Equal Temperament

Any system of tuning in which the octave is divided into a number of equal intervals. In western music, the octave is divided into twelve exactly equal intervals called semitones. The semitone represents an interval between two tones whose frequency ratio is the 12th root of 2. This ratio is further subdivided into 100 cents.

Tuning in equal temperament alters the traditional intervals of just intonation, except the octave, which remains the same. The fifth is lowered by 2 cents, which cannot be perceived, but the major third is raised by 14 cents, to which most people are now accustomed. See interval for a comparison of intervals expressed in equal temperament and other tunings; see also Appendix C.

Although clearly formulated by Mersenne in 1635, equal temperament did not become generally established in practice until 1800 in Germany and later in England and France. Its historical importance is that the major and minor scales being used became transposable for all twelve semitones; that is, the scale could begin on any semitone and still consist of the same frequency ratios in the scale. This system allowed musicians to modulate from one key or tonality to any other without sounding out of tune, that process not being practical in a system of just intonation.

Compare: Intonation, Just Intonation, Pythagorean Scale, Temperament, Tempered Tuning. See: Flat, Quarter Tone, Sharp.