Pitch Interval in Cents

This formula converts a frequency ratio into cents, a logarithmic unit that musicians and acousticians use to measure very small or very large pitch differences on a consistent scale. It works because equal musical intervals correspond to equal frequency ratios, not equal frequency differences; using a base-2 logarithm makes an octave, where the frequency doubles, equal to 1200 cents. That means the cents scale matches how pitch is perceived and how musical intervals repeat across octaves.

Use this when comparing two pitches, checking tuning accuracy, or analyzing intervals in equal temperament, just intonation, or recorded audio. It is especially useful whenever the frequencies are known and you want the interval size in a standard musical unit.

• Using the frequency difference (f2 - f1) instead of the ratio f2/f1
• Forgetting that the logarithm is base 2, not base 10 or natural log unless you convert correctly
• Reversing the frequencies so the ratio becomes less than 1, which gives a negative value instead of the size of an upward interval