|
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to measure small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be heard between successive notes. Alexander J. Ellis based the measure on the ''acoustic logarithms'' decimal semitone system developed by Gaspard de Prony in the 1830s, at Robert Holford Macdowell Bosanquet's suggestion. Ellis made extensive measurements of musical instruments from around the world, using cents extensively to report and compare the scales employed,〔Alexander Ellis: (On the Musical Scales of Various Nations ) HTML transcription of the 1885 article in the Journal of the Society of Arts (Accessed September 2008)〕 and further described and employed the system in his edition of Hermann von Helmholtz's ''On the Sensations of Tone''. It has become the standard method of representing and comparing musical pitches and intervals with relative accuracy. ==Use== Like a decibel's relation to intensity, a cent is a ratio between two close frequencies. For the ratio to remain constant over the frequency spectrum, the frequency range encompassed by a cent must be proportional to the two frequencies. An equally tempered semitone (the interval between two adjacent piano keys) spans 100 cents by definition. An octave—two notes that have a frequency ratio of 2:1 -- spans twelve semitones and therefore 1200 cents. Since a frequency raised by one cent is simply multiplied by this constant cent value, and 1200 cents doubles a frequency, the ratio of frequencies one cent apart is precisely equal to 21/1200, the 1200th root of 2, which is approximately 1.0005777895. If one knows the frequencies ''a'' and ''b'' of two notes, the number of cents measuring the interval from ''a'' to ''b'' may be calculated by the following formula (similar to the definition of decibel): : Likewise, if one knows a note ''a'' and the number ''n'' of cents in the interval from ''a'' to ''b'', then ''b'' may be calculated by: : 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cent (music)」の詳細全文を読む スポンサード リンク
|