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Difference between revisions of "Cent (music)"

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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|Error in playing a note of specified pitch.<ref name=Ohgushi/>}}
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{{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/>}}
 
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/>
  
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.<ref name=tune/> Recent observations suggest errors of 5-15 cents when playing a specific pitch are common on an instrument tuned to ''A''4=440 Hz, with errors of 20-50 cents for pitches above ''A''7 (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.<ref name=Ohgushi/>
+
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.<ref name=tune/> Recent observations suggest errors of 5-15 cents when playing a specific pitch are common on an instrument tuned to ''A''4=442 Hz, with errors of 20-50 cents for pitches above ''A''7 (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.<ref name=Ohgushi/>
  
 
==References==
 
==References==

Revision as of 16:45, 14 July 2012

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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.

(PD) Image: John R Brews

The cent appears in an article Alexander Ellis published in 1885[1] 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,[2] also published as the translation On the sensations of tone of Die Lehre von den Tonempfindungen.[3]

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.[1] 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.[4]

References

  1. 1.0 1.1 Alexander J Ellis (March 25, 1885). "On the musical scales of various nations; §III.–Cents". Journal of the Society of Arts 33: p. 487.
  2. 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. 
  3. Herman von Helmholtz (1954). On the sensations of tone, Reprint of 1885 translation by Alexander Ellis. Courier Dover Publications. ISBN 0486607534. 
  4. 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.