Equal Temperament By Young, Gayle
Equal temperament is a musical tuning strategy which deals mathematically with musical intervals in order to allow perfect transposition; it replaced the Pythagorean approach. The octave can be divided into equal steps of many different sizes, ranging from step sizes larger than the standard 12-tone equal temperament (such as five, seven, eight, or ten equal steps per octave) to much smaller step sizes. Calculations of the sizes of intervals use ‘cents’, with each of the 12 semi-tones described as a 100-cent interval. There are 1,200 cents in every octave. Pitches organised in 24 equal steps are referred to as quarter-tones, each 50 cents. Some composers prefer to work with multiples of 12, such as 36-tone (33.3 cents), 48-tone (25 cents), and the division of the octave into 96 equal steps of 12.5 cents, as proposed by Mexican composer Juliàn Carillo. Many composers work with seemingly arbitrary divisions of the octave, such as 19-tone (63.2 cents) and 31-tone (38.7 cents). These tunings include pitches that come close to key intervals in just intonation (see below). The advantage of using an equal-tempered tuning to access these tunings is that any equal-tempered pitch structure can easily be transposed.