Equal temperament

An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent pitches is separated by the same interval. In other words, the pitches of an equal temperament can be produced by repeating a generating interval. Equal intervals also means equal ratios between 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). For 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. 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 pitch is tuned to A440, and all other pitches are some multiple of semitones away from that in either direction, although the standard pitch has not always been 440 and has fluctuated and generally risen over the past few hundred years.