Diminished seventh chord.

A chord formed from a diminished triad with added diminished 7th, for example B–D–F–A; it thus contains two tritones (B–F and D–A) and is tonally unstable. It is typically found on the raised 7th degree of a minor key and functions, in its standard resolution to the tonic (ex.1a), like a dominant chord, the 7th (G in ex.1a) rising by semitone to the tonic while the other notes fall; it is commonly borrowed for equivalent use in the major mode (ex.1b). Its root may be defined conventionally, as the lowest note when the chord is rearranged as a sequence of thirds (G in ex.1a and b; see also Root, ex.1a); however, because of the manner of its resolution, the chord is sometimes interpreted as an incomplete dominant 9th with the root omitted (in ex.1a and b the ‘missing root’ would be E).

Because the four notes in the diminished 7th chord are a minor 3rd (or augmented 2nd) apart, the chord divides the octave into four equal segments (ex.2); as a result of this symmetry and of the phenomenon of enharmonic equivalence, the multiplicity of possible diminished 7th chords may be reduced to three distinct pitch collections (B–D–F–A, B–D–F–A and C–E–G–B), with all their respellings and inversions. By means of such reinterpretation, and by permitting resolutions in which the lowest note either falls by semitone or remains at the same pitch, any one of these pitch collections can resolve to a major or minor triad on any pitch. Ex.3 sets out 24 possible resolutions of the collection B–D–F–A: in ex.3a the lowest note rises by semitone, while in ex.3b it falls by semitone, and in ex.3c it stays constant. The existence of so many different possibilities for resolution gives the diminished 7th chord ambiguous tonal implications, making it an important tool in modulation (see J. Saslaw: ‘Gottfried Weber and Multiple Meaning’, Theoria, v (1990–91), 74–103).

JANNA SASLAW