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) decidedly spans 100 cents. 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.
Read more about this topic: Cent (music)
Famous quotes containing the word use:
“... it is use, and use alone, which leads one of us, tolerably trained to recognize any criterion of grace or any sense of the fitness of things, to tolerate ... the styles of dress to which we are more or less conforming every day of our lives. Fifty years hence they will seem to us as uncultivated as the nose-rings of the Hottentot seem today.”
—Elizabeth Stuart Phelps (1844–1911)