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Section 23.3 The Fully Diminished Seventh as Pivot Chord

Each diminished seventh sonority implies four different keys. Play and sing through the example below.

Figure 23.3.1 The Four Resolutions of a Diminished Seventh Sonority

In the example above, each note of the \(\left.\text{vii}^{\circ}{}^{7}\right.\) chord was treated in turn as the \(\hat{7}\) scale degree and resolved up by half step. In the example below, each note of the chord is resolved as if it were the 7th of the chord, moving down by half step to the root of a dominant seventh chord.

Figure 23.3.2 Resolutions of a Diminished Seventh Sonority to a Dominant Seventh Sonority

This means that for any diminished seventh chord, you should be able to imagine the other three respellings in the same way you can imagine other spellings of words like two (i.e., to and too) or there (their and they’re).

In the following examples, a \(\left.\text{vii}^{\circ}{}^{7}\right.\) chord is enharmonically reinterpreted in a new key.

In the first example, Beethoven enharmonically reinterprets \(\left.\text{F}^♯{}^{\circ}{}^{7}\middle/\text{C}\right.\) in G minor (\(\left.\text{vii}^{\circ}{}^{4}_{3}\right.\)) as \(\left.\text{vii}^{\circ}{}^{4}_{2}\right.\) in E minor (\(\left.\text{D}^♯{}^{\circ}{}^{7}\middle/\text{C}\right.\)), which resolves to a \(\left.\text{V}^{7}\right.\) chord in E minor.

Figure 23.3.3 Beethoven, Pathétique Sonata, Op. 13, I (1798)

In the next example from the second movement of Beethoven’s Fifth Symphony, Beethoven modulates from C major to A♭ major by enharmonically reinterpreting an \(\left.\text{E}^{\circ}{}^{7}\right.\) chord in C (\(\left.\text{vii}^{\circ}{}^{7}\middle/\text{IV}\right.\)) as \(\left.\text{vii}^{\circ}{}^{4}_{2}\right.\) in A♭ (\(\left.\text{G}^{\circ}{}^{7}\middle/\text{F}^{♭}\right.\)). Notice the unusual resolution of the \(\left.\text{vii}^{\circ}{}^{4}_{2}\right.\) chord to a \(\left.\text{Ger}^{+6}\right.\) chord by leading all three of the upper voices of the \(\left.\text{vii}^{\circ}{}^{4}_{2}\right.\) up by half step to the \(\left.\text{Ger}^{+6}\right.\), which itself is unusually spelled in the key of A♭ major (E–A♭–C♭–D instead of F♭–A♭–C♭–D).

Figure 23.3.4 Beethoven, Symphony No. 5, Op. 67, II (1808)

In the final example of this section, Schubert reinterprets a \(\left.\text{G}^♯{}^{\circ}{}^{7}\right.\) in G minor as an \(\left.\text{E}^♯{}^{\circ}{}^{7}\right.\) chord in B minor (\(\left.\text{vii}^{\circ}{}^{6}_{5}\middle/\text{V}\right.\)). The \(\left.\text{G}^♯{}^{\circ}{}^{7}\right.\) chord in G minor is analyzed as \(\left.\text{vii}^{\circ}{}^{4}_{2}\middle/\text{iv}\right.\), meaning it could resolve to a C minor chord, but it could also have been interpreted as \(\left.\text{vii}^{\circ}{}^{4}_{3}\middle/\text{VI}\right.\), or as tonicizing an E♭ major chord. Because the chord never resolves in G minor, one cannot be certain of the intended resolution. Remember that diminished triads are not tonicized, so the \(\left.\text{G}^♯{}^{\circ}{}^{7}\right.\) would not be considered as tonicizing the note A (the root of the \(\left.\text{ii}^{\circ}{}\right.\) chord) or F♯ (the root of the \(\left.\text{vii}^{\circ}{}\right.\) chord).

Figure 23.3.5 Schubert, Schwanegesang, D. 957, “Der Atlas” (1828)