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That's funny because B+G, C+G to me says G major: a major third, then a fourth. Is the ear guided to keys by inversion, some inversions more natural or root-y than others?

I've been composing pop music for a long time without knowing stuff like this.

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I can see the G major argument. That would be a I/3 into IV. My professor would have said that answer is wrong due to voice leading, the 7 to 1 is very powerful. And the last chord is C, in root, meaning that's where you have resolved. Had the second interval been G+B, it would make the GMaj argument stronger. Ultimately, it's really context. You're really just asking about cadences, very roughly translated means "how chords resolve".

B+G is a minor sixth, not a major third. If you invert it, it's a major third.

B+G followed by C+G is most likely going to sound like a cadence in C Major. You could claim it is G major only if you considered it unresolved transition to the subdominant.

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