981edo - Revision history

FloraC: Update

2026-05-19T09:32:15Z

Update

← Older revision		Revision as of 09:32, 19 May 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[~~ennealimmia~~]], which ~~also~~ tempers out 4096/4095.		981edo is a good [[13-limit\|13-]] and [[17-limit]] system, [[consistent]] to the [[17-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], [[4459/4455]] and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealympic]], which additionally tempers out 4096/4095.

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 981 factors into primes as 3<sup>2</sup> × 109, 981edo has subset edos 3, 9, 109, and 327.		Since 981 factors into primes as {{nowrap\| 3<sup>2</sup> × 109 }}, 981edo has subset edos {{EDOs\| 3, 9, 109, and 327 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 17:		Line 17:
	! 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
	\|-		\|-
Line 24:		Line 24:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 1555 -981 }}		\| {{Monzo\| 1555 -981 }}
	\| {{~~mapping~~\| 981 1555 }}		\| {{Mapping\| 981 1555 }}
	\| −0.0586		\| −0.0586
	\| 0.0586		\| 0.0586
Line 31:		Line 31:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 1 -27 18 }}, {{monzo\| 85 -17 -25 }}		\| {{Monzo\| 1 -27 18 }}, {{monzo\| 85 -17 -25 }}
	\| {{~~mapping~~\| 981 1555 2278 }}		\| {{Mapping\| 981 1555 2278 }}
	\| −0.0722		\| −0.0722
	\| 0.0515		\| 0.0515
Line 39:		Line 39:
	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 4375/4374, {{monzo\| 79 -25 -23 5 }}		\| 2401/2400, 4375/4374, {{monzo\| 79 -25 -23 5 }}
	\| {{~~mapping~~\| 981 1555 2278 2754 }}		\| {{Mapping\| 981 1555 2278 2754 }}
	\| −0.0385		\| −0.0385
	\| 0.0562		\| 0.0562
Line 46:		Line 46:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470		\| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470
	\| {{~~mapping~~\| 981 1555 2278 2754 3394 }}		\| {{Mapping\| 981 1555 2278 2754 3394 }}
	\| −0.0630		\| −0.0630
	\| 0.0545		\| 0.0545
Line 53:		Line 53:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470		\| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470
	\| {{~~mapping~~\| 981 1555 2278 2754 3394 3630 }}		\| {{Mapping\| 981 1555 2278 2754 3394 3630 }}
	\| −0.0453		\| −0.0453
	\| 0.0636		\| 0.0636
Line 60:		Line 60:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913		\| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913
	\| {{~~mapping~~\| 981 1555 2278 2754 3394 3630 4010 }}		\| {{Mapping\| 981 1555 2278 2754 3394 3630 4010 }}
	\| −0.0473		\| −0.0473
	\| 0.0591		\| 0.0591
Line 70:		Line 70:
	\|+ 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 83:		Line 83:
	\|-		\|-
	\| 9		\| 9
	\| 258\981<br />(40\981)		\| 258\981<br>(40\981)
	\| 315.60<br />(48.93)		\| 315.60<br>(48.93)
	\| 6/5<br />(36/35)		\| 6/5<br>(36/35)
	\| [[Ennealimmal]] / ~~ennealimmia~~		\| [[Ennealimmal]] / ennealympic
	\|}		\|}
	<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

	[[Category:Ennealimmic]]		[[Category:Ennealimmic]]
	[[Category:~~Ennealimmia~~]]		[[Category:Ennealimmal]]

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"

2026-03-13T13:32:39Z

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 88:		Line 88:
	\| [[Ennealimmal]] / ennealimmia		\| [[Ennealimmal]] / ennealimmia
	\|}		\|}
	<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

	[[Category:Ennealimmic]]		[[Category:Ennealimmic]]
	[[Category:Ennealimmia]]		[[Category:Ennealimmia]]

ArrowHead294 at 23:09, 20 February 2025

2025-02-20T23:09:18Z

← Older revision		Revision as of 23:09, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|981~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:40:25Z

Theory: cleanup

← Older revision		Revision as of 16:40, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. It [[tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.		981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 981 ~~= {{factorization\|981}}~~, 981edo has subset edos 3, 9, 109, and 327.		Since 981 factors into primes as 3<sup>2</sup> × 109, 981edo has subset edos 3, 9, 109, and 327.

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

ArrowHead294 at 18:59, 15 January 2025

2025-01-15T18:59:00Z

← Older revision		Revision as of 18:59, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. ~~The equal temperament~~ [[~~Tempering out\|~~tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.		981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. It [[tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 26:		Line 26:
	\| {{monzo\| 1555 -981 }}		\| {{monzo\| 1555 -981 }}
	\| {{mapping\| 981 1555 }}		\| {{mapping\| 981 1555 }}
	\| ~~−0~~.0586		\| −0.0586
	\| 0.0586		\| 0.0586
	\| 4.79		\| 4.79
Line 33:		Line 33:
	\| {{monzo\| 1 -27 18 }}, {{monzo\| 85 -17 -25 }}		\| {{monzo\| 1 -27 18 }}, {{monzo\| 85 -17 -25 }}
	\| {{mapping\| 981 1555 2278 }}		\| {{mapping\| 981 1555 2278 }}
	\| ~~−0~~.0722		\| −0.0722
	\| 0.0515		\| 0.0515
	\| 4.21		\| 4.21
Line 40:		Line 40:
	\| 2401/2400, 4375/4374, {{monzo\| 79 -25 -23 5 }}		\| 2401/2400, 4375/4374, {{monzo\| 79 -25 -23 5 }}
	\| {{mapping\| 981 1555 2278 2754 }}		\| {{mapping\| 981 1555 2278 2754 }}
	\| ~~−0~~.0385		\| −0.0385
	\| 0.0562		\| 0.0562
	\| 4.59		\| 4.59
Line 47:		Line 47:
	\| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470		\| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470
	\| {{mapping\| 981 1555 2278 2754 3394 }}		\| {{mapping\| 981 1555 2278 2754 3394 }}
	\| ~~−0~~.0630		\| −0.0630
	\| 0.0545		\| 0.0545
	\| 4.46		\| 4.46
Line 54:		Line 54:
	\| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470		\| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470
	\| {{mapping\| 981 1555 2278 2754 3394 3630 }}		\| {{mapping\| 981 1555 2278 2754 3394 3630 }}
	\| ~~−0~~.0453		\| −0.0453
	\| 0.0636		\| 0.0636
	\| 5.20		\| 5.20
Line 61:		Line 61:
	\| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913		\| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913
	\| {{mapping\| 981 1555 2278 2754 3394 3630 4010 }}		\| {{mapping\| 981 1555 2278 2754 3394 3630 4010 }}
	\| ~~−0~~.0473		\| −0.0473
	\| 0.0591		\| 0.0591
	\| 4.83		\| 4.83
Line 88:		Line 88:
	\| [[Ennealimmal]] / ennealimmia		\| [[Ennealimmal]] / ennealimmia
	\|}		\|}
	<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

	[[Category:Ennealimmic]]		[[Category:Ennealimmic]]
	[[Category:Ennealimmia]]		[[Category:Ennealimmia]]

ArrowHead294: Partial undo

2024-11-16T12:58:39Z

Partial undo

← Older revision		Revision as of 12:58, 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 55:		Line 64:
	\| 0.0591		\| 0.0591
	\| 4.83		\| 4.83
	~~{{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
Line 71:		Line 87:
	\| 6/5<br />(36/35)		\| 6/5<br />(36/35)
	\| [[Ennealimmal]] / ennealimmia		\| [[Ennealimmal]] / ennealimmia
	~~{{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

	[[Category:Ennealimmic]]		[[Category:Ennealimmic]]
	[[Category:Ennealimmia]]		[[Category:Ennealimmia]]

ArrowHead294 at 03:03, 16 November 2024

2024-11-16T03:03:16Z

← Older revision		Revision as of 03:03, 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\| 1555 -981 }}		\| {{monzo\| 1555 -981 }}
	\| {{mapping\| 981 1555 }}		\| {{mapping\| 981 1555 }}
	\| -0.0586		\| −0.0586
	\| 0.0586		\| 0.0586
	\| 4.79		\| 4.79
Line 32:		Line 24:
	\| {{monzo\| 1 -27 18 }}, {{monzo\| 85 -17 -25 }}		\| {{monzo\| 1 -27 18 }}, {{monzo\| 85 -17 -25 }}
	\| {{mapping\| 981 1555 2278 }}		\| {{mapping\| 981 1555 2278 }}
	\| -0.0722		\| −0.0722
	\| 0.0515		\| 0.0515
	\| 4.21		\| 4.21
Line 39:		Line 31:
	\| 2401/2400, 4375/4374, {{monzo\| 79 -25 -23 5 }}		\| 2401/2400, 4375/4374, {{monzo\| 79 -25 -23 5 }}
	\| {{mapping\| 981 1555 2278 2754 }}		\| {{mapping\| 981 1555 2278 2754 }}
	\| -0.0385		\| −0.0385
	\| 0.0562		\| 0.0562
	\| 4.59		\| 4.59
Line 46:		Line 38:
	\| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470		\| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470
	\| {{mapping\| 981 1555 2278 2754 3394 }}		\| {{mapping\| 981 1555 2278 2754 3394 }}
	\| -0.0630		\| −0.0630
	\| 0.0545		\| 0.0545
	\| 4.46		\| 4.46
Line 53:		Line 45:
	\| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470		\| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470
	\| {{mapping\| 981 1555 2278 2754 3394 3630 }}		\| {{mapping\| 981 1555 2278 2754 3394 3630 }}
	\| -0.0453		\| −0.0453
	\| 0.0636		\| 0.0636
	\| 5.20		\| 5.20
Line 60:		Line 52:
	\| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913		\| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913
	\| {{mapping\| 981 1555 2278 2754 3394 3630 4010 }}		\| {{mapping\| 981 1555 2278 2754 3394 3630 4010 }}
	\| -0.0473		\| −0.0473
	\| 0.0591		\| 0.0591
	\| 4.83		\| 4.83
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center~~-~~all left-5"~~		{{rank-2 begin}}
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 80:		Line 67:
	\|-		\|-
	\| 9		\| 9
	\| 258\981<br>(40\981)		\| 258\981<br />(40\981)
	\| 315.60<br>(48.93)		\| 315.60<br />(48.93)
	\| 6/5<br>(36/35)		\| 6/5<br />(36/35)
	\| [[Ennealimmal]] / ennealimmia		\| [[Ennealimmal]] / ennealimmia
	\|}		{{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}}

	[[Category:Ennealimmic]]		[[Category:Ennealimmic]]
	[[Category:Ennealimmia]]		[[Category:Ennealimmia]]

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T11:18:56Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 11:18, 2 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. The equal temperament [[Tempering out\|tempers out]] [[2080/2079]], [[2401/2400]], 2431/2430, [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and 4914/4913 in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.		981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. The equal temperament [[Tempering out\|tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 981 = ~~3<sup>2</sup> × 109~~, 981edo has subset edos 3, 9, 109, and 327.		Since 981 = {{factorization\|981}}, 981edo has subset edos 3, 9, 109, and 327.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 24:		Line 24:
	\| 2.3		\| 2.3
	\| {{monzo\| 1555 -981 }}		\| {{monzo\| 1555 -981 }}
	\| [{{~~val~~\| 981 1555 }}]		\| {{mapping\| 981 1555 }}
	\| -0.0586		\| -0.0586
	\| 0.0586		\| 0.0586
Line 31:		Line 31:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 1 -27 18 }}, {{monzo\| 85 -17 -25 }}		\| {{monzo\| 1 -27 18 }}, {{monzo\| 85 -17 -25 }}
	\| [{{~~val~~\| 981 1555 2278 }}]		\| {{mapping\| 981 1555 2278 }}
	\| -0.0722		\| -0.0722
	\| 0.0515		\| 0.0515
Line 38:		Line 38:
	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 4375/4374, {{monzo\| 79 -25 -23 5 }}		\| 2401/2400, 4375/4374, {{monzo\| 79 -25 -23 5 }}
	\| [{{~~val~~\| 981 1555 2278 2754 }}]		\| {{mapping\| 981 1555 2278 2754 }}
	\| -0.0385		\| -0.0385
	\| 0.0562		\| 0.0562
Line 45:		Line 45:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470		\| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470
	\| [{{~~val~~\| 981 1555 2278 2754 3394 }}]		\| {{mapping\| 981 1555 2278 2754 3394 }}
	\| -0.0630		\| -0.0630
	\| 0.0545		\| 0.0545
Line 52:		Line 52:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470		\| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470
	\| [{{~~val~~\| 981 1555 2278 2754 3394 3630 }}]		\| {{mapping\| 981 1555 2278 2754 3394 3630 }}
	\| -0.0453		\| -0.0453
	\| 0.0636		\| 0.0636
Line 59:		Line 59:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913		\| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913
	\| [{{~~val~~\| 981 1555 2278 2754 3394 3630 4010 }}]		\| {{mapping\| 981 1555 2278 2754 3394 3630 4010 }}
	\| -0.0473		\| -0.0473
	\| 0.0591		\| 0.0591
Line 70:		Line 70:
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 77:		Line 77:
	\| 500.306		\| 500.306
	\| 8192/6137		\| 8192/6137
	\| [[~~Langwidge~~]] ~~(2.17.19 subgroup)~~		\| [[Protolangwidge]]
	\|-		\|-
	\| 9		\| 9

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

2023-10-19T16:07:02Z

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

← Older revision		Revision as of 16:07, 19 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	981edo is a good 13- and 17-limit system. It tempers out [[2080/2079]], [[2401/2400]], 2431/2430, [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and 4914/4913 in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.		981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. The equal temperament [[Tempering out\|tempers out]] [[2080/2079]], [[2401/2400]], 2431/2430, [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and 4914/4913 in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 68:		Line 68:
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	! 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 85:		Line 85:
	\| [[Ennealimmal]] / ennealimmia		\| [[Ennealimmal]] / ennealimmia
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Ennealimmic]]		[[Category:Ennealimmic]]
	[[Category:Ennealimmia]]		[[Category:Ennealimmia]]

FloraC: -redundant category

2023-08-14T03:18:12Z

-redundant category

← Older revision		Revision as of 03:18, 14 August 2023
Line 77:		Line 77:
	\| 500.306		\| 500.306
	\| 8192/6137		\| 8192/6137
	\| [[Langwidge]] (2.17.19)		\| [[Langwidge]] (2.17.19 subgroup)
	\|-		\|-
	\| 9		\| 9
Line 86:		Line 86:
	\|}		\|}

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Ennealimmic]]		[[Category:Ennealimmic]]
	[[Category:Ennealimmia]]		[[Category:Ennealimmia]]