21.3: Uses for Diminished Chords
- Page ID
- 258605
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Dominant Function
The most common use for either a diminished triad or seventh chord is in a dominant function. If we consider the diagram from 16.5: Overview of Functional Harmony, we find the vii° chord with the dominant (V) in brackets. Though this is not the only use for a vii° chord, this is the most common. The fascinating reason why the vii° chord can be used with this function is due to the scale degrees the two chords share.
- The dominant triad (V) is made up of sol-ti-re
- The dominant seventh (V7) chord is made up of sol-ti-re-fa
- The leading tone triad (vii°) is made up of ti-re-fa
- The leading tone seventh (viiø7 or vii°7) chord is made up of ti-re-fa-la (or le)
Leading to Do
The leading tone of the key (seventh scale degree) always wants to resolve up by a step to do. This tendency tone leads our ear from the seventh scale degree to the tonic.
At the same time, the presence of re can either move down a step to do or up a step to mi. This tendency is not quite as strong as ti-do, but adds to the dominant pull to the tonic.
The strong tendency for fa to move down a step to mi is an additional pull of movement that gives these chords a dominant sound. When we compare the strong tendency tones that are present in the dominant seventh (V7) to the strong tendency tones that are present in both the leading tone triad (vii°) and leading tone seventh chord (viiø7 or vii°7), they both contain these strong tones.
Modulation
The fully diminished (vii°7) chord can be used to modulate because, as mentioned before, the four pitches that are each a minor third apart evenly break up the 12 tones within an octave. These pitches can be used with one spelling in one key, and then rewritten enharmonically in a new key. This concept will be covered in more detail in more advanced music theory classes.
Embellishment
The use of a diminished chord as embellishment is related to the same tendency tones detailed above. Creating a diminished chord that then resolves up a step can momentarily give extra emphasis to that new note. We can use this technique to bring in chromatic notes (notes not originally part of the key) through the use of accidentals.
This example is in the key of C major. We know this because there are no sharps or flats in the key signature and it starts on a C chord and ends on a C chord. We also have a clear cadence at the end in the key of C. However, at the end of the second measure, we have an F-sharp. If we were to analyze the notes sounding at that moment, we would find: F-sharp, A, and E. Even though the C has been omitted, this is implying a half-diminished seventh chord with F-sharp as the root. There are two ways to think about this chord: (1) that it is briefly borrowed from the key of G major (one sharp) to give emphasis to the G chord, or (2) that this sonority was created as a result of lower neighbor and upper neighbor embellishing tones.