# Cent (music)  Main Article Discussion Related Articles  [?] Bibliography  [?] External Links  [?] Citable Version  [?] This editable Main Article is under development and subject to a disclaimer. [edit intro]

The cent is a logarithmic measure of a musical interval introduced by Alexander Ellis. A cent is the logarithmic division of the equitempered semitone into 100 equal parts.

## Formula

In terms of a formula, the separation or interval between two frequencies ƒ1 and ƒ2 in cents is determined as:

$c=1200\log _{2}\left({\frac {f_{1}}{f_{2}}}\right)\ .$ Consequently, two frequencies ƒ1 and ƒ2 separated by an interval of 1 cent are in the ratio:

${\frac {f_{1}}{f_{2}}}=2^{1/1200}\approx 1.005777895\ ,$ that is, by a ratio given by the 1200th root of 2.

## Background

The cent appears in an article Alexander Ellis published in 1885 and also in an appendix he added to his translation of Herman von Helmholtz's Die Lehre von den Tonempfindungen published in translation as On the Sensation of Tone As a Physiological Basis for the Theory of Music, and also as On the sensations of tone. (PD) Image: John R Brews
Audible difference in frequency Δƒ/ƒ at two sound levels heard in rapid succession vs. frequency ƒ. (PD) Image: John R Brews
Average error of nine flutists in playing a note of specified pitch after listening to a pitch A4 = 442 Hz from a piano.