Dominant seventh chord: Difference between revisions

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In the [[5-limit]]:

* [[36:45:54:64]] (~~1⁄1–5⁄4–3⁄2–[[16/9|16⁄9]]~~), the ''Ptolemaic dominant seventh chord'', is found on the dominant scale degree ([[3/2|3⁄2]] or V) of [[Zarlino|Ptolemy's intense diatonic scale (Zarlino)]], perhaps the most common 5-limit diatonic.

* [[36:45:54:64]] (1⁄1–5⁄4–3⁄2–16⁄9), the ''Ptolemaic dominant seventh chord'', is found on the dominant scale degree ([[3/2|3⁄2]] or V) of [[Zarlino|Ptolemy's intense diatonic scale (Zarlino)]], perhaps the most common 5-limit diatonic.

* [[20:25:30:36]] (~~1⁄1–5⁄4–3⁄2–[[9/5|9⁄5]]~~), the ''major-minor seventh chord'', combines a major third with the [[consonant]] seventh that would be found in a [[Ptolemaic minor seventh chord]] built on the same root. It is found rooted at 1⁄1 (I) and 4⁄3 (IV) in the [[duodene]].

* [[20:25:30:36]] (1⁄1–5⁄4–3⁄2–9⁄5), the ''major-minor seventh chord'', combines a major third with the [[consonant]] seventh that would be found in a [[Ptolemaic minor seventh chord]] built on the same root. It is found rooted at 1⁄1 (I) and 4⁄3 (IV) in the [[duodene]].

* [[108:135:160:192]] (~~1⁄1–5⁄4–[[40/27|40⁄27]]–[[16/9|16⁄9]]~~) is found on the dominant scale degree (3⁄2 or V) of a diatonic scale with the second degree tuned a comma lower than in Zarlino (10⁄9 instead of 9⁄8), such as in left-handed [[nicetone]].

* [[108:135:160:192]] (1⁄1–5⁄4–40⁄27–16⁄9) is found on the dominant scale degree (3⁄2 or V) of a diatonic scale with the second degree tuned a comma lower than in Zarlino (10⁄9 instead of 9⁄8), such as in left-handed [[nicetone]].

* [[128:160:192:225]] (~~1⁄1–5⁄4–3⁄2–[[225/128|225⁄128]]~~), an inversion of the ''Neapolitan''[https://en.wikipedia.org/wiki/Neapolitan_chord] or ''German sixth''[https://en.wikipedia.org/wiki/Augmented_sixth_chord#German_sixth] chord, is found rooted at [[16/15|16⁄15]] (♭II) and [[8/5|8⁄5]] (♭VI) in the [[duodene]]. (Although [[225/128]] is often considered an augmented sixth rather than a minor seventh, in [[Meantone_family#Septimal_meantone|septimal meantone]] it is tuned identically to the [[7/4|harmonic seventh]].)

* [[128:160:192:225]] (1⁄1–5⁄4–3⁄2–225⁄128), an inversion of the ''Neapolitan''[https://en.wikipedia.org/wiki/Neapolitan_chord] or ''German sixth''[https://en.wikipedia.org/wiki/Augmented_sixth_chord#German_sixth] chord, is found rooted at [[16/15|16⁄15]] (♭II) and [[8/5|8⁄5]] (♭VI) in the [[duodene]]. (Although [[225/128]] is often considered an augmented sixth rather than a minor seventh, in [[Meantone_family#Septimal_meantone|septimal meantone]] it is tuned identically to the [[7/4|harmonic seventh]].)

In the [[7-limit]]:

@@ Line 13: / Line 13: @@
 In the [[5-limit]]:
-* [[36:45:54:64]] (1⁄1–5⁄4–3⁄2–[[16/9|16⁄9]]), the ''Ptolemaic dominant seventh chord'', is found on the dominant scale degree ([[3/2|3⁄2]] or V) of [[Zarlino|Ptolemy's intense diatonic scale (Zarlino)]], perhaps the most common 5-limit diatonic.
+* [[36:45:54:64]] (1⁄1–5⁄4–3⁄2–16⁄9), the ''Ptolemaic dominant seventh chord'', is found on the dominant scale degree ([[3/2|3⁄2]] or V) of [[Zarlino|Ptolemy's intense diatonic scale (Zarlino)]], perhaps the most common 5-limit diatonic.
-* [[20:25:30:36]] (1⁄1–5⁄4–3⁄2–[[9/5|9⁄5]]), the ''major-minor seventh chord'', combines a major third with the [[consonant]] seventh that would be found in a [[Ptolemaic minor seventh chord]] built on the same root. It is found rooted at 1⁄1 (I) and 4⁄3 (IV) in the [[duodene]].
+* [[20:25:30:36]] (1⁄1–5⁄4–3⁄2–9⁄5), the ''major-minor seventh chord'', combines a major third with the [[consonant]] seventh that would be found in a [[Ptolemaic minor seventh chord]] built on the same root. It is found rooted at 1⁄1 (I) and 4⁄3 (IV) in the [[duodene]].
-* [[108:135:160:192]] (1⁄1–5⁄4–[[40/27|40⁄27]]–[[16/9|16⁄9]]) is found on the dominant scale degree (3⁄2 or V) of a diatonic scale with the second degree tuned a comma lower than in Zarlino (10⁄9 instead of 9⁄8), such as in left-handed [[nicetone]].
+* [[108:135:160:192]] (1⁄1–5⁄4–40⁄27–16⁄9) is found on the dominant scale degree (3⁄2 or V) of a diatonic scale with the second degree tuned a comma lower than in Zarlino (10⁄9 instead of 9⁄8), such as in left-handed [[nicetone]].
-* [[128:160:192:225]] (1⁄1–5⁄4–3⁄2–[[225/128|225⁄128]]), an inversion of the ''Neapolitan''[https://en.wikipedia.org/wiki/Neapolitan_chord] or ''German sixth''[https://en.wikipedia.org/wiki/Augmented_sixth_chord#German_sixth] chord, is found rooted at [[16/15|16⁄15]] (♭II) and [[8/5|8⁄5]] (♭VI) in the [[duodene]]. (Although [[225/128]] is often considered an augmented sixth rather than a minor seventh, in [[Meantone_family#Septimal_meantone|septimal meantone]] it is tuned identically to the [[7/4|harmonic seventh]].)
+* [[128:160:192:225]] (1⁄1–5⁄4–3⁄2–225⁄128), an inversion of the ''Neapolitan''[https://en.wikipedia.org/wiki/Neapolitan_chord] or ''German sixth''[https://en.wikipedia.org/wiki/Augmented_sixth_chord#German_sixth] chord, is found rooted at [[16/15|16⁄15]] (♭II) and [[8/5|8⁄5]] (♭VI) in the [[duodene]]. (Although [[225/128]] is often considered an augmented sixth rather than a minor seventh, in [[Meantone_family#Septimal_meantone|septimal meantone]] it is tuned identically to the [[7/4|harmonic seventh]].)
 In the [[7-limit]]: