How do we calculate the frequency of a second note according to the cents that separate it?

This formula allows us to calculate the frequency of a note (f 2 ) if we know the frequency of a note (f 1 ) and the distance in cents (c):

\[ f_2 = f_1 * 2^ { \frac{c}{1200} } \]

Do you want to see how we got to this formula?

For example, to calculate the frequency of a C#5 above an A4 (440) using equal temperament (a major third major in equal temperament has 400 cents):

\[ C\#5 = 440 * 2^ { \frac{400}{1200} } = 440 * 2^ { \frac{1}{3} } = 554.37 \]

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