Dominant (temperament) - Revision history

FloraC: Cleanup on infobox

2026-02-09T09:07:23Z

Cleanup on infobox

← Older revision		Revision as of 09:07, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Dominant		\| Title = Dominant
	\| Subgroups = 2.3.5.7		\| Subgroups = 2.3.5.7
	\| Comma basis = [[36/35]], [[64/63]]		\| Comma basis = [[36/35]], [[64/63]]
	\| Edo join 1 = 12 \| Edo join 2 = 17c		\| Edo join 1 = 12 \| Edo join 2 = 17c
	\| ~~Generator~~ = 3/2 \| ~~Generator~~ tuning = 701.1 \| Optimization method = CWE		\| Generators = 3/2 \| Generators tuning = 701.1 \| Optimization method = CWE
	\| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]]		\| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]]
	\| Mapping = 1; 1 4 -2		\| Mapping = 1; 1 4 -2

Overthink: /* Tuning spectrum */ bold monotone tunings

2026-01-02T05:55:25Z

Tuning spectrum: bold monotone tunings

← Older revision		Revision as of 05:55, 2 January 2026
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	=== Tuning spectrum ===		=== Tuning spectrum ===
			{{todo\|complete table\|comment=add the missing 11- and 13-limit eigenmonzo tunings}}
	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|-		\|-
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	\| [[1/5-comma meantone\|1/5 syntonic comma]]		\| [[1/5-comma meantone\|1/5 syntonic comma]]
	\|-		\|-
	\| [[12edo\|7\12]]		\| '''[[12edo\|7\12]]'''
	\|		\|
	\| 700.000		\| '''700.000'''
	\| Lower bound of 7- and 9-odd-limit diamond monotone		\| '''Lower bound of 7- and 9-odd-limit diamond monotone'''
	\|-		\|-
	\|		\|
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	\| 1/2 septimal comma		\| 1/2 septimal comma
	\|-		\|-
	\| [[5edo\|3\5]]		\| '''[[5edo\|3\5]]'''
	\|		\|
	\| 720.000		\| '''720.000'''
	\| Upper bound of 7- and 9-odd-limit diamond monotone		\| '''Upper bound of 7- and 9-odd-limit diamond monotone'''
	\|-		\|-
	\|		\|

FloraC: /* Chords and harmony */ - typo

2025-12-27T16:59:32Z

Chords and harmony: - typo

← Older revision		Revision as of 16:59, 27 December 2025
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	== Chords and harmony ==		== Chords and harmony ==
	Much of 12edo harmony can be used. Dominant enables chords of [[didymic chords\|didymic]] and [[archytas chords\|archytas]]. The dominant seventh chord represents the harmonic seventh chord, whereas the [[German sixth chord\|(German) augmented sixth chord]] is more of less equivalent to meantone's dominant seventh chord, as a tuning of [[28:35:42:50\|1–5/4–3/2–25/14]].		Much of 12edo harmony can be used. Dominant enables chords of [[didymic chords\|didymic]] and [[archytas chords\|archytas]]. The dominant seventh chord represents the harmonic seventh chord, whereas the [[German sixth chord\|(German) augmented sixth chord]] is more or less equivalent to meantone's dominant seventh chord, as a tuning of [[28:35:42:50\|1–5/4–3/2–25/14]].

	== Tunings ==		== Tunings ==

FloraC: /* Chords and harmony */ expand

2025-12-21T13:09:38Z

Chords and harmony: expand

← Older revision		Revision as of 13:09, 21 December 2025
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	== Chords and harmony ==		== Chords and harmony ==
	Much of 12edo harmony can be used. Dominant enables chords of [[didymic chords\|didymic]] and [[archytas chords\|archytas]].		Much of 12edo harmony can be used. Dominant enables chords of [[didymic chords\|didymic]] and [[archytas chords\|archytas]]. The dominant seventh chord represents the harmonic seventh chord, whereas the [[German sixth chord\|(German) augmented sixth chord]] is more of less equivalent to meantone's dominant seventh chord, as a tuning of [[28:35:42:50\|1–5/4–3/2–25/14]].

	== Tunings ==		== Tunings ==

FloraC: Better equal temp join, Misc. cleanup

2025-12-21T12:56:42Z

Better equal temp join, Misc. cleanup

← Older revision		Revision as of 12:56, 21 December 2025
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	\| Subgroups = 2.3.5.7		\| Subgroups = 2.3.5.7
	\| Comma basis = [[36/35]], [[64/63]]		\| Comma basis = [[36/35]], [[64/63]]
	\| Edo join 1 = 5 \| Edo join 2 = 7		\| Edo join 1 = 12 \| Edo join 2 = 17c
	\| Generator = 3/2 \| Generator tuning = 701.1 \| Optimization method = CWE		\| Generator = 3/2 \| Generator tuning = 701.1 \| Optimization method = CWE
	\| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]]		\| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]]
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	\| Odd limit 2 = (7-limit) 27 \| Mistuning 2 = 26.3 \| Complexity 2 = 12		\| Odd limit 2 = (7-limit) 27 \| Mistuning 2 = 26.3 \| Complexity 2 = 12
	}}		}}
	'''Dominant''' is a [[regular temperament\|temperament]] which is an [[extension]] of both [[meantone]] and [[archy]]. It is defined by [[tempering out]] the [[81/80\|syntonic comma (81/80)]] and [[64/63\|septimal comma (64/63)]] in the 7-limit. It also tempers out the [[36/35\|septimal quartertone (36/35)]], as 36/35 = (64/63)(81/80). It is the unique temperament that identifies the [[harmonic seventh chord]] with the [[dominant seventh chord]], which is a familiar feature from [[12edo]].		'''Dominant''' is a [[regular temperament\|temperament]] which is an [[extension]] of both [[meantone]] and [[archy]]. It is defined by [[tempering out]] the [[81/80\|syntonic comma (81/80)]] and [[64/63\|septimal comma (64/63)]] in the 7-limit. It also tempers out the [[36/35\|septimal quartertone (36/35)]], as 36/35 = (64/63)⋅(81/80). It is the unique temperament that identifies the [[harmonic seventh chord]] with the [[dominant seventh chord]], which is a familiar feature from [[12edo]].

	However, it is not very accurate for the same reason that 12edo is inaccurate in the 7-limit, as either 5/4 or 7/4 must be tuned very sharply (with 5/4 reaching over 462 cents in the best tuning of 7/4, and likewise 7/4 reaching over 1006 cents in the best tuning of 5/4). Thus, the "best tuning" is a compromise between the two, tuning 3/2 basically just.		However, it is not very accurate for the same reason that 12edo is inaccurate in the 7-limit, as either 5/4 or 7/4 must be tuned very sharply (with 5/4 reaching over 462 cents in the best tuning of 7/4, and likewise 7/4 reaching over 1006 cents in the best tuning of 5/4). Thus, the best tuning is a compromise between the two, tuning 3/2 basically just.

	The most obvious extension to the 11 and 13-limit is treating the major and minor thirds as [[14/11]] and [[13/11]] as well as 5/4 and 6/5, tempering out [[56/55]] and [[66/65]]. This favors even sharper fifths on the edge of the [[gentle region]]. 29edo tunes this about as well as possible, albeit using the second best approximation of most harmonics.		The most obvious extension to the 11- and 13-limit is treating the major and minor thirds as [[14/11]] and [[13/11]] as well as 5/4 and 6/5, tempering out [[56/55]] and [[66/65]]. This favors even sharper fifths on the edge of the [[gentle region]]. [[29edo]] tunes this about as well as possible, albeit using the second best approximation of most harmonics.

	Other possible tunings include [[17edo]] (17c val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].		Other possible tunings include [[17edo]] (17c val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].
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	\| 7 \|\| 107.8 \|\| 15/14		\| 7 \|\| 107.8 \|\| 15/14
	\|}		\|}
	<nowiki />* In 7-limit [[CWE]] tuning		<nowiki/>* In 7-limit [[CWE]] tuning

	== Chords and harmony ==		== Chords and harmony ==
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	\| [[7/5]]		\| [[7/5]]
	\| 702.915		\| 702.915
	\| 7 & 9-odd limit minimax tuning		\| 7- & 9-odd-limit minimax tuning
	\|-		\|-
	\|		\|
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	\| Full septimal comma		\| Full septimal comma
	\|}		\|}
	<nowiki />* Besides the octave		<nowiki/>* Besides the octave

	== References ==		== References ==

FloraC: /* Tunings */ + basic norm-based tunings

2025-12-21T12:53:40Z

Tunings: + basic norm-based tunings

@@ Line 52: / Line 52: @@
 == Tunings ==
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"

Overthink: Added Infobox Regtemp

2025-11-27T23:41:14Z

Added Infobox Regtemp

← Older revision		Revision as of 23:41, 27 November 2025
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			{{Infobox Regtemp
			\| Title = Dominant
			\| Subgroups = 2.3.5.7
			\| Comma basis = [[36/35]], [[64/63]]
			\| Edo join 1 = 5 \| Edo join 2 = 7
			\| Generator = 3/2 \| Generator tuning = 701.1 \| Optimization method = CWE
			\| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]]
			\| Mapping = 1; 1 4 -2
			\| Pergen = (P8, P5)
			\| Odd limit 1 = 7 \| Mistuning 1 = 25.3 \| Complexity 1 = 7
			\| Odd limit 2 = (7-limit) 27 \| Mistuning 2 = 26.3 \| Complexity 2 = 12
			}}
	'''Dominant''' is a [[regular temperament\|temperament]] which is an [[extension]] of both [[meantone]] and [[archy]]. It is defined by [[tempering out]] the [[81/80\|syntonic comma (81/80)]] and [[64/63\|septimal comma (64/63)]] in the 7-limit. It also tempers out the [[36/35\|septimal quartertone (36/35)]], as 36/35 = (64/63)(81/80). It is the unique temperament that identifies the [[harmonic seventh chord]] with the [[dominant seventh chord]], which is a familiar feature from [[12edo]].		'''Dominant''' is a [[regular temperament\|temperament]] which is an [[extension]] of both [[meantone]] and [[archy]]. It is defined by [[tempering out]] the [[81/80\|syntonic comma (81/80)]] and [[64/63\|septimal comma (64/63)]] in the 7-limit. It also tempers out the [[36/35\|septimal quartertone (36/35)]], as 36/35 = (64/63)(81/80). It is the unique temperament that identifies the [[harmonic seventh chord]] with the [[dominant seventh chord]], which is a familiar feature from [[12edo]].

Yourmusic Productions: More on higher limit extensions.

2025-10-06T20:53:16Z

FloraC: + history

2025-08-26T12:29:02Z

+ history

← Older revision		Revision as of 12:29, 26 August 2025
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	Other possible tunings include [[17edo]] (17c val), [[29edo]] (29cd val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].		Other possible tunings include [[17edo]] (17c val), [[29edo]] (29cd val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].

			Dominant was known as ''dominant seventh'' in 2003, but the ''seventh'' part was dropped shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10437.html Yahoo! Tuning Group \| ''The meantone family'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10864.html#10870 Yahoo! Tuning Group \| ''names and definitions: meantone'']</ref>.

	See [[Meantone family #Dominant]] for technical data.		See [[Meantone family #Dominant]] for technical data.
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	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	\|-		\|-
	! &#~~35;~~ !! Cents* !! Approximate Ratios		! # !! Cents* !! Approximate Ratios
	\|-		\|-
	\| 0 \|\| 0.0 \|\| '''1/1'''		\| 0 \|\| 0.0 \|\| '''1/1'''
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|-		\|-
	! Edo<br />~~Generator~~		! Edo<br>generator
	! [[Eigenmonzo\|Eigenmonzo<br />(~~Unchanged~~-interval)]]*		! [[Eigenmonzo\|Eigenmonzo<br>(unchanged-interval)]]*
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
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	\|}		\|}
	<nowiki />* Besides the octave		<nowiki />* Besides the octave

			== References ==

	[[Category:Dominant\| ]] <!-- Main article -->		[[Category:Dominant\| ]] <!-- Main article -->

VectorGraphics at 02:51, 17 May 2025

2025-05-17T02:51:42Z

← Older revision		Revision as of 02:51, 17 May 2025
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	'''Dominant''' is a [[regular temperament\|temperament]] which is an [[extension]] of both [[meantone]] and [[archy]]. It is defined by [[tempering out]] the [[81/80\|syntonic comma (81/80)]] and [[64/63\|septimal comma (64/63)]] in the 7-limit. It also tempers out the [[36/35\|septimal quartertone (36/35)]], as 36/35 = (64/63)(81/80). It is the unique temperament that identifies the [[harmonic seventh chord]] with the [[dominant seventh chord]], which is a familiar feature from [[12edo]].		'''Dominant''' is a [[regular temperament\|temperament]] which is an [[extension]] of both [[meantone]] and [[archy]]. It is defined by [[tempering out]] the [[81/80\|syntonic comma (81/80)]] and [[64/63\|septimal comma (64/63)]] in the 7-limit. It also tempers out the [[36/35\|septimal quartertone (36/35)]], as 36/35 = (64/63)(81/80). It is the unique temperament that identifies the [[harmonic seventh chord]] with the [[dominant seventh chord]], which is a familiar feature from [[12edo]].

			However, it is not very accurate for the same reason that 12edo is inaccurate in the 7-limit, as either 5/4 or 7/4 must be tuned very sharply (with 5/4 reaching over 462 cents in the best tuning of 7/4, and likewise 7/4 reaching over 1006 cents in the best tuning of 5/4). Thus, the "best tuning" is a compromise between the two, tuning 3/2 basically just.

	Other possible tunings include [[17edo]] (17c val), [[29edo]] (29cd val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].		Other possible tunings include [[17edo]] (17c val), [[29edo]] (29cd val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].

← Older revision		Revision as of 20:53, 6 October 2025
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	However, it is not very accurate for the same reason that 12edo is inaccurate in the 7-limit, as either 5/4 or 7/4 must be tuned very sharply (with 5/4 reaching over 462 cents in the best tuning of 7/4, and likewise 7/4 reaching over 1006 cents in the best tuning of 5/4). Thus, the "best tuning" is a compromise between the two, tuning 3/2 basically just.		However, it is not very accurate for the same reason that 12edo is inaccurate in the 7-limit, as either 5/4 or 7/4 must be tuned very sharply (with 5/4 reaching over 462 cents in the best tuning of 7/4, and likewise 7/4 reaching over 1006 cents in the best tuning of 5/4). Thus, the "best tuning" is a compromise between the two, tuning 3/2 basically just.

	Other possible tunings include [[17edo]] (17c ~~val), [[29edo]] (29cd~~ val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].		The most obvious extension to the 11 and 13-limit is treating the major and minor thirds as [[14/11]] and [[13/11]] as well as 5/4 and 6/5, tempering out [[56/55]] and [[66/65]]. This favors even sharper fifths on the edge of the [[gentle region]]. 29edo tunes this about as well as possible, albeit using the second best approximation of most harmonics.

			Other possible tunings include [[17edo]] (17c val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].

	Dominant was known as ''dominant seventh'' in 2003, but the ''seventh'' part was dropped shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10437.html Yahoo! Tuning Group \| ''The meantone family'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10864.html#10870 Yahoo! Tuning Group \| ''names and definitions: meantone'']</ref>.		Dominant was known as ''dominant seventh'' in 2003, but the ''seventh'' part was dropped shortly after<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10437.html Yahoo! Tuning Group \| ''The meantone family'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10864.html#10870 Yahoo! Tuning Group \| ''names and definitions: meantone'']</ref>.
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	\|		\|
	\| 703.448		\| 703.448
	\| ~~29cd~~ val		\| 29cdef val
	\|-		\|-
	\|		\|