Dominant seventh chord: Difference between revisions
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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 {{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. | ||
== In | == In temperaments == | ||
In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the dominant seventh chord has an [[intervallic odd limit]] of 25: | In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the dominant seventh chord has an [[intervallic odd limit]] of 25: | ||
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Note the ~9/5 is simultaneously ~[[16/9]], and the interval between the ~5/4 and ~9/5 is [[36/25]]~[[64/45]]. | Note the ~9/5 is simultaneously ~[[16/9]], and the interval between the ~5/4 and ~9/5 is [[36/25]]~[[64/45]]. | ||
In [[septimal meantone]] | In [[septimal meantone]] (which is well-represented by the historically prevalent [[quarter-comma meantone]]), that ~[[36/25]]~[[64/45]] is tempered to ~[[10/7]], making the chord an [[essentially tempered chord]] in the [[9-odd-limit]]. (→ [[Didymic chords #Dominant seventh chord]]) | ||
<!-- TODO: There are two temperings happening in two different interpretations of this chord: starling takes ~36/25 to ~10/7, and marvel takes ~64/45 to ~10/7. Septimal meantone equates both of those preimages, but we should describe them separately. --> | |||
== In just intonation == | == In just intonation == | ||
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In the [[5-limit]]: | In the [[5-limit]]: | ||
* [[36:45:54:64]] | * [[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]], 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]]. | * [[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]]. | ||
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* [[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]]. | * [[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]], 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 | * [[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 [[3-limit]]: | In the [[3-limit]]: | ||
* [[576:729:864:1024]] | * [[576:729:864:1024]] is found on the dominant scale degree (V or {{Frac|3|2}}) of the [[Pythagorean tuning|Pythagorean]] diatonic scale. | ||
== See also == | == See also == | ||
Revision as of 03:05, 28 August 2024
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 dominant seventh chord has an intervallic odd limit of 25:
Note the ~9/5 is simultaneously ~16/9, and the interval between the ~5/4 and ~9/5 is 36/25~64/45.
In septimal meantone (which is well-represented by the historically prevalent quarter-comma meantone), that ~36/25~64/45 is tempered to ~10/7, making the chord an essentially tempered chord in the 9-odd-limit. (→ Didymic chords #Dominant seventh chord)
In just intonation
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.
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 3-limit:
- 576:729:864:1024 is found on the dominant scale degree (V or 3⁄2) of the Pythagorean diatonic scale.