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Encyclopedia > Cent (music)

The cent is a logarithmic unit of measure used for musical intervals. Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard. A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. ... In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... This page is about musical systems of tuning, for the musical process of tuning see tuning. ...


1200 cents are equal to one octave — a frequency ratio of 2:1 — and an equally tempered semitone (two adjacent piano keys) is equal to 100 cents. This means that a cent is precisely equal to 21/1200, the 1200th root of 2, which is approximately 1.0005777895. In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ... The musical interval of a half step, semitone, or minor second is the relationship between the leading tone and the first note (the root or tonic) in a major scale. ...


If you know the frequencies a and b of two notes, the number of cents measuring the interval between them may be calculated by the following formula:

To compute the frequencies of an equal-tempered scale starting at A-220 (the A below middle C), use the following formula: Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ...

 A = 220Hz A# = 220 * TRT (233.08Hz, 100 cents higher) B = 220 * TRT2 (246.94Hz, 200 cents higher) C = 220 * TRT3 (261.63Hz, 300 cents higher) 

etc., where TRT is the twelfth root of two, approximately 1.05946. The difference between the frequencies of adjacent notes is approximately 6 percent. The hertz (symbol Hz) is the SI unit of frequency. ... The hertz (symbol Hz) is the SI unit of frequency. ... The hertz (symbol Hz) is the SI unit of frequency. ... The hertz (symbol Hz) is the SI unit of frequency. ...


To compare different tuning systems, convert the various interval sizes into cents. For example, in just intonation the major third is represented by the frequency ratio 5:4. Applying the formula at the top shows this to be about 386 cents. The equivalent interval on the equal-tempered piano would be 400 cents. The difference, 14 cents, is about a seventh of a half step, easily audible. The just noticeable difference for this unit is about 6 cents. Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. ... In psychophysics, the just noticeable difference (usually abbreviated as jnd, using lowercase letters) is the smallest difference in a sensory input that is perceivable by a human being or other animal. ...


The measure was developed by A. J. Ellis around the 1870s, and was published in his edition of Hermann von Helmholtz's On the Sensations of Tone. It has since become the standard way of measuring intervals in equal temperament systems or for comparison with equal temperament systems. Events and Trends Technology The invention of the telephone (1876) by Alexander Graham Bell. ... Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist. ... Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ...


See also

In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... This page is about musical systems of tuning, for the musical process of tuning see tuning. ...

External links


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Cent (currency) — a one-hundredth subdivision of several units of currency.
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This is a disambiguation page, a list of pages that otherwise might share the same title.
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