Cent (music)

From Freepedia

The cent is a unit in a logarithmic scale of relative pitch or intervals. 1200 cents are equal to one octave, and an equally tempered semitone is equal to 100 cents. The formula to determine the value in cents between two notes with frequencies a and b is:

<math>n = 1200 \log_2 \left( \frac{a}{b} \right) \approx 3986 \log_{10} \left( \frac{a}{b} \right)</math>

The ratio of two notes a and b with a difference in frequency of one cent is 1:2^1/1200 which is approx. 1.0005777895.

The measure was developed by A. J. Ellis around the 1870s, and was published in his edition of Hermann von Helmholtz's On the Sensations of Tone. It has since become the standard way of measuring intervals in equal temperament systems or for comparison with equal temperament systems.