CHAPTER VII

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PIANOFORTE STRINGS AND THEIR PROPER DIMENSIONS.

The strings of a modern pianoforte are made of cast steel and possess a relatively great thickness and stiffness. That is to say, they enjoy these characteristics to a far greater degree than do the strings of any other musical instruments that employ such agents for the purpose of generating musical sounds. The strings of any member of the viol family, for example, are so totally unlike those of the pianoforte that no comparison of their respective behavior when subjected to tension can be of interest to any save the scientist. In dealing with the strings of the pianoforte then, we face an isolated and unusual problem which we shall have to consider at some length. We shall investigate the peculiar effects produced by the high tension, great thickness and great stiffness of the strings, as well as the singular phenomena exhibited in the case of the covered bass strings. We shall note that the strings are responsible for many unpleasant things of which they are seldom accused, and that their proportions as to length and tension do not comprehend in themselves the whole problem that the scaling of them presents to the designer. This matter of the internal nature of the steel and other wire has not, unhappily, received that attention to which its importance justly entitles it. No treatment of the principles of pianoforte design could be considered complete, however, without some discussion of the phenomena thus presented. The investigation which we shall undertake will lead us to the development of more of those general principles that we are now engaged in enunciating, and we shall then be able to formulate certain rules of wide application which may be employed in the practical consideration of the problems with which the whole matter of pianoforte design abounds.

As is generally known, the strings that are charged with the duty of emitting the sounds comprehended within the two lowest octaves on the pianoforte are customarily constructed of a combination of steel wire and some other, usually copper or iron. The latter is wound over a core of the former wire, and this winding is graduated, as to the amount and thickness of the material employed, according to the pitch to which it is desired that each string shall be tuned. There is an obvious reason for this procedure. For, as we have already shown, two strings whose lengths are as 2:1 will, other things being equal, emit musical sounds separated by the interval of an octave. Consequently, under perfect mechanical conditions, the length of each string of a pianoforte should conform to the rule thus indicated, and should be one-half or double the length of that which produces the octave above or below it; the absolute application of this rule, however, being subject to certain practical modifications throughout the entire compass. These will be discussed later.

Even in the absence of such considerations, however, this ideal condition could not be attained. The mechanical difficulties presented would always operate to forbid the carrying out of such an arrangement throughout the whole compass of the instrument. For, to follow the rule with entire consistency would necessitate a length of 256 inches for the lowest C, on an assumed length of 2 inches for the highest note of the same denomination. As this would imply a length or height of the instrument of nearly 24 feet it is not difficult to see that such construction is impossible. Furthermore, evenness of tone quality would be seriously hindered if the lowest strings were of any such dimensions. To secure equality of tonal result it is necessary, as has been noted above, that we should be able to equalize, as far as possible, the particular forms of vibration that pertain to each string. Obviously, the nature of the blow that would produce a given form of vibration in a string of 256 inches in length must be very different from that which would produce similar forms in a string only one-tenth as long. Again, to maintain such long strings at the required tension involves mechanical problems that savor more of engineering than of pianoforte building.

For these and cognate reasons, therefore, the practice has arisen of artificially slowing the rate of vibration in the bass strings by wrapping them with brass, iron or copper wire. Naturally, the form of the vibrations excited in these wrapped strings is entirely different from any that the plain steel wire is capable of producing. The iron or copper wire is itself thrown into vibration both independently of and together with the cord of steel, so that we have the phenomenon of one string emitting two separate series of vibrations, with resultant disarrangement of the generated upper partials and concomitant production of beats in a more or less appreciable quantity. Now if, in addition, the bass strings are not scaled with approximate correctness as to their relative lengths, thicknesses, and other dimensions, it follows that there will be two distinct and different causes of dissonance and unevenness of tone-quality, either of which is sufficient, in itself, to produce very unpleasant tonal results. It is clear, then, that particular attention must be paid to the designing of the string arrangement, if excellence of tone-quality is to be anywhere approached.

It is, fortunately, possible to give quite precise directions for the calculating of string dimensions. As a preliminary, we must remind the reader of the rules that were laid down in