What defines a half diminished seventh chord?

A half diminished seventh chord is specifically characterized by its structure, which comprises a diminished triad along with a major third on top, resulting in a unique sound that distinguishes it from other seventh chords.

To break this down, a diminished triad is made up of two minor thirds stacked on top of each other. When a major third is added above this diminished triad, it achieves the half-diminished quality. For example, in the key of C, the half-diminished seventh chord would consist of the notes B, D, F, and A. Here, B is the root, D is a minor third (making the diminished triad), F is a diminished fifth, and A is a major seventh.

This structure provides the half-diminished seventh chord with its distinct, somewhat unresolved quality that is often utilized in various harmonic contexts, particularly in jazz and classical music. The inclusion of the major third rather than a minor or diminished seventh plays a crucial role in its identification and classification, which is why the correct answer emphasizes this major third on top of a diminished triad.