Diminished seventh

diminished seventh

Inverse	augmented second
Name
Other names	-
Abbreviation	d7[1]
Size
Semitones	9
Interval class	3
Just interval	128:75[2] or 216:125[3]
Cents
Equal temperament	900
24 equal temperament	900
Just intonation	925 or 947

Diminished seventh  Play (help·info).

In classical music from Western culture, a diminished seventh ( play (help·info)) is an interval produced by narrowing a minor seventh by a chromatic semitone^[1][4]. For instance, the interval from A to G is a minor seventh, ten semitones wide, and both the intervals from A♯ to G, and from A to G♭ are diminished sevenths, spanning nine semitones. Being diminished, it is considered a dissonant interval^[5].

The diminished seventh is enharmonically equivalent to a major sixth. Its inversion is the augmented second.

The diminished seventh is used quite readily in the minor key, where it is present in the harmonic minor scale between the seventh scale step and the sixth scale step in the octave above.

In an equal tempered tuning, a diminished seventh is equal to nine semitones, a ratio of 2^9/12:1 (approximately 1.682), or 900 cents. There is no standard just tuning of this interval, but one possibility, assuming the flat submediant is a perfect (5:4) major third below the octave, and the leading tone to be 15:16, would lead to an interval of 128:75, about 925 cents; another interval is 216:125, which is three minor thirds.

See also

• Diminished seventh chord

Sources

1. ^ ^{a b} Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 978-0-07-294262-0. Specific example of an d7 not given but general example of minor intervals described.
2. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 0824747143. Diminished seventh.
3. ^ Haluska (2003), p.xxvi. Acute diminished seventh.
4. ^ Hoffmann, F.A. (1881). Music: Its Theory & Practice, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007.
5. ^ Benward & Saker (2003), p.92.