Dominant seventh chord

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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 meantone

See also: Didymic chords

In meantone (including 12edo), on which traditional tonal harmony is built, the dominant seventh chord has an intervallic odd limit of 25:

• (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 ~5/4 and ~9/5 is ~36/25.

However, in septimal meantone, which is well-represented by the historically prevalent quarter-comma meantone, that ~36/25 is tempered to ~10/7, making the chord an essentially tempered chord in the 9-odd-limit.

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, 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 some meantone tunings this chord is tuned identically to other “dominant seventh” chords such as 4:5:6:7, 36:45:54:64, and 20:25:30:36.)

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.

See also

• Well Tuned Dominant Sevenths by Graham Breed