# Cents

### Definition

Cents provide a linear unit of measurement for frequency ratios. Cents are to frequency as decibels are to amplitude. A cent is 1/100th of an equal-tempered semitone, which is itself 1/12 of an octave.

The following formula converts a frequency ratio to a pitch interval in cents:

cents = 1200 × log2(ratio)

The following formula converts a pitch interval in cents to a frequency ratio:

ratio = 2(cents/1200)

### Examples

Wikipedia gives the just-noticeable difference for “two tones in quick succession” above 1000 Hz. as “about 10 cents”. The following table compares low-integer frequency ratios with the equal-tempered chromatic scale.

 Cents TemperedInterval Ratio 000 Unison 1:1 100 Minor Second 200 Major Second 204 9:8 231 8:7 300 Minor Third 316 6:5 386 5:4 400 Major Third 498 4:3 500 Perfect Fourth 551 11:8 600 Tritone 649 16:11 700 Perfect Fifth 702 3:2 800 Minor Sixth 814 8:5 884 5:3 9000 Major Sixth 969 7:4 996 16:7 1000 Minor Seventh 1100 Major Seventh 1200 Octave 2:1

 © Charles Ames Page created: 2014-03-04 Last updated: 2015-04-14