Cent (music): Difference between revisions
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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. | 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 ƒ<sub>1</sub> and ƒ<sub>2</sub> in ''cents'' is determined as: | ||
:<math> c = 1200 \log _2 \left( \frac {f_1}{f_2} \right) \ . </math> | |||
Consequently, two frequencies ƒ<sub>1</sub> and ƒ<sub>2</sub> separated by an interval of 1 cent are in the ratio: | |||
:<math>\frac{f_1}{f_2}=2^{1/1200} \approx 1.005777895 \ , </math> | |||
that is, by a ratio given by the 1200th root of 2. | |||
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/> | ||
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/> 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/> However, more recent estimates 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''). This error was traced to the response of auditory nerves in the ear, which exhibit a systematic error.<ref name=Ohgushi/> | |||
==References== | ==References== | ||
Revision as of 11:42, 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]
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] 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] However, more recent estimates 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). This error was traced to the response of auditory nerves in the ear, which exhibit a systematic error.[4]
References
- ↑ 1.0 1.1 1.2 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.
- ↑ Cite error: Invalid
<ref>tag; no text was provided for refs namedOhgushi