299edo - Revision history

FloraC: /* Regular temperament properties */ + heptacot

2026-05-20T12:15:34Z

Regular temperament properties: + heptacot

← Older revision		Revision as of 12:15, 20 May 2026
Line 17:		Line 17:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[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
	\|-		\|-
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	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 474 -299 }}		\| {{Monzo\| 474 -299 }}
	\| {{~~mapping~~\| 299 474 }}		\| {{Mapping\| 299 474 }}
	\| −0.1218		\| −0.1218
	\| 0.1218		\| 0.1218
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	\| 2.3.5		\| 2.3.5
	\| 15625/15552, {{monzo\| 80 -49 -1 }}		\| 15625/15552, {{monzo\| 80 -49 -1 }}
	\| {{~~mapping~~\| 299 474 694 }}		\| {{Mapping\| 299 474 694 }}
	\| +0.0665		\| +0.0665
	\| 0.2844		\| 0.2844
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	\| 2.3.5.7		\| 2.3.5.7
	\| 10976/10935, 15625/15552, 823543/819200		\| 10976/10935, 15625/15552, 823543/819200
	\| {{~~mapping~~\| 299 474 694 839 }}		\| {{Mapping\| 299 474 694 839 }}
	\| +0.1925		\| +0.1925
	\| 0.3291		\| 0.3291
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 385/384, 6250/6237, 10976/10935, 12005/11979		\| 385/384, 6250/6237, 10976/10935, 12005/11979
	\| {{~~mapping~~\| 299 474 694 839 1034 }}		\| {{Mapping\| 299 474 694 839 1034 }}
	\| +0.2399		\| +0.2399
	\| 0.3092		\| 0.3092
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 325/324, 385/384, 625/624, 10648/10647, 10976/10935		\| 325/324, 385/384, 625/624, 10648/10647, 10976/10935
	\| {{~~mapping~~\| 299 474 694 839 1034 1106 }}		\| {{Mapping\| 299 474 694 839 1034 1106 }}
	\| +0.2779		\| +0.2779
	\| 0.2948		\| 0.2948
Line 60:		Line 60:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619		\| 325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619
	\| {{~~mapping~~\| 299 474 694 839 1034 1106 1222 }}		\| {{Mapping\| 299 474 694 839 1034 1106 1222 }}
	\| +0.2595		\| +0.2595
	\| 0.2767		\| 0.2767
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	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444		\| 325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444
	\| {{~~mapping~~\| 299 474 694 839 1034 1106 1222 1270 }}		\| {{Mapping\| 299 474 694 839 1034 1106 1222 1270 }}
	\| +0.2424		\| +0.2424
	\| 0.2627		\| 0.2627
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	\|+ style="font-size: 105%;" \| 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
			\|-
			\| 1
			\| 25\299
			\| 100.33
			\| 1323/1250
			\| [[Heptacot]] (7-limit)
	\|-		\|-
	\| 1		\| 1
Line 101:		Line 107:
	\| [[Marfifths]]		\| [[Marfifths]]
	\|}		\|}
	<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		<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:Enlil]]		[[Category:Enlil]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

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"

2026-03-13T13:33:07Z

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 13:33, 13 March 2026
Line 101:		Line 101:
	\| [[Marfifths]]		\| [[Marfifths]]
	\|}		\|}
	<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:Enlil]]		[[Category:Enlil]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

ArrowHead294 at 14:30, 20 February 2025

2025-02-20T14:30:52Z

← Older revision		Revision as of 14:30, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|299~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T15:47:59Z

Theory: cleanup

← Older revision		Revision as of 15:47, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	In the 5-limit, 299et [[tempers out]] the [[kleisma]], 15625/15552, in the 7-limit [[10976/10935]], in the 11-limit [[385/384]]; and in the 13-limit [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.		In the 5-limit, 299et [[tempering out\|tempers out]] the [[kleisma]], 15625/15552, in the [[7-limit]] [[10976/10935]], in the [[11-limit]] [[385/384]]; and in the [[13-limit]] [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 299 factors into ~~{{factorization\|299}}~~, 299edo contains [[13edo]] and [[23edo]] as subsets.		Since 299 factors into 13 × 23, 299edo contains [[13edo]] and [[23edo]] as subsets.

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 19:34, 15 January 2025

2025-01-15T19:34:30Z

← Older revision		Revision as of 19:34, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	In the 5-limit, 299et [[~~tempering out\|~~tempers out]] the [[kleisma]], 15625/15552, in the 7-limit [[10976/10935]], in the 11-limit [[385/384]]; and in the 13-limit [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.		In the 5-limit, 299et [[tempers out]] the [[kleisma]], 15625/15552, in the 7-limit [[10976/10935]], in the 11-limit [[385/384]]; and in the 13-limit [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| {{monzo\| 474 -299 }}		\| {{monzo\| 474 -299 }}
	\| {{mapping\| 299 474 }}		\| {{mapping\| 299 474 }}
	\| ~~−0~~.1218		\| −0.1218
	\| 0.1218		\| 0.1218
	\| 3.04		\| 3.04
Line 101:		Line 101:
	\| [[Marfifths]]		\| [[Marfifths]]
	\|}		\|}
	<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:Enlil]]		[[Category:Enlil]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

ArrowHead294: Partial undo

2024-11-16T12:57:36Z

Partial undo

← Older revision		Revision as of 12:57, 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 62:		Line 71:
	\| 0.2627		\| 0.2627
	\| 6.54		\| 6.54
	~~{{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 84:		Line 100:
	\| 75/56		\| 75/56
	\| [[Marfifths]]		\| [[Marfifths]]
	~~{{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:Enlil]]		[[Category:Enlil]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

ArrowHead294 at 03:07, 16 November 2024

2024-11-16T03:07:39Z

← Older revision		Revision as of 03:07, 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\| 474 -299 }}		\| {{monzo\| 474 -299 }}
	\| {{mapping\| 299 474 }}		\| {{mapping\| 299 474 }}
	\| -0.1218		\| −0.1218
	\| 0.1218		\| 0.1218
	\| 3.04		\| 3.04
Line 70:		Line 62:
	\| 0.2627		\| 0.2627
	\| 6.54		\| 6.54
	\|}		{{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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	\| 75/56		\| 75/56
	\| [[Marfifths]]		\| [[Marfifths]]
	\|}		{{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:Enlil]]		[[Category:Enlil]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

FloraC: /* Theory */ +subsets and supersets

2024-03-04T07:56:07Z

Theory: +subsets and supersets

← Older revision		Revision as of 07:56, 4 March 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	In the 5-limit, 299et tempers out the [[kleisma]], 15625/15552, in the 7-limit [[10976/10935]], in the 11-limit [[385/384]]; and in the 13-limit [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.		In the 5-limit, 299et [[tempering out\|tempers out]] the [[kleisma]], 15625/15552, in the 7-limit [[10976/10935]], in the 11-limit [[385/384]]; and in the 13-limit [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|299}}		{{Harmonics in equal\|299}}

			=== Subsets and supersets ===
			Since 299 factors into {{factorization\|299}}, 299edo contains [[13edo]] and [[23edo]] as subsets.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: /* Regular temperament properties */ clarify

2024-03-04T07:53:23Z

Regular temperament properties: clarify

← Older revision		Revision as of 07:53, 4 March 2024
Line 73:		Line 73:
	\|+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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	\| [[Marfifths]]		\| [[Marfifths]]
	\|}		\|}
			<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:Enlil]]		[[Category:Enlil]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]

FloraC: Cleanup +1

2023-09-09T13:03:12Z

Cleanup +1

← Older revision		Revision as of 13:03, 9 September 2023
Line 21:		Line 21:
	\| 2.3		\| 2.3
	\| {{monzo\| 474 -299 }}		\| {{monzo\| 474 -299 }}
	\| [{{~~val~~\| 299 474 }}]		\| {{mapping\| 299 474 }}
	\| -0.1218		\| -0.1218
	\| 0.1218		\| 0.1218
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	\| 2.3.5		\| 2.3.5
	\| 15625/15552, {{monzo\| 80 -49 -1 }}		\| 15625/15552, {{monzo\| 80 -49 -1 }}
	\| [{{~~val~~\| 299 474 694 }}]		\| {{mapping\| 299 474 694 }}
	\| +0.0665		\| +0.0665
	\| 0.2844		\| 0.2844
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	\| 2.3.5.7		\| 2.3.5.7
	\| 10976/10935, 15625/15552, 823543/819200		\| 10976/10935, 15625/15552, 823543/819200
	\| [{{~~val~~\| 299 474 694 839 }}]		\| {{mapping\| 299 474 694 839 }}
	\| +0.1925		\| +0.1925
	\| 0.3291		\| 0.3291
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 385/384, 6250/6237, 10976/10935, 12005/11979		\| 385/384, 6250/6237, 10976/10935, 12005/11979
	\| [{{~~val~~\| 299 474 694 839 1034 }}]		\| {{mapping\| 299 474 694 839 1034 }}
	\| +0.2399		\| +0.2399
	\| 0.3092		\| 0.3092
Line 49:		Line 49:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 325/324, 385/384, 625/624, 10648/10647, 10976/10935		\| 325/324, 385/384, 625/624, 10648/10647, 10976/10935
	\| [{{~~val~~\| 299 474 694 839 1034 1106 }}]		\| {{mapping\| 299 474 694 839 1034 1106 }}
	\| +0.2779		\| +0.2779
	\| 0.2948		\| 0.2948
Line 56:		Line 56:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619		\| 325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619
	\| [{{~~val~~\| 299 474 694 839 1034 1106 1222 }}]		\| {{mapping\| 299 474 694 839 1034 1106 1222 }}
	\| +0.2595		\| +0.2595
	\| 0.2767		\| 0.2767
Line 63:		Line 63:
	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444		\| 325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444
	\| [{{~~val~~\| 299 474 694 839 1034 1106 1222 1270 }}]		\| {{mapping\| 299 474 694 839 1034 1106 1222 1270 }}
	\| +0.2424		\| +0.2424
	\| 0.2627		\| 0.2627