![]() We can define C according to the fingerings we're used to on our instruments - which most people are going to find easier - or we can say that C is still 523Hz, in which case if someone says "play C", I must fret the D position. If I'm in a band, and we all decide it would sound better if we all dropped our tunings by a tone, we have a choice.When I play the third fret relative to the capo, I can call it D - so all the chord shapes I know have changed their names - or I can continue to call it C, even though its pitch has risen by a tone. If I decide a song would be easier to sing if I put a capo on the 2nd fret, I have a choice.If I tune my guitar with a tuning fork or an electronic tuner, then C is about 523Hz - unless I change my tuner to a difference reference pitch.So C is 4 semitones lower than whatever arbitrary pitch the E string is at. ![]() If I tune my guitar by ear, without external reference, then as long as the E string feels about right, I'll probably tune everything else relative to that.Even if the guitar is only "in tune" relative to itself. When I pick up my guitar, for me C is the pitch I get when I play the third fret of the A string.However, the mapping of absolute pitches to note names is only a convention, and in reality the absolute pitch of C only needs to be agreed between the people performing a piece of music. The very simplest answer is that A is 440Hz (* 2^n, as you say) and that C is a minor third higher than that (523.251 Hz).
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