The diminished seven (1-b3-b5-bb7) and half diminished seven (1-b3-b5-b7) chords are built upon a diminished triad. Despite this similarity and despite the tendency of some musicians to treat these chords the same, the two can function very differently. Each can serve in a dominant function and resolve to a major or minor triad whose root is a half-step higher. However, the half diminished seven also functions as a subdominant chord in minor keys (iiø7 – V7 – i7). The ii-V relationship is one of the most common harmonic idioms in jazz and popular music. The fully diminished seven chord almost always functions in a dominant capacity. It is one of the most easily transposable chords in music and serves as a handy device for transposing to far-off keys. All this put aside, let it be said that these two chords offer very different possibilities for use in music.
The Diminished Seven Chord
The Half Diminished Seven Chord