Dominant seventh chord: Difference between revisions

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In the [[3-limit]]:

* [[576:729:864:1024]] ~~(1⁄1–81⁄64–3⁄2–[[16/9|16⁄9]])~~, the ''Pythagorean dominant seventh chord'', is found on the dominant scale degree ([[3/2~~|3⁄2]] or V~~) of the [[Pythagorean tuning|Pythagorean]] diatonic scale.

* [[576:729:864:1024]], the ''Pythagorean dominant seventh chord'', is found on the dominant scale degree (V or {{Frac|3|2}}) of the [[Pythagorean tuning|Pythagorean]] diatonic scale.

In the [[5-limit]]:

* [[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.

* [[36:45:54:64]], the ''Ptolemaic dominant seventh chord'', is found on the dominant scale degree (V or {{Frac|3|2}}) of 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)~~, 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]], 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 the I ({{Frac|1|1}}) and IV ({{Frac|4|3}}) of the [[duodene]].

* [[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]].

* [[108:135:160:192]] is found on the dominant scale degree (V or {{Frac|3|2}}) 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)~~, 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]], 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 the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of 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]]:

* [[4:5:6:7]] ~~(1⁄1–5⁄4–3⁄2–7⁄4)~~, the ''harmonic seventh chord'', is a [[consonant]] chord in the 7-limit, often used as a tuning target in barbershop music[https://en.wikipedia.org/wiki/Harmonic_seventh_chord#Barbershop_seventh].

* [[4:5:6:7]], the ''harmonic seventh chord'', is a [[consonant]] chord in the 7-limit, often used as a tuning target in barbershop music[https://en.wikipedia.org/wiki/Harmonic_seventh_chord#Barbershop_seventh].

== See also ==

@@ Line 9: / Line 9: @@
 In the [[3-limit]]:
-* [[576:729:864:1024]] (1⁄1–81⁄64–3⁄2–[[16/9|16⁄9]]), the ''Pythagorean dominant seventh chord'', is found on the dominant scale degree ([[3/2|3⁄2]] or V) of the [[Pythagorean tuning|Pythagorean]] diatonic scale.
+* [[576:729:864:1024]], the ''Pythagorean dominant seventh chord'', is found on the dominant scale degree (V or {{Frac|3|2}}) of the [[Pythagorean tuning|Pythagorean]] diatonic scale.
 In the [[5-limit]]:
-* [[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.
+* [[36:45:54:64]], the ''Ptolemaic dominant seventh chord'', is found on the dominant scale degree (V or {{Frac|3|2}}) of 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), 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]], 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 the I ({{Frac|1|1}}) and IV ({{Frac|4|3}}) of the [[duodene]].
-* [[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]].
+* [[108:135:160:192]] is found on the dominant scale degree (V or {{Frac|3|2}}) 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), 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]], 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 the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of 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]]:
-* [[4:5:6:7]] (1⁄1–5⁄4–3⁄2–7⁄4), the ''harmonic seventh chord'', is a [[consonant]] chord in the 7-limit, often used as a tuning target in barbershop music[https://en.wikipedia.org/wiki/Harmonic_seventh_chord#Barbershop_seventh].
+* [[4:5:6:7]], the ''harmonic seventh chord'', is a [[consonant]] chord in the 7-limit, often used as a tuning target in barbershop music[https://en.wikipedia.org/wiki/Harmonic_seventh_chord#Barbershop_seventh].
 == See also ==