Dominant (temperament): Difference between revisions

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'''Dominant''' is a [[regular temperament|temperament]] [[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]].

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.

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{| class="wikitable center-1 right-2"

|-

! &#~~35;~~ !! Cents* !! Approximate Ratios

! # !! Cents* !! Approximate Ratios

|-

| 0 || 0.0 || '''1/1'''

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{| class="wikitable center-all left-4"

|-

! Edo<br />~~Generator~~

! Edo<br>generator

! [[Eigenmonzo|Eigenmonzo<br />(~~Unchanged~~-interval)]]*

! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*

! Generator (¢)

! Comments

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| [[5/4]]

| 696.578

| [[Quarter-comma meantone|1/4 syntonic comma]], 5-odd-limit minimax

| [[Quarter-comma meantone|1/4 syntonic comma]], [[5-odd-limit]] minimax

|-

|

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|-

|

| 11/10

| [[11/10]]

| 703.499

| 11-odd limit minimax tuning

| [[11-odd-limit]] minimax tuning

|-

|

| 13/10

| [[13/10]]

| 703.522

| 13-odd limit minimax tuning

| [[13-odd-limit]] minimax tuning

|-

| [[17edo|10\17]]

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<nowiki />* Besides the octave

~~[[Category:Temperaments]]~~

== References ==

[[Category:Dominant| ]]

[[Category:Dominant| ]]

[[Category:Rank-2 temperaments]]

[[Category:Meantone family]]

[[Category:Archytas clan]]

[[Category:Mint temperaments]]

@@ Line 1: / Line 1: @@
-'''Dominant''' is a [[regular temperament|temperament]] [[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]].
+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.
@@ Line 10: / Line 14: @@
 {| class="wikitable center-1 right-2"
 |-
-! &#35; !! Cents* !! Approximate Ratios
+! # !! Cents* !! Approximate Ratios
 |-
 | 0 || 0.0 || '''1/1'''
@@ Line 37: / Line 41: @@
 {| class="wikitable center-all left-4"
 |-
-! Edo<br />Generator
+! Edo<br>generator
-! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]]*
+! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
 ! Generator (¢)
 ! Comments
@@ Line 55: / Line 59: @@
 | [[5/4]]
 | 696.578
-| [[Quarter-comma meantone|1/4 syntonic comma]], 5-odd-limit minimax
+| [[Quarter-comma meantone|1/4 syntonic comma]], [[5-odd-limit]] minimax
 |-
 |
@@ Line 93: / Line 97: @@
 |-
 |
-| 11/10
+| [[11/10]]
 | 703.499
-| 11-odd limit minimax tuning
+| [[11-odd-limit]] minimax tuning
 |-
 |
-| 13/10
+| [[13/10]]
 | 703.522
-| 13-odd limit minimax tuning
+| [[13-odd-limit]] minimax tuning
 |-
 | [[17edo|10\17]]
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 <nowiki />* Besides the octave
-[[Category:Temperaments]]
+== References ==
-[[Category:Dominant| ]] <!-- ain article -->
+[[Category:Dominant| ]] <!-- Main article -->
+[[Category:Rank-2 temperaments]]
 [[Category:Meantone family]]
 [[Category:Archytas clan]]
 [[Category:Mint temperaments]]