The fundamental (not necessary the only) point of the key signature is that it allows you to use fewer accidentals when writing it, which is a convenience. The key is always determined by what the harmony actually does. ALWAYS.Then what's the point of the key signature if it doesn't tell what key the music is written in? To keep with my original example, if the key signature is 3b, is the music not written either in Eb Major, or C minor?
If not, what purpose does the key signature have, and how (short of reading the music all the way through) would you know what key it is in? I'm still very new to Theory.
Plenty of music is best written without any key signature at all, for example if it isn't easily definable in terms of the accepted keys of functional Western tonality. I have a book of Hermeto Pascoal compositions, not one of which has any key signature. (And no, that doesn't mean the key is C. Not one of the tunes has anything to do with the key of C.)
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