Dominant seventh chord: Difference between revisions
→In JI: Rephrased to emphasize why 225/128 may be considered a seventh. Tags: Mobile edit Mobile web edit |
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In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the dominant seventh chord is a [[9-odd-limit]] [[essentially tempered chord]]: | 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 | * (Meantone) 1/1 ‒ [[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. | 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 == | == In JI == | ||
Revision as of 00:12, 14 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:
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 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 it is tuned identically to the 7/4 seventh.)
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.