equaltemperament

Equal temperament is a tuning system in which the octave is divided into equal steps, so that every adjacent pitch has the same frequency ratio. In the common 12-tone equal temperament (12-TET), the octave is divided into 12 equal parts, and each semitone represents a frequency ratio of 2^(1/12). After 12 steps the pitch doubles, completing the octave. This arrangement makes all semitones equal across the keyboard and allows seamless transposition and modulation between keys.

Historically, many tunings sought to preserve consonant intervals such as the perfect fifth or the major third, often at the expense of other keys. Meantone and other temperaments produced varied interval sizes, which caused some keys to sound more in tune than others and could yield “wolf” intervals in certain keys. In the 17th to 19th centuries, temperaments such as well temperament, Werckmeister, and Kirnberger offered compromises. By the 19th century, 12-TET became the standard in Western music due to its practicality for keyboard instruments and its ability to keep keys uniform across the repertoire.

Advantages of equal temperament include the ability to modulate freely to any key, consistent fingering across keys, and straightforward construction for instruments and electronic tunings. Disadvantages include the deliberate deviation of intervals from their pure just intonation values; in 12-TET, the major third and the perfect fifth are slightly tempered compared with their just ratios.

Beyond 12-TET, other equal temperaments divide the octave into n equal parts, such as 19-TET, 24-TET, 31-TET, and 53-TET. Some of these offer closer approximations to just intonation or enable microtonal approaches (e.g., 24-TET includes quarter tones). Despite this diversity, 12-TET remains the dominant standard in Western music and in most modern tuning systems for keyboards and digital instruments.