12 equal temperament

12 equal temperament (12-ET)^[a] is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (¹²√2 ≈ 1.05946). That resulting smallest interval, 1⁄12 the width of an octave, is called a semitone or half step.

Twelve-tone equal temperament is the most widespread system in music today. It has been the predominant tuning system of Western music, starting with classical music, since the 18th century, and Europe almost exclusively used approximations of it for millennia before that.^{[citation needed]} It has also been used in other cultures.

In modern times, 12-ET is usually tuned relative to a standard pitch of 440 Hz, called A440, meaning one note, A, is tuned to 440 hertz and all other notes are defined as some multiple of semitones apart from it, either higher or lower in frequency. The standard pitch has not always been 440 Hz. It has varied and generally risen over the past few hundred years.^[1]

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