Skip to main content
Humanities LibreTexts

23.3: The Fully Diminished Seventh as Pivot Chord

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

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


    Figure \(\PageIndex{1}\): The Four Resolutions of a Diminished Seventh Sonority

    In the example above, each note of the viivii∘7 chord was treated in turn as scale degree 7^ and resolved up by half step. In the example below, each note of the chord resolves as if it were the 7th of the chord, moving down by half step to the root of a dominant seventh chord.


    Figure \(\PageIndex{2}\): 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 viivii∘7 chord is enharmonically reinterpreted in a new key.

    In the first example, Beethoven enharmonically reinterprets FCF♯∘7/C in G minor (viivii∘34) as viivii∘24 in E minor (DCD♯∘7/C), which resolves to a VV7 chord in E minor.



    Figure \(\PageIndex{3}\): 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 EE∘7 chord in C (viiIVvii∘7/IV) as viivii∘24 in A♭ (GFG∘7/F♭). Notice the unusual resolution of the viivii∘24 chord to a GerGer+6 chord by leading all three of the upper voices of the viivii∘24 up by half step to the GerGer+6, which itself is unusually spelled in the key of A♭ major (E–A♭–C♭–D instead of F♭–A♭–C♭–D).



    Figure \(\PageIndex{4}\): Beethoven, Symphony No. 5, Op. 67, II (1808)

    In the final example of this section, Schubert reinterprets a GG♯∘7 in G minor as an EE♯∘7 chord in B minor (viiVvii∘56/V). The GG♯∘7 chord in G minor is analyzed as viiivvii∘24/iv, meaning it could resolve to a C minor chord, but it could also have been interpreted as viiVIvii∘34/VI, 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 GG♯∘7 would not be considered as tonicizing the note A (the root of the iiii∘ chord) or F♯ (the root of the viivii∘ chord).



    Figure \(\PageIndex{5}\): Schubert, Schwanegesang, D. 957, “Der Atlas” (1828)

    This page titled 23.3: The Fully Diminished Seventh as Pivot Chord is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Robert Hutchinson via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.