Diminished seventh chord

diminished seventh
Component intervals from root
	diminished seventh
	diminished fifth (tritone)
	minor third
	root
Tuning
	125:150:180:216
Forte no. / Complement
	4–28 / 8–28

The diminished seventh chord is a four-note chord (a seventh chord) composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root: (1, ♭3, ♭5, 7). For example, the diminished seventh chord built on B, commonly written as B^o⁷, has pitches B-D-F-A♭:

${ \omit Score.TimeSignature \relative c' { <b d f aes>1 } }$

The chord consists of a diminished triad plus the diminished seventh above the root. These four notes form a stack of three intervals which are all minor thirds. Since stacking yet another minor third returns to the root note, the four inversions of a diminished seventh chord are symmetrical. The integer notation is {0, 3, 6, 9}.

Since the diminished seventh interval is enharmonically equivalent to a major sixth, the chord is enharmonically equivalent to (1, ♭3, ♭5, ♮6).

The diminished seventh chord occurs as a leading-tone seventh chord in the harmonic minor scale. It typically has dominant function and contains two diminished fifths, which often resolve inwards.^[2]

The chord notation for the diminished seventh chord (assuming root C) is Cdim⁷ or C^o⁷ (or Cm^6♭5 for the enharmonic variant). The notation Cdim or C^o normally denotes a (three-note) diminished triad, but some jazz charts or other music literature may intend for these to denote the four-note diminished seventh chord instead.

François-Joseph Fétis tuned the chord 10:12:14:17 (17-limit tuning).^[3]

^ Shirlaw, Matthew (1900). The Theory of Harmony, p. 86. ISBN 978-1-4510-1534-8. "G♯–B–D–F."
^ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p. 219. Seventh Edition. ISBN 978-0-07-294262-0.
^ Fétis, François-Joseph and Arlin, Mary I. (1994). Esquisse de l'histoire de l'harmonie, p. 139n9. ISBN 978-0-945193-51-7.

[1] Shirlaw, Matthew (1900). The Theory of Harmony, p. 86. ISBN 978-1-4510-1534-8. "G♯–B–D–F."

[2] Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p. 219. Seventh Edition. ISBN 978-0-07-294262-0.

[3] Fétis, François-Joseph and Arlin, Mary I. (1994). Esquisse de l'histoire de l'harmonie, p. 139n9. ISBN 978-0-945193-51-7.

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