Harmonic seventh

harmonic seventh
InverseSeptimal major second
Name
Other namesseptimal minor seventh, subminor seventh, acute diminished just seventh, quarter comma augmented sixth
Abbreviationm 7, H 7, min 7, accdim 7, Aug 6
Size
Semitones~9.7
Interval class~2.3
Just interval7:4
Cents
Just intonation968.826

The harmonic seventh interval, also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969 cents). This is about 32 cents narrower, with a more stable and consonant sound, than a minor seventh in equal temperament, and is up to 49 cents narrower than and is, "particularly sweet", "sweeter in quality" than an "ordinary" just minor seventh, which has an intonation ratio of 9:5 (about 1018 cents).

The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic (second octave of the fundamental) and the seventh harmonic; in that octave, harmonics 4, 5, 6, and 7 constitute the four notes (in order) of a purely consonant major chord (root position) with an added minor seventh (or augmented sixth, depending on the tuning system used).