296edo - 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"

2026-03-13T13:32:50Z

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
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	\| [[Dzelic]]		\| [[Dzelic]]
	\|}		\|}
	<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:Sabric]]		[[Category:Sabric]]

ArrowHead294 at 14:30, 20 February 2025

2025-02-20T14:30:19Z

← Older revision		Revision as of 14:30, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|296~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:50, 15 January 2025

2025-01-15T18:50:06Z

← Older revision		Revision as of 18:50, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 296 factors into ~~2<sup>3</sup> × 37~~, 296edo has subset edos {{EDOs\| 2, 4, 8, 37, 74 and 148 }}.		Since 296 factors into {{factorisation\|296}}, 296edo has subset edos {{EDOs\| 2, 4, 8, 37, 74 and 148 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 105:		Line 105:
	\| [[Dzelic]]		\| [[Dzelic]]
	\|}		\|}
	<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:Sabric]]		[[Category:Sabric]]

ArrowHead294: Partial undo

2024-11-16T12:34:16Z

Partial undo

← Older revision		Revision as of 12:34, 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 48:		Line 57:
	\| 0.2206		\| 0.2206
	\| 5.44		\| 5.44
	~~{{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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	\| 117/100<br />(?)		\| 117/100<br />(?)
	\| [[Dzelic]]		\| [[Dzelic]]
	~~{{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:Sabric]]		[[Category:Sabric]]

ArrowHead294 at 04:24, 16 November 2024

2024-11-16T04:24:23Z

← Older revision		Revision as of 04:24, 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
Line 56:		Line 48:
	\| 0.2206		\| 0.2206
	\| 5.44		\| 5.44
	\|}		{{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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	\|-		\|-
	\| 8		\| 8
	\| 144\296<br>(4\296)		\| 144\296<br />(4\296)
	\| 583.78<br>(16.22)		\| 583.78<br />(16.22)
	\| 7/5<br>(126/125)		\| 7/5<br />(126/125)
	\| [[Octoid]]		\| [[Octoid]]
	\|-		\|-
	\| 37		\| 37
	\| 67\296<br>(3\296)		\| 67\296<br />(3\296)
	\| 271.62<br>(12.16)		\| 271.62<br />(12.16)
	\| 117/100<br>(?)		\| 117/100<br />(?)
	\| [[Dzelic]]		\| [[Dzelic]]
	\|}		{{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:Sabric]]		[[Category:Sabric]]

FloraC: Cleanup

2024-03-04T08:31:37Z

Cleanup

← Older revision		Revision as of 08:31, 4 March 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo\| -16 35 -17 }}. It is also an interesting temperament in higher limits, being ~~distinctly~~ [[consistent]] through to the [[15-odd-limit]]. In the 7-limit it tempers out 4375/4374 ([[ragisma]]), 16875/16807 (mirkwai), and 118098/117649 (stearnsma), [[support]]ing 7-limit [[octoid]] and [[sabric]]. In the 11-limit, [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[6250/6237]] and [[9801/9800]]; in the 13-limit, [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], and [[6656/6655]], so that it also supports the 11- and 13-limit versions of octoid. It allows [[swetismic chords]] and [[squbemic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.		In the 5-limit, 296et not only [[tempering out\|tempers out]] the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo\| -16 35 -17 }}. It is also an interesting temperament in higher limits, being [[consistency\|distinctly consistent]] through to the [[15-odd-limit]]. In the 7-limit it tempers out 4375/4374 ([[ragisma]]), 16875/16807 (mirkwai), and 118098/117649 (stearnsma), [[support]]ing 7-limit [[octoid]] and [[sabric]]. In the 11-limit, [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[6250/6237]] and [[9801/9800]]; in the 13-limit, [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], and [[6656/6655]], so that it also supports the 11- and 13-limit versions of octoid. It allows [[swetismic chords]] and [[squbemic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 24:		Line 24:
	\| 2.3		\| 2.3
	\| {{monzo\| -469 296 }}		\| {{monzo\| -469 296 }}
	\| [{{~~val~~\| 296 469 }}]		\| {{mapping\| 296 469 }}
	\| +0.1904		\| +0.1904
	\| 0.1905		\| 0.1905
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	\| 2.3.5		\| 2.3.5
	\| 2109375/2097152, {{monzo\| -16 35 -17 }}		\| 2109375/2097152, {{monzo\| -16 35 -17 }}
	\| [{{~~val~~\| 296 469 687 }}]		\| {{mapping\| 296 469 687 }}
	\| +0.2962		\| +0.2962
	\| 0.2158		\| 0.2158
Line 38:		Line 38:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 16875/16807, 2100875/2097152		\| 4375/4374, 16875/16807, 2100875/2097152
	\| [{{~~val~~\| 296 469 687 831 }}]		\| {{mapping\| 296 469 687 831 }}
	\| +0.2138		\| +0.2138
	\| 0.2350		\| 0.2350
Line 45:		Line 45:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 540/539, 1375/1372, 4000/3993, 2100875/2097152		\| 540/539, 1375/1372, 4000/3993, 2100875/2097152
	\| [{{~~val~~\| 296 469 687 831 1024 }}]		\| {{mapping\| 296 469 687 831 1024 }}
	\| +0.1691		\| +0.1691
	\| 0.2284		\| 0.2284
Line 52:		Line 52:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 540/539, 625/624, 729/728, 1375/1372, 15379/15360		\| 540/539, 625/624, 729/728, 1375/1372, 15379/15360
	\| [{{~~val~~\| 296 469 687 831 1024 1095 }}]		\| {{mapping\| 296 469 687 831 1024 1095 }}
	\| +0.2012		\| +0.2012
	\| 0.2206		\| 0.2206
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	\|+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
	\|-		\|-
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	\| [[Dzelic]]		\| [[Dzelic]]
	\|}		\|}
			<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:Sabric]]		[[Category:Sabric]]

FloraC: Cleanup; linking; style

2023-07-02T11:45:22Z

Cleanup; linking; style

← Older revision		Revision as of 11:45, 2 July 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''296 equal divisions of the octave''' ('''296edo'''), or the '''296(-tone) equal temperament''' ('''296tet''', '''296et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO\|~~equal division of the octave]] into~~ 296 ~~parts of about 4.05 [[cent]]s each.~~		{{EDO intro\|296}}

	== Theory ==		== Theory ==
	In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo\| -16 35 -17 }}. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out 4375/4374 ([[ragisma]]), 16875/16807 (mirkwai), and 118098/117649 (stearnsma), [[support~~\|supporting~~]] 7-limit [[octoid]] ~~temperament~~. In the 11-limit, [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[6250/6237]] and [[9801/9800]]; in the 13-limit, [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], and [[6656/6655]], so that it also supports the 11- and 13-limit versions of octoid. It allows [[swetismic chords]] and [[squbemic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.		In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo\| -16 35 -17 }}. It is also an interesting temperament in higher limits, being distinctly [[consistent]] through to the [[15-odd-limit]]. In the 7-limit it tempers out 4375/4374 ([[ragisma]]), 16875/16807 (mirkwai), and 118098/117649 (stearnsma), [[support]]ing 7-limit [[octoid]] and [[sabric]]. In the 11-limit, [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[6250/6237]] and [[9801/9800]]; in the 13-limit, [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], and [[6656/6655]], so that it also supports the 11- and 13-limit versions of octoid. It allows [[swetismic chords]] and [[squbemic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.

	~~296 is divisible by {{EDOs\| 2, 4, 8, 37, 74 and 148 }}~~.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|296\|columns=11}}		{{Harmonics in equal\|296\|columns=11}}

			=== Subsets and supersets ===
			Since 296 factors into 2<sup>3</sup> × 37, 296edo has subset edos {{EDOs\| 2, 4, 8, 37, 74 and 148 }}.

	== 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]]		! 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]] (¢)
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	\|+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
	\|-		\|-
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	\| 182.43		\| 182.43
	\| 10/9		\| 10/9
	\| [[~~Minortone]] / [[mitonic~~]]		\| [[Mitonic]]
	\|-		\|-
	\| 1		\| 1
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	\| 271.62		\| 271.62
	\| 75/64		\| 75/64
	\| [[~~Orson]] / [[sabric~~]]		\| [[Sabric]]
	\|-		\|-
	\| 1		\| 1
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	\|}		\|}

	[[Category:~~Equal divisions of the octave\|###]] <!-- 3-digit number -->~~		[[Category:Sabric]]
	~~[[Category:Orson~~]]

Eliora: /* Rank-2 temperaments */ oops

2023-03-20T18:47:02Z

Rank-2 temperaments: oops

← Older revision		Revision as of 18:47, 20 March 2023
Line 97:		Line 97:
	\|-		\|-
	\| 37		\| 37
	\| ~~271.62~~<br>(3\296)		\| 67\296<br>(3\296)
	\| ~~583~~.78<br>(12.16)		\| 271.62<br>(12.16)
	\| 117/100<br>(?)		\| 117/100<br>(?)
	\| [[Dzelic]]		\| [[Dzelic]]

Eliora: /* Rank-2 temperaments */ dzelic

2023-03-13T21:58:57Z

Rank-2 temperaments: dzelic

← Older revision		Revision as of 21:58, 13 March 2023
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	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per ~~octave~~		! Periods<br>per 8ve
	! Generator<br>(reduced)		! Generator<br>(reduced)
	! Cents<br>(reduced)		! Cents<br>(reduced)
Line 95:		Line 95:
	\| 7/5<br>(126/125)		\| 7/5<br>(126/125)
	\| [[Octoid]]		\| [[Octoid]]
			\|-
			\| 37
			\| 271.62<br>(3\296)
			\| 583.78<br>(12.16)
			\| 117/100<br>(?)
			\| [[Dzelic]]
	\|}		\|}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Orson]]		[[Category:Orson]]

Plumtree: Infobox ET now computes most parameters automatically

2022-10-04T16:22:46Z

Infobox ET now computes most parameters automatically

← Older revision		Revision as of 16:22, 4 October 2022
Line 1:		Line 1:
	{{Infobox ET		{{Infobox ET}}
	~~\| Prime factorization = 2<sup>3</sup> × 37~~
	~~\| Step size = 4.05405¢~~
	~~\| Fifth = 173\296 (701.35¢)~~
	~~\| Semitones = 27:23 (109.46¢ : 93.24¢)~~
	~~\| Consistency = 15~~
	}}
	The '''296 equal divisions of the octave''' ('''296edo'''), or the '''296(-tone) equal temperament''' ('''296tet''', '''296et''') when viewed from a [[regular temperament]] perspective, is the [[EDO\|equal division of the octave]] into 296 parts of about 4.05 [[cent]]s each.		The '''296 equal divisions of the octave''' ('''296edo'''), or the '''296(-tone) equal temperament''' ('''296tet''', '''296et''') when viewed from a [[regular temperament]] perspective, is the [[EDO\|equal division of the octave]] into 296 parts of about 4.05 [[cent]]s each.