634edo - Revision history

FloraC: /* Regular temperament properties */ + heptacot

2026-05-20T12:08:11Z

Regular temperament properties: + heptacot

← Older revision		Revision as of 12:08, 20 May 2026
Line 68:		Line 68:
	! Associated<br>ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
			\|-
			\| 1
			\| 53\634
			\| 100.32
			\| 675/637
			\| [[Heptacot]]
	\|-		\|-
	\| 1		\| 1

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

2026-05-20T11:48:01Z

Regular temperament properties: countritonic -> garitritonic

← Older revision		Revision as of 11:48, 20 May 2026
Line 84:		Line 84:
	\| 311\634		\| 311\634
	\| 588.64		\| 588.64
	\| ~~{{monzo\| -14 15 -4 }}~~		\| 351/250
	\| [[~~Countritonic~~]] ~~(5-limit)~~		\| [[Garitritonic]]
	\|-		\|-
	\| 2		\| 2

FloraC: +1 temp

2026-05-15T12:40:05Z

+1 temp

← Older revision		Revision as of 12:40, 15 May 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~~\| 1005 -634 }}		\| {{Monzo\| 1005 -634 }}
	\| {{~~mapping~~\| 634 1005 }}		\| {{Mapping\| 634 1005 }}
	\| −0.0799		\| −0.0799
	\| 0.0799		\| 0.0799
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| -53 10 16 }}, {{monzo\| 33 -34 9 }}		\| {{Monzo\| -53 10 16 }}, {{monzo\| 33 -34 9 }}
	\| {{~~mapping~~\| 634 1005 1472 }}		\| {{Mapping\| 634 1005 1472 }}
	\| −0.0254		\| −0.0254
	\| 0.1009		\| 0.1009
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	\| 2.3.5.7		\| 2.3.5.7
	\| 420175/419904, 703125/702464, 33554432/33480783		\| 420175/419904, 703125/702464, 33554432/33480783
	\| {{~~mapping~~\| 634 1005 1472 1780 }}		\| {{Mapping\| 634 1005 1472 1780 }}
	\| −0.0422		\| −0.0422
	\| 0.0921		\| 0.0921
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 9801/9800, 19712/19683, 41503/41472, 703125/702464		\| 9801/9800, 19712/19683, 41503/41472, 703125/702464
	\| {{~~mapping~~\| 634 1005 1472 1780 2193 }}		\| {{Mapping\| 634 1005 1472 1780 2193 }}
	\| −0.0031		\| −0.0031
	\| 0.1135		\| 0.1135
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 1716/1715, 2080/2079, 4096/4095, 14641/14625, 31250/31213		\| 1716/1715, 2080/2079, 4096/4095, 14641/14625, 31250/31213
	\| {{~~mapping~~\| 634 1005 1472 1780 2193 2346 }}		\| {{Mapping\| 634 1005 1472 1780 2193 2346 }}
	\| +0.0041		\| +0.0041
	\| 0.1048		\| 0.1048
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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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	\| {{monzo\| -14 15 -4 }}		\| {{monzo\| -14 15 -4 }}
	\| [[Countritonic]] (5-limit)		\| [[Countritonic]] (5-limit)
			\|-
			\| 2
			\| 263\634<br>(54\634)
			\| 497.79<br>(102.21)
			\| 4/3<br>(35/33)
			\| [[Gariwizmic]]
	\|-		\|-
	\| 2		\| 2
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	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
	<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"

2026-03-13T13:32:34Z

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 93:		Line 93:
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
	<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

Francium: changed EDO intro to ED intro

2025-02-21T06:28:55Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:28, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|634~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:31:20Z

Theory: cleanup

← Older revision		Revision as of 16:31, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	634edo is a good 13-limit and no-17 higher-limit system. It [[tempers out]] {{monzo\| -53 10 16 }} ([[kwazy comma]]) and {{monzo\| 33 -34 9 }} (countritonic comma) in the 5-limit; 420175/419904 ([[wizma]]), 703125/702464 ([[meter]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[9801/9800]], [[19712/19683]], [[41503/41472]] in the 11-limit; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 14641/14625, and 31250/31213 in the 13-limit.		634edo is a good 13-limit and no-17 higher-limit system. As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| -53 10 16 }} ([[kwazy comma]]) and {{monzo\| 33 -34 9 }} (countritonic comma) in the 5-limit; 420175/419904 ([[wizma]]), 703125/702464 ([[meter]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[9801/9800]], [[19712/19683]], [[41503/41472]] in the 11-limit; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 14641/14625, and 31250/31213 in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 634 factors into ~~{{factorization\|634}}~~, 634edo has [[2edo]] and [[317edo]] as its subsets.		Since 634 factors into 2 × 317, 634edo has [[2edo]] and [[317edo]] as its subsets.

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

ArrowHead294 at 19:52, 15 January 2025

2025-01-15T19:52:29Z

← Older revision		Revision as of 19:52, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	634edo is a good 13-limit and no-17 higher-limit system. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] {{monzo\| -53 10 16 }} ([[kwazy comma]]) and {{monzo\| 33 -34 9 }} (countritonic comma) in the 5-limit; 420175/419904 ([[wizma]]), 703125/702464 ([[meter]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[9801/9800]], [[19712/19683]], [[41503/41472]] in the 11-limit; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 14641/14625, and 31250/31213 in the 13-limit.		634edo is a good 13-limit and no-17 higher-limit system. It [[tempers out]] {{monzo\| -53 10 16 }} ([[kwazy comma]]) and {{monzo\| 33 -34 9 }} (countritonic comma) in the 5-limit; 420175/419904 ([[wizma]]), 703125/702464 ([[meter]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit; [[9801/9800]], [[19712/19683]], [[41503/41472]] in the 11-limit; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 14641/14625, and 31250/31213 in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

ArrowHead294 at 19:51, 15 January 2025

2025-01-15T19:51:42Z

← Older revision		Revision as of 19:51, 15 January 2025
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	\| {{monzo\| 1005 -634 }}		\| {{monzo\| 1005 -634 }}
	\| {{mapping\| 634 1005 }}		\| {{mapping\| 634 1005 }}
	\| ~~−0~~.0799		\| −0.0799
	\| 0.0799		\| 0.0799
	\| 4.22		\| 4.22
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	\| {{monzo\| -53 10 16 }}, {{monzo\| 33 -34 9 }}		\| {{monzo\| -53 10 16 }}, {{monzo\| 33 -34 9 }}
	\| {{mapping\| 634 1005 1472 }}		\| {{mapping\| 634 1005 1472 }}
	\| ~~−0~~.0254		\| −0.0254
	\| 0.1009		\| 0.1009
	\| 5.33		\| 5.33
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	\| 420175/419904, 703125/702464, 33554432/33480783		\| 420175/419904, 703125/702464, 33554432/33480783
	\| {{mapping\| 634 1005 1472 1780 }}		\| {{mapping\| 634 1005 1472 1780 }}
	\| ~~−0~~.0422		\| −0.0422
	\| 0.0921		\| 0.0921
	\| 4.86		\| 4.86
Line 47:		Line 47:
	\| 9801/9800, 19712/19683, 41503/41472, 703125/702464		\| 9801/9800, 19712/19683, 41503/41472, 703125/702464
	\| {{mapping\| 634 1005 1472 1780 2193 }}		\| {{mapping\| 634 1005 1472 1780 2193 }}
	\| ~~−0~~.0031		\| −0.0031
	\| 0.1135		\| 0.1135
	\| 6.00		\| 6.00
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	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T12:59:11Z

Partial undo

← Older revision		Revision as of 12:59, 16 November 2024
Line 12:		Line 12:

	== 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
Line 51:		Line 60:

	=== 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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	\| 1125/1024		\| 1125/1024
	\| [[Kwazy]]		\| [[Kwazy]]
	~~{{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

ArrowHead294 at 02:59, 16 November 2024

2024-11-16T02:59:57Z

← Older revision		Revision as of 02:59, 16 November 2024
Line 12:		Line 12:

	== 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		\| 2.3
	\| {{monzo\| 1005 -634 }}		\| {{monzo\| 1005 -634 }}
	\| {{mapping\| 634 1005 }}		\| {{mapping\| 634 1005 }}
	\| -0.0799		\| −0.0799
	\| 0.0799		\| 0.0799
	\| 4.22		\| 4.22
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	\| {{monzo\| -53 10 16 }}, {{monzo\| 33 -34 9 }}		\| {{monzo\| -53 10 16 }}, {{monzo\| 33 -34 9 }}
	\| {{mapping\| 634 1005 1472 }}		\| {{mapping\| 634 1005 1472 }}
	\| -0.0254		\| −0.0254
	\| 0.1009		\| 0.1009
	\| 5.33		\| 5.33
Line 39:		Line 31:
	\| 420175/419904, 703125/702464, 33554432/33480783		\| 420175/419904, 703125/702464, 33554432/33480783
	\| {{mapping\| 634 1005 1472 1780 }}		\| {{mapping\| 634 1005 1472 1780 }}
	\| -0.0422		\| −0.0422
	\| 0.0921		\| 0.0921
	\| 4.86		\| 4.86
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	\| 9801/9800, 19712/19683, 41503/41472, 703125/702464		\| 9801/9800, 19712/19683, 41503/41472, 703125/702464
	\| {{mapping\| 634 1005 1472 1780 2193 }}		\| {{mapping\| 634 1005 1472 1780 2193 }}
	\| -0.0031		\| −0.0031
	\| 0.1135		\| 0.1135
	\| 6.00		\| 6.00
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	=== 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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	\| 1125/1024		\| 1125/1024
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		{{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}}