432edo - 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"

2026-03-13T13:32:19Z

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 67:		Line 67:
	\| [[Undim]]		\| [[Undim]]
	\|}		\|}
	<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

Francium: changed EDO intro to ED intro

2025-02-21T06:20:12Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:20, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|432~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:05, 15 January 2025

2025-01-15T17:05:50Z

← Older revision		Revision as of 17:05, 15 January 2025
Line 26:		Line 26:
	\| {{monzo\| 685 -432 }}		\| {{monzo\| 685 -432 }}
	\| {{mapping\| 432 685 }}		\| {{mapping\| 432 685 }}
	\| ~~−0~~.2596		\| −0.2596
	\| 0.2595		\| 0.2595
	\| 9.34		\| 9.34
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	\| {{monzo\| 41 -20 -4 }}, {{monzo\| -3 -23 17 }}		\| {{monzo\| 41 -20 -4 }}, {{monzo\| -3 -23 17 }}
	\| {{mapping\| 432 685 1003 }}		\| {{mapping\| 432 685 1003 }}
	\| ~~−0~~.1440		\| −0.1440
	\| 0.2676		\| 0.2676
	\| 9.63		\| 9.63
Line 40:		Line 40:
	\| 5120/5103, 703125/702464, 6565234375/6530347008		\| 5120/5103, 703125/702464, 6565234375/6530347008
	\| {{mapping\| 432 685 1003 1213 }}		\| {{mapping\| 432 685 1003 1213 }}
	\| ~~−0~~.1631		\| −0.1631
	\| 0.2341		\| 0.2341
	\| 8.43		\| 8.43
Line 67:		Line 67:
	\| [[Undim]]		\| [[Undim]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T13:16:16Z

Partial undo

← Older revision		Revision as of 13:16, 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 34:		Line 43:
	\| 0.2341		\| 0.2341
	\| 8.43		\| 8.43
	~~{{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 50:		Line 66:
	\| 4/3		\| 4/3
	\| [[Undim]]		\| [[Undim]]
	~~{{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

ArrowHead294 at 01:45, 16 November 2024

2024-11-16T01:45:08Z

← Older revision		Revision as of 01:45, 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\| 685 -432 }}		\| {{monzo\| 685 -432 }}
	\| {{mapping\| 432 685 }}		\| {{mapping\| 432 685 }}
	\| -0.2596		\| −0.2596
	\| 0.2595		\| 0.2595
	\| 9.34		\| 9.34
Line 33:		Line 24:
	\| {{monzo\| 41 -20 -4 }}, {{monzo\| -3 -23 17 }}		\| {{monzo\| 41 -20 -4 }}, {{monzo\| -3 -23 17 }}
	\| {{mapping\| 432 685 1003 }}		\| {{mapping\| 432 685 1003 }}
	\| -0.1440		\| −0.1440
	\| 0.2676		\| 0.2676
	\| 9.63		\| 9.63
Line 40:		Line 31:
	\| 5120/5103, 703125/702464, 6565234375/6530347008		\| 5120/5103, 703125/702464, 6565234375/6530347008
	\| {{mapping\| 432 685 1003 1213 }}		\| {{mapping\| 432 685 1003 1213 }}
	\| -0.1631		\| −0.1631
	\| 0.2341		\| 0.2341
	\| 8.43		\| 8.43
	\|}		{{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
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	\| 4/3		\| 4/3
	\| [[Undim]]		\| [[Undim]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:05, 16 November 2024

2024-11-16T01:05:56Z

← Older revision		Revision as of 01:05, 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 46:		Line 47:
	=== 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 60:		Line 62:
	\|-		\|-
	\| 4		\| 4
	\| 179\432<br>(37\432)		\| 179\432<br />(37\432)
	\| 497.22<br>(102.78)		\| 497.22<br />(102.78)
	\| 4/3		\| 4/3
	\| [[Undim]]		\| [[Undim]]
	\|}		\|}
	~~<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}}

FloraC: -typo

2023-11-09T13:59:26Z

-typo

← Older revision		Revision as of 13:59, 9 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	432edo has a reasonable approximation to the 7-limit, where the equal temperament [[tempering out\|tempers out]] [[5120/5103], [[703125/702464]], [[40353607/40310784]], 102760448/102515625, and 283115520/282475249. It [[support]]s and provides a good tuning for the 5-limit [[maja]] temperament.		432edo has a reasonable approximation to the 7-limit, where the equal temperament [[tempering out\|tempers out]] [[5120/5103]], [[703125/702464]], [[40353607/40310784]], 102760448/102515625, and 283115520/282475249. It [[support]]s and provides a good tuning for the 5-limit [[maja]] temperament.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: Review

2023-11-09T13:59:15Z

Review

← Older revision		Revision as of 13:59, 9 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~432et~~ tempers out ~~283115520~~/~~282475249~~, [[703125/702464]], ~~102760448/102515625 and~~ [[40353607/40310784]] ~~in the 7-limit~~. It provides ~~the optimal patent val~~ for the [[maja]] temperament.		432edo has a reasonable approximation to the 7-limit, where the equal temperament [[tempering out\|tempers out]] [[5120/5103], [[703125/702464]], [[40353607/40310784]], 102760448/102515625, and 283115520/282475249. It [[support]]s and provides a good tuning for the 5-limit [[maja]] temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|432}}		{{Harmonics in equal\|432}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	432 is a highly factorable number~~. It factors~~ into ~~2<sup>4</sup> × 3<sup>3</sup>~~, ~~with~~ subset edos {{EDOs\|2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, and 216}}.		432 is a highly factorable number, factoring into {{factorization\|432}}, so 432edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, and 216 }}.

	== 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\|685 -432}}		\| {{monzo\| 685 -432 }}
	\|{{mapping\|432 685}}		\| {{mapping\| 432 685 }}
	\| -0.2596		\| -0.2596
	\| 0.2595		\| 0.2595
	\| 9.34		\| 9.34
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|41 -20 -4}}, {{monzo\|-3 -23 17}}		\| {{monzo\| 41 -20 -4 }}, {{monzo\| -3 -23 17 }}
	\|{{mapping\|432 685 1003}}		\| {{mapping\| 432 685 1003 }}
	\| -0.1440		\| -0.1440
	\| 0.2676		\| 0.2676
	\| 9.63		\| 9.63
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|5120/5103, 703125/702464, 6565234375/6530347008		\| 5120/5103, 703125/702464, 6565234375/6530347008
	\|{{mapping\|432 685 1003 1213}}		\| {{mapping\| 432 685 1003 1213 }}
	\| -0.1631		\| -0.1631
	\| 0.2341		\| 0.2341
Line 51:		Line 53:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|163\432		\| 163\432
	\|452.78		\| 452.78
	\|125/96		\| 125/96
	\|[[Maja]]		\| [[Maja]]
	\|-		\|-
	\|4		\| 4
	\|179\432<br>(37\432)		\| 179\432<br>(37\432)
	\|497.22<br>(102.78)		\| 497.22<br>(102.78)
	\|4/3		\| 4/3
	\|[[Undim]]		\| [[Undim]]
	\|}		\|}

	<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

Francium: Created page with "{{Infobox ET}} {{EDO intro|432}} == Theory == 432et tempers out 283115520/282475249, 703125/702464, 102760448/102515625 and 40353607/40310784 in the 7-limit. It provi..."

2023-11-07T16:57:03Z

Created page with "{{Infobox ET}} {{EDO intro|432}} == Theory == 432et tempers out 283115520/282475249, 703125/702464, 102760448/102515625 and 40353607/40310784 in the 7-limit. It provi..."

New page

{{Infobox ET}}
{{EDO intro|432}}

== Theory ==
432et tempers out 283115520/282475249, [[703125/702464]], 102760448/102515625 and [[40353607/40310784]] in the 7-limit. It provides the optimal patent val for the [[maja]] temperament.
=== Odd harmonics ===
{{Harmonics in equal|432}}
=== Subsets and supersets ===
432 is a highly factorable number. It factors into 24 × 33, with subset edos {{EDOs|2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, and 216}}.

== 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|685 -432}}
|{{mapping|432 685}}
| -0.2596
| 0.2595
| 9.34
|-
|2.3.5
|{{monzo|41 -20 -4}}, {{monzo|-3 -23 17}}
|{{mapping|432 685 1003}}
| -0.1440
| 0.2676
| 9.63
|-
|2.3.5.7
|5120/5103, 703125/702464, 6565234375/6530347008
|{{mapping|432 685 1003 1213}}
| -0.1631
| 0.2341
| 8.43
|}

=== 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
|163\432
|452.78
|125/96
|[[Maja]]
|-
|4
|179\432 (37\432)
|497.22 (102.78)
|4/3
|[[Undim]]
|}

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