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Cent (music)

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The cent is a logarithmic measure of a musical interval introduced by Alexander Ellis. It first appears 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.[1] 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.[2]


  1. 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. 
  2. Alexander J Ellis (March 25, 1885). "On the musical scales of various nations; §III.–Cents". Journal of the Society of Arts 33: p. 487.