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	Tempered Interval	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