PIANOFORTE MANUFACTURE. There are eighty eight notes in the full compass keyboard of the pianoforte, which gives a range of 7 4 octaves. The fifty-second note from the bass end of the scale is called "Pitch C," and serves as the standard from which all the others are tuned. Since each note has to vibrate twice as fast as the note of the same an octave below, and there are twelve semitones to the octave, it follows that the semi tone ratio from note to note must be the twelfth root of 2, namely 1.05946, which is a geometrical progression giving the now gen erally adopted "equal temperament" tuning. Purely mathematical considerations make it essential that the string lengths should also proceed in geometrical progression, but in a slightly smaller octave ratio than In Germany the ratio most favoured is 1.875:1, and in Great Britain 1.89:1. Both of these ratios approxi mately allow of half-size increases in the gauge of wire used, twice per octave, without departing far from the uniform tension initially decided upon. The English Music Wire Gauge advances one-thousandth of an inch in diameter per half size, while the New Westphalian Gauge advances 0.025 millimetre per half size, but there are irregularities in the English Gauge at various places, for reasons apparently unknown.
In small instruments, whether Brands or uprights, it is im possible to carry theoretical string lengths throughout the piano, and compromises have to be made by shortening and thickening them in order to maintain the necessary high tension. Since short and thick strings give a different and inferior tone quality it must not be expected that small instruments will give a pure and balanced "timbre" throughout the scale.
Cold drawn steel wire of the highest quality is specially made for the pianoforte industry, with a breaking strength of about I5o tons per square inch. Three types are now in favour, the polished, the plated and the rust-resisting. The last has been suc cessfully developed, and is especially useful for export models.
are always between 5.o and 5.5 centimetres in length, the shorter length being used for small instruments. From this starting point the succeeding lengths are calculated mathematically until it becomes necessary to employ heavier strings weighted by means of one or two layers of copper wire closely and tightly spun upon them. In order to gain in length and to fix the bridge to a sensitive part of the sound-board, well away from its edges, about fifty of the bass strings (12 singles and 19 bichords) are planned to cross over the others, reaching to a separate and higher bridge. This method of "overstringing" is now general in all but the cheapest pianos. The lengths of the copper-covered strings are not cal culated mathematically but are made so that the lowest note is as long as possible. Additional length is often secured by means of a "suspended" bridge, as shown in fig. 1, which transmits the vibrations of the bridge to a point which should be at least six inches from the edge of the sound-board.
It has been found that a tension of about 160 lb. is advisable for the uncovered strings, and the diameter of wire is calculated from the after which the nearest gauge to this nl diameter is selected, it being impracticable to manufacture a different diameter for each note. In the formula, "n" is the number of vibrations per second, "T" the tension in lb., and "1" the length of the vibrating portion of the string, in centimetres.
For the copper-covered strings some makers employ the formula 'Nt 20,00o which gives the all-over diameter of the required nl string. Others calculate the weight per centimetre instead of the iii,25o T diameter, using the formula afterwards spinning strings of the required weight, as found by experimental determinations. For bichord bass strings a considerable increase of tension is pro vided, varying from 1 o to 15%, and for the single bass strings a further increase of 15% and upwards, according to the size of the instrument.