


A cent is a measure of an interval in music developed by Alexander Ellis, and which received great exposure in Ellis’ contributions to English editions of Helmholtz’ treatise on music (Helmholtz & Ellis, 1954). Ellis took a musical octave and divided it into 1200 cents, recognizing that to move an octave higher than some frequency f that this frequency had to be doubled (that is, 1200 cents is derived from the ratio 1:2). In equal tempered tuning, the interval between semitones (that is, the interval between adjacent keys of a modern piano) is equal to 100 cents (Benson, 2007; Isacoff, 2001). The cent scale is logarithmic. If one knows the frequencies of two tones, then the number of cents between the tones is equal to 1200 times the basetwo logarithm of the ratio of the two frequencies. A cent is too small an interval to be distinguished by human hearing. However, the cent is an extremely useful measure when used to compare different musical intervals in an experiment, or musical intervals generated by different means (for example, by different instruments).
References:
 Benson, D. J. (2007). Music: A Mathematical Offering. Cambridge, UK ; New York: Cambridge University Press.
 Helmholtz, H. v., & Ellis, A. J. (1954). On the sensations of tone as a physiological basis for the theory of music (2d English ed.). New York,: Dover Publications.
 Isacoff, S. (2001). Temperament: The Idea That Solved Music's Greatest Riddle (1st ed.). New York: Alfred A. Knopf.



