33:08Z

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 13:33, 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

Overthink: link

2025-12-13T20:17:43Z

link

← Older revision		Revision as of 20:17, 13 December 2025
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	== Theory ==		== Theory ==
	Using the patent val, it tempers out {{monzo\| 20 -17 3 }} (rodan comma) and {{monzo\| 23 6 -14 }} ([[vishnuzma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[390625/388962]] in the 7-limit; 1331/1323, 1375/1372, [[2200/2187]], and [[16384/16335]] in the 11-limit; [[325/324]], [[352/351]], [[1001/1000]], [[1573/1568]], and 2704/2695 in the 13-limit.		Using the patent val, it tempers out {{monzo\| 20 -17 3 }} ([[rodan comma]]) and {{monzo\| 23 6 -14 }} ([[vishnuzma]]) in the 5-limit; [[6144/6125]], [[10976/10935]], and [[390625/388962]] in the 7-limit; 1331/1323, 1375/1372, [[2200/2187]], and [[16384/16335]] in the 11-limit; [[325/324]], [[352/351]], [[1001/1000]], [[1573/1568]], and 2704/2695 in the 13-limit.

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

ArrowHead294 at 22:49, 20 February 2025

2025-02-20T22:49:25Z

← Older revision		Revision as of 22:49, 20 February 2025
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	{{Infobox ET}}{{todo\|expand}}		{{Infobox ET}}{{todo\|expand}}
	{{~~EDO~~ intro~~\|220~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:46, 15 January 2025

2025-01-15T18:46:48Z

← Older revision		Revision as of 18:46, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 220 factors into ~~2<sup>2</sup> × 5 × 11~~, 220edo has subset edos {{EDOs\| 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110 }}		Since 220 factors into {{factorisation\|220}}, 220edo has subset edos {{EDOs\| 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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	\| {{monzo\| 349 -220 }}		\| {{monzo\| 349 -220 }}
	\| {{mapping\| 220 349 }}		\| {{mapping\| 220 349 }}
	\| ~~−0~~.5304		\| −0.5304
	\| 0.5302		\| 0.5302
	\| 9.72		\| 9.72
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	\| {{monzo\| 20 -17 3 }}, {{monzo\| 23 6 -14 }}		\| {{monzo\| 20 -17 3 }}, {{monzo\| 23 6 -14 }}
	\| {{mapping\| 220 349 511 }}		\| {{mapping\| 220 349 511 }}
	\| ~~−0~~.4912		\| −0.4912
	\| 0.4364		\| 0.4364
	\| 8.00		\| 8.00
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	\| 6144/6125, 10976/10935, 390625/388962		\| 6144/6125, 10976/10935, 390625/388962
	\| {{mapping\| 220 349 511 618 }}		\| {{mapping\| 220 349 511 618 }}
	\| ~~−0~~.5538		\| −0.5538
	\| 0.3932		\| 0.3932
	\| 7.21		\| 7.21
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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 ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

BudjarnLambeth: Typo

2025-01-07T05:15:14Z

Typo

← Older revision		Revision as of 05:15, 7 January 2025
Line 1:		Line 1:
	{{Infobox ET}}{{todo\|expand}#		{{Infobox ET}}{{todo\|expand}}
	{{EDO intro\|220}}		{{EDO intro\|220}}

BudjarnLambeth: Todo

2025-01-02T00:35:05Z

Todo

← Older revision		Revision as of 00:35, 2 January 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}{{todo\|expand}#
	{{EDO intro\|220}}		{{EDO intro\|220}}

BudjarnLambeth: Undo revision 173913: EDOs this big should not have auto interval tables

2024-12-31T01:09:27Z

Undo revision 173913: EDOs this big should not have auto interval tables

← Older revision		Revision as of 01:09, 31 December 2024
Line 10:		Line 10:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 220 factors into 2<sup>2</sup> × 5 × 11, 220edo has subset edos {{EDOs\| 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110 }}		Since 220 factors into 2<sup>2</sup> × 5 × 11, 220edo has subset edos {{EDOs\| 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110 }}

	~~== Intervals ==~~
	~~{{Interval table}}~~

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

MisterShafXen: /* Theory */

2024-12-30T15:14:59Z

Theory

← Older revision		Revision as of 15:14, 30 December 2024
Line 10:		Line 10:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 220 factors into 2<sup>2</sup> × 5 × 11, 220edo has subset edos {{EDOs\| 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110 }}		Since 220 factors into 2<sup>2</sup> × 5 × 11, 220edo has subset edos {{EDOs\| 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110 }}

			== Intervals ==
			{{Interval table}}

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

ArrowHead294: Partial undo

2024-11-16T13:10:22Z

Partial undo

← Older revision		Revision as of 13:10, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
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	\| 0.3932		\| 0.3932
	\| 7.21		\| 7.21
	~~{{comma basis end}~~}		\|}

	=== 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