Cents converter
Convert a musical interval between cents and the frequency ratio it stands for. An octave is 1,200 cents and exactly double the frequency.
That's about the same as a pure fifth. That is a frequency ratio of about 1.5.
What it means
How wide is that interval?
Cents describe intervals, not pitches. A note needs a reference — usually A = 440 Hz — before an interval becomes a frequency.
Every unit
Your interval in every unit
Learn
Three things worth knowing
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1,200 cents = one octave = ratio 2
And each semitone is 100 cents, a ratio of 2^(1/12) = 1.0595. Adding cents multiplies ratios, which is the whole point of the unit.
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Ellis, in 1885
Alexander Ellis divided the semitone into a hundred parts so that the tunings of different cultures could be compared numerically rather than by ear.
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A pure fifth is not 700 cents
It is 701.955. The two-cent gap is what forces every piano to compromise, and the 23.5 cents it accumulates over twelve fifths is the Pythagorean comma.
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Background
About cents
Pitch is logarithmic: an octave is always double the frequency, whether you start at 100 Hz or 1,000. So intervals are ratios, and cents are the logarithm that turns multiplying ratios back into adding numbers.
There are 1,200 cents in an octave and 100 in an equal-tempered semitone. The ear can just hear about 5.