Temperament

Temperament is a system of compromise in the tuning of keyed instruments. Though the various intervals of the scale are spoken of broadly as consisting of tones and semitones, the successive tones are not all equal when given in just intonation according to harmonic law—i.e. so that the consonant intervals are in perfect tune; and as every note in the scale may become the keynote of another scale, if all these scales are to be given exactly a complete set of keys for each would be necessary. But it has been found in practice that by only a slight deviation from just intonation a much more limited keyboard, of twelve notes to the octave, gives results which do not offend the ordinary ear, though the discrepancy is distinguishable by a trained one. Up till about the beginning of the 19th century in Germany, till 1835 in France, and 1846 in Britain, the system adopted was that known as mean temperament, by which the intervals in some keys were more exactly in tune than in others; some of the intervals in the less favoured keys, known as wolf intervals, being so unpleasantly out of tune as to cause composers to avoid these keys. This was remedied in a few instances by the use of two divided keys, one of which gave separately D$\backslash sharp$ and E$\backslash flat$, and the other F$\backslash sharp$ and G$\backslash flat$. The present practice, known as equal temperament, makes each tone and semitone in the octave approximately equal, so that every key is equally available; while at the same time every interval except the octave deviates slightly from just intonation. This deviation is more obvious on the organ, or still more the harmonium, than on the pianoforte; but it is of more practical moment in the orchestra, where keyed instruments are heard along with others playing in just intonation. There are many advocates of a system of just intonation, at all events as applied to special instruments; and various keyboards have been invented to obviate the mechanical difficulties. The subject is still a favourite battlefield of theorists. See Bosanquet on Musical Intervals and Temperament, and Helmholtz' Sensations of Tone.