What are cents in music?

This formula allows us to calculate the frequency of a note (f₂) if we know the frequency of a note (f₁) and the distance in cents (c):

We start from the formula to calculate cents between two notes:

\[ cents = log_2 \left( \frac{f_2}{f_1} \right) *1200 \]

Divide both sides by 1200:

\[ \frac{cents}{1200} = log_2 \left( \frac{f_2}{f_1} \right) \]

The equation tells us that 2 raised to the power \( \frac {cents} {1200} \) is equal to \( \frac {f_2} {f_1} \) . Thus:

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

Multiplying each side by f₁, we arrive at the final formula:

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

or:

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

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):

Enter the frequency of a first note and the cents that separate it to calculate the frequency of the second note. Click Calculate frequency: