![]() ![]() 5 Other representations of intervals by logarithmsĪlexander J. ![]() It has become the standard method of representing and comparing musical pitches and intervals. He made extensive measurements of musical instruments from around the world, using cents extensively to report and compare the scales employed, and further described and employed 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. 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, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be perceived between successive notes.Ĭents, as described by Alexander J. 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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