574edo - Revision history

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"

2026-03-13T13:32:32Z

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:
	\| [[Vishnu]] (574d)		\| [[Vishnu]] (574d)
	\|}		\|}
	<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

2025-02-21T06:31:09Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:31, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|574~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:26:40Z

Theory: cleanup

← Older revision		Revision as of 16:26, 17 January 2025
Line 5:		Line 5:
	574edo shares the [[harmonic]] [[3/1\|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.		574edo shares the [[harmonic]] [[3/1\|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.

	The 574d val [[tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.		The 574d val [[tempering out\|tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.

	The patent val tempers out 2100875/2097152 ([[rainy comma]]), 6115295232/6103515625 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.		The patent val tempers out 2100875/2097152 ([[rainy comma]]), 6115295232/6103515625 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] 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 574 factors into ~~{{factorization\|574}}~~, 574edo has subset edos {{EDOs\| 2, 7, 14, 41, 82, and 287 }}.		Since 574 factors into 2 × 7 × 41, 574edo has subset edos {{EDOs\| 2, 7, 14, 41, 82, and 287 }}.

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

ArrowHead294 at 14:07, 16 January 2025

2025-01-16T14:07:19Z

← Older revision		Revision as of 14:07, 16 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~574 = 14 × 41, and~~ 574edo shares the [[harmonic]] [[3/1\|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.		574edo shares the [[harmonic]] [[3/1\|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.

	The 574d val [[~~tempering out\|~~tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.		The 574d val [[tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.

	The patent val tempers out 2100875/2097152 ([[rainy comma]]), 6115295232/6103515625 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.		The patent val tempers out 2100875/2097152 ([[rainy comma]]), 6115295232/6103515625 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.
Line 30:		Line 30:
	\| {{monzo\| 23 6 -14 }}, {{monzo\| 42 -47 14 }}		\| {{monzo\| 23 6 -14 }}, {{monzo\| 42 -47 14 }}
	\| {{mapping\| 574 910 1333 }}		\| {{mapping\| 574 910 1333 }}
	\| ~~−0~~.1658		\| −0.1658
	\| 0.1260		\| 0.1260
	\| 6.03		\| 6.03
Line 37:		Line 37:
	\| 4375/4374, 29360128/29296875, 40500000/40353607		\| 4375/4374, 29360128/29296875, 40500000/40353607
	\| {{mapping\| 574 910 1333 1612 }} (574d)		\| {{mapping\| 574 910 1333 1612 }} (574d)
	\| ~~−0~~.2320		\| −0.2320
	\| 0.1583		\| 0.1583
	\| 7.57		\| 7.57
Line 44:		Line 44:
	\| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607		\| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607
	\| {{mapping\| 574 910 1333 1612 1986 }} (574d)		\| {{mapping\| 574 910 1333 1612 1986 }} (574d)
	\| ~~−0~~.2202		\| −0.2202
	\| 0.1435		\| 0.1435
	\| 6.87		\| 6.87
Line 51:		Line 51:
	\| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503		\| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503
	\| {{mapping\| 574 910 1333 1612 1986 2124 }} (574d)		\| {{mapping\| 574 910 1333 1612 1986 2124 }} (574d)
	\| ~~−0~~.1786		\| −0.1786
	\| 0.1607		\| 0.1607
	\| 7.69		\| 7.69
Line 58:		Line 58:
	\| 10976/10935, 2100875/2097152, 49009212/48828125		\| 10976/10935, 2100875/2097152, 49009212/48828125
	\| {{mapping\| 574 910 1333 1611 }} (574)		\| {{mapping\| 574 910 1333 1611 }} (574)
	\| ~~−0~~.0459		\| −0.0459
	\| 0.2347		\| 0.2347
	\| 11.23		\| 11.23
Line 65:		Line 65:
	\| 5632/5625, 10976/10935, 131072/130977, 166698/166375		\| 5632/5625, 10976/10935, 131072/130977, 166698/166375
	\| {{mapping\| 574 910 1333 1611 1986 }} (574)		\| {{mapping\| 574 910 1333 1611 1986 }} (574)
	\| ~~−0~~.0713		\| −0.0713
	\| 0.2160		\| 0.2160
	\| 10.33		\| 10.33
Line 72:		Line 72:
	\| 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375		\| 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375
	\| {{mapping\| 574 910 1333 1611 1986 2124 }} (574)		\| {{mapping\| 574 910 1333 1611 1986 2124 }} (574)
	\| ~~−0~~.0544		\| −0.0544
	\| 0.2007		\| 0.2007
	\| 9.60		\| 9.60
Line 93:		Line 93:
	\| [[Vishnu]] (574d)		\| [[Vishnu]] (574d)
	\|}		\|}
	<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

2024-11-16T12:25:49Z

Partial undo

← Older revision		Revision as of 12:25, 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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	\| 0.2007		\| 0.2007
	\| 9.60		\| 9.60
	~~{{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
	\|-		\|-
	\| 2		\| 2
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	\| 25/24		\| 25/24
	\| [[Vishnu]] (574d)		\| [[Vishnu]] (574d)
	~~{{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 04:43, 16 November 2024

2024-11-16T04:43:40Z

← Older revision		Revision as of 04:43, 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\| 23 6 -14 }}, {{monzo\| 42 -47 14 }}		\| {{monzo\| 23 6 -14 }}, {{monzo\| 42 -47 14 }}
	\| {{mapping\| 574 910 1333 }}		\| {{mapping\| 574 910 1333 }}
	\| -0.1658		\| −0.1658
	\| 0.1260		\| 0.1260
	\| 6.03		\| 6.03
	\|-		\|- style="border-top: double;"
	\| style="border-top: double;" \| 2.3.5.7		\| 2.3.5.7
	~~\| style="border-top: double;"~~ \| 4375/4374, 29360128/29296875, 40500000/40353607		\| 4375/4374, 29360128/29296875, 40500000/40353607
	~~\| style="border-top: double;"~~ \| {{mapping\| 574 910 1333 1612 }} (574d)		\| {{mapping\| 574 910 1333 1612 }} (574d)
	\| ~~style="border-top: double~~;~~" \| -~~0.2320		\| −0.2320
	~~\| style="border-top: double;"~~ \| 0.1583		\| 0.1583
	~~\| style="border-top: double;"~~ \| 7.57		\| 7.57
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607		\| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607
	\| {{mapping\| 574 910 1333 1612 1986 }} (574d)		\| {{mapping\| 574 910 1333 1612 1986 }} (574d)
	\| -0.2202		\| −0.2202
	\| 0.1435		\| 0.1435
	\| 6.87		\| 6.87
Line 50:		Line 42:
	\| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503		\| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503
	\| {{mapping\| 574 910 1333 1612 1986 2124 }} (574d)		\| {{mapping\| 574 910 1333 1612 1986 2124 }} (574d)
	\| -0.1786		\| −0.1786
	\| 0.1607		\| 0.1607
	\| 7.69		\| 7.69
	\|-		\|- style="border-top: double;"
	\| style="border-top: double;" \| 2.3.5.7		\| 2.3.5.7
	~~\| style="border-top: double;"~~ \| 10976/10935, 2100875/2097152, 49009212/48828125		\| 10976/10935, 2100875/2097152, 49009212/48828125
	~~\| style="border-top: double;"~~ \| {{mapping\| 574 910 1333 1611 }} (574)		\| {{mapping\| 574 910 1333 1611 }} (574)
	\| ~~style="border-top: double~~;~~" \| -~~0.0459		\| −0.0459
	~~\| style="border-top: double;"~~ \| 0.2347		\| 0.2347
	~~\| style="border-top: double;"~~ \| 11.23		\| 11.23
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 5632/5625, 10976/10935, 131072/130977, 166698/166375		\| 5632/5625, 10976/10935, 131072/130977, 166698/166375
	\| {{mapping\| 574 910 1333 1611 1986 }} (574)		\| {{mapping\| 574 910 1333 1611 1986 }} (574)
	\| -0.0713		\| −0.0713
	\| 0.2160		\| 0.2160
	\| 10.33		\| 10.33
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	\| 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375		\| 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375
	\| {{mapping\| 574 910 1333 1611 1986 2124 }} (574)		\| {{mapping\| 574 910 1333 1611 1986 2124 }} (574)
	\| -0.0544		\| −0.0544
	\| 0.2007		\| 0.2007
	\| 9.60		\| 9.60
	\|}		{{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~~
	\|-		\|-
	\| 2		\| 2
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	\| 25/24		\| 25/24
	\| [[Vishnu]] (574d)		\| [[Vishnu]] (574d)
	\|}		{{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}}

Godtone at 17:42, 8 April 2024

2024-04-08T17:42:05Z

← Older revision		Revision as of 17:42, 8 April 2024
Line 7:		Line 7:
	The 574d val [[tempering out\|tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.		The 574d val [[tempering out\|tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.

	The patent val tempers out 2100875/2097152 ([[rainy comma]]), ~~67108864~~/~~66976875~~ ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.		The patent val tempers out 2100875/2097152 ([[rainy comma]]), 6115295232/6103515625 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.

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

FloraC: Adopt template: Factorization

2023-11-02T13:40:32Z

Adopt template: Factorization

← Older revision		Revision as of 13:40, 2 November 2023
Line 13:		Line 13:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 574 factors into ~~2 × 7 × 41~~, 574edo has subset edos {{EDOs\| 2, 7, 14, 41, 82, and 287 }}.		Since 574 factors into {{factorization\|574}}, 574edo has subset edos {{EDOs\| 2, 7, 14, 41, 82, and 287 }}.

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

FloraC: /* Regular temperament properties */ correct vals

2023-10-29T08:49:57Z

Regular temperament properties: correct vals

← Older revision		Revision as of 08:49, 29 October 2023
Line 42:		Line 42:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607		\| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607
	\| {{mapping\| 574 910 1333 1612 }} (574d)		\| {{mapping\| 574 910 1333 1612 1986 }} (574d)
	\| -0.2202		\| -0.2202
	\| 0.1435		\| 0.1435
Line 49:		Line 49:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503		\| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503
	\| {{mapping\| 574 910 1333 1612 }} (574d)		\| {{mapping\| 574 910 1333 1612 1986 2124 }} (574d)
	\| -0.1786		\| -0.1786
	\| 0.1607		\| 0.1607

FloraC: /* Regular temperament properties */ +574d val

2023-10-29T08:48:17Z

Regular temperament properties: +574d val

← Older revision		Revision as of 08:48, 29 October 2023
Line 33:		Line 33:
	\| 6.03		\| 6.03
	\|-		\|-
	\| 2.3.5.7		\| style="border-top: double;" \| 2.3.5.7
	\| 10976/10935, 2100875/2097152, 49009212/48828125		\| style="border-top: double;" \| 4375/4374, 29360128/29296875, 40500000/40353607
	\| {{mapping\| 574 910 1333 1611 }} (574)		\| style="border-top: double;" \| {{mapping\| 574 910 1333 1612 }} (574d)
	\| -0.0459		\| style="border-top: double;" \| -0.2320
	\| 0.2347		\| style="border-top: double;" \| 0.1583
	\| 11.23		\| style="border-top: double;" \| 7.57
			\|-
			\| 2.3.5.7.11
			\| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607
			\| {{mapping\| 574 910 1333 1612 }} (574d)
			\| -0.2202
			\| 0.1435
			\| 6.87
			\|-
			\| 2.3.5.7.11.13
			\| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503
			\| {{mapping\| 574 910 1333 1612 }} (574d)
			\| -0.1786
			\| 0.1607
			\| 7.69
			\|-
			\| style="border-top: double;" \| 2.3.5.7
			\| style="border-top: double;" \| 10976/10935, 2100875/2097152, 49009212/48828125
			\| style="border-top: double;" \| {{mapping\| 574 910 1333 1611 }} (574)
			\| style="border-top: double;" \| -0.0459
			\| style="border-top: double;" \| 0.2347
			\| style="border-top: double;" \| 11.23
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11