12TET

12TET, or twelve-tone equal temperament, is a tuning system that divides the octave into 12 equal steps called semitones. Each successive semitone multiplies the previous frequency by the twelfth root of two, about 1.059463. Because the octave represents a 2:1 frequency ratio, the frequency of any note can be calculated as f = f0 × 2^(n/12). In 12TET, notes separated by octave are given the same name across octaves, and enharmonic pitches (for example, C♯ and D♭) are identical.

The system yields an equal, logarithmic spacing of the 12 semitones, which enables consistent transposition and modulation to any key. It also provides uniform seconds per octave, simplifying instrument design and keyboard layout, especially for keyboards and electronically tuned instruments.

History and adoption: prior temperaments, such as just intonation and mean-tone, tuned intervals more purely in some keys but sounded out of tune in others. Equal temperament gained prominence in Europe from the 18th into the 19th century and became the standard tuning in Western classical and popular music, facilitated by keyboard instruments and later electronic tuners. Modern concert pitch commonly uses A4 = 440 Hz, though others such as 435 Hz are used in some contexts.

Limitations and alternatives: 12TET sacrifices perfectly pure intervals found in just intonation, producing slight deviations in some chords. Some composers and theorists explore alternative systems (e.g., 19-TET, 31-TET, or microtonal tunings) to preserve different tunings or to explore new sonorities.