Diminished 7th

Notes and formula

The formula is 1 – ♭3 – ♭5 – ♭♭7, or 0 – 3 – 6 – 9 in semitones. Every gap is three semitones, including the one from the top note back to the root.

The double flat on the seventh is not pedantry. Spelling it B♭♭ rather than A keeps the chord a stack of thirds on paper, which is how its function stays readable; players who write A instead lose the ability to see at a glance which key the chord is aiming at.

Symmetry and its consequences

Because all four intervals are equal, every inversion of the chord is another diminished seventh. C–E♭–G♭–A, E♭–G♭–A–C and G♭–A–C–E♭ are the same four notes, so one chord serves as four, each with a different root.

It follows that there are only three distinct diminished seventh chords in all of music: start on C, on C♯ or on D, and the fourth start repeats the first. Learning one shape on guitar and moving it three frets gives every chord it can produce.

How to play it

On piano the chord is C–E♭–G♭–A, four keys spaced identically, and the pattern transfers to any root without rethinking.

On guitar the usual form is x3424x, sounding C–G♭–A–E♭. Sliding it up three frets gives the same chord named from a different note; sliding it one fret gives one of the other two.

What it does

Its everyday role is the passing chord. Drop a diminished seventh between two chords a tone apart and every voice moves by a semitone, which is why it appears constantly in ragtime, in early jazz and in the second bar of a great many standards.

Its second role is disguise. Cdim7 shares three of its four notes with A♭7♭9, and the same is true at each of its four roots, so one diminished seventh can stand in for four different dominants. That ambiguity is exactly what nineteenth-century composers used it for: it is the chord that lets music change key without announcing it.

Diminished seventh or half-diminished

The two are routinely confused because both are written with a circle. Cdim7 is C–E♭–G♭–A and passes. Cm7♭5, the half-diminished, is C–E♭–G♭–B♭ and rests — it is the ii of a minor ii–V–i, a chord to sit on rather than travel through.

One note separates them, and it is the note that decides whether the chord is symmetrical. Half-diminished chords have a perfect fifth inside them between E♭ and B♭; fully diminished ones have none at all.

Scales that contain it

The whole–half diminished scale is built from the chord by filling each three-semitone gap with a passing note. It is symmetrical for the same reason the chord is, so it repeats every three semitones and only three of them exist.

When the chord is standing in for a dominant, players often use the half–whole scale of that dominant instead. Both contain all four chord tones; they differ in which notes they add, and the choice decides whether the bar sounds like classical chromaticism or like bebop.

Frequently asked questions