
The cent is a
logarithmic unit of measure used for
musical intervals.
Twelve-tone equal temperament
12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (\sqrt 2/math> ≈ 1.05946). That resul ...
divides the
octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
into 12
semitone
A semitone, also called a minor second, half step, or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between ...
s of 100 cents each. Typically, cents are used to express small intervals, to
check intonation, or to compare the sizes of comparable intervals in different
tuning systems. For humans, a single cent is too small to be perceived between successive notes.
Cents, as described by
Alexander John Ellis
Alexander John Ellis (14 June 1814 – 28 October 1890) was an English mathematician, philologist and early phonetician who also influenced the field of musicology. He changed his name from his father's name, Sharpe, to his mother's maiden nam ...
, follow a tradition of measuring intervals by
logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
s that began with
Juan Caramuel y Lobkowitz in the 17th century. Ellis chose to base his measures on the hundredth part of a semitone,