halfdiminished

Half-diminished refers to a four-note seventh chord built on a root with a diminished triad plus a minor seventh. It is commonly notated as m7b5 or with the symbol ø7. The chord tones are 1, ♭3, ♭5, ♭7 relative to the root.

For example, C half-diminished seventh (Cø7) consists of C, E♭, G♭, and B♭. The triad C–E♭–G♭ is diminished, and the seventh above C is a minor seventh (B♭), giving the full chord C–E♭–G♭–B♭.

Usage and function: half-diminished chords are a prevalent harmonic device in tonal and jazz harmony. In major keys, the ii chord is often a iiø7, and such chords frequently appear in ii–V–I progressions, where the half-diminished chord functions as a predominant chord leading toward the dominant V7 and then to the tonic I. They are valued for their strong pull to the dominant while maintaining a darker, more tense color than a simple minor or diminished chord.

Relation to fully diminished: a half-diminished seventh has a diminished triad with a minor seventh (1–♭3–♭5–♭7), whereas a fully diminished seventh adds a diminished seventh above the root (1–♭3–♭5–♭♭7). Enharmonic spellings may vary in context, but the presence of a minor seventh distinguishes half-diminished from fully diminished.

In practice, players encounter half-diminished chords in many genres, and they may be inverted or extended with added tones while preserving the characteristic 1–♭3–♭5–♭7 structure.