Dominant seventh flat five chord

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Dominant seventh flat five chord

A dominant seventh flat five chord is a tetrad comprising a root, a major third, a diminished fifth, and a minor seventh.

In temperaments

In meantone (including 12edo), on which traditional tonal harmony is built, the interval of a diminished fifth tempers together 36/25~64/45~1024/729, and the minor seventh tempers together 9/5~16/9, giving a chord with an intervallic odd limit of 125:

• (Meantone) 1/1 ‒ 5/4 ‒ 36/25 ‒ 9/5

In marvel temperament, which tempers out 225/224, a ~16/9 minor seventh is equated with ~25/14, which combines with a 10/7~64/45 diminished fifth to give a 9-odd-limit essentially tempered chord:

• (Marvel) 1/1 ‒ 5/4 ‒ 10/7 ‒ 16/9, with steps 5/4, 8/7, 5/4

Similarly, in starling temperament, which tempers out 126/125, a ~9/5 minor seventh is equated with ~25/14, which combines with a 10/7~36/25 diminished fifth to give a 9-odd-limit essentially tempered chord:

• (Starling) 1/1 ‒ 5/4 ‒ 10/7 ‒ 9/5, with steps 5/4, 8/7, 5/4

Septimal meantone, which is well-represented by the historically prevalent quarter-comma meantone, tempers together all of the above chords, so any of the those interpretations may be relevant for dominant seventh flat five chords found in common-practice music.

In just intonation

In the 7-limit:

• 20:25:28:35 (1/1 - 5/4 - 7/5 - 7/4)
• 28:35:40:50, found in genus 5² ⋅ 7, corresponds to a just interpretation of the essentially-tempered chords of marvel and starling temperament.

In the 5-limit:

• 180:225:256:320 is a found rooted on V (3⁄2) and II (9⁄8) in the duodene.
• 100:125:144:180 is another interpretation of the chord from meantone temperament, found in genus 3² ⋅ 5³.

See also

• French sixth chord, a chord that is enharmonically equivalent to a dominant seventh flat five chord in 12edo.