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Chapter 20 Answer Key

Applications

Exercises

1. Spell and resolve dominant ninth chords in four voices.

2. Spell and resolve altered dominants in four voices.

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3. Embellish the given tonic chords with either CTO7 or CT+6. Observe the chord member that is doubled in the provided chords.

Brain Teasers

1. Unlike V7, which may be complete or incomplete, why should altered dom-inants (V+7 and VO34) be complete?Answer: An incomplete chord lacks its fifth. For reasons discussed in Chapter 12, this chord member is somewhat expendable relative to the root, third, and seventh. For altered dominants, the fifth is either raised or low-ered by half step. If the fifth were absent, the chord would cease to be an altered dominant.

2. Why is V+ much more effective, and common, in major keys (rather than minor keys)?Answer: The raised fifth of V+ is #2̂. This altered scale degree is enharmonic with 3̂ in minor keys (e.g., in C minor, #2̂ is D# and 3̂ is Eb). Therefore, rather than resolving up by half step, the raised fifth would act as an enharmonic common tone with the third of i.

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3. What is the relationship between VO34 in C major and Fr+6 in F major? Might this relationship enable a certain modulatory process? Why or why not?Answer: VO34 in C major and Fr+6 in F major are the exact same sonorities—they have identical spellings (D b–F–G–Bn) but different functions (D and PD, respectively). This relationship seems similar to the enharmonic rela-tionship between V7 and Gr+6. However, in this case, modulation via en-harmonic reinterpretation is not possible because the chord members resolve in the same manner regardless of function. In other words, both VO34 in C major and Fr+6 in F major resolve to a C major chord (I in C major and V in F major, respectively).

4. Two chords in Example 16-9 are analyzable as dominant ninth chords. Which ones?Answer: In. m. 4, Fn turns V7 into V9. In the first half of m. 7, A is the ninth of a complete dominant ninth chord in first inversion.

Thinking Critically

1. Spell V+ in F major. Then plot the chord on a pitch-class (pc) wheel. Describe its structure as viewed on the pc wheel.Discussion: This + triad is symmetrical—it divides the octave into three M3 units.

2. Revisit the enharmonic reinterpretation of viiO7 discussed in Chapter 19. Based on the structural properties of V+ uncovered in the previous Thinking Critically question, how might this chord be used to modulate?Discussion: The chord may be reinterpreted enharmonically. Any pc may serve as the root, which recontextualizes the other pcs as the two tendency

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tones, 7̂ and #2̂. The chord may serve as a C–C pivot chord to modulate ei-ther up or down a M3 from the original tonic. As the diagram below shows, V+ in F major may be reinterpreted to modulate up a M3 to A major, or down a M3 to Db major (or C# major). This form of enharmonic reinterpre-tation is less common than the types discussed in Chapter 19.