- Dominant chords may feature an augmented or diminished fifth, indicated in analysis by “+” beside the Roman numeral. Diminished fifths are indicated by a “o” beside the Roman numeral.
- When the fifth of a major triad is raised, it becomes an augmented triad, which is symmetrical and easily subject to enharmonic reinterpretation.
- Augmented dominant chords typically have the augmented fifth resolving up to the third of the chord. These most commonly are found resolving to major triads
- Diminished fifths typically resolve down by semitone to the root of the following chord
- A dominant-seventh chord with a diminished fifth, when placed in second inversion, is enharmonically equivalent to a French augmented-sixth chord
To this point, many of the chromatic harmonies we have explored have been explained in terms of either secondary function or modal borrowing. None of these harmonies include alterations to the perfect fifth of the chord; a practice we will now discuss in some detail. When the fifth of a triad is raised or lowered, it becomes either augmented or diminished. While we have seen diminished triads and seventh chords that feature diminished fifths, we have yet to discuss the possibility of a chord with a major third and either an augmented or diminished fifth. These chords are commonly referred to as “altered chords.” Although there is no standard analytical notation, augmented fifths are often indicated in analysis by “+” beside the Roman numeral. Diminished fifths are indicated by a “o” beside the Roman numeral. We will adopt this practice here.
The Dominant with an augmented fifth
If you raise the fifth of a major triad, it will become an augmented triad. Typically, raised fifths resolve upward by step to the third of its target chord. In Example 1, Franck abruptly modulates from f-sharp minor to D major by way of a dominant seventh chord with an augmented fifth. Note the resolution moves upward to the third of the target chord (in this case, tonic in D major). This is the most common resolution of this chromatic pitch.
The dominant chord with augmented fifth can be used as an applied chord, as well, as you can hear in the excerpt from Strauss’s “Till Eulenspiegel’s Merry Pranks” in Example 2.
Importantly, these chords do not resolve easily to minor triads, since the augmented fifth would not be able to resolve upward by step. In Example 3, the dominant chord with an augmented fifth is used in first inversion, with the chromaticized fifth resolving upward again.
Note that the augmented triad is a symmetrical chord than can be interpreted in multiple ways, making it difficult to identify its root without proper surrounding context. In Example 3, Brahms makes it clear that chord is functioning as the dominant of Bb, but one could easily re-interpret the bass note as the root of an A augmented triad. Like the diminished-seventh chord, the augmented triad can be a pathway to distant, chromatic modulations. Example 4 shows the three possible enharmonic interpretations and resolutions of the C augmented triad.
The Dominant with Diminished Fifth
Flattening the fifth of a major triad results in a strange chord quality that we have not encountered thus far. This alteration makes a diminished fifth above the root, and this tone tends to resolve downward by step to the root of its target chord. Although it is possible to use this triad, it is far more common to use the diminished fifth in a dominant-seventh chord. In Example 5, an excerpt from the opera Salome by Richard Strauss, the cadential dominant includes a diminished fifth, which provides a delightful dissonance leading to the tonic. In this example, Strauss is more liberal with the resolution of the flattened fifth, and doesn’t bother resolving the pitch to the root of the tonic chord.
Like the augmented triads and diminished-seventh chords, the dominant seventh with a diminished fifth is symmetrical. Moreover, the chord is equivalent to a French augmented-sixth chord. This equivalence becomes even clearer when you use the Vo7 chord in second inversion, leaving the lowered fifth in the bass voice to resolve downward by step. For example, in C major, the Vo4/3 chord is identical to the French augmented-sixth chord in F major. Similarly, the Vo4/3/V is equivalent to the French augmented-sixth chord in the home key of C major. Technically, the root-position dominant seventh chord with a diminished fifth is also equivalent to a French augmented-sixth chord, though this requires some enharmonic respelling to become clear. Example 6 shows all of these equivalences.
To finish off our discussion of altered dominants, consider Example 7, from the second movement of Tchaikovsky’s Symphony No. 5. In this excerpt, emerging from a chromatic quagmire of half-diminished and fully-diminished seventh chords is a relatively surprising diatonic ii7 chord. This chord resolves via stepwise motion, through another half-diminished seventh chord, to the cadential dominant of the passage: a Vo4/3 chord. Typically, cadential dominants are only effective in root position, however this chord is emblematic of nineteenth-century chromaticism and ambiguity. The lowered fifth resolves downward by step, much like an augmented-sixth chord, to the D major tonic.
To this point, we have only used harmonies that form triads or seventh chords. It is possible, and indeed, many Romantic-era composers and beyond did this, to continue to superimpose thirds beyond the seventh above the root of a chord. You can do this only so far, though, before you reach the root of the chord again, as you can see in Example 8a). In jazz theory, chord members beyond the seventh are referred to as extensions, and we will adopt this practice here. Importantly, extensions rely on their voicing to determine their meaning. In Example 8b) and 8c), two different voicings of the same four pitches are given. In Example 8b), the chord can clearly be contextualized as V13/7 in the key of C major. Example 8c) is much less clear; it could be some kind of inversion of the chord in 8b), or we could consider it to be an extended iii chord. In either case, the context is made unclear by the chord’s voicing. Because of this, we tend to only use extended chords in root position (as the extensions are truly defined by the chord root).
When composing these chords in a four-voice texture, you need to decide which notes to leave out. These chords will always include the root and the chordal seventh.
The V9 chord replaces a doubled root with a ninth. The ninth should resolve down by step.
The V11 chord replaces the third with an eleventh. The eleventh “resolves” by common-tone. This chord typically includes both the ninth and the eleventh, and resembles a IV chord with scale-degree 5 in the bass.
The V13 chord replaces the fifth with a thirteenth. The thirteenth “resolves” by leaping down by third to scale-degree 1.
- Coming soon!