REED, FLUE AND STRINGED IN STRUMENTS, TEMPERAMENT, TUN ING AND VOICING OF. Temperament.— The intervals of the perfect octave are divided naturally into 53 parts or commas, the succes sive sounds of the diatonic scale being separated by these commas into the following intervals: Naturei arbitrary division of the octave, into intervals of exact dimensions, is not satis factory, nor does it admit of an exact equaliz ing; the only possible approach to it being by the method known as the seven temperament,' which method or principle was discovered and established by John Sebastian Bach, in the early part of the 18th century, who learned that cer tain intervals would bear being tuned sharp (in excess of) or fiat (short of) perfect; the thirds and fourths being tuned sharp and the fifth tuned flat of perfect, thus distributing among all the 12 keys of the octave, the three commas or points by which the major tones exceeded the minor, thus rendering equal the five tones in the diatonic series. Previous to this time, it had been the custom to tune to perfect inter vals, those keys having not over three or flats and play in those keys only. The prob lem to be solved was to so divide the octave into 12 semitones by fixed sounds, that each one of the 12 sounds could be made the key note which a properly proportioned dia tonic scale could be based, either in the major or minor form, and a melodic or harmonic pro gretision made possible through the whole 24 major and minor scales; so that from any one of these 12 notes a uniform chromatic scale could be constructed, thus making possible modulations of unlimited variety and beauty.
The method then of tempering the notes of keyed instruments consists in arbitrarily ad justing the enharmonic thesis, that is, the dis tinction there is naturally between D sharp and E flat, G sharp and A flat, by tuning these notes too sharp for one and too flat for the other of these natural tones or intervals, and by making a similar compromise between the more minute discrepancies of the diatonic scale. Thus while no interval will be exactly true, yet none will be so adjusted as to shock the ear by false intonation, but rather add a color or quality to the tonality of the instrument, which, though harmonious, would otherwise be characterless.
Rule for Tempering Pianos and Organs.— Tune middle C to desired pitch, then tune F fifth below —sharp of C, until between C and F, there result three beats in five seconds. Next tune A-sharp — fourth above F-sharp of the latter, until there results one beat, each second. Next tune G— fourth below middle C— flat of C, by one beat a second; then tune D — fifth above—flat to G, by three beats in five sec onds; A— fourth below—flat to D; E— fifth above — flat to A; B — fourth below — flat to E; F-sharp— fourth below—flat to B; C sharp— fifth above—fiat to F-sharp; G-sharp — fourth below — flat to C-sharp; II-sharp fifth above—flat to G-sharp, which will make D-sharp as sharp of A-sharp, as the latter is sharp of the first F tuned.
In all the above intervals, the fifths beat three times in five seconds; the fourths beat once a second, or five times in five seconds. All the 12 notes, from F beloiv middle C to first E above, have now been tuned; the temperament has been confined to the smallest possible com pass to lessen the liability of errors, and if the first F above middle C is now tuned three beats in five seconds, fiat of A-sharp below, it will be a perfect octave to the first F tuned.
Tuning.—The art, principle or act of so adjusting the intonations of keyed musical in struments as to make possible consecutive mu sical tones agreeable to the ear. The method varies according to the kind or character of the instrument. Where strings are used, as in pianofortes, harps, violins, violas, guitars, zith ers, etc., tuning consists in adjusting the ten sion of the strings by turning the pins or pegs around which the strings are wound. In band and orchestral wind instruments, a crook or Joint is used, sometimes called a slide, because it slides in and out to adjust the length of the column of air in the tube to the point where the desired pitch of the fundamental note is obtained.