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Logarithms and cents
Since intervals combine by multiplying, it is hard to compare their sizes directly. Logarithms help, because they turn multiplication into addition. Musicians use a logarithmic unit called the cent. An octave is 1200 cents and each semitone of the piano is exactly 100. A pure fifth, ratio 3:2, is about 702 cents, and the piano's fifth is 700, so they differ by two cents, a fiftieth of a semitone. Most listeners only start to notice differences of around five to ten cents.