In music, there is the frequency of notes and the pitch of notes. They are logarithmically related. As stated before, the simplest way to find out a new pitch is when the frequency doubles, the pitch is raised one octave. Here is a table of the frequencies of the G Major Scale:
 
 

Notice in the table that when the G note is raised one octave, the frequency doubles.  If the note was raised to another octave, it would be 4 times the original frequency (which comes to about 1148 Hz)

    The change in pitch, is measured in cents. There are 1200 cents in one octave.  Calculating the cent value for a pitch change can be found using the formula:

    C is equal to the cent value, and f and g are the two frequencies. Since we are using a twelve step scale and there are 1200 cents per one octave, 100 cents is equal to half a step. If one has two frequencies, 800 Hz and 400 Hz, one could determine the cent value easily because the ratio of the two frequencies is 2:1. However, when one has frequencies which are, let's say 457.7 Hz and 305.5 Hz, the exact interval is harder to find and can not be exactly measured using the equation above, if we fill in f and g, we get:

C = 3986 (log 457.7 - log 305.5)
C = 3986 (2.6606 - 2.4850)
C = 3986 (.1756)
C = 699.8

The cent value is approximately 700. That is equivalent to 7 half steps, which comes out to the fifth major interval. Cent values are an easy way to express frequencies. Here is a graph of the change in frequency to the interval measured in cents. Notice the frequency changes faster than the interval.

In summation, Cent values can be used to determine changes in intervals. Math not only can be found in the tonal part of music, but it is also in rhythm, duration, and tempo. Music basically is math in application.

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