1547edo - 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"

2026-03-13T13:32:18Z

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 117:		Line 117:
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
	<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 ==

ArrowHead294 at 23:08, 20 February 2025

2025-02-20T23:08:29Z

← Older revision		Revision as of 23:08, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1547~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:43:57Z

Theory: cleanup

← Older revision		Revision as of 16:43, 17 January 2025
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	== Theory ==		== Theory ==
	1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. It [[tempers out]] [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma.		1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. As an equal temperament, it [[tempering out\|tempers out]] [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma.

	In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo\| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].		In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo\| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1547 factors into ~~{{factorization\|1547}}~~, 1547edo has subset edos {{EDOs\| 7, 13, 17, 91, 119, and 221 }}.		Since 1547 factors into 7 × 13 × 17, 1547edo has subset edos {{EDOs\| 7, 13, 17, 91, 119, and 221 }}.

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

ArrowHead294 at 18:45, 15 January 2025

2025-01-15T18:45:47Z

← Older revision		Revision as of 18:45, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. It [[~~Tempering out\|~~tempers out]] [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma.		1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. It [[tempers out]] [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma.

	In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo\| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].		In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo\| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].

	In the 7-limit, it provides the [[optimal patent val]] for 7-limit [[brahmagupta]], the 441 & 1106 temperament, and supports an alternative 11-limit extension to it. It also supports [[semidimi]], the 171 & 1376 temperament.		In the 7-limit, it provides the [[optimal patent val]] for 7-limit [[brahmagupta]], the {{nowrap\|441 & 1106}} temperament, and supports an alternative 11-limit extension to it. It also supports [[semidimi]], the {{nowrap\|171 & 1376}} temperament.

	In the 11-limit, 1547edo provides the optimal patent val for the [[aluminium]] temperament, which maps 135/128 to 1/13th of the occtave. It also tempers out 117649/117612, and is a tuning for the rank-3 temperament [[heimdall]]. In higher limits, it supports 91th-octave temperament [[protactinium]].		In the 11-limit, 1547edo provides the optimal patent val for the [[aluminium]] temperament, which maps 135/128 to 1/13th of the occtave. It also tempers out 117649/117612, and is a tuning for the rank-3 temperament [[heimdall]]. In higher limits, it supports 91th-octave temperament [[protactinium]].
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	\| {{monzo\| 2452 -1547 }}		\| {{monzo\| 2452 -1547 }}
	\| {{mapping\| 1547 2542 }}		\| {{mapping\| 1547 2542 }}
	\| ~~−0~~.015		\| −0.015
	\| 0.015		\| 0.015
	\| 1.99		\| 1.99
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	\| {{monzo\| -52 -17 34 }}, {{monzo\| 40 -56 21 }}		\| {{monzo\| -52 -17 34 }}, {{monzo\| 40 -56 21 }}
	\| {{mapping\| 1547 2542 3592 }}		\| {{mapping\| 1547 2542 3592 }}
	\| ~~−0~~.008		\| −0.008
	\| 0.017		\| 0.017
	\| 2.14		\| 2.14
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	\| 4375/4374, {{monzo\| -1 4 11 -11 }}, {{monzo\| 46 -14 -3 -6 }}		\| 4375/4374, {{monzo\| -1 4 11 -11 }}, {{monzo\| 46 -14 -3 -6 }}
	\| {{mapping\| 1547 2542 3592 4343 }}		\| {{mapping\| 1547 2542 3592 4343 }}
	\| ~~−0~~.007		\| −0.007
	\| 0.014		\| 0.014
	\| 1.86		\| 1.86
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	\| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325		\| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325
	\| {{mapping\| 1547 2542 3592 4343 5352 }}		\| {{mapping\| 1547 2542 3592 4343 5352 }}
	\| ~~−0~~.017		\| −0.017
	\| 0.024		\| 0.024
	\| 3.10		\| 3.10
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	\| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683		\| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683
	\| {{mapping\| 1547 2542 3592 4343 5352 5725 }}		\| {{mapping\| 1547 2542 3592 4343 5352 5725 }}
	\| ~~−0~~.029		\| −0.029
	\| 0.034		\| 0.034
	\| 4.42		\| 4.42
Line 117:		Line 117:
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
	<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 ==

ArrowHead294: Partial undo

2024-11-16T12:27:36Z

Partial undo

← Older revision		Revision as of 12:27, 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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	\| 0.034		\| 0.034
	\| 4.42		\| 4.42
	~~{{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 />(176/175)		\| 4/3<br />(176/175)
	\| [[Protactinium]]		\| [[Protactinium]]
	~~{{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 04:38, 16 November 2024

2024-11-16T04:38:37Z

← Older revision		Revision as of 04:38, 16 November 2024
Line 18:		Line 18:

	== 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 8ve<br>Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 2452 -1547 }}		\| {{monzo\| 2452 -1547 }}
	\| {{mapping\| 1547 2542 }}		\| {{mapping\| 1547 2542 }}
	\| -0.015		\| −0.015
	\| 0.015		\| 0.015
	\| 1.99		\| 1.99
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	\| {{monzo\| -52 -17 34 }}, {{monzo\| 40 -56 21 }}		\| {{monzo\| -52 -17 34 }}, {{monzo\| 40 -56 21 }}
	\| {{mapping\| 1547 2542 3592 }}		\| {{mapping\| 1547 2542 3592 }}
	\| -0.008		\| −0.008
	\| 0.017		\| 0.017
	\| 2.14		\| 2.14
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	\| 4375/4374, {{monzo\| -1 4 11 -11 }}, {{monzo\| 46 -14 -3 -6 }}		\| 4375/4374, {{monzo\| -1 4 11 -11 }}, {{monzo\| 46 -14 -3 -6 }}
	\| {{mapping\| 1547 2542 3592 4343 }}		\| {{mapping\| 1547 2542 3592 4343 }}
	\| -0.007		\| −0.007
	\| 0.014		\| 0.014
	\| 1.86		\| 1.86
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	\| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325		\| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325
	\| {{mapping\| 1547 2542 3592 4343 5352 }}		\| {{mapping\| 1547 2542 3592 4343 5352 }}
	\| -0.017		\| −0.017
	\| 0.024		\| 0.024
	\| 3.10		\| 3.10
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	\| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683		\| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683
	\| {{mapping\| 1547 2542 3592 4343 5352 5725 }}		\| {{mapping\| 1547 2542 3592 4343 5352 5725 }}
	\| -0.029		\| −0.029
	\| 0.034		\| 0.034
	\| 4.42		\| 4.42
	\|}		{{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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	\|-		\|-
	\| 7		\| 7
	\| 670\1547<br>(7\1547)		\| 670\1547<br />(7\1547)
	\| 519.715<br>(5.429)		\| 519.715<br />(5.429)
	\| 27/20<br>(325/324)		\| 27/20<br />(325/324)
	\| [[Brahmagupta]] (7-limit)		\| [[Brahmagupta]] (7-limit)
	\|-		\|-
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	\|-		\|-
	\| 13		\| 13
	\| 642\1547<br>(47\1547)		\| 642\1547<br />(47\1547)
	\| 497.996<br>(36.458)		\| 497.996<br />(36.458)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Aluminium]]		\| [[Aluminium]]
	\|-		\|-
	\| 17		\| 17
	\| 321\1547<br>(48\1547)		\| 321\1547<br />(48\1547)
	\| 248.998<br>(37.233)		\| 248.998<br />(37.233)
	\| {{monzo\| -23 5 9 -2 }}<br>(100352/98415)		\| {{monzo\| -23 5 9 -2 }}<br />(100352/98415)
	\| [[Chlorine]]		\| [[Chlorine]]
	\|-		\|-
	\| 91		\| 91
	\| 642\1547<br>(13\1547)		\| 642\1547<br />(13\1547)
	\| 497.996<br>(10.084)		\| 497.996<br />(10.084)
	\| 4/3<br>(176/175)		\| 4/3<br />(176/175)
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		{{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 ==

FloraC: Adopt template: Factorization

2023-10-30T14:03:03Z

Adopt template: Factorization

← Older revision		Revision as of 14:03, 30 October 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	1547 has subset edos {{EDOs\| 7, 13, 17, 91, 119, and 221 }}.		Since 1547 factors into {{factorization\|1547}}, 1547edo has subset edos {{EDOs\| 7, 13, 17, 91, 119, and 221 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+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
	\|-		\|-

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

2023-10-17T07:34:47Z

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

← Older revision		Revision as of 07:34, 17 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. It tempers out [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma.		1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. It [[Tempering out\|tempers out]] [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma.

	In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo\| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].		In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo\| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].
Line 14:		Line 14:
	{{Harmonics in equal\|1547}}		{{Harmonics in equal\|1547}}

	=== ~~Divisors~~ ===		=== Subsets and supersets ===
	1547 has subset edos {{EDOs\| 7, 13, 17, 91, 119, and 221 }}.		1547 has subset edos {{EDOs\| 7, 13, 17, 91, 119, and 221 }}.

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	\| 2.3		\| 2.3
	\| {{monzo\| 2452 -1547 }}		\| {{monzo\| 2452 -1547 }}
	\| [{{~~val~~\| 1547 2542 }}]		\| {{mapping\| 1547 2542 }}
	\| -0.015		\| -0.015
	\| 0.015		\| 0.015
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	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -52 -17 34 }}, {{monzo\| 40 -56 21 }}		\| {{monzo\| -52 -17 34 }}, {{monzo\| 40 -56 21 }}
	\| [{{~~val~~\| 1547 2542 3592 }}]		\| {{mapping\| 1547 2542 3592 }}
	\| -0.008		\| -0.008
	\| 0.017		\| 0.017
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	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, {{monzo\| -1 4 11 -11 }}, {{monzo\| 46 -14 -3 -6 }}		\| 4375/4374, {{monzo\| -1 4 11 -11 }}, {{monzo\| 46 -14 -3 -6 }}
	\| [{{~~val~~\| 1547 2542 3592 4343 }}]		\| {{mapping\| 1547 2542 3592 4343 }}
	\| -0.007		\| -0.007
	\| 0.014		\| 0.014
Line 51:		Line 51:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325		\| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325
	\| [{{~~val~~\| 1547 2542 3592 4343 5352 }}]		\| {{mapping\| 1547 2542 3592 4343 5352 }}
	\| -0.017		\| -0.017
	\| 0.024		\| 0.024
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683		\| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683
	\| [{{~~val~~\| 1547 2542 3592 4343 5352 5725 }}]		\| {{mapping\| 1547 2542 3592 4343 5352 5725 }}
	\| -0.029		\| -0.029
	\| 0.034		\| 0.034
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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
Line 115:		Line 115:
	\| [[Protactinium]]		\| [[Protactinium]]
	\|}		\|}
			<nowiki>*</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 ==
	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=oac5JZ9FtB8 Prelude and Fugue in Two Elements ~~(Op. 2, No. 6)~~]		* [https://www.youtube.com/watch?v=oac5JZ9FtB8 ''Prelude and Fugue in Two Elements'']

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

BudjarnLambeth at 06:54, 9 July 2023

2023-07-09T06:54:59Z

← Older revision		Revision as of 06:54, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1547}}		{{EDO intro\|1547}}

BudjarnLambeth at 05:06, 9 July 2023

2023-07-09T05:06:03Z

← Older revision		Revision as of 05:06, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	{{EDO intro\|1547}}		{{EDO intro\|1547}}