A diminished seventh chord consists of a stack of minor thirds, or a diminished triad with an additional third on top.
The diminished seventh between the chord's root and seventh gives it its name. (It is often called a fully diminished seventh to distinguish it from the half diminished seventh.) Note that this seventh can be respelled as a major sixth, thus changing the implied root of the chord:
In fact, by enharmonically respelling the different members of the chord, we can make any one of them its apparent root:
Composers have traditionally used the diminished seventh in two ways: as a leading tone seventh and as a common tone seventh.
viio7 occurs naturally in (harmonic minor). It can occur in the major mode through mixture. In a leading tone seventh, every note typically resolves by step to the major or minor triad whose root is a diatonic semitone above the root of the seventh:
A substitute for the dominant seventh, the leading tone seventh can resolve to either the major or minor form of its tonic; a viio7 on B, for instance, can resolve to either a C major or a C minor triad. Because of its tricky enharmonic properties, the viio7 on B is equivalent to a third-inversion seventh on D, a second-inversion seventh on F, and to a first-inversion seventh on G# or A-flat. The same chord, therefore, can resolve to either the major or minor forms of four different tonics a minor third apart.
By contrast to the dominant-to-tonic relationship implied by viio7, common tone resolutions of the fully diminished seventh do not imply dominant to tonic motion (hence the omission of the Roman numeral vii in labeling these chords). In a common-tone resolution of a leading tone seventh, at least one chord tone is held in common with the chord of resolution while the other three notes of the seventh move by step. Sometimes not one, but two adjacent members of the seventh chord -- root and third, third and fifth, fifth and seventh, or seventh and root -- will be held in common:
Contrapuntal diminished 7th (Po7, No7)
Sometimes a diminished seventh neither functions as a leading tone seventh nor resolves as a common tone seventh. Sometimes all of its members move by step or skip to the next sonority, but not in such a way as to suggest dominant harmony. Such chords invariably play a contrapuntal, or linear role, behaving as either a neighboring or passing harmony to the sonority that precedes or follows them. In the passage below, three different kinds of diminished seventh occur. The one in m. 41 is a common tone seventh; the one in m. 45 is a leading tone seventh. The one in m. 44 serves as a passing chord joining the sonority in m. 43 to the sonority in m. 45; note that one voice moves by skip, the other three by step.
The nineteenth century (especially the music of Chopin, Liszt, Wagner, Strauss, etc.) is full of unexpected resolutions of o7. As that century progressed, composers increasingly became aware of the possibilities of this chord as a way of challenging the structural supremacy of the tonic-dominant axis. Perhaps its most revolutionary characteristic is the way in which the fully diminished seventh divides the octave into four equal parts, each three semitones in size:
It almost literally does have 101 uses!