Twelve-tone equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio (rather than the same absolute change in frequency). In other words, there are equal ratios of the frequencies of any adjacent pair, and, since pitch is perceived roughly as the logarithm of frequency, equal perceived "distance" from every note to its nearest neighbor.
In equal temperament tunings, the generating interval is often found by dividing some larger desired interval, often the octave (ratio 2:1), into a number of smaller equal steps (equal frequency ratios between successive notes). In classical music and Western music in general, the most common tuning system for the past few hundred years has been and remains twelve-tone equal temperament (also known as 12 equal temperament, 12-TET, or 12-ET), which divides the octave into 12 parts, all of which are equal 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. In modern times, 12TET is usually tuned relative to a standard pitch of 440 Hz, called A440, meaning one note is tuned to A440, and all other notes are some multiple of semitones away from that in either direction. The standard pitch has not always been 440 but has varied and generally risen over the past few hundred years.
Other equal temperaments exist. They divide the octave differently. For example, some music has been written in 19-TET and 31-TET. Arabic music uses 24-TET. In Western countries, when people use the term equal temperament without qualification, they usually mean 12-TET. To avoid ambiguity between equal temperaments that divide the octave and ones that divide some other interval (or that use an arbitrary generator without first dividing a larger interval), the term equal division of the octave, or EDO is preferred for the former. According to this naming system, 12-TET is called 12-EDO, 31-TET is called 31-EDO, and so on.
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