The cent is a logarithmic measure of a musical interval introduced by Alexander Ellis. It appears in an article he published in 1885 and also in the appendix he added to his translation of Herman von Helmholtz's On the Sensation of Tone As a Physiological Basis for the Theory of Music, also published as Die Lehre von den Tonempfindungen, translated as On the sensations of tone. A cent is the logarithmic division of the equitempered semitone into 100 equal parts. It is therefore the 1200th root of 2, a ratio approximately equal to (1:1.0005777895).
When two notes are played together, a difference of 2 cents is noticeable, and a difference of 5 cents is heard as out of tune.
- Alexander J Ellis (March 25, 1885). "On the musical scales of various nations; §III.–Cents". Journal of the Society of Arts 33: p. 487.
- Herman von Helmholtz (1912). “Footnote, p. 41 and Appendix XX, Section C”, On the Sensation of Tone As a Physiological Basis for the Theory of Music, Alexander Ellis translation of 4th German ed. Longmans, Green.
- Herman von Helmholtz (1954). On the sensations of tone, Reprint of 1885 translation by Alexander Ellis. Courier Dover Publications. ISBN 0486607534.