149edo - Revision history

FloraC: + note about 894edo

2026-06-18T07:15:49Z

+ note about 894edo

← Older revision		Revision as of 07:15, 18 June 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]], [[676/675]] and [[729/728]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[~~Gamelismic~~ family #Ominous\|ominous]] in the 13- and 17-limit.		149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp.

			In the 5-limit it [[tempering out\|tempers out]] the [[sensipent comma]], 78732/78125; in the [[7-limit]], [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the [[11-limit]] [[385/384]] and [[441/440]]; in the [[13-limit]] [[351/350]], [[676/675]] and [[729/728]]; in the [[17-limit]] [[273/272]] and [[561/560]]; in the [[19-limit]] [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[gamelismic family #Ominous\|ominous]] in the 13- and 17-limit.

	It is also usable in the [[23-limit]], only missing [[19/11]], [[21/11]], and their [[octave complement]]s in the [[23-odd-limit]]. In the [[27-odd-limit]], additional inconsistencies include [[25/21]], [[25/22]], [[27/20]], [[27/25]], [[27/19]], and their octave complements.		It is also usable in the [[23-limit]], only missing [[19/11]], [[21/11]], and their [[octave complement]]s in the [[23-odd-limit]]. In the [[27-odd-limit]], additional inconsistencies include [[25/21]], [[25/22]], [[27/20]], [[27/25]], [[27/19]], and their octave complements.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	149edo is the 35th [[prime edo]].		149edo is the 35th [[prime edo]]. As such, it does not contain any nontrivial subset edos.

			[[894edo]], which slices its step in six, is a notable system for the higher-limit, also consistent to the 17-odd-limit.

	== Regular temperament properties ==		== Regular temperament properties ==
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	! 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~~\| -236 149 }}		\| {{Monzo\| -236 149 }}
	\| {{~~mapping~~\| 149 236 }}		\| {{Mapping\| 149 236 }}
	\| +0.405		\| +0.405
	\| 0.405		\| 0.405
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	\| 2.3.5		\| 2.3.5
	\| 78732/78125, {{monzo\| -34 20 1 }}		\| 78732/78125, {{monzo\| -34 20 1 }}
	\| {{~~mapping~~\| 149 236 346 }}		\| {{Mapping\| 149 236 346 }}
	\| +0.232		\| +0.232
	\| 0.411		\| 0.411
Line 41:		Line 45:
	\| 2.3.5.7		\| 2.3.5.7
	\| 1029/1024, 3136/3125, 19683/19600		\| 1029/1024, 3136/3125, 19683/19600
	\| {{~~mapping~~\| 149 236 346 418 }}		\| {{Mapping\| 149 236 346 418 }}
	\| +0.386		\| +0.386
	\| 0.445		\| 0.445
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 385/384, 441/440, 3136/3125, 19683/19600		\| 385/384, 441/440, 3136/3125, 19683/19600
	\| {{~~mapping~~\| 149 236 346 418 515 }}		\| {{Mapping\| 149 236 346 418 515 }}
	\| +0.521		\| +0.521
	\| 0.481		\| 0.481
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 351/350, 385/384, 441/440, 676/675, 847/845		\| 351/350, 385/384, 441/440, 676/675, 847/845
	\| {{~~mapping~~\| 149 236 346 418 515 551 }}		\| {{Mapping\| 149 236 346 418 515 551 }}
	\| +0.567		\| +0.567
	\| 0.451		\| 0.451
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	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 273/272, 351/350, 385/384, 441/440, 676/675, 847/845		\| 273/272, 351/350, 385/384, 441/440, 676/675, 847/845
	\| {{~~mapping~~\| 149 236 346 418 515 551 609 }}		\| {{Mapping\| 149 236 346 418 515 551 609 }}
	\| +0.495		\| +0.495
	\| 0.453		\| 0.453
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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
	\|-		\|-
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	\| [[Heinz]]		\| [[Heinz]]
	\|}		\|}
	<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:Heinz]]		[[Category:Heinz]]

Overthink: /* Theory */ another important comma

2026-04-10T20:14:15Z

Theory: another important comma

← Older revision		Revision as of 20:14, 10 April 2026
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	== Theory ==		== Theory ==
	149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] ~~and~~ [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limit.		149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]], [[676/675]] and [[729/728]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limit.

	It is also usable in the [[23-limit]], only missing [[19/11]], [[21/11]], and their [[octave complement]]s in the [[23-odd-limit]]. In the [[27-odd-limit]], additional inconsistencies include [[25/21]], [[25/22]], [[27/20]], [[27/25]], [[27/19]], and their octave complements.		It is also usable in the [[23-limit]], only missing [[19/11]], [[21/11]], and their [[octave complement]]s in the [[23-odd-limit]]. In the [[27-odd-limit]], additional inconsistencies include [[25/21]], [[25/22]], [[27/20]], [[27/25]], [[27/19]], and their octave complements.

Overthink: /* Theory */ note 23-limit

2026-03-20T16:58:56Z

Theory: note 23-limit

← Older revision		Revision as of 16:58, 20 March 2026
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	== Theory ==		== Theory ==
	149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limit.		149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limit.

			It is also usable in the [[23-limit]], only missing [[19/11]], [[21/11]], and their [[octave complement]]s in the [[23-odd-limit]]. In the [[27-odd-limit]], additional inconsistencies include [[25/21]], [[25/22]], [[27/20]], [[27/25]], [[27/19]], and their octave complements.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	149edo is the 35th [[prime edo]].		149edo is the 35th [[prime edo]].

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

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"

2026-03-13T13:31:52Z

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 142:		Line 142:
	\| [[Heinz]]		\| [[Heinz]]
	\|}		\|}
	<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:Heinz]]		[[Category:Heinz]]

ArrowHead294 at 17:05, 18 February 2025

2025-02-18T17:05:37Z

← Older revision		Revision as of 17:05, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|149~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:53, 15 January 2025

2025-01-15T18:53:25Z

← Older revision		Revision as of 18:53, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28 ~~cents~~ flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limit.		149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| [[Heinz]]		\| [[Heinz]]
	\|}		\|}
	<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:Heinz]]		[[Category:Heinz]]

ArrowHead294: Partial undo

2024-11-16T12:33:33Z

Partial undo

← Older revision		Revision as of 12:33, 16 November 2024
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	== 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
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	\| 0.453		\| 0.453
	\| 5.62		\| 5.62
	~~{{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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	\| 11/8		\| 11/8
	\| [[Heinz]]		\| [[Heinz]]
	~~{{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:Heinz]]		[[Category:Heinz]]

ArrowHead294 at 04:25, 16 November 2024

2024-11-16T04:25:56Z

← Older revision		Revision as of 04:25, 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
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	\| 0.453		\| 0.453
	\| 5.62		\| 5.62
	\|}		{{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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	\| 11/8		\| 11/8
	\| [[Heinz]]		\| [[Heinz]]
	\|}		{{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:Heinz]]		[[Category:Heinz]]

FloraC: Rework and cleanup

2024-05-14T09:33:16Z

Rework and cleanup

← Older revision		Revision as of 09:33, 14 May 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	149edo is the smallest division which is ~~uniquely~~ [[consistent]] through the [[17-odd-limit]]. ~~It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limits.~~ It has a general flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]].		149edo is the smallest division which is [[consistency\|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 24:		Line 24:
	\| 2.3		\| 2.3
	\| {{monzo\| -236 149 }}		\| {{monzo\| -236 149 }}
	\| [{{~~val~~\| 149 236 }}]		\| {{mapping\| 149 236 }}
	\| +0.405		\| +0.405
	\| 0.405		\| 0.405
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	\| 2.3.5		\| 2.3.5
	\| 78732/78125, {{monzo\| -34 20 1 }}		\| 78732/78125, {{monzo\| -34 20 1 }}
	\| [{{~~val~~\| 149 236 346 }}]		\| {{mapping\| 149 236 346 }}
	\| +0.232		\| +0.232
	\| 0.411		\| 0.411
Line 38:		Line 38:
	\| 2.3.5.7		\| 2.3.5.7
	\| 1029/1024, 3136/3125, 19683/19600		\| 1029/1024, 3136/3125, 19683/19600
	\| [{{~~val~~\| 149 236 346 418 }}]		\| {{mapping\| 149 236 346 418 }}
	\| +0.386		\| +0.386
	\| 0.445		\| 0.445
Line 45:		Line 45:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 385/384, 441/440, 3136/3125, 19683/19600		\| 385/384, 441/440, 3136/3125, 19683/19600
	\| [{{~~val~~\| 149 236 346 418 515 }}]		\| {{mapping\| 149 236 346 418 515 }}
	\| +0.521		\| +0.521
	\| 0.481		\| 0.481
Line 52:		Line 52:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 351/350, 385/384, 441/440, 676/675, 847/845		\| 351/350, 385/384, 441/440, 676/675, 847/845
	\| [{{~~val~~\| 149 236 346 418 515 551 }}]		\| {{mapping\| 149 236 346 418 515 551 }}
	\| +0.567		\| +0.567
	\| 0.451		\| 0.451
Line 59:		Line 59:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 273/272, 351/350, 385/384, 441/440, 676/675, 847/845		\| 273/272, 351/350, 385/384, 441/440, 676/675, 847/845
	\| [{{~~val~~\| 149 236 346 418 515 551 609 }}]		\| {{mapping\| 149 236 346 418 515 551 609 }}
	\| +0.495		\| +0.495
	\| 0.453		\| 0.453
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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
	\|-		\|-
Line 96:		Line 96:
	\| 193.29		\| 193.29
	\| 28/25		\| 28/25
	\| [[~~Luna]] / [[hemithirds~~]]		\| [[Hemithirds]]
	\|-		\|-
	\| 1		\| 1
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	\| [[Heinz]]		\| [[Heinz]]
	\|}		\|}
			<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:Heinz]]		[[Category:Heinz]]

FloraC: Cleanup; linking; style

2023-08-29T06:18:13Z

Cleanup; linking; style

← Older revision		Revision as of 06:18, 29 August 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''149edo''' is the [[equal division of the octave]] into~~ 149 ~~equal parts of 8.054 [[cent]]s each.~~		{{EDO intro\|149}}

	== Theory ==		== Theory ==
	149edo is the smallest division which is uniquely [[consistent]] through the [[17-odd-limit]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limits. It has a general flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]].		149edo is the smallest division which is uniquely [[consistent]] through the [[17-odd-limit]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[Gamelismic family #Ominous\|ominous]] in the 13- and 17-limits. It has a general flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the [[sensipent comma]], 78732/78125; in the 7-limit, [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the 11-limit [[385/384]] and [[441/440]]; in the 13-limit [[351/350]] and [[676/675]]; in the 17-limit [[273/272]] and [[561/560]]; in the 19-limit [[286/285]] and [[343/342]].

	~~149edo is the 35th [[prime EDO]].~~		=== Prime harmonics ===
			{{Harmonics in equal\|149}}

	=== ~~Prime harmonics~~ ===		=== Subsets and supersets ===
	~~{{Primes in~~ edo~~\|149}}~~		149edo is the 35th [[prime edo]].

	== 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]] (¢)
Line 67:		Line 68:
	{\| 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)
	! Associated<br>~~ratio~~		! Associated<br>Ratio
	! Temperaments		! Temperaments
	\|-		\|-
Line 140:		Line 141:
	\|}		\|}

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