Half-Diminished 7th
m7b5
0 - 3 - 6 - 10Diminished triad + minor 7th
About Half-Diminished 7th
A half-diminished seventh chord is a four-note chord built from a diminished triad plus a minor seventh — in C that is C, E♭, G♭ and B♭, written Cm7♭5 or Cø7. It is the chord that opens almost every minor-key jazz cadence, and its name records exactly how it differs from the fully diminished seventh: one note, and the whole of its behaviour.
Notes and formula
The formula is 1 – ♭3 – ♭5 – ♭7, or 0 – 3 – 6 – 10 in semitones. A diminished triad with a minor seventh on top rather than a diminished one.
That seventh is what makes the chord usable as a resting point. Between E♭ and B♭ there is a perfect fifth — an interval the fully diminished seventh does not contain anywhere — and it gives the chord a floor to stand on while the tritone below stays unresolved.
How to play it
On piano the chord is C–E♭–G♭–B♭. As with any four-note chord, the fifth can go: C–E♭–B♭ states it, and pianists comping a minor ii–V often play only the third and seventh.
On guitar the movable form is x3434x, sounding C–G♭–B♭–E♭ with the root on the fifth string. It is one of the few extended shapes that needs no barre, which is why it turns up early in any jazz method.
What it does
Its job is the ii of a minor ii–V–i: Dm7♭5, G7, Cm. In that position it is not a passing chord but a destination for a bar or two, and the flattened fifth is heard as a colour rather than as an error.
It also appears as the vii of a major key with a seventh added — Bm7♭5 in C major — where it substitutes for the dominant. The two uses sound different because of what follows, not because of what the chord is.
The chord it shares its notes with
Cm7♭5 spelled from E♭ is E♭–G♭–B♭–C, an E♭ minor sixth chord. The identity works in both directions and is the fastest way to find either shape from the other, which is why jazz players learn them as one hand position with two names.
The name that applies depends on the bass. Under a C the chord is a half-diminished seventh heading for a dominant; under an E♭ it is a minor sixth that has already arrived.
Half-diminished or fully diminished
Cm7♭5 is C–E♭–G♭–B♭; Cdim7 is C–E♭–G♭–A. Both carry the circle in some chord charts, and reading one as the other is the most common mistake in written jazz.
The behaviour differs completely. The fully diminished chord is symmetrical and passes through; the half-diminished has a perfect fifth inside it, rests, and belongs to a key.
Scales that contain it
Locrian fits without alteration and is the textbook answer. In practice most players prefer Locrian ♮2, the sixth mode of melodic minor, because it raises the second degree and removes the one note that clashes with the chord in a minor ii–V.
The choice is audible: plain Locrian sounds severe, Locrian ♮2 sounds like the chord was meant to be there.
Frequently asked questions
What notes are in a Cm7♭5 chord?
C, E♭, G♭ and B♭. On guitar the movable shape is x3434x, with the root on the fifth string.
Is m7♭5 the same as half-diminished?
Yes — two names for one chord. The circle with a slash through it, ø, means the same thing; a plain circle means the fully diminished seventh, which has a different top note.
Which scale works over a half-diminished chord?
Locrian ♮2 in a minor ii–V, plain Locrian if the chord stands alone. Both contain every chord tone; the raised second is what keeps the line from sounding sour.