487edo - 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"

2026-03-13T13:32:14Z

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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	\| [[Tritriple]] (5-limit)		\| [[Tritriple]] (5-limit)
	\|}		\|}
	<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

	== Scales ==		== Scales ==

ArrowHead294 at 23:07, 20 February 2025

2025-02-20T23:07:28Z

← Older revision		Revision as of 23:07, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|487~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:19:32Z

Theory: cleanup

← Older revision		Revision as of 16:19, 17 January 2025
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	== Theory ==		== Theory ==
	487edo is [[consistency\|distinctly consistent]] to the [[13-odd-limit]]. It [[tempers out]] {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].		487edo is [[consistency\|distinctly consistent]] to the [[13-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|487~~\|columns=11~~}}		{{Harmonics in equal\|487}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	487edo is the 93rd [[prime edo]].		487edo is the 93rd [[prime edo]].

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

ArrowHead294 at 18:55, 15 January 2025

2025-01-15T18:55:32Z

← Older revision		Revision as of 18:55, 15 January 2025
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	== Theory ==		== Theory ==
	487edo is [[consistency\|distinctly consistent]] to the [[13-odd-limit]]. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].		487edo is [[consistency\|distinctly consistent]] to the [[13-odd-limit]]. It [[tempers out]] {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| {{monzo\| 772 -487 }}		\| {{monzo\| 772 -487 }}
	\| {{mapping\| 487 772 }}		\| {{mapping\| 487 772 }}
	\| ~~−0~~.0958		\| −0.0958
	\| 0.0958		\| 0.0958
	\| 3.89		\| 3.89
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	\| {{monzo\| 24 -21 4 }}, {{monzo\| 55 -1 -23 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| 55 -1 -23 }}
	\| {{mapping\| 487 772 1131 }}		\| {{mapping\| 487 772 1131 }}
	\| ~~−0~~.1421		\| −0.1421
	\| 0.1020		\| 0.1020
	\| 4.14		\| 4.14
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	\| 4375/4374, 235298/234375, 33554432/33480783		\| 4375/4374, 235298/234375, 33554432/33480783
	\| {{mapping\| 487 772 1131 1367 }}		\| {{mapping\| 487 772 1131 1367 }}
	\| ~~−0~~.0667		\| −0.0667
	\| 0.1577		\| 0.1577
	\| 6.40		\| 6.40
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	\| 4375/4374, 5632/5625, 12005/11979, 41503/41472		\| 4375/4374, 5632/5625, 12005/11979, 41503/41472
	\| {{mapping\| 487 772 1131 1367 1685 }}		\| {{mapping\| 487 772 1131 1367 1685 }}
	\| ~~−0~~.0899		\| −0.0899
	\| 0.1485		\| 0.1485
	\| 6.03		\| 6.03
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	\| 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979		\| 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979
	\| {{mapping\| 487 772 1131 1367 1685 1802 }}		\| {{mapping\| 487 772 1131 1367 1685 1802 }}
	\| ~~−0~~.0623		\| −0.0623
	\| 0.1490		\| 0.1490
	\| 6.05		\| 6.05
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	\| [[Tritriple]] (5-limit)		\| [[Tritriple]] (5-limit)
	\|}		\|}
	<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

	== Scales ==		== Scales ==

ArrowHead294: Partial undo

2024-11-16T12:55:56Z

Partial undo

← Older revision		Revision as of 12:55, 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
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	\| 0.1490		\| 0.1490
	\| 6.05		\| 6.05
	~~{{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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	\| 864/625		\| 864/625
	\| [[Tritriple]] (5-limit)		\| [[Tritriple]] (5-limit)
	~~{{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

	== Scales ==		== Scales ==

ArrowHead294 at 03:13, 16 November 2024

2024-11-16T03:13:09Z

← Older revision		Revision as of 03:13, 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\| 772 -487 }}		\| {{monzo\| 772 -487 }}
	\| {{mapping\| 487 772 }}		\| {{mapping\| 487 772 }}
	\| -0.0958		\| −0.0958
	\| 0.0958		\| 0.0958
	\| 3.89		\| 3.89
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	\| {{monzo\| 24 -21 4 }}, {{monzo\| 55 -1 -23 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| 55 -1 -23 }}
	\| {{mapping\| 487 772 1131 }}		\| {{mapping\| 487 772 1131 }}
	\| -0.1421		\| −0.1421
	\| 0.1020		\| 0.1020
	\| 4.14		\| 4.14
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	\| 4375/4374, 235298/234375, 33554432/33480783		\| 4375/4374, 235298/234375, 33554432/33480783
	\| {{mapping\| 487 772 1131 1367 }}		\| {{mapping\| 487 772 1131 1367 }}
	\| -0.0667		\| −0.0667
	\| 0.1577		\| 0.1577
	\| 6.40		\| 6.40
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	\| 4375/4374, 5632/5625, 12005/11979, 41503/41472		\| 4375/4374, 5632/5625, 12005/11979, 41503/41472
	\| {{mapping\| 487 772 1131 1367 1685 }}		\| {{mapping\| 487 772 1131 1367 1685 }}
	\| -0.0899		\| −0.0899
	\| 0.1485		\| 0.1485
	\| 6.03		\| 6.03
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	\| 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979		\| 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979
	\| {{mapping\| 487 772 1131 1367 1685 1802 }}		\| {{mapping\| 487 772 1131 1367 1685 1802 }}
	\| -0.0623		\| −0.0623
	\| 0.1490		\| 0.1490
	\| 6.05		\| 6.05
	\|}		{{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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	\| 864/625		\| 864/625
	\| [[Tritriple]] (5-limit)		\| [[Tritriple]] (5-limit)
	\|}		{{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}}

	== Scales ==		== Scales ==

FloraC: Cleanup; clarify the title row of the rank-2 temp table; -redundant categories

2023-11-03T06:14:39Z

Cleanup; clarify the title row of the rank-2 temp table; -redundant categories

← Older revision		Revision as of 06:14, 3 November 2023
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	== Theory ==		== Theory ==
	~~487et~~ tempers out {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].		487edo is [[consistency\|distinctly consistent]] to the [[13-odd-limit]]. The equal temperament [[tempering out\|tempers out]] {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| 2.3		\| 2.3
	\| {{monzo\| 772 -487 }}		\| {{monzo\| 772 -487 }}
	\| [{{~~val~~\| 487 772 }}]		\| {{mapping\| 487 772 }}
	\| -0.0958		\| -0.0958
	\| 0.0958		\| 0.0958
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	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 24 -21 4 }}, {{monzo\| 55 -1 -23 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| 55 -1 -23 }}
	\| [{{~~val~~\| 487 772 1131 }}]		\| {{mapping\| 487 772 1131 }}
	\| -0.1421		\| -0.1421
	\| 0.1020		\| 0.1020
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	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 235298/234375, 33554432/33480783		\| 4375/4374, 235298/234375, 33554432/33480783
	\| [{{~~val~~\| 487 772 1131 1367 }}]		\| {{mapping\| 487 772 1131 1367 }}
	\| -0.0667		\| -0.0667
	\| 0.1577		\| 0.1577
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 4375/4374, 5632/5625, 12005/11979, 41503/41472		\| 4375/4374, 5632/5625, 12005/11979, 41503/41472
	\| [{{~~val~~\| 487 772 1131 1367 1685 }}]		\| {{mapping\| 487 772 1131 1367 1685 }}
	\| -0.0899		\| -0.0899
	\| 0.1485		\| 0.1485
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979		\| 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979
	\| [{{~~val~~\| 487 772 1131 1367 1685 1802 }}]		\| {{mapping\| 487 772 1131 1367 1685 1802 }}
	\| -0.0623		\| -0.0623
	\| 0.1490		\| 0.1490
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	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Tritriple]] (5-limit)		\| [[Tritriple]] (5-limit)
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==
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	* [[Silver17]]		* [[Silver17]]

	~~[[Category:487edo\| ]] <!-- main article -->~~
	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	~~[[Category:Prime EDO]]~~
	[[Category:Silver]]		[[Category:Silver]]

FloraC: +counterwuerschmidt

2023-10-03T13:17:38Z

+counterwuerschmidt

← Older revision		Revision as of 13:17, 3 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	487et tempers out {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 55 -1 -23 }} in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].		487et tempers out {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 55 -1 -23 }} (counterwürschmidt comma) in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|487\|columns=11}}		{{Harmonics in equal\|487\|columns=11}}

	=== ~~Miscellaneous properties~~ ===		=== Subsets and supersets ===
	487edo is the 93rd [[prime edo]].		487edo is the 93rd [[prime edo]].

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	\| 3087/2560		\| 3087/2560
	\| [[Seniority]]		\| [[Seniority]]
			\|-
			\| 1
			\| 157\487
			\| 386.86
			\| 5/4
			\| [[Counterwürschmidt]]
	\|-		\|-
	\| 1		\| 1

BudjarnLambeth at 06:36, 9 July 2023

2023-07-09T06:36:46Z

← Older revision		Revision as of 06:36, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|487}}		{{EDO intro\|487}}

BudjarnLambeth at 05:45, 9 July 2023

2023-07-09T05:45:53Z

← Older revision		Revision as of 05:45, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|487}}		{{EDO intro\|487}}