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: | 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/ | * (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. | 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/ | * (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]]: | 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 | * (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). | [[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]].--> | <!-- 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 == | ||
Latest revision as of 05:57, 29 January 2026
A dominant seventh chord is a tetrad comprising a root, major third, fifth, and minor seventh.
The name of the chord derives from the 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.
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:
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:
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 essentially just 7-odd-limit chord that tempers together 4:5:6:7 and 36:45:54:64:
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).
In just intonation
In the 3-limit:
- 576:729:864:1024 is found on the dominant scale degree (V or 3⁄2) of the Pythagorean diatonic scale.
In the 5-limit:
- 36:45:54:64 is found on the dominant scale degree (V or 3⁄2) of Ptolemy's intense diatonic scale (Zarlino), perhaps the most common 5-limit diatonic.
- 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 (1⁄1) and IV (4⁄3) of the duodene.
- 108:135:160:192 is found on the dominant scale degree (V or 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, a 5-limit interpretation of an inversion of the Neapolitan or German sixth chord, is found rooted at the ♭II (16⁄15) and ♭VI (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:
- 4:5:6:7, the harmonic seventh chord, is a concord in the 7-limit, often used as a tuning target in 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.