The cent system had already been defined in his History of Musical Pitch, where Ellis writes: "If we supposed that, between each pair of adjacent notes, forming an equal semitone, 99 other notes were interposed, making exactly equal intervals with each other, we should divide the octave into 1200 equal hundrecths of an equal semitone, or cents as they may be briefly called." Įllis defined the pitch of a musical note in his 1880 work History of Musical Pitch to be "the number of double or complete vibrations, backwards and forwards, made in each second by a particle of air while the note is heard". History Īlexander John Ellis' paper On the Musical Scales of Various Nations, published by the Journal of the Society of Arts in 1885, officially introduced the cent system to be used in exploring, by comparing and contrasting, musical scales of various nations. It has become the standard method of representing and comparing musical pitches and intervals. Making extensive measurements of musical instruments from around the world, Ellis used cents to report and compare the scales employed, and further described and utilized the system in his 1875 edition of Hermann von Helmholtz's On the Sensations of Tone. Ellis chose to base his measures on the hundredth part of a semitone, 1200√ 2, at Robert Holford Macdowell Bosanquet's suggestion. ![]() For humans, a single cent is too small to be perceived between successive notes.Ĭents, as described by Alexander John Ellis, follow a tradition of measuring intervals by logarithms that began with Juan Caramuel y Lobkowitz in the 17th century. Typically, cents are used to express small intervals, to check intonation, or to compare the sizes of comparable intervals in different tuning systems. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. The cent is a logarithmic unit of measure used for musical intervals. ![]() Octaves are equally spaced when measured on a logarithmic scale (cents).
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