Half-diminished seventh chord
Diminished triad with a minor seventh. Softer than the fully diminished one and with an unambiguous root.
What it means
The half-diminished seventh chord consists of a diminished triad with an added minor seventh — from below thus minor third, minor third, major third. It is called half-diminished because only the fifth is diminished, not the seventh; with the fully diminished seventh chord the latter is diminished as well.
Musical use
Within the scale it stands in major on the seventh degree and in minor on the second. These two places correspond to two different functions.
On the second degree in minor it is a subdominant sonority: it arises from the minor subdominant with an added sixth that is placed in the bass, and leads to the dominant. In the minor cadence it is therefore a familiar sonority before the V7; in jazz the corresponding turn of half-diminished chord, dominant, and tonic is a basic building block.
On the seventh degree in major it is interpreted as a dominant sonority — as V7 with the root omitted and an added ninth, or simply as an abbreviated dominant. It resolves accordingly into the tonic.
Compared with the fully diminished seventh chord it sounds softer, because the minor seventh is less tense than the diminished. Above all, however, it has an unambiguous root, whereas the fully diminished one divides the octave evenly and is therefore ambiguous. In jazz the Locrian scale belongs to this chord as its pool of notes.
In functional theory it counts as an abbreviated dominant seventh-ninth chord without root or, in minor, as a subdominant with sixth. In jazz it stands as m7♭5 at the beginning of the minor cadence ii–V–i. The best-known example is the so-called Tristan chord at the beginning of Wagner's Tristan und Isolde, which corresponds in sound to a half-diminished seventh chord but appears notated as F–B–D♯–G♯.
Performance practice
First determine on which degree the sonority stands — on it depends whether it leads to the dominant or to the tonic. Lead the diminished fifth inward and the seventh downward. And distinguish exactly in the score between minor and diminished seventh; the difference is a semitone and clearly audible.