The diminished seventh chord can act a multi-functional secondary dominant that enables the composer to modulate to near and distant key areas with the implementation of a single sonority. This is because every diminished seventh chord has multiple enharmonic spellings, each with a different possible resolution.
1. Original Spelling and Function. If we build a diminished seventh chord on the seventh scale degree of any key, it functions much the same as a dominant chord in that it will normally resolve to the tonic. However, as discussed in another chapter on the function of chords, this makes the analysis of the chord ambivalent since it appears to be built on one scale (vii) degree but functions as if built on another (V), even if the root of that chord does not appear. We can look at it from both points of view.
In C Major, the creation of a diminished seventh chord built on the seventh scale degree results in a sonority spelled B-D-F-Ab and will normally resolve to the tonic triad. If interpreted as a function of the dominant, the missing root is G, and we need to analyze it as such. Either way, the result is the same. The Ab will resolve down to the G, the F down to the E, the D down to the tonic, and the B ascending to double the tonic.
2. Enharmonic Spellings and New Meanings. The key to any diminished seventh chord is its repeating structure of minor thirds. Since the chord has no changes within its internal intervallic properties it will sound the same no matter what note sounds as its root. For example, if we respell the Ab as G# we can reconfigure the chord by rearranging the series of thirds with G# as the 'root' (now with E as the actual dominant root). We now have a secondary dominant to vi in C.
3. Other Configurations. To continue the trend we have established, any note in a diminished seventh chord can act as the leading tone of a different key. If we wish the D to function as a leading tone we can respell the B as Cb and reconfigure the chord into a series of thirds with D as the 'root' (now with Bb as the actual dominant root). We now have a secondary dominant to Eb.
The only remaining note we have not used as a leading tone is F. If we respell it as E# and the Ab as G# we can reconfigure the chord with E# as the 'root' (C# as the actual secondary dominant root) and modulate to arguably the most distant relationship with our home key, the tritone F#.
4. Modulation Choices and Notational Options. Of course, any of these secondary dominants can resolve to either the major or minor version of the tonality to which they are associated. The resolution to a minor can just as logically resolve to A major, the Eb major or eb minor, and the F# major to its enharmonic Gb major or their parallel minors.
Regarding the notation of diminished seventh chords when the resolution is not going to be the tonic, some composers spell the chord in its original fashion and simply resolve to another chord. However, it is perhaps better to choose to respell it in the fashion of the key to which one is modulating, thus providing for clearer visual voice leading indications for the performer.
