text: Yes.  Because the frequency of the notes are a geometric sequence with a factor of 2^(1/12) between each note, and 2^(n/12) is irrational except for when n is divisible by 12.  There are 12 half-steps in an octave.\n\nThe frequency of A (just below middle C) is 220 Hz.  So the frequency of a note that is one half-step above A is 220*(2^(1/12)).  Two half-steps up is 220*(2^(2/12)).