Twelve-tone equal temperament is a tuning system that divides every octave into twelve tones, all of which are spaced equally on a logarithmic scale, with a ratio equal to the twelfth root of 2 (which is approximately 1.05946). The resulting interval, 1⁄12 the width of an octave, is a semitone.
Musicians have been aware of equal temperament since ancient times, and it became dominant in Western music several hundred years ago. Its main advantages over other tuning systems are a convenient fit for conventional keyboard layouts and complete harmonic freedom; its disadvantage is a small amount of harmonic impurity for each interval.
In recent decades, twelve-tone equal temperament is usually tuned relative to a standard pitch of 440 Hz for the note A, and all other notes are defined as some multiple of semitones from it. The standard pitch has varied over time and has generally risen over the past few hundred years.