The interval between two frequencies in cents and semitones, or turn a cents value back into a frequency ratio. 100 cents = 1 semitone.
Cents = 1200 × log2(f2 ÷ f1); 100 cents is one equal-tempered semitone, 1200 a full octave. A pure perfect fifth (ratio 3:2) is 701.96 cents, two cents wider than the equal-tempered fifth — the gap temperament smooths over.
A hundredth of an equal-tempered semitone, so an octave is 1200 cents. It is the standard unit for tuning: guitar tuners typically show how many cents sharp or flat a string is.
Cents = 1200 × log2 of the frequency ratio. From 440 to 466.16 Hz is 100 cents (one semitone); a 3:2 ratio is 701.96 cents, the pure perfect fifth.
Trained listeners notice about 5-10 cents on sustained tones; around 20-25 cents sounds clearly out of tune to most ears. Vibrato and short notes hide more.