308edo - 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 64:		Line 64:
	\| [[Oquatonic]] (308)		\| [[Oquatonic]] (308)
	\|}		\|}
	<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

2025-02-21T06:22:14Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:22, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|308~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:53, 15 January 2025

2025-01-15T16:53:08Z

← Older revision		Revision as of 16:53, 15 January 2025
Line 13:		Line 13:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 308 factors into 2<sup>2</sup> × 7 × 11, 308edo has subset edos {{EDOs\| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}.		Since 308 factors into {{nowrap\|2<sup>2</sup> × 7 × 11}}, 308edo has subset edos {{EDOs\| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 30:		Line 30:
	\| {{monzo\| -122 77 }}		\| {{monzo\| -122 77 }}
	\| {{mapping\| 308 488 }}		\| {{mapping\| 308 488 }}
	\| 0.2070		\| +0.2070
	\| 0.2071		\| 0.2071
	\| 5.32		\| 5.32
Line 37:		Line 37:
	\| {{monzo\| -36 11 8 }}, {{monzo\| -7 22 -12 }}		\| {{monzo\| -36 11 8 }}, {{monzo\| -7 22 -12 }}
	\| {{mapping\| 308 488 715 }}		\| {{mapping\| 308 488 715 }}
	\| 0.2241		\| +0.2241
	\| 0.1708		\| 0.1708
	\| 4.38		\| 4.38
Line 64:		Line 64:
	\| [[Oquatonic]] (308)		\| [[Oquatonic]] (308)
	\|}		\|}
	<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

2024-11-16T13:14:24Z

Partial undo

← Older revision		Revision as of 13:14, 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 31:		Line 40:
	\| 0.1708		\| 0.1708
	\| 4.38		\| 4.38
	~~{{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 47:		Line 63:
	\| 4/3<br />(126/125)		\| 4/3<br />(126/125)
	\| [[Oquatonic]] (308)		\| [[Oquatonic]] (308)
	~~{{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 01:49, 16 November 2024

2024-11-16T01:49:42Z

← Older revision		Revision as of 01:49, 16 November 2024
Line 16:		Line 16:

	== 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 40:		Line 31:
	\| 0.1708		\| 0.1708
	\| 4.38		\| 4.38
	\|}		{{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 63:		Line 47:
	\| 4/3<br />(126/125)		\| 4/3<br />(126/125)
	\| [[Oquatonic]] (308)		\| [[Oquatonic]] (308)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:11, 16 November 2024

2024-11-16T01:11:25Z

← Older revision		Revision as of 01:11, 16 November 2024
Line 17:		Line 17:
	== 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 43:		Line 44:
	=== 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 57:		Line 59:
	\|-		\|-
	\| 28		\| 28
	\| 128\308<br>(4\308)		\| 128\308<br />(4\308)
	\| 498.70<br>(15.58)		\| 498.70<br />(15.58)
	\| 4/3<br>(126/125)		\| 4/3<br />(126/125)
	\| [[Oquatonic]] (308)		\| [[Oquatonic]] (308)
	\|}		\|}
	~~<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

2024-02-21T10:54:23Z

Review

← Older revision		Revision as of 10:54, 21 February 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~308et~~ only is consistent in the 5-limit. Ignoring the ~~harmonics~~ 7, 11 and 13, ~~308et~~ is strong in the 2.3.5.17.19.23.29.31 subgroup.		308edo only is [[consistent]] in the [[5-odd-limit]]. Ignoring the [[harmonic]]s [[7/1\|7]], [[11/1\|11]] and [[13/1\|13]], it is strong in the 2.3.5.17.19.23.29.31 [[subgroup]].

	~~308et tempers out following commas:~~		Using the [[patent val]] nonetheless, the equal temperament [[tempering out\|tempers out]] [[19683/19600]], [[65625/65536]], and [[390625/388962]] in the 7-limit, and [[243/242]], 1375/1372, [[6250/6237]], [[9801/9800]], and 14700/14641 in the 11-limit.

	~~7-limit commas: 4096000/4084101,~~ [[~~390625/388962~~]], ~~26873856/26796875,~~ [[~~19683/19600~~]], [[~~78125000~~/~~78121827~~]], [[65625/65536]], [[~~1640558367~~/~~1638400000~~]]

	11-limit ~~commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375~~, [[243/242]], ~~[[131072~~/~~130977]]~~, [[6250/6237]]~~, 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883~~, [[9801/9800]], ~~539055~~/~~537824, 202397184/201768035~~

	Using the 308d val, it supports [[unidec]] and [[gammic]].		Using the 308d val, it supports [[unidec]] and [[gammic]].
Line 17:		Line 13:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	308 factors into 2<sup>2</sup> x 7 x 11, ~~with~~ subset edos {{EDOs\| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154}}.		Since 308 factors into 2<sup>2</sup> × 7 × 11, 308edo has subset edos {{EDOs\| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}.

	==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]]
Line 27:		Line 23:
	! 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\| -122 77 }}		\| {{monzo\| -122 77 }}
	\| {{~~val~~\| 308 488 }}		\| {{mapping\| 308 488 }}
	\| 0.2070		\| 0.2070
	\| 0.2071		\| 0.2071
Line 39:		Line 35:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -36 11 8 }}, {{monzo\| -7 22 -12 }}		\| {{monzo\| -36 11 8 }}, {{monzo\| -7 22 -12 }}
	\| {{~~val~~\| 308 488 715 }}		\| {{mapping\| 308 488 715 }}
	\| 0.2241		\| 0.2241
	\| 0.1708		\| 0.1708
Line 49:		Line 45:
	\|+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
	\|-		\|-
Line 63:		Line 59:
	\| 128\308<br>(4\308)		\| 128\308<br>(4\308)
	\| 498.70<br>(15.58)		\| 498.70<br>(15.58)
	\| 4/3<br>(~~2048~~/~~2025~~)		\| 4/3<br>(126/125)
	\| [[Oquatonic]]		\| [[Oquatonic]] (308)
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct
	~~{{Todo~~\| ~~review }}~~

FloraC: The val must be specified if nonpatent

2023-05-16T14:18:27Z

The val must be specified if nonpatent

← Older revision		Revision as of 14:18, 16 May 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|308}}		{{EDO intro\|308}}

	== Theory ==		== Theory ==
	308et only is consistent in the 5-limit. Ignoring the harmonics 7, 11 and 13, 308et is strong in the 2.3.5.17.19.23.29.31 subgroup.		308et only is consistent in the 5-limit. Ignoring the harmonics 7, 11 and 13, 308et is strong in the 2.3.5.17.19.23.29.31 subgroup.
Line 10:		Line 11:
	11-limit commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375, [[243/242]], [[131072/130977]], [[6250/6237]], 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883, [[9801/9800]], 539055/537824, 202397184/201768035		11-limit commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375, [[243/242]], [[131072/130977]], [[6250/6237]], 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883, [[9801/9800]], 539055/537824, 202397184/201768035

	Using the 308d val, it supports [[~~Unidec~~]] and [[~~Gammic~~]].		Using the 308d val, it supports [[unidec]] and [[gammic]].
	===Prime harmonics===
			=== Prime harmonics ===
	{{Harmonics in equal\|308}}		{{Harmonics in equal\|308}}
	===Subsets and supersets===
			=== Subsets and supersets ===
	308 factors into 2<sup>2</sup> x 7 x 11, with subset edos {{EDOs\| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154}}.		308 factors into 2<sup>2</sup> x 7 x 11, with subset edos {{EDOs\| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154}}.

	==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\|-122 77}}		\| {{monzo\| -122 77 }}
	\|{{val\|308 488}}		\| {{val\| 308 488 }}
	\| 0.2070		\| 0.2070
	\| 0.2071		\| 0.2071
	\| 5.32		\| 5.32
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-36 11 8}}, {{monzo\|-7 22 -12}}		\| {{monzo\| -36 11 8 }}, {{monzo\| -7 22 -12 }}
	\|{{val\|308 488 715}}		\| {{val\| 308 488 715 }}
	\| 0.2241		\| 0.2241
	\| 0.1708		\| 0.1708
Line 46:		Line 49:
	\|+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<br>(Reduced)
	! Cents<br>(~~reduced~~)		! Cents<br>(Reduced)
	! Associated<br>~~ratio~~		! Associated<br>Ratio
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|9\308		\| 9\308
	\|35.06		\| 35.06
	\|128/125		\| 128/125
	\|[[Gammic]]		\| [[Gammic]] (308d)
	\|-		\|-
	\|28		\| 28
	\|128\308<br>(4\308)		\| 128\308<br>(4\308)
	\|498.70<br>(15.58)		\| 498.70<br>(15.58)
	\|4/3<br>(2048/2025)		\| 4/3<br>(2048/2025)
	\|[[Oquatonic]]		\| [[Oquatonic]]
	\|}		\|}

			{{Todo\| review }}

Francium: Created page because the category already existed

2023-05-15T10:38:14Z

Created page because the category already existed

New page

{{Infobox ET}}
{{EDO intro|308}}
== Theory ==
308et only is consistent in the 5-limit. Ignoring the harmonics 7, 11 and 13, 308et is strong in the 2.3.5.17.19.23.29.31 subgroup.

308et tempers out following commas:

7-limit commas: 4096000/4084101, [[390625/388962]], 26873856/26796875, [[19683/19600]], [[78125000/78121827]], [[65625/65536]], [[1640558367/1638400000]]

11-limit commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375, [[243/242]], [[131072/130977]], [[6250/6237]], 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883, [[9801/9800]], 539055/537824, 202397184/201768035

Using the 308d val, it supports [[Unidec]] and [[Gammic]].
===Prime harmonics===
{{Harmonics in equal|308}}
===Subsets and supersets===
308 factors into 22 x 7 x 11, with subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154}}.

==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|-122 77}}
|{{val|308 488}}
| 0.2070
| 0.2071
| 5.32
|-
|2.3.5
|{{monzo|-36 11 8}}, {{monzo|-7 22 -12}}
|{{val|308 488 715}}
| 0.2241
| 0.1708
| 4.38
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator (reduced)
! Cents (reduced)
! Associated ratio
! Temperaments
|-
|1
|9\308
|35.06
|128/125
|[[Gammic]]
|-
|28
|128\308 (4\308)
|498.70 (15.58)
|4/3 (2048/2025)
|[[Oquatonic]]
|}