Sharp Fourth Scale Degree in the Goldberg Variation "Aria"
My question relates to the C# in the 3rd measure.
I understand that the section eventually modulates to D major which contains that C#, but that does not seem to happen until the 9th measure. What would be the customary harmonic analysis of the 3 measure?
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Although there are answers in the comments, I thought I'd provide an official one.
You're correct that the music has not yet modulated to D, as evidenced by (among other things) the C? that appears in the bass at the end of m. 4.
Measure 4 is clearly a V chord (D), and that C? clearly suggests a tonicization of that V chord. When we stack that chord in m. 3 in thirds, we get C?–E–G, which is a vii° triad (the ° means diminished) in the key of D. With the E in the bass it's in first inversion, so this chord is best called a vii°6/V (read "seven-diminished six of five"), which is a very common occurrence in step-descent basses like this one.
And as some of the comments above discuss, if one wishes to include the A in the chord, we're left with A–C?–E–G, which is a V7 chord in D, but now in second inversion. If you include the A, the chord is then best labeled V43/V.
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