Varieties of equal temperament

12-tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending^ⓘ

An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same. This system yields pitch steps perceived as equal in size, due to the logarithmic changes in pitch frequency.

In classical music, the most common tuning system since the 18th century has been an equal temperament that divides the octave into 12 parts. The system uses a logarithmic scale with a ratio equal to the 12th root of 2, ( ${\textstyle {\sqrt[{12}]{2}}}$ ≈ 1.05946). That resulting smallest interval, ⁠1/12⁠ the width of an octave, is called a semitone or half step.

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

Other equal temperaments divide the octave differently. For example, some music has been written in 19 TET and 31 TET, while the Arab tone system uses 24 TET.

Instead of dividing an octave, an equal temperament can also divide a different interval, like the equal-tempered version of the Bohlen–Pierce scale, which divides the just interval of an octave and a fifth (ratio 3:1), called a "tritave" or a "pseudo-octave" in that system, into 13 equal parts.

For tuning systems that divide the octave equally, but are not approximations of just intervals, the term equal division of the octave, or EDO can be used.