897edo - Revision history

FloraC: /* Regular temperament properties */ countritonic -> ragitritonic

2026-05-20T11:50:27Z

Regular temperament properties: countritonic -> ragitritonic

← Older revision		Revision as of 11:50, 20 May 2026
Line 21:		Line 21:
	! 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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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 33 -34 9 }}, {{monzo\| 70 -9 -24 }}		\| {{Monzo\| 33 -34 9 }}, {{monzo\| 70 -9 -24 }}
	\| {{~~mapping~~\| 897 1422 2083 }}		\| {{Mapping\| 897 1422 2083 }}
	\| −0.1255		\| −0.1255
	\| 0.0996		\| 0.0996
Line 36:		Line 36:
	\| 2.3.5.7		\| 2.3.5.7
	\| 250047/250000, 67108864/66976875, 28824005/28697814		\| 250047/250000, 67108864/66976875, 28824005/28697814
	\| {{~~mapping~~\| 897 1422 2083 2518 }} (897)		\| {{Mapping\| 897 1422 2083 2518 }} (897)
	\| −0.0706		\| −0.0706
	\| 0.1283		\| 0.1283
Line 43:		Line 43:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814		\| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
	\| {{~~mapping~~\| 897 1422 2083 2518 3103 }} (897)		\| {{Mapping\| 897 1422 2083 2518 3103 }} (897)
	\| −0.0480		\| −0.0480
	\| 0.1234		\| 0.1234
Line 50:		Line 50:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814		\| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
	\| {{~~mapping~~\| 897 1422 2083 2518 3103 3319 }} (897)		\| {{Mapping\| 897 1422 2083 2518 3103 3319 }} (897)
	\| −0.0222		\| −0.0222
	\| 0.1265		\| 0.1265
Line 60:		Line 60:
	\|+ 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
	\|-		\|-
Line 76:		Line 76:
	\| 588.63		\| 588.63
	\| 128/91		\| 128/91
	\| [[~~Countritonic~~]] (897df)		\| [[Ragitritonic]] (897df)
	\|-		\|-
	\| 3		\| 3
Line 84:		Line 84:
	\| [[Avicenna (temperament)\|Avicenna]] (897)		\| [[Avicenna (temperament)\|Avicenna]] (897)
	\|}		\|}
	<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

	== Music ==		== Music ==

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"

2026-03-13T13:32:55Z

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
Line 84:		Line 84:
	\| [[Avicenna (temperament)\|Avicenna]] (897)		\| [[Avicenna (temperament)\|Avicenna]] (897)
	\|}		\|}
	<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 ==

Francium: changed EDO intro to ED intro

2025-02-21T06:30:34Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:30, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|897~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 14:05, 16 January 2025

2025-01-16T14:05:23Z

← Older revision		Revision as of 14:05, 16 January 2025
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	\| {{monzo\| 33 -34 9 }}, {{monzo\| 70 -9 -24 }}		\| {{monzo\| 33 -34 9 }}, {{monzo\| 70 -9 -24 }}
	\| {{mapping\| 897 1422 2083 }}		\| {{mapping\| 897 1422 2083 }}
	\| ~~−0~~.1255		\| −0.1255
	\| 0.0996		\| 0.0996
	\| 7.44		\| 7.44
Line 37:		Line 37:
	\| 250047/250000, 67108864/66976875, 28824005/28697814		\| 250047/250000, 67108864/66976875, 28824005/28697814
	\| {{mapping\| 897 1422 2083 2518 }} (897)		\| {{mapping\| 897 1422 2083 2518 }} (897)
	\| ~~−0~~.0706		\| −0.0706
	\| 0.1283		\| 0.1283
	\| 9.59		\| 9.59
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	\| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814		\| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
	\| {{mapping\| 897 1422 2083 2518 3103 }} (897)		\| {{mapping\| 897 1422 2083 2518 3103 }} (897)
	\| ~~−0~~.0480		\| −0.0480
	\| 0.1234		\| 0.1234
	\| 9.22		\| 9.22
Line 51:		Line 51:
	\| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814		\| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
	\| {{mapping\| 897 1422 2083 2518 3103 3319 }} (897)		\| {{mapping\| 897 1422 2083 2518 3103 3319 }} (897)
	\| ~~−0~~.0222		\| −0.0222
	\| 0.1265		\| 0.1265
	\| 9.46		\| 9.46
Line 84:		Line 84:
	\| [[Avicenna (temperament)\|Avicenna]] (897)		\| [[Avicenna (temperament)\|Avicenna]] (897)
	\|}		\|}
	<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 ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13\|3\|23''] (2023) ~~–~~ 3-, 13-, and 23edo polymicrotonal		* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13\|3\|23''] (2023) – 3-, 13-, and 23edo polymicrotonal

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T12:42:18Z

Partial undo

← Older revision		Revision as of 12:42, 16 November 2024
Line 16:		Line 16:

	== 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]] (%)
	\|-		\|-
	\| 2.3.5		\| 2.3.5
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	\| 0.1265		\| 0.1265
	\| 9.46		\| 9.46
	~~{{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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	\| 13/12		\| 13/12
	\| [[Avicenna (temperament)\|Avicenna]] (897)		\| [[Avicenna (temperament)\|Avicenna]] (897)
	~~{{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 04:08, 16 November 2024

2024-11-16T04:08:42Z

← Older revision		Revision as of 04:08, 16 November 2024
Line 16:		Line 16:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 33 -34 9 }}, {{monzo\| 70 -9 -24 }}		\| {{monzo\| 33 -34 9 }}, {{monzo\| 70 -9 -24 }}
	\| {{mapping\| 897 1422 2083 }}		\| {{mapping\| 897 1422 2083 }}
	\| -0.1255		\| −0.1255
	\| 0.0996		\| 0.0996
	\| 7.44		\| 7.44
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	\| 250047/250000, 67108864/66976875, 28824005/28697814		\| 250047/250000, 67108864/66976875, 28824005/28697814
	\| {{mapping\| 897 1422 2083 2518 }} (897)		\| {{mapping\| 897 1422 2083 2518 }} (897)
	\| -0.0706		\| −0.0706
	\| 0.1283		\| 0.1283
	\| 9.59		\| 9.59
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	\| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814		\| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
	\| {{mapping\| 897 1422 2083 2518 3103 }} (897)		\| {{mapping\| 897 1422 2083 2518 3103 }} (897)
	\| -0.0480		\| −0.0480
	\| 0.1234		\| 0.1234
	\| 9.22		\| 9.22
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	\| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814		\| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
	\| {{mapping\| 897 1422 2083 2518 3103 3319 }} (897)		\| {{mapping\| 897 1422 2083 2518 3103 3319 }} (897)
	\| -0.0222		\| −0.0222
	\| 0.1265		\| 0.1265
	\| 9.46		\| 9.46
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 13/12		\| 13/12
	\| [[Avicenna (temperament)\|Avicenna]] (897)		\| [[Avicenna (temperament)\|Avicenna]] (897)
	\|}		{{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 ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13\|3\|23''] (2023) – 3-, 13- and 23edo polymicrotonal		* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13\|3\|23''] (2023) – 3-, 13-, and 23edo polymicrotonal

			[[Category:Listen]]

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T11:33:00Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 11:33, 2 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	897edo shares the same approximation to [[3/1\|harmonic 3]] as [[299edo]]. It has sharp approximations to [[5/1\|5]] and flat ones starting with [[7/1\|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val\| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val\| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.		897edo shares the same approximation to [[3/1\|harmonic 3]] with [[299edo]]. It has sharp approximations to [[5/1\|5]] and flat ones starting with [[7/1\|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val\| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val\| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.

	The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, and 172032/171875 in the 11-limit; [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.		The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, and 172032/171875 in the 11-limit; [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.
Line 13:		Line 13:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 897 factors into ~~3 × 13 × 23~~, 897edo has subset edos {{EDOs\| 3, 13, 23, 39, 69, and 299 }}.		Since 897 factors into {{factorization\|897}}, 897edo has subset edos {{EDOs\| 3, 13, 23, 39, 69, and 299 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-

FloraC: /* Regular temperament properties */ specificity of the link

2023-10-20T09:28:53Z

Regular temperament properties: specificity of the link

← Older revision		Revision as of 09:28, 20 October 2023
Line 80:		Line 80:
	\| 137.79		\| 137.79
	\| 13/12		\| 13/12
	\| [[Avicenna]] (897)		\| [[Avicenna (temperament)\|Avicenna]] (897)
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

FloraC: +subsets and supersets

2023-10-20T09:20:09Z

+subsets and supersets

← Older revision		Revision as of 09:20, 20 October 2023
Line 9:		Line 9:
	The 897def val tempers out [[4375/4374]] in the 7-limit; [[4000/3993]], 46656/46585, and 172032/171875 in the 11-limit; [[1716/1715]], and [[10648/10647]] in the 13-limit.		The 897def val tempers out [[4375/4374]] in the 7-limit; [[4000/3993]], 46656/46585, and 172032/171875 in the 11-limit; [[1716/1715]], and [[10648/10647]] in the 13-limit.

	=== ~~Prime~~ harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|897}}		{{Harmonics in equal\|897}}

			=== Subsets and supersets ===
			Since 897 factors into 3 × 13 × 23, 897edo has subset edos {{EDOs\| 3, 13, 23, 39, 69, and 299 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperaments		! Temperaments
	\|-
	~~\| 3~~
	~~\| 103\897~~
	~~\| 137.79~~
	~~\| 13/12~~
	~~\| [[Avicenna]] (897)~~
	\|-		\|-
	\| 1		\| 1
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	\| 128/91		\| 128/91
	\| [[Countritonic]] (897df)		\| [[Countritonic]] (897df)
			\|-
			\| 3
			\| 103\897
			\| 137.79
			\| 13/12
			\| [[Avicenna]] (897)
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

FloraC: Rework +1

2023-10-20T09:17:47Z

Rework +1

← Older revision		Revision as of 09:17, 20 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	897edo ~~has sharp approximations~~ to ~~harmonics~~ [[3/1\|3]] ~~and~~ [[5/1\|5]] and flat ones starting with [[7/1\|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val\| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val\| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.		897edo shares the same approximation to [[3/1\|harmonic 3]] as [[299edo]]. It has sharp approximations to [[5/1\|5]] and flat ones starting with [[7/1\|7]]. In the 13-limit at least, we want to consider the [[patent val]] {{val\| 897 1422 2083 '''2518''' '''3103''' '''3319''' }} as well as the 897def [[val]] {{val\| 897 1422 2083 '''2519''' '''3104''' '''3320''' }}.

	The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 102487/102400, [[131072/130977]], 160083/160000, and 172032/171875 in the 11-limit; [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.		The patent val tempers out [[250047/250000]] in the 7-limit; [[3025/3024]], [[5632/5625]], 42592/42525, 102487/102400, [[131072/130977]], 160083/160000, and 172032/171875 in the 11-limit; [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.

	The 897def val tempers out [[4375/4374]] in the 7-limit; [[4000/3993]], 46656/46585, and 172032/171875 in the 11-limit; [[1716/1715]], and [[10648/10647]] in the 13-limit.		The 897def val tempers out [[4375/4374]] in the 7-limit; [[4000/3993]], 46656/46585, and 172032/171875 in the 11-limit; [[1716/1715]], and [[10648/10647]] in the 13-limit.
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	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-
	~~\| 2.3~~
	~~\| {{monzo\| 474 -299 }}~~
	~~\| {{mapping\| 897 1422 }}~~
	~~\| -0.1218~~
	~~\| 0.1218~~
	~~\| 9.10~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
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	\| {{mapping\| 897 1422 2083 }}		\| {{mapping\| 897 1422 2083 }}
	\| -0.1255		\| -0.1255
	\| 0.~~010~~		\| 0.0996
	\| 0.75		\| 7.44
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
Line 45:		Line 38:
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 5632/5625, ~~160083~~/~~160000~~, 28824005/28697814		\| 3025/3024, 5632/5625, 102487/102400, 28824005/28697814
	\| {{mapping\| 897 1422 2083 2518 3103 }} (897)		\| {{mapping\| 897 1422 2083 2518 3103 }} (897)
	\| -0.0480		\| -0.0480
Line 52:		Line 45:
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| ~~2080~~/~~2079~~, 1001/1000, 3025/3024, 4096/4095, ~~2058857500~~/~~2051893701~~		\| 676/675, 1001/1000, 3025/3024, 4096/4095, 28824005/28697814
	\| {{mapping\| 897 1422 2083 2518 3103 3319 }} (897)		\| {{mapping\| 897 1422 2083 2518 3103 3319 }} (897)
	\| -0.0222		\| -0.0222
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	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperaments		! Temperaments
			\|-
			\| 3
			\| 103\897
			\| 137.79
			\| 13/12
			\| [[Avicenna]] (897)
	\|-		\|-
	\| 1		\| 1
	\| 419\897		\| 419\897
	\| 560.~~535~~		\| 560.54
	\| 864/625		\| 864/625
	\| [[Whoosh]]		\| [[Whoosh]]
			\|-
			\| 1
			\| 440\897
			\| 588.63
			\| 128/91
			\| [[Countritonic]] (897df)
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct
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	== Music ==		== Music ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13\|3\|23''] – 3-, 13- and 23edo polymicrotonal		* [https://www.youtube.com/watch?v=opR71xbJ-PQ ''13\|3\|23''] (2023) – 3-, 13- and 23edo polymicrotonal