How does 12-tone equal temperament divide an octave?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

In equal temperament, the octave is divided into 12 semitones of equal size.1

This system functions as a "divisional" tuning method where each semitone is measured at 100 cents, with one cent defined as 1/1,200 of an octave. Mathematically, each semitone step increases in frequency by a factor of the 12th root of 2, which is approximately 1.059. By the time the 12th semitone is reached, the cumulative multiplier equals 2, effectively completing the octave.1

This approach ensures that intonational defects are distributed equally across the chromatic scale, allowing keyboard instruments to play in all keys with only minor adjustments to pure intervals, such as narrowing the perfect fifth by 2 cents.1