The fourth family of Chord and Scale Qualities is Half-Diminished.
Half Diminished scales and chords have a flatted third scale degree, a flatted fifth scale degree, and and a flatted seventh scale degree.
They are designated by a circle with a line cutting it in half (Ø). Due to early issues with computer typesetting, it is often written out as "minor 7 flat 5" (e.g. AØ becomes A-7b5), which is technically incorrect as it identifies it as being part of the Minor family which it is not. But be prepared to see it written both ways!
There is no half-diminished triad, as it requires 4 notes (R b3 b5 b7) to construct.