The equal temperament scale of tuning is which the octave is divided into a number of equal intervals. 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.
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. The perfect fourths and fifths are close to pure, not being in uncomfortable harmony, while the major thirds and sixths are quite different from those of pure temperament, which causes a slight loss in harmony.
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 pure temperament.
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