MUSIC THEORY FUNDAMENTALS - Chapter 9, Exercise 1 Solution
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Finding the Second Theme's Key in a C Major Sonata

PROBLEM
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A piece in C major (a major key) is in sonata form. Using this chapter's
own real tonal-plan rule for the exposition, name the key the second
theme would modulate to.

SOLUTION
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This chapter's own tonal-plan rule states that in a major-key sonata-form
work, the exposition's first theme stays in the tonic key, while the
second theme modulates to the DOMINANT key.

The tonic of C major is C. Per Chapter 7's own real scale-degree naming,
the dominant is the 5th scale degree of the tonic's own major scale.

    C major scale: C - D - E - F - G - A - B
                    1   2   3   4   5

The 5th degree of C major is G.

ANSWER: The second theme would modulate to G major, the dominant key.

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WHY THIS WORKS AS AN ANSWER

This is a direct application of this chapter's own real major-key sonata
rule (tonic -> dominant), combined with Chapter 7's own real definition
of the dominant as the 5th scale degree. The real reason this specific
modulation is so common: G major and C major are directly adjacent on
Chapter 3's own circle of fifths, sharing six of seven scale tones,
which makes the exposition's own move away from "home" feel like a
genuine but not overly distant harmonic journey - exactly the kind of
smooth, closely-related modulation Chapter 7 already covered.