Resonance may be defined as the property which one sonorous body possesses of impressing its vibrations upon another sonorous body. The existence of this power may be demonstrated in a variety of ways. The most simple proofs are afforded by the pianoforte itself. For example, if we strike any key upon the instrument and at the same time gently press down the corresponding key one octave higher, so as to raise the damper without at the same time raising the hammer, we shall find that if the first key be released while the other is held open, the string corresponding to the latter will continue to give its proper sound. In this case the vibrations excited in the first string travel along the belly-bridge until they reach the nearest open string whose vibration rate is synchronous with that of the original sounding string. When such a string is reached it is immediately impressed with the motions excited in the former string, with the results above described. This is a case of resonance of two attached bodies. Peculiar as it may seem, however, it is not essential as a preliminary condition to the existence of resonance between them that two sonorous bodies be tangibly connected. For instance, the foregoing experiment may be varied by employing two pianofortes and choosing one of the sounds from each. The result will be precisely the same. It will, however, be noted that only such sounds as have either synchronous or nearly synchronous rates of vibration will exhibit the phenomena of resonance when separated from each other. Where they are connected, however, especially when the connecting body is a sound-board prepared for the purpose, synchronism is not necessary. In fact, it is a matter of common observation that the sound-board of the pianoforte, in conjunction with the belly-bridge, operates to set up more or less intense vibration in every string within the compass of the instrument when the dampers are raised, even if only one string be struck. When the damper pedal is raised in playing, every string throughout the instrument is immediately thrown into a state of vibration, and begins to sound. The result is a large augmentation of the total volume of sound produced. Of course, the sound of any one string thus sympathetically excited is relatively feeble, but the total volume is considerable, with especial strength in the particular partials of each string that are more or less synchronous, as to their vibration rates, with the sounds originally produced by striking the keys. When the dampers are permitted to rest in their normal positions, on the other hand, the sound-board exercises its resonant powers in a different manner. Whenever a string or group of strings are struck, the board is thrown into a state of vibration which affects only itself and not the strings that remain damped. The result of this excitement is to expose a relatively great vibrating surface to the atmosphere, with the immediate consequence that the quantity of air impelled into a state of periodic motion is multiplied many times. Thus the size of the impelled layers of air, and the resultant sonorous waves is augmented until we obtain sounds of the intensity and richness which we are accustomed to associate with the pianoforte.
Now, from what we have already learned of the laws of tone-quality, it is obvious that the resonant medium must be capable of reinforcing not only the fundamental but the partials of all the tones which it influences. To this end we must provide a substance that combines elasticity with the freedom of vibration that is, of course, essential. It is not possible to employ metal on account of its excessive stiffness and consequent resistance to the influence of impressed vibrations; while on the other hand a wooden body will not be sufficiently stiff and rigid unless artificially strengthened. For this reason it is customary to construct sound-boards of a freely-vibrating wood (the spruce-fir is generally employed for this purpose) and to strengthen them by fastening to one side bars of hard wood called “ribs.” In this manner the requisite stiffness is imparted to the board, which at the same time is sufficiently susceptible to the impressed vibrations from the strings.
It is a fact that this accepted and universal form of resonance table is essentially similar to that which was used in the ancient harpsichord and spinet. While there has been much experimentation along these lines, it does not appear that any lasting improvements have been devised as yet, at least in the governing principles of sound-board construction. We may then confine ourselves to a description of the accepted styles.
The wood used in the construction of sound-boards is the spruce-fir, which, as stated above, has been found to be the best possible for the purpose. It is prepared in a sheet of suitable size, and is arranged so that the grain runs approximately at right angles to the plane of the belly-bridge.
It can easily be understood that the thickness of the board must vary according to the dimensions of the strings that act upon it. In other words, we can perceive that more resonating power is required for the relatively weaker treble strings than for the relatively stronger bass strings. The actual thicknesses vary with individual makers. From 3⁄8 inch in the treble to 1⁄4 of an inch in the bass may be regarded as a fair approximation. Nevertheless, it is necessary to bear in mind that these dimensions are subject to modification according to the variations in the total amount of tension that the instrument is made to bear. Other things being equal, an increased tension load implies a thicker board, and vice-versa.
After the dimensions and material of the board are thus determined, it remains to consider the bridging, the reinforcement, and the adjustment of the board. We shall consider these in their natural order, as given above.
The belly-bridges are placed upon the surface of the board, as we know, for the purpose of conveying to the latter the minute blows that are inflicted by the vibrating strings, in order that the vibrations may be impressed upon the board and there amplified and intensified as described at the beginning of this chapter. A secondary duty is that of delimiting the lower boundaries of the speaking length of the strings. The bridges must naturally be constructed with a curved outline that is determined during the draughting of the scale. The actual shape of this curve has no effect per se, upon the activities of the bridge, but has to do entirely with the string lengths. The bridge which carries the overstrung portion of the scale may be considered as being similarly affected, as to outline, by the exigencies of the bass string dimensions. The bridges are made of hard wood, and their sizes are usually from one inch and one-quarter to one inch and one-half high, and in width about one-eighth of an inch less all round. The variations occur principally on account of the necessity which arises of giving a bearing to the strings as they cross over the bridges.
It is necessary that the strings be raised at the bridges in order that they may be firmly held at the points of contact by means of the strain imposed by them on the surface of the bridge when they are stretched at proper tension. Of course it is most essential that this bearing be not too high, as in that case the strain becomes too much for the board to bear with facility and its durability is thereby impaired. The necessary immobility of the portions of the strings that lie upon the bridge is secured by diverting the line of travel, and causing them to bear against pins placed on either edge of the bridge, so as to slant the line of the string as it passes over. The waste ends should run parallel to the speaking-length after the bridge has been crossed.
It may be further properly remarked that there are interesting and complicated problems to be overcome in choosing the material and the exact method of building the belly-bridges. It is desired to combine extreme facility of vibration with the requisite resisting power. In other words, the bridge must allow the fullest possible scope to the impressed vibrations from the strings and, at the same time, must possess such strength that it can successfully resist the torsions imposed upon it by the pull of the strings. The only method that appears to be thoroughly practical and, at the same time, acoustically correct is one which most manufacturers have already had the acuteness to adopt. The bridge, according to this method, is built up of a number of layers of hard wood (generally maple) which are glued together in such a way that the grain of each layer crosses that of the other. In this way both the requisite strength and more or less facility of vibration are obtained. But it has remained for one distinguished piano maker to go a step further, and to apply thoroughly scientific methods to the design of the belly-bridges. In the instruments made by him, he has built the bridges in such a way that the impressed vibrations will travel in the line of the grain instead of across it. The bridges, in fact, are built of end-grain and not, as is general, of cross-grain wood. This ingenious and simple device facilitates the passage of the impressed vibrations and, in consequence, tends to impart a greater clarity to the various partials of the compound tones. Some existing pianofortes might be greatly improved as to their clarity of speech if a similar device for increasing the power of resonance were fitted to them.
There is another point to be emphasized in reference to the bridges. In some makes of pianos the line of the bridge construction is permitted to be broken wherever there is a corresponding break in the hammer line caused by the interposition of the various braces of the iron frame. The obvious result of such a method of construction is that the resonance of the board is much interfered with and the consequent tonal efficiency of the instrument lessened. For it is easy to see that if the bridge line be broken at any point, the vibrations that are carried from any sounding string along the bridge to the surface of the sound-board will be stopped at the break and will be unable to reach those parts of the board that are remote from its path, with rapidity and ease. Incontestably, therefore, the bridge line should, if possible, be continuous. Many manufacturers, however, while apparently recognizing the force of this proposition, seem to be afraid to follow it out to its logical conclusion. They are willing to make the line of bridge continuous until the end of the plain wire strings is reached. After that point they seem to think that it is no longer necessary that continuity of communication between the various sounding members of the scale should subsist. This idea is, of course, quite fallacious. The bass strings are simply a continuation of the higher ones, and are, in fact, precisely similar except in regard to the details of thickness and length. Moreover, it is quite as important that the portions of the board over which the bass bridge exercises control should be made freely resonant, as it is that this process should be applied to the others. The bass bridge ought invariably, therefore, to be connected with the bridges that serve the rest of the strings.