The keyboard of the piano, with each octave divided into 12 equal steps, and with the upper note of each octave exactly doubling the vibrations per second of the one below, might seem a reflection of mathematical symmetry, but it's actually a subtle perversion of it. Medieval musicians discovered that some mathematically "perfect" harmonies were so painful on the ear that they dubbed them "wolf" tones, and avoiding "wolves" became an important part of the composer's task. Handel split the octave into so many finely graduated steps that wolves were largely eliminated. Finally it was found that by slightly sharpening some notes and slightly flattening others, a system known as "equal temperament" could eliminate them entirely. JS Bach's collection of 48 preludes and fugues, which range through all the keys, was the first big celebration of this system: hence its title, The Well-Tempered Clavier.