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V. Chromaticism
Altered and Extended Dominant Chords

### Core Idea

Altered dominant chords feature either an augmented or diminished fifth. Augmented fifths are indicated in analysis by “+” beside the Roman numeral. Diminished fifths are indicated by a “o” beside the Roman numeral. Dominant with an augmented fifth

### Explanation

Altered dominant chords

Altered dominant chords feature either an augmented or diminished fifth. Augmented fifths are indicated in analysis by “+” beside the Roman numeral. Diminished fifths are indicated by a “o” beside the Roman numeral.

Dominant with an augmented fifth

If you raise the fifth of a dominant triad, it will become an augmented triad. Typically, raised fifths resolve upward by step to the third of its target chord. 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. Like the diminished-seventh chord, this means that the augmented triad can be a pathway to distant, chromatic modulations. See Example 1, which shows the three possible enharmonic interpretations and resolutions of the C augmented triad.

Importantly, these chords do not resolve easily to minor triads, since the augmented fifth would not be able to resolve upward by step.

Example 1: The three possible resolutions of the C augmented triad.

The Dominant with Diminished Fifth

When you add a 7th to a Vo chord, you get a chord that sounds precisely like 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. As Example 2 shows, the chords Vo4/3/V and the French augmented-sixth chord are identical.

Example 2: The dominant chord with a diminished fifth, and its equivalence with the French augmented-sixth chord.

Extended dominant chords

Extensions can be added to dominant chords to create new and interesting sonorities. These chords are typically found only in root position.

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.

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### Key Quote

Augmented fifths are indicated in analysis by “+” beside the Roman numeral.

### Application Scenarios

If you raise the fifth of a dominant triad, it will become an augmented triad. Typically, raised fifths resolve upward by step to the third of its target chord. 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. Like the diminished-seventh chord, this means that the augmented triad can be a pathway to distant, chromatic modulations. See Example 1, which shows the three possible enharmonic interpretations and resolutions of the C augmented triad.

Example 1: The three possible resolutions of the C augmented triad.

When you add a 7th to a Vo chord, you get a chord that sounds precisely like 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. As Example 2 shows, the chords Vo4/3/V and the French augmented-sixth chord are identical.

Example 2: The dominant chord with a diminished fifth, and its equivalence with the French augmented-sixth chord.

### Key Terminology

second inversion augmented triad chordal seventh seventh chord root position chromatic texture scale triad chord root note
Source: https://viva.pressbooks.pub/openmusictheory/chapter/altered-and-extended-dominant-chords/
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