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Since the time of Bach evenly tempered scale containing 12 semitones in each octave is used in music. If the string length l (for a given tension) produces a sound "do" the first octave, corresponding to the frequency f, equal to 512 vibrations per second, the string length 
(stringed instruments, this length is obtained by pressing a finger in the appropriate place) makes a sound, having frequency 
(original fifth), and the string length 
produces a sound having a frequency 2f (octave). Our ear when comparing two sounds captures not the attitude of their frequencies, and the logarithm of this ratio. Naturally just take the binary logarithm to one octave interval was measured as a unit:
Why is there the division of octave to 12 intervals? To make octave and natural quint fit into the same equal temperament (the division of the octave into equal intervals by ear), octave should be divided into so many parts to make number of 
close to the selected fraction denominator. Suitable fractions among
will be shot
Approximation 1 and 1/ 2 is too rough. Approximation 3/5 corresponds to the pentatonic that existed among the peoples of the East, and the approach of 7/12 - the most suitable. Error
audibly indistinguishable.
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| Usage in physics. | | | Usage of the continued fractions in other spheres |