The first equation is a mathematical representation of ascale as geometric series that sets aside the perfect fifth. Basically, thisequation represents that fact that an interval is necessary which upon transpositioning 7 times would give the 7 semitones. Whereas, the second equationrepresents the fact that, the geometric scale is for a scale of 12 notes.

Thereason being that, 12 perfect fifths did not round off to precisely to an evenoctave, instead it exceeded it by a small ratio. This ratio is called the Pythagoreancomma. “It is the small interval that exists between two notes with identicalpitch, but has different names and different roles in harmony.” (Halpin)  Now, when bothequations are solved for x, it is quite evident that, the two solutions willnot be equal, which then brings up the question, which to rely upon or ? 

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