music

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.

Interval
Frequency ratio from starting point
Cents from starting point

Unison

1:1

0

Semitone or minor second

1.059463:1

100

Whole tone or major second

1.122462:1

200

Minor third

1.189207:1

300

Major third

1.259921:1

400

Perfect fourth

1.334840:1

500

Augmented fourth/Diminished fifth

1.414214:1

600

Perfect fifth

1.498307:1

700

Minor sixth

1.587401:1

800

Major sixth

1.681793:1

900

Minor seventh

1.781797:1

1,000

Major seventh

1.887749:1

1,100

Octave

2:1

1,200

Scale of equal temperament.

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.

Scale of 12-tone equal temperament.