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{{Wikipedia|Dominant seventh chord}}
{{Wikipedia|Dominant seventh chord}}
A '''dominant seventh chord''' is a [[tetrad]] comprising a root, [[major]] third, fifth, and [[minor]] seventh.


A '''dominant seventh chord''' is a [[tetrad]] comprising a root, a [[major]] third, a fifth, and a [[minor]] seventh.
The name of the chord derives from the {{w|Dominant (music)|dominant}} scale degree, which is the only degree of a [[diatonic scale]] on which it is found. However, in many musical genres, “dominant seventh chord” informally refers to any chord with this general structure, regardless of where it appears in the overall scale.


The name of the chord derives from the dominant[https://en.wikipedia.org/wiki/Dominant_(music)] scale degree, which is the only degree of a [[diatonic scale]] on which it is found. However, in many musical genres, “dominant seventh chord” informally refers to any chord with this general structure, regardless of where it appears in the overall scale.
== In temperaments ==
In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the interval of a minor seventh represents [[9/5]][[~]][[16/9]], and the tritone between ~5/4 and ~9/5 represents [[36/25]]~[[64/45]]~[[1024/729]], all [[tempered together]] into a single chord:


== JI Tunings ==
* (Meantone) 1/1 – [[5/4]] – [[3/2]] – [[9/5]], with steps 5/4, 6/5, 6/5.


This chord tempers together [[36:45:54:64]], [[20:25:30:36]], and [[108:135:160:192]], with a resulting [[intervallic odd limit]] of 25 due to the simplest interpretation of its tritone being ~36/25.
[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]], tempers the tritone to ~[[10/7]], making the chord an [[essentially tempered chord]] in the [[9-odd-limit]]. In fact, tempering out the starling comma [[126/125]] alone is enough to convert it to a 9-odd-limit essentially tempered chord:
* (Starling) 1/1 – [[5/4]] – [[3/2]] – [[9/5]]
However, in [[starling]] the seventh of this chord represents 9/5~[[25/14]], but not 16/9. Septimal meantone tempering is necessary to temper together all three of the sevenths (9/5~16/9~25/14), so either of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])
In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[Dyadic chord#Essentially tempered dyadic chord|essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:
* (Archytas) 1/1 – [[5/4]] – [[3/2]] – [[7/4]]
[[Dominant (temperament)|Dominant temperament]] combines archytas with meantone, tempering out both 81/80 and 64/63, and as a result also tempers out [[36/35]], equating 4:5:6:7 with all of the 5-limit dominant seventh chords of meantone. Since [[12edo]] is a good tuning of Dominant temperament, this simpler septimal interpretation may also be relevant for dominant seventh chords in music originally composed for 12edo — particularly in performance styles that use more flexible intonation (such as Barbershop).
<!-- Note: 12edo also supports Mint temperament via Dominant, but I'm intentionally omitting it here for simplicity. It's easy enough to find via [[36/35]].-->
== In just intonation ==
In the [[3-limit]]:
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]] is found on the dominant scale degree (V or {{Frac|3|2}}) of the [[Pythagorean tuning|Pythagorean]] diatonic scale.


In the [[5-limit]]:
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]] 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]], a 5-limit interpretation of an inversion of the {{w|Neapolitan chord|''Neapolitan''}} or {{w|Augmented sixth chord #German sixth|''German sixth chord''}}, is found rooted at the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of the [[duodene]]. ([[225/128]] is often considered an augmented sixth rather than a minor seventh, but in septimal meantone and [[marvel]] temperament this chord is tuned identically to 4:5:6:7, and in [[12edo]] and its multiples it is tuned identically to 36:45:54:64 and 20:25:30:36.)


In the [[7-limit]]:
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 [[concord]] in the 7-limit, often used as a tuning target in {{w|Harmonic seventh chord #Barbershop seventh|barbershop music}}.
 
* [[70:90:105:126]] (1/1–9/7–3/2–9/5) is the ''subharmonic seventh chord'', a [[utonal]] [[9-odd-limit]] tetrad which is the inversion of [[6:7:9:10]], the subharmonic sixth chord.
 
* [[28:35:42:50]] is a [[condissonant]] chord, and one of the possible interpretations of the dominant seventh in the starling, marvel, and septimal meantone temperaments.
 
* [[28:36:42:49]] is a septimal dominant seventh chord. A tempered version of this chord is found in the diatonic scale of [[superpyth]] temperament.


== See also ==
== See also ==
* [https://x31eq.com/dominant.html Well Tuned Dominant Sevenths]
* [https://x31eq.com/dominant.html ''Well Tuned Dominant Sevenths''] by [[Graham Breed]]


[[Category:Dominant seventh chords| ]] <!-- main article -->
[[Category:Dominant seventh chords| ]] <!-- main article -->
[[Category:Tetrads]]
[[Category:Just intonation chords]]
[[Category:Essentially tempered chords]]
[[Category:9-odd-limit chords]]
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