332edo - 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"

2026-03-13T13:31:58Z

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 13:31, 13 March 2026
Line 84:		Line 84:
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
	<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:Sedia]]		[[Category:Sedia]]

Francium: changed EDO intro to ED intro

2025-02-21T06:21:05Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:21, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|332~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:06, 15 January 2025

2025-01-15T17:06:48Z

← Older revision		Revision as of 17:06, 15 January 2025
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 332 factors into ~~2<sup>2</sup> × 83~~, 332edo has subset edos {{EDOs\| 2, 4, 83, and 166 }}.		Since 332 factors into {{factorisation\|332}}, 332edo has subset edos {{EDOs\| 2, 4, 83, and 166 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 26:		Line 26:
	\| {{monzo\| -13 17 -6 }}, {{monzo\| -53 10 16 }}		\| {{monzo\| -13 17 -6 }}, {{monzo\| -53 10 16 }}
	\| {{mapping\| 332 526 771 }}		\| {{mapping\| 332 526 771 }}
	\| 0.0955		\| +0.0955
	\| 0.2778		\| 0.2778
	\| 7.69		\| 7.69
Line 33:		Line 33:
	\| 2401/2400, 19683/19600, 29360128/29296875		\| 2401/2400, 19683/19600, 29360128/29296875
	\| {{mapping\| 332 526 771 932 }}		\| {{mapping\| 332 526 771 932 }}
	\| 0.0851		\| +0.0851
	\| 0.2412		\| 0.2412
	\| 6.67		\| 6.67
Line 84:		Line 84:
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
	<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:Sedia]]		[[Category:Sedia]]

ArrowHead294: Partial undo

2024-11-16T13:14:05Z

Partial undo

← Older revision		Revision as of 13:14, 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]] (%)
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 27:		Line 36:
	\| 0.2412		\| 0.2412
	\| 6.67		\| 6.67
	~~{{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 67:		Line 83:
	\| 1125/1024		\| 1125/1024
	\| [[Kwazy]]		\| [[Kwazy]]
	~~{{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:Sedia]]		[[Category:Sedia]]

ArrowHead294 at 01:50, 16 November 2024

2024-11-16T01:50:38Z

← Older revision		Revision as of 01:50, 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]] (%)~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 36:		Line 27:
	\| 0.2412		\| 0.2412
	\| 6.67		\| 6.67
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 83:		Line 67:
	\| 1125/1024		\| 1125/1024
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

	[[Category:Sedia]]		[[Category:Sedia]]

ArrowHead294 at 01:12, 16 November 2024

2024-11-16T01:12:46Z

← Older revision		Revision as of 01:12, 16 November 2024
Line 13:		Line 13:
	== 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
	\|-		\|-
Line 39:		Line 40:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+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 71:		Line 73:
	\|-		\|-
	\| 2		\| 2
	\| 143\332<br>(23\332)		\| 143\332<br />(23\332)
	\| 516.87<br>(83.13)		\| 516.87<br />(83.13)
	\| 27/20<br>(21/20)		\| 27/20<br />(21/20)
	\| [[Harry]]		\| [[Harry]]
	\|-		\|-
Line 82:		Line 84:
	\| [[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
	~~<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:Sedia]]		[[Category:Sedia]]

FloraC: Review

2023-12-05T16:41:07Z

Review

← Older revision		Revision as of 16:41, 5 December 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|332}}		{{EDO intro\|332}}

	== Theory ==		== Theory ==
	332edo tempers out 118098/117649, ~~134217728/133984375,~~ 29360128/29296875 ~~and [[2401/2400]]~~ in the 7-limit. It provides the optimal patent val ~~for [[majvamoid~~]] and [[sedia]].		332edo is [[consistent]] to the [[7-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]], 118098/117649, and 29360128/29296875 in the 7-limit. It provides the [[optimal patent val]] for 11-, 13-, and 17-limit [[sedia]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal}}		{{Harmonics in equal\|332}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	332 factors into 2<sup>2</sup> × 83, ~~with~~ subset edos {{EDOs\|2, 4, 83, and 166}}.		Since 332 factors into 2<sup>2</sup> × 83, 332edo has subset edos {{EDOs\| 2, 4, 83, and 166 }}.

	== 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~~		\| 2.3.5
	~~\|{{monzo\|-263 166}}~~		\| {{monzo\| -13 17 -6 }}, {{monzo\| -53 10 16 }}
	~~\|{{mapping\|332 526}}~~		\| {{mapping\| 332 526 771 }}
	~~\| 0.2367~~
	~~\| 0.2367~~
	~~\| 6.55~~
	\|-
	\|2.3.5
	\|{{monzo\|-13 17 -6}}, {{monzo\|-53 10 16}}
	\|{{mapping\|332 526 771}}
	\| 0.0955		\| 0.0955
	\| 0.2778		\| 0.2778
	\| 7.69		\| 7.69
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|2401/2400, 19683/19600, 29360128/29296875		\| 2401/2400, 19683/19600, 29360128/29296875
	\|{{mapping\|332 526 771 932}}		\| {{mapping\| 332 526 771 932 }}
	\| 0.0851		\| 0.0851
	\| 0.2412		\| 0.2412
Line 49:		Line 46:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|33\332		\| 33\332
	\|119.28		\| 119.28
	\|15/14		\| 15/14
	\|[[Septidiasemi]]		\| [[Septidiasemi]]
	\|-		\|-
	\|1		\| 1
	\|75\332		\| 75\332
	\|271.08		\| 271.08
	\|1024/875		\| 1024/875
	\|[[Quasiorwell]]		\| [[Quasiorwell]]
	\|-		\|-
	\|1		\| 1
	\|127\332		\| 127\332
	\|459.04		\| 459.04
	\|125/96		\| 125/96
	\|[[Majvam]]		\| [[Majvam]]
	\|-		\|-
	\|1		\| 1
	\|143\332		\| 143\332
	\|516.87		\| 516.87
	\|27/20		\| 27/20
	\|[[Gravity]]		\| [[Gravity]]
	\|-		\|-
	\|2		\| 2
	\|143\332<br>(23\332)		\| 143\332<br>(23\332)
	\|516.87<br>(83.13)		\| 516.87<br>(83.13)
	\|27/20<br>(21/20)		\| 27/20<br>(21/20)
	\|[[Harry]]		\| [[Harry]]
	\|-		\|-
	\|2		\| 2
	\|45\332		\| 45\332
	\|162.65		\| 162.65
	\|1125/1024		\| 1125/1024
	\|[[Kwazy]]		\| [[Kwazy]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	~~<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:Sedia]]

Francium at 15:47, 7 November 2023

2023-11-07T15:47:55Z

← Older revision		Revision as of 15:47, 7 November 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro}}		{{EDO intro\|332}}
	== Theory ==		== Theory ==
	332edo tempers out 118098/117649, 134217728/133984375, 29360128/29296875 and [[2401/2400]] in the 7-limit. It provides the optimal patent val for [[majvamoid]] and [[sedia]].		332edo tempers out 118098/117649, 134217728/133984375, 29360128/29296875 and [[2401/2400]] in the 7-limit. It provides the optimal patent val for [[majvamoid]] and [[sedia]].

Francium: Created page with "{{Infobox ET}} {{EDO intro}} == Theory == 332edo tempers out 118098/117649, 134217728/133984375, 29360128/29296875 and 2401/2400 in the 7-limit. It provides the optimal pa..."

2023-11-07T15:47:01Z

Created page with "{{Infobox ET}} {{EDO intro}} == Theory == 332edo tempers out 118098/117649, 134217728/133984375, 29360128/29296875 and 2401/2400 in the 7-limit. It provides the optimal pa..."

New page

{{Infobox ET}}
{{EDO intro}}
== Theory ==
332edo tempers out 118098/117649, 134217728/133984375, 29360128/29296875 and [[2401/2400]] in the 7-limit. It provides the optimal patent val for [[majvamoid]] and [[sedia]].
=== Prime harmonics ===
{{Harmonics in equal}}
=== Subsets and supersets ===
332 factors into 22 × 83, with subset edos {{EDOs|2, 4, 83, and 166}}.
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-263 166}}
|{{mapping|332 526}}
| 0.2367
| 0.2367
| 6.55
|-
|2.3.5
|{{monzo|-13 17 -6}}, {{monzo|-53 10 16}}
|{{mapping|332 526 771}}
| 0.0955
| 0.2778
| 7.69
|-
|2.3.5.7
|2401/2400, 19683/19600, 29360128/29296875
|{{mapping|332 526 771 932}}
| 0.0851
| 0.2412
| 6.67
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator*
! Cents*
! Associated Ratio*
! Temperaments
|-
|1
|33\332
|119.28
|15/14
|[[Septidiasemi]]
|-
|1
|75\332
|271.08
|1024/875
|[[Quasiorwell]]
|-
|1
|127\332
|459.04
|125/96
|[[Majvam]]
|-
|1
|143\332
|516.87
|27/20
|[[Gravity]]
|-
|2
|143\332 (23\332)
|516.87 (83.13)
|27/20 (21/20)
|[[Harry]]
|-
|2
|45\332
|162.65
|1125/1024
|[[Kwazy]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct