The 12-Note System

Western music divides the octave into 12 equal steps called semitones. Each semitone multiplies the frequency by the twelfth root of 2 (approximately 1.0595). This equal temperament system is a mathematical compromise — no interval except the octave is a perfect ratio, but every key sounds equally good.

Before equal temperament, pure-ratio tunings sounded out of tune once you changed key. Bach's Well-Tempered Clavier — pieces in all 24 keys — proved you could roam freely across them. But "well-tempered" meant an unequal tuning, not today's equal temperament, standardized long after his death.