MUSIC THEORY FUNDAMENTALS - Chapter 7, Exercise 3 Solution
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Why C Major and G Major Share Six of Seven Scale Tones

PROBLEM
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Explain, using this chapter's own material and Chapter 3's circle of
fifths, why C major and G major share six of their seven scale tones,
and name the one note that differs between them.

SOLUTION
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C major and G major are directly adjacent on Chapter 3's own circle of
fifths - G is exactly one real perfect fifth above C. Per Chapter 3's
own key-signature rule, moving one step around the circle of fifths adds
or removes exactly one sharp or flat.

Comparing the actual pitch content of both scales (not scale-degree
order, just which notes appear):

    C major pitches: C, D, E, F, G, A, B
    G major pitches: G, A, B, C, D, E, F#

Comparing the two sets: C, D, E, G, A, B all appear in BOTH scales -
that is six shared notes. The only note that differs is F (natural, in
C major) versus F# (sharp, in G major).

ANSWER: C major and G major share six scale tones (C, D, E, G, A, B),
differing only in F (C major) versus F# (G major) - exactly one real
accidental, matching G major's own real key signature of 1 sharp.

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WHY THIS WORKS AS AN ANSWER

This is a direct, real consequence of Chapter 3's own key-signature
rule: since G major has exactly one more sharp than C major (1 sharp
versus 0), and that one sharp is specifically F#, the two scales can
only possibly differ in that single note. Every other note the two
keys share in common is unaffected, which is exactly what makes
neighboring keys on the circle of fifths sound so closely related.