Dominant seventh chord: Difference between revisions
→In JI: internalize Wikipedia links. Distinguish concordance and consonance (it's not consonant if it's built on the fifth degree) |
→In JI: 7/4 is an A6 in septimal meantone, and the normal interpretation of the augmented sixth chord is simiply 4:5:6:7 |
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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]], 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]]. ( | * [[128:160:192:225]], a 5-limit interperation 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, and especially in [[septimal meantone]] it is tuned identically to [[7/4]].) | ||
In the [[7-limit]]: | In the [[7-limit]]: | ||
Revision as of 08:05, 13 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 meantone
In meantone (including 12edo), on which traditional tonal harmony is built, the dominant seventh chord is a 9-odd-limit essentially tempered chord:
- (Meantone) 1-5/4-3/2-9/5 with steps 5/4, 6/5, 6/5.
Note the ~9/5 is simultaneously ~16/9, and the interval between the third and seventh is ~10/7. Therefore, every interval of this chord is within the 9-odd-limit tonality diamond.
In JI
There are many possibilities of chords outside meantone, each with its own strengths and weaknesses.
In the 3-limit:
- 576:729:864:1024, the Pythagorean dominant seventh chord, is found on the dominant scale degree (V or 3⁄2) of the Pythagorean diatonic scale.
In the 5-limit:
- 36:45:54:64, the Ptolemaic dominant seventh chord, 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 interperation 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, and especially in septimal meantone it is tuned identically to 7/4.)
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.