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There are several aspects. One main relation, which is quite interesting is the frequency of the musical notes. A difference of one octave corresponds to a vibration ratio of 2:1. That is, if a certain "C" has a certain frequency, then the next "C" (further to the right on the piano) has twice that frequency. Each octave is divided into 12 equal intervals; thus, the frequency ratio of one semi-note is 1 : 12th. root of 2, or about 1 : 1.0595. (On the piano, a semi-note is the interval between a white key and the black key next to it, or between two white keys if there is no black key in between.)
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