Half-diminished chords
A half-diminished chord is a 4-note chord — the root plus a minor third, a diminished fifth and a minor seventh above it. It is a diminished triad with a minor seventh on top, which is why it is also called half-diminished.
It sounds moody and jazzy — most often the ii chord in a minor key. Below are the half-diminished chords for all twelve keys, from C to B — pick any chart for its full set of voicings, the piano shape and how it's built.