# Appendix 3: Converting between Frequency Ratios and Cents

The cent is defined as one hundredth of an equal tempered semitone, which is equivalent to one twelve-hundredth of an octave since there are 12 semitones to the octave. Thus one cent can be expressed as:

The frequency ratio of any interval (F1/F2) can therefore be calculated from that interval in cents (*c*) as follows:

and the number of cents can be calculated from the frequency ratio by rearranging to give:

Therefore:

$c=1200\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{log}}_{2}\left[\frac{F1}{F2}\right]$ | (A3.1) |

For calculation convenience, a logarithm to base 2 can be expressed as a logarithm ...

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