Dominant seventh chord
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.
In starling temperament, which tempers out 126/125 and tempers together 9/5~25/14, the ~36/25 tritone is tempered together with ~10/7, making the chord an essentially tempered chord in the 9-odd-limit. However, note that in starling temperament the seventh of this chord does not also represent the ~16/9 seventh.
Septimal meantone, which is well-represented by the historically prevalent quarter-comma meantone, tempers 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 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.
- 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.
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.