This equalization is, of course, only approximate. For the forms of vibration excited in two strings of the same pitch will be different whenever the various factors that govern the emission of sound by them are variable. Thus when the factor of length is varied, no counter-adjustment of tension, thickness or density can restore to the string so modified the exact form of vibration that it may have originally possessed. Consequently it becomes impossible to induce from artificially weighted strings precisely the same series of partial tones that a plain wire filament will emit, even when the tones generated by the two strings are of the same pitch.
The lesson of this is plain. As perfection of tonal quality can only be attained in part, it especially behooves us to pay strict attention to such scaling of the bass strings as will furnish a complement of sound producing agencies that may be relied upon to induce as nearly as possible the same successions of partials as are habitually emitted throughout the higher sections of the piano. Thus it becomes evident that the greatest practicable length and the least practicable weight are the chief factors that must govern the designer in laying out the scale for the bass strings.
The relative densities of the wrapping material employed in the manufacture of bass strings have been the subject of considerable study. Brass, which was the earliest object of experiment, has long been superseded by either copper or iron. As to the relative advantages possessed by these two materials, it can be said at once that the chief and almost the only advantage presented by the latter lies in its relative cheapness. Acoustically, however, copper forms by all means the most suitable material for the winding of bass strings, and this for the following reasons: The specific gravity of copper is 8.78, while that of iron is but 7.78. Again, the former metal, while inferior in tenacity to the latter, possesses, on the other hand, the great advantage of higher ductility, so that its elastic qualities are very marked. It is thus evident that copper is a more suitable material for the generation of musical sound than is iron, and the qualities which we have just noted as pertaining to it are precisely those most useful in the production of harmonic progressions of partial tones. It is therefore clear that as between copper and iron all the advantages lie with the former.
The thickest wire used for the uncovered strings is generally No. 24. In beginning the scaling of the bass strings, however, we choose No. 17 or No. 18 for the notes nearest to the treble. The covering is usually from No. 25 to No. 28 (standard, not music, wire gauge) according to the size of the piano and the practicable string-length. Of course, longer strings may be covered with lighter wire. The first covered string is generally approximately one-sixth shorter than the string immediately above it. This proportion, as suggested above, may, however, be profitably disregarded, if it thereby be possible to lengthen the bass strings. There are always two of these strings to each tone and the thickness of covering wire must be progressively increased as the scale descends. A descending increase of one number in thickness of the covering wire for each pair of strings may properly be allowed, unless the lengths are too closely alike, or vice-versa, in which cases suitable modifications may be made. But assuming that the descending lengths are arranged in arithmetical progression with a mean of 3⁄4 of an inch, and supposing the highest covered string to be 45 inches long; then the suggested increase of thickness should under all circumstances hold good. It may often be found, however, that the space limitations of an instrument or other practical considerations make it impossible to follow out these rules with exactitude. In any case, we must remember that all such rules are themselves the fruit of empirical observation and to such observations we must look, when it becomes necessary to revise them in order to satisfy the requirements of some particular situation.
CHAPTER VIII.
RESONANCE AND THE RESONANCE-APPARATUS OF THE PIANOFORTE.
We have now made a somewhat lengthy and thorough investigation into the nature and behavior of the various materials and substances that are employed in the construction of pianoforte strings. From this inquiry we have been able to deduce a set of rules which, when practically applied, will furnish us with a guide to the solution of many perplexing problems which take their root in the conditions imposed upon the designer by the limitations of space and the other mechanical conditions of pianoforte construction. It would not be proper, however, to proceed forthwith to the practical questions of support for the strings. For we must still find the correct solutions of another series of problems that spring, not from the strings themselves, but from their important and necessary accessories, the sound-board and belly bridges.
The belly-bridge is the medium of connection between the strings and the sound-board. Through it the vibrations excited in the strings are conveyed to the freely vibrating surface of the sound-board, and the sonority of the generated sounds is thereby enormously increased. This is the process in bare outline, but, in order to obtain a proper view of the matter under discussion it will be necessary to examine the phenomena to which the juxtaposition of strings, bridge and sound-board give rise. We must, in fact, make another brief excursion into the realms of acoustics.
The property which the sound-board possesses of reinforcing and emphasizing the sounds generated by the strings is called “resonance.” Important as this property of sonorous bodies is to musicians and the makers of musical instruments, the fact remains that it is a matter very little understood by the mass of them. This is the more remarkable when one considers that, without resonant properties, no musical instruments would be possible. For it is not difficult to perceive that music, as we know it, could not exist were the means of expressing it limited to the actual and immediate bodies that perform the motions which are the direct causes of musical sounds. This fact is most clearly illustrated in the case of the pianoforte. The unaided sound of a pianoforte string is ridiculously feeble; in fact, it is quite inaudible at the distance of a few feet. Yet we are all familiar with the wonderfully harmonious and powerful sounds that the same string will be the means of producing when aided by the sound-board.