12ET

Twelve-tone equal temperament (12ET) is a tuning system in which the octave is divided into 12 equal steps, or semitones. Each adjacent semitone multiplies pitch by the same factor, the twelfth root of two (approximately 1.05946), so an octave spans a factor of two. Because the octave is the basic repeating unit, there are 12 pitch classes within each octave, often designated as C, C sharp, D, D sharp, E, F, F sharp, G, G sharp, A, A sharp, and B.

In 12ET, enharmonic notes such as C sharp and D flat are considered the same pitch class, which allows consistent transposition and modulation across keys. The standard tuning reference used in many contexts is A4 = 440 Hz, though exact concert pitch varies by ensemble and locale.

History and adoption: 12ET emerged from earlier temperaments that aimed to balance purity of intervals with key flexibility. By the 18th and 19th centuries, it became the dominant tuning in Western classical music, particularly for keyboard instruments, because it enables smooth modulation and uniform intonation across all keys. It gradually supplanted many meantone and other temperaments, which favored some keys over others and produced wolf intervals.

Applications and implications: 12ET underpins most modern Western music, providing a fixed framework for scales, chords, and tuning across instruments. While it offers practical consistency, it compromises some interval purity compared with just intonation, a trade that has prompted ongoing exploration of alternative tunings and microtonal systems.