339edo - 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"

2026-03-13T13:31:43Z

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 61:		Line 61:
	\| [[Tritriple]] (339d)		\| [[Tritriple]] (339d)
	\|}		\|}
	<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

ArrowHead294 at 12:19, 21 February 2025

2025-02-21T12:19:28Z

← Older revision		Revision as of 12:19, 21 February 2025
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	\| {{monzo\| -13 17 -6 }}, {{monzo\| -44 -3 21 }}		\| {{monzo\| -13 17 -6 }}, {{monzo\| -44 -3 21 }}
	\| {{mapping\| 339 537 787 }}		\| {{mapping\| 339 537 787 }}
	\| 0.2930		\| +0.2930
	\| 0.2828		\| 0.2828
	\| 7.99		\| 7.99

Francium: changed EDO intro to ED intro

2025-02-21T06:21:16Z

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~~\|339~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:07, 15 January 2025

2025-01-15T16:07:23Z

← Older revision		Revision as of 16:07, 15 January 2025
Line 61:		Line 61:
	\| [[Tritriple]] (339d)		\| [[Tritriple]] (339d)
	\|}		\|}
	<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

2024-11-16T13:15:34Z

Partial undo

← Older revision		Revision as of 13:15, 16 November 2024
Line 14:		Line 14:

	== 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 22:		Line 31:
	\| 0.2828		\| 0.2828
	\| 7.99		\| 7.99
	~~{{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 44:		Line 60:
	\| 864/625		\| 864/625
	\| [[Tritriple]] (339d)		\| [[Tritriple]] (339d)
	~~{{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 01:47, 16 November 2024

2024-11-16T01:47:31Z

← Older revision		Revision as of 01:47, 16 November 2024
Line 14:		Line 14:

	== 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 31:		Line 22:
	\| 0.2828		\| 0.2828
	\| 7.99		\| 7.99
	\|}		{{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 60:		Line 44:
	\| 864/625		\| 864/625
	\| [[Tritriple]] (339d)		\| [[Tritriple]] (339d)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:08, 16 November 2024

2024-11-16T01:08:09Z

← Older revision		Revision as of 01:08, 16 November 2024
Line 15:		Line 15:
	== 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 34:		Line 35:
	=== 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 59:		Line 61:
	\| [[Tritriple]] (339d)		\| [[Tritriple]] (339d)
	\|}		\|}
	~~<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: Review

2024-01-21T09:54:57Z

Review

← Older revision		Revision as of 09:54, 21 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~339et~~ is ~~only consistent to~~ the [[~~5-odd~~-limit]]~~. It can be used for~~ the ~~2.3.5.13.19.23.31.41~~ [[~~subgroup~~]], ~~tempering out 780/779,~~ [[~~621/620~~]]~~, 1426/1425, 1026/1025, 2945/2944, 14391/14375 and 73853/73800~~. Using the 339d val ({{val\|339 537 787 '''951'''}}) in the 7-limit and the 339de val ({{val\|339 537 787 '''951''' '''1172'''}}) in the 11-limit, it [[support]]s [[tritriple]].		339edo is [[enfactoring\|enfactored]] in the [[3-limit]] with the same tuning as [[113edo]], and is only [[consistent]] to the [[5-odd-limit]]. Using the 339d val ({{val\| 339 537 787 '''951''' }}) in the 7-limit and the 339de val ({{val\| 339 537 787 '''951''' '''1172''' }}) in the 11-limit, it [[support]]s [[tritriple]].

			It can be used for the 2.3.5.13.19.23.31.41 [[subgroup]], where it [[tempering out\|tempers out]] [[621/620]], 780/779, 1026/1025, 1426/1425, 2945/2944, 14391/14375 and 73853/73800.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	339 factors into 3 × 113, ~~with~~ [[3edo]] and [[113edo]] as its ~~subset edos~~. [[1017edo]], which triples it, gives a good correction to the harmonics 7 and 11.		Since 339 factors into 3 × 113, 339edo has [[3edo]] and 113edo as its subsets. [[1017edo]], which triples it, gives a good correction to the harmonics 7 and 11.

	== 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\|-179 113}}~~		\| {{monzo\| -13 17 -6 }}, {{monzo\| -44 -3 21 }}
	~~\|{{mapping\|339 537}}~~		\| {{mapping\| 339 537 787 }}
	~~\| 0.3376~~
	~~\| 0.3377~~
	~~\| 9.54~~
	\|-
	\|2.3.5
	\|{{monzo\|-13 17 -6}}, {{monzo\|-44 -3 21}}
	\|{{mapping\|339 537 787}}
	\| 0.2930		\| 0.2930
	\| 0.2828		\| 0.2828
Line 46:		Line 41:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|32\339		\| 32\339
	\|113.27		\| 113.27
	\|16/15		\| 16/15
	\|[[Misneb]]		\| [[Misneb]]
	\|-		\|-
	\|1		\| 1
	\|146\339		\| 146\339
	\|516.81		\| 516.81
	\|27/20		\| 27/20
	\|[[Gravity]]		\| [[Gravity]]
	\|-		\|-
	\|1		\| 1
	\|158\339		\| 158\339
	\|559.29		\| 559.29
	\|864/625		\| 864/625
	\|[[Tritriple]] (339d)		\| [[Tritriple]] (339d)
	\|}		\|}

	<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|339}} == Theory == 339et is only consistent to the 5-odd-limit. It can be used for the 2.3.5.13.19.23.31.41 subgroup, tempering out 780/779..."

2024-01-17T20:26:50Z

Created page with "{{Infobox ET}} {{EDO intro|339}} == Theory == 339et is only consistent to the 5-odd-limit. It can be used for the 2.3.5.13.19.23.31.41 subgroup, tempering out 780/779..."

New page

{{Infobox ET}}
{{EDO intro|339}}

== Theory ==
339et is only consistent to the [[5-odd-limit]]. It can be used for the 2.3.5.13.19.23.31.41 [[subgroup]], tempering out 780/779, [[621/620]], 1426/1425, 1026/1025, 2945/2944, 14391/14375 and 73853/73800. Using the 339d val ({{val|339 537 787 '''951'''}}) in the 7-limit and the 339de val ({{val|339 537 787 '''951''' '''1172'''}}) in the 11-limit, it [[support]]s [[tritriple]].

=== Odd harmonics ===
{{Harmonics in equal|339}}

=== Subsets and supersets ===
339 factors into 3 × 113, with [[3edo]] and [[113edo]] as its subset edos. [[1017edo]], which triples it, gives a good correction to the harmonics 7 and 11.

== 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<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-179 113}}
|{{mapping|339 537}}
| 0.3376
| 0.3377
| 9.54
|-
|2.3.5
|{{monzo|-13 17 -6}}, {{monzo|-44 -3 21}}
|{{mapping|339 537 787}}
| 0.2930
| 0.2828
| 7.99
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|1
|32\339
|113.27
|16/15
|[[Misneb]]
|-
|1
|146\339
|516.81
|27/20
|[[Gravity]]
|-
|1
|158\339
|559.29
|864/625
|[[Tritriple]] (339d)
|}

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