Cent (music): Difference between revisions
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that is, by a ratio given by the 1200th root of 2. | that is, by a ratio given by the 1200th root of 2. | ||
{{Image|Tuning error.png|right|250px|Average error of nine flutists in playing a note of specified pitch after listening to a pitch ''A''4 = 442 Hz from a piano.<ref name=Ohgushi/>}} | {{Image|Tuning error.png|right|250px|Average error of nine flutists in playing a note of specified pitch after listening to a pitch ''A''4 <nowiki>=</nowiki> 442 Hz from a piano.<ref name=Ohgushi/>}} | ||
The ''cent'' appears in an article Alexander Ellis published in 1885<ref name=tune/> 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'',<ref name=Ellis/> also published as the translation ''On the sensations of tone'' of ''Die Lehre von den Tonempfindungen''.<ref name=sensations/> | The ''cent'' appears in an article Alexander Ellis published in 1885<ref name=tune/> 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'',<ref name=Ellis/> also published as the translation ''On the sensations of tone'' of ''Die Lehre von den Tonempfindungen''.<ref name=sensations/> | ||
Revision as of 10:47, 14 July 2012
The cent is a logarithmic measure of a musical interval introduced by Alexander Ellis. A cent is the logarithmic division of the equitempered semitone into 100 equal parts. In terms of a formula, the separation or interval between two frequencies ƒ1 and ƒ2 in cents is determined as:
Consequently, two frequencies ƒ1 and ƒ2 separated by an interval of 1 cent are in the ratio:
that is, by a ratio given by the 1200th root of 2.
Average error of nine flutists in playing a note of specified pitch after listening to a pitch A4 = 442 Hz from a piano.[1]
The cent appears in an article Alexander Ellis published in 1885[2] 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,[3] also published as the translation On the sensations of tone of Die Lehre von den Tonempfindungen.[4]
According to Ellis, 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] Recent observations suggest errors of 5-15 cents when playing a specific pitch are common on an instrument tuned to A4=442 Hz, with errors of 20-50 cents for pitches above A7 (the 7th octave, 3 octaves above the octave containing middle C). The increased error at higher pitch was traced to a systematic error in the response of auditory nerves in the ear.[1]
References
- ↑ 1.0 1.1 Ohgushi, K and Ano, Y (2005). "The Relationship between Musical Pitch and Temporal Responses of the Auditory Nerve Fibers". Journal of Physiological Anthropology and Applied Human Science 24 (1): pp. 99-101.
- ↑ 2.0 2.1 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.