Cent (music): Difference between revisions
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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 ''Die Lehre von den Tonempfindungen'', translated as ''On the sensations of tone''.<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 ''Die Lehre von den Tonempfindungen'', translated as ''On the sensations of tone''.<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 in pitch estimates are common, with errors of 20-50 cents 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== | ||
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<ref name=Ellis> | <ref name=Ellis> | ||
{{cite book |title=On the Sensation of Tone As a Physiological Basis for the Theory of Music |author=Herman von Helmholtz |url= http://books.google.com/books?id=wY2fAAAAMAAJ&pg=PA41 |edition=Alexander Ellis translation of 4th German ed |chapter=Footnote, p. 41 and Appendix XX, Section C|year=1912 |publisher=Longmans, Green}} | {{cite book |title=On the Sensation of Tone As a Physiological Basis for the Theory of Music |author=Herman von Helmholtz |url= http://books.google.com/books?id=wY2fAAAAMAAJ&pg=PA41 |edition=Alexander Ellis translation of 4th German ed |chapter=Footnote, p. 41 and Appendix XX, Section C|year=1912 |publisher=Longmans, Green}} | ||
</ref> | |||
<ref name=Ohgushi> | |||
{{cite journal |title=The Relationship between Musical Pitch and Temporal Responses of | |||
the Auditory Nerve Fibers |journal=Journal of Physiological Anthropology and Applied Human Science |volume=24 |issue=1 |pages=pp. 99-101 |year=2005 |author=Ohgushi, K and Ano, Y |url=http://www.brainmusic.org/EducationalActivitiesFolder/Ohgushi_pitch2005.pdf }} | |||
</ref> | </ref> | ||
Revision as of 11:53, 13 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.
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 Die Lehre von den Tonempfindungen, translated as On the sensations of tone.[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 in pitch estimates are common, with errors of 20-50 cents 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
- ↑ 1.0 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.
- ↑ 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.
- ↑ Ohgushi, K and Ano, Y (2005). [http://www.brainmusic.org/EducationalActivitiesFolder/Ohgushi_pitch2005.pdf "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.