If a piano tuner starts by tuning a C, then tunes a G so that it is exactly 1 ½ times the frequency of the C, he can continue tuning in fifths (a D, then an A etc.) until he arrives back at C again. However, he will find that, for mathematical reasons, the last C is not in tune with the first C. This was discovered long ago by Pythagoras and is called “the comma of Pythagoras”.