I was talking with a student the other day and we got into the subject of diminished seventh chords and how they are used in jazz. It got me thinking about how many different ways this chord can be resolved based on how it is used by composers of jazz as well as classical music. Most of us think of this chord as having a leading-tone function or wanting to resolve up a semi-tone to another chord. This seems to be the most common usage. But what about the other situations where we find the chord moving down a half-step or where we find the diminished seventh chord with the same root as the chord it moves to? What is going on in these cases?
We can classify the diminished seventh chord in three different ways. The first would be the leading-tone function. The second would be a common-tone classification in which the root of the chord of resolution is any one of the tones of the diminished seventh. The third would also be a common-tone classification but in this case the fifth of the chord of resolution is any one of the tones of the diminished seventh chord. Since jazz harmony rarely uses triads my examples have two common tones (under the common-tone examples) as I have used Major 6th and Minor 7th chords as chords of resolution. All three of these classifications involve chromatic voice-leading with sixths or tenths which serve to pass between two chords or to embellish a single chord. Let’s examine some typical examples.
A typical usage of the dim7 would be an ascending pass between two diatonic chords that are a whole step apart. For example in the key of C major we can connect the ii chord (Dm7) and the iii chord (Em7) by placing a dim7 chord between them: Dm7 - D#dim7 - Em7. This would be the most common leading-tone function since the D#dim7 resolves up by half-step. Note the chromatic tenths that really drive this progression forward.
The second type is an embellishment or prolongation of a single chord in which the root (and in my examples the sixth) of the chord to be embellished is a member of the dim7 chord and the two other voices are chromatic neighbor notes a sixth apart: C6 – Cdim7 – C6. This will be considered a common-tone classification.
The third type is the reverse of the first type in which two chords a whole step apart are connected with a descending dim7 chord: Em7 – Ebdim7 – Dm7. This is also a common-tone pattern in which the fifth (and in my examples the seventh) of the chord of resolution is a member of the dim7 chord. Again the chromatic tenths drive this progression.
Since the diminished seventh chord is a symmetrical structure consisting of consecutive minor thirds any of the four tones can be considered the root. In practice the spelling of the dim7 usually helps us determine its function. It is then possible to say that we can resolve this chord in twelve different ways based on our three classifications. Four roots times three classifications equals twelve different resolutions of one chord type! This means we can go anywhere within our twelve-tone system with this chord. Of course this dim7 chord does not occur in isolation but in a context that usually involves some sort of chromatic voice-leading.
To summarize let’s make three simple rules to remember the three types:
1) The diminished seventh chord resolves up by half-step to next chord (leading-tone).
2) The diminished seventh chord has the same root as the chord of resolution (common-tone, root).
3) The diminished seventh chord resolves down by half-step to the next chord (common-tone, fifth).
I have included musical examples below to show these resolutions. I decided to name the diminished seventh chord the same way each time for easier understanding since my purpose was to show the twelve resolutions possible with the same chord. I used enharmonic spellings to better show the common tones and voice-leading. Notice how the roots of the chords of resolution (when reading from the bottom to the top on the first three lines of music) form the complete chromatic scale!