Dominant seventh chord: Difference between revisions
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{{Wikipedia}} | {{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, [[major]] third, fifth, and [[minor]] seventh. | ||
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== In temperaments == | == 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: | |||
* (Meantone) 1/1 – [[5/4]] – [[3/2]] – [[9/5]], with steps 5/4, 6/5, 6/5. | |||
* (Meantone) 1/ | |||
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 just intonation == | ||
In the [[3-limit]]: | |||
* [[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]]: | ||
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* [[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.) | * [[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 [[ | In the [[7-limit]]: | ||
* [[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 == | ||
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[[Category:Dominant seventh chords| ]] <!-- main article --> | [[Category:Dominant seventh chords| ]] <!-- main article --> | ||
[[Category:Just intonation chords]] | [[Category:Just intonation chords]] | ||
[[Category:Essentially tempered chords]] | |||
[[Category:9-odd-limit chords]] | |||