330edo - 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"

2026-03-13T13:32:34Z

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 83:		Line 83:
	\| [[Major arcana]] (5-limit)		\| [[Major arcana]] (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

	[[Category:Canou]]		[[Category:Canou]]
	[[Category:Semicanousmic]]		[[Category:Semicanousmic]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

Lériendil: Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

2025-04-17T02:30:10Z

Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

← Older revision		Revision as of 02:30, 17 April 2025
Line 63:		Line 63:
	\| 498.182		\| 498.182
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|-		\|-
	\| 3		\| 3

Sintel: fix helmholtz link

2025-04-16T15:38:07Z

fix helmholtz link

← Older revision		Revision as of 15:38, 16 April 2025
Line 63:		Line 63:
	\| 498.182		\| 498.182
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|-		\|-
	\| 3		\| 3

ArrowHead294 at 22:49, 20 February 2025

2025-02-20T22:49:11Z

← Older revision		Revision as of 22:49, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|330~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:47, 15 January 2025

2025-01-15T19:47:07Z

← Older revision		Revision as of 19:47, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 330 factors into ~~2 × 3 × 5 × 11~~, 330edo has subset edos {{EDOs\| 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165 }}.		Since 330 factors into {{factorisation\|330}}, 330edo has subset edos {{EDOs\| 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 83:		Line 83:
	\| [[Major arcana]] (5-limit)		\| [[Major arcana]] (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

	[[Category:Canou]]		[[Category:Canou]]
	[[Category:Semicanousmic]]		[[Category:Semicanousmic]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

ArrowHead294: Partial undo

2024-11-16T12:39:05Z

Partial undo

← Older revision		Revision as of 12:39, 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		\| 2.3
Line 38:		Line 47:
	\| 0.2212		\| 0.2212
	\| 6.08		\| 6.08
	~~{{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 />({{monzo\| 16 -13 2 }})		\| 4/3<br />({{monzo\| 16 -13 2 }})
	\| [[Major arcana]] (5-limit)		\| [[Major arcana]] (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

	[[Category:Canou]]		[[Category:Canou]]
	[[Category:Semicanousmic]]		[[Category:Semicanousmic]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

ArrowHead294 at 04:13, 16 November 2024

2024-11-16T04:13:14Z

← Older revision		Revision as of 04:13, 16 November 2024
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	== 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
Line 46:		Line 38:
	\| 0.2212		\| 0.2212
	\| 6.08		\| 6.08
	\|}		{{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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	\|-		\|-
	\| 3		\| 3
	\| 137\330<br>(27\330)		\| 137\330<br />(27\330)
	\| 498.182<br>(98.182)		\| 498.182<br />(98.182)
	\| 4/3<br>(200/189)		\| 4/3<br />(200/189)
	\| [[Term (temperament)\|Term]]		\| [[Term (temperament)\|Term]]
	\|-		\|-
	\| 6		\| 6
	\| 137\330<br>(27\330)		\| 137\330<br />(27\330)
	\| 498.182<br>(98.182)		\| 498.182<br />(98.182)
	\| 4/3<br>(200/189)		\| 4/3<br />(200/189)
	\| [[Semiterm]] (330eff)		\| [[Semiterm]] (330eff)
	\|-		\|-
	\| 22		\| 22
	\| 137\330<br>(2\330)		\| 137\330<br />(2\330)
	\| 498.182<br>(7.273)		\| 498.182<br />(7.273)
	\| 4/3<br>({{monzo\| 16 -13 2 }})		\| 4/3<br />({{monzo\| 16 -13 2 }})
	\| [[Major arcana]] (5-limit)		\| [[Major arcana]] (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}}

	[[Category:Canou]]		[[Category:Canou]]
	[[Category:Semicanousmic]]		[[Category:Semicanousmic]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

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

2024-01-22T08:05:37Z

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

← Older revision		Revision as of 08:05, 22 January 2024
Line 2:		Line 2:
	{{EDO intro\|330}}		{{EDO intro\|330}}

	==Theory==		== Theory ==
			330edo has a flat tendency, with its [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] tuned progressively flatter. In the 11-limit, the 330e [[val]] {{val\| 330 523 766 926 '''1141''' }} scores significantly better in [[TE error]] than its [[patent val]] {{val\| 330 523 766 926 '''1142''' }} and allows an extension to the 13-limit.

	330edo has a flat tendency, with its 3rd, 5th, and 7th harmonics tuned progressively flatter. In the 11-limit, the 330e [[val]] {{val\| 330 523 766 926 '''1141''' }} scores significantly better in [[TE error]] than its [[patent val]] {{val\| 330 523 766 926 '''1142''' }} and allows an extension to the 13-limit.		The equal temperament tempers out 32805/32768 ([[schisma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]), 703125/702464 ([[meter]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]]. Using the 330e val, it tempers out 385/384 ([[keenanisma]]), 9801/9800 ([[kalisma]]), and 14641/14580 ([[semicanousma]]) in the [[11-limit]]; 847/845 ([[847/845\|cuthbert]]) and 1001/1000 ([[1001/1000\|sinbadma]]) in the [[13-limit]].

	It tempers out 32805/32768 ([[schisma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]), 703125/702464 ([[~~meter comma\|~~meter]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]]. Using the 330e val, it tempers out 385/384 ([[keenanisma]]), 9801/9800 ([[kalisma]]), and 14641/14580 ([[semicanousma]]) in the [[11-limit]]; 847/845 ([[847/845\|cuthbert]]) and 1001/1000 ([[1001/1000\|sinbadma]]) in the [[13-limit]].

	It provides a nice tuning for [[keenanismic family\|keenanismic]], the rank-4 temperament that tempers out 385/384 (even better than its [[optimal patent val]] [[284edo]]), and actually a close-to-optimal tuning for 11-limit [[Canou family #semicanou\|semicanou]], the rank-3 temperament that tempers out 9801/9800 and 14641/14580.		It provides a nice tuning for [[keenanismic family\|keenanismic]], the rank-4 temperament that tempers out 385/384 (even better than its [[optimal patent val]] [[284edo]]), and actually a close-to-optimal tuning for 11-limit [[Canou family #semicanou\|semicanou]], the rank-3 temperament that tempers out 9801/9800 and 14641/14580.
Line 14:		Line 13:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 330 factors into 2 × 3 × 5 × 11, it has subset edos {{EDOs\| 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165 }}.		Since 330 factors into 2 × 3 × 5 × 11, 330edo has subset edos {{EDOs\| 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165 }}.

	==Regular temperament properties==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|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
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|-523 330}}		\| {{monzo\| -523 330 }}
	\|{{~~val~~\|330 523}}		\| {{mapping\| 330 523 }}
	\| 0.0432		\| +0.0432
	\| 0.0432		\| 0.0432
	\| 1.19		\| 1.19
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|32805/32768, {{monzo\|-2 -50 35}}		\| 32805/32768, {{monzo\| -2 -50 35 }}
	\|{{~~val~~\|330 523 766}}		\| {{mapping\| 330 523 766 }}
	\| 0.1521		\| +0.1521
	\| 0.1581		\| 0.1581
	\| 4.35		\| 4.35
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|32805/32768, 250047/250000, ~~703125~~/~~702464~~		\| 32805/32768, 250047/250000, 823543/819200
	\|{{~~val~~\|330 523 766 926}}		\| {{mapping\| 330 523 766 926 }}
	\| 0.2524		\| +0.2524
	\| 0.2212		\| 0.2212
	\| 6.08		\| 6.08
Line 53:		Line 52:
	\|+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
	\|-		\|-
	\|1		\| 1
	\|137\330		\| 137\330
	\|498.182		\| 498.182
	\|4/3		\| 4/3
	\|[[Helmholtz]]		\| [[Helmholtz]]
			\|-
			\| 3
			\| 137\330<br>(27\330)
			\| 498.182<br>(98.182)
			\| 4/3<br>(200/189)
			\| [[Term (temperament)\|Term]]
	\|-		\|-
	\|3		\| 6
	\|137\330<br>(27\330)		\| 137\330<br>(27\330)
	\|498.182<br>(98.182)		\| 498.182<br>(98.182)
	\|4/3<br>(200/189)		\| 4/3<br>(200/189)
	\|[[~~Term~~]]		\| [[Semiterm]] (330eff)
	\|-		\|-
	\|22		\| 22
	\|137\330<br>(2\330)		\| 137\330<br>(2\330)
	\|498.182<br>(7.273)		\| 498.182<br>(7.273)
	\|4/3<br>({{monzo\|16 -13 2}})		\| 4/3<br>({{monzo\| 16 -13 2 }})
	\|[[Major arcana]] (5-limit)		\| [[Major arcana]] (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

	[[Category:Canou]]		[[Category:Canou]]
	[[Category:Semicanousmic]]		[[Category:Semicanousmic]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

Eliora: /* Rank-2 temperaments */

2023-11-08T20:09:54Z

Rank-2 temperaments

← Older revision		Revision as of 20:09, 8 November 2023
Line 71:		Line 71:
	\|-		\|-
	\|22		\|22
	\|137\330		\|137\330<br>(2\330)
	(2\330)		\|498.182<br>(7.273)
	\|498.182		\|4/3<br>({{monzo\|16 -13 2}})
	(7.273)
	\|4/3
	({{monzo\|16 -13 2}})
	\|[[Major arcana]] (5-limit)		\|[[Major arcana]] (5-limit)
	\|}		\|}

Eliora: /* Theory */ +major arcana

2023-11-08T20:09:34Z

Theory: +major arcana

← Older revision		Revision as of 20:09, 8 November 2023
Line 69:		Line 69:
	\|4/3<br>(200/189)		\|4/3<br>(200/189)
	\|[[Term]]		\|[[Term]]
			\|-
			\|22
			\|137\330
			(2\330)
			\|498.182
			(7.273)
			\|4/3
			({{monzo\|16 -13 2}})
			\|[[Major arcana]] (5-limit)
	\|}		\|}