Dominant seventh chord: Difference between revisions

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* 36:45:54:64 (1⁄1–5⁄4–3⁄2–[[16/9|16⁄9]]), the the [[Ptolemaic dominant seventh chord]], is found on the dominant scale degree ([[3/2|3⁄2]] or V) of [[Ptolemy's intense diatonic scale (Zarlino)|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 ~~on the minor chords~~ rooted at [[5/4|5⁄4]] (III) and [[15/8|15⁄8]] (VI) in the [[duodene]].

* 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 [[5/4|5⁄4]] (III) and [[15/8|15⁄8]] (VI) 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 if the second degree of the diatonic scale is 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|40⁄27]]–[[16/9|16⁄9]]) is found on the dominant scale degree (V) if the second degree of the diatonic scale is 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]]), the [[~~Neapolitan~~ chord]], is found ~~on the chords~~ 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 [[harmonic seventh ~~chord~~]].)

* [[128:160:192:225]] (1⁄1–5⁄4–3⁄2–[[225/128|225⁄128]]), 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]]:

* 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].

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 * 36:45:54:64 (1⁄1–5⁄4–3⁄2–[[16/9|16⁄9]]), the the [[Ptolemaic dominant seventh chord]], is found on the dominant scale degree ([[3/2|3⁄2]] or V) of  [[Ptolemy's intense diatonic scale (Zarlino)|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 on the minor chords rooted at [[5/4|5⁄4]] (III) and [[15/8|15⁄8]] (VI) in the [[duodene]].
+* 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 [[5/4|5⁄4]] (III) and [[15/8|15⁄8]] (VI) 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 if the second degree of the diatonic scale is 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|40⁄27]]–[[16/9|16⁄9]]) is found on the dominant scale degree (V) if the second degree of the diatonic scale is 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]]), the [[Neapolitan chord]], is found on the chords 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 [[harmonic seventh chord]].)
+* [[128:160:192:225]] (1⁄1–5⁄4–3⁄2–[[225/128|225⁄128]]), 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]]:
 * 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].