idea
The Pythagorean comma
Start on a note and go up by twelve pure fifths. You pass through all twelve notes of the piano and arrive near the starting note, seven octaves higher. But not exactly: you overshoot by about 23.5 cents, almost a quarter of a semitone. This small difference is the Pythagorean comma. Because of it, an instrument with fixed notes, like a piano or an organ, cannot have all its fifths and all its octaves perfectly pure at the same time.