Diminished major seventh chord

In music theory, a diminished major seventh chord is a seventh chord composed of a diminished triad and a major seventh.[1] Thus, it is composed of a root note, together with a minor third, a diminished fifth, and a major seventh above the root: (1, ♭3, ♭5, 7). For example, the diminished major seventh chord built on C, commonly written as C^oM7, has pitches C–E♭–G♭–B:

diminished major seventh

Component intervals from root
major seventh
diminished fifth (tritone)
minor third
root
Forte no. / Complement
4-18 / 8-18

Diminished major seventh chords are very dissonant, containing the dissonant intervals of the tritone and the major seventh. They are frequently encountered, especially in jazz, as a diminished seventh chord with an appoggiatura, especially when the melody has the leading note of the given chord: the ability to resolve this dissonance smoothly to a diatonic triad with the same root allows it to be used as a temporary tension before tonic resolution. It is nevertheless infrequently used as a chord in itself.

The chord can be represented by the integer notation {0, 3, 6, 11}.

Diminished major seventh chord table

Chord	Root	Minor third	Diminished fifth	Major seventh
C^o^M7	C	E♭	G♭	B
C♯^o^M7	C♯	E	G	B♯ (C)
D♭^o^M7	D♭	F♭ (E)	A (G)	C
D^o^M7	D	F	A♭	C♯
D♯^o^M7	D♯	F♯	A	C (D)
E♭^o^M7	E♭	G♭	B (A)	D
E^o^M7	E	G	B♭	D♯
F^o^M7	F	A♭	C♭ (B)	E
F♯^o^M7	F♯	A	C	E♯ (F)
G♭^o^M7	G♭	B (A)	D (C)	F
G^o^M7	G	B♭	D♭	F♯
G♯^o^M7	G♯	B	D	F (G)
A♭^o^M7	A♭	C♭ (B)	E (D)	G
A^o^M7	A	C	E♭	G♯
A♯^o^M7	A♯	C♯	E	G (A)
B♭^o^M7	B♭	D♭	F♭ (E)	A
B^o^M7	B	D	F	A♯

Sources

1. Jamini, Deborah. (2005). Harmony And Composition: Basics to Intermediate, p.204. ISBN 978-1-4120-3333-6.