re: min maj 6ths "Ok so say for example I hit c and a, to create a major 6th.
Does the c string vibrate at the c frequency and the a string at the a frequency and the composite that is produced vibrate as if it where a major 6th?"
The frequency of the vibration of the strings do not change on a piano. The freq is a function of the length and to some degree, mass of the string. The term maj 6th, refers to a relationship between notes.
The composite you refer to is a reccognisable sound for each intervall and in fact there is a third vbration which occurs as the vib of the 2 strings combine in the medium, such as the air and your basilar membrane inside the cochlear. This is easily heard when you play a minor 2nd, c-d flat, and is sometimes called the beat frequency.
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