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Why is it C's Major scale that comes without accidentals instead of A?

The C Major scale is played C D E F G A B C

The C chromatic scale is played C C# D D# E F F# G G# A A# B C

Why was it decided that instead of (Shifting the letters of C chromatic down two) A A# B B# C D D# E E# F F# G A

Basically if you wrote on the white piano keys, the A would be written on the C key.

My question is more about why it's called C instead of A, rather than having anything to do with the pitches. As a related side question, what importance does A have besides being a tuning reference.

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