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