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.
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.
The reinforcement of the board is accomplished by gluing ribs of
wood across its back surface in a direction crossing the grain of
the board. These ribs are usually made about one inch square in the
middle portions. This size is continued until near the edge of the
board on each side, when they are gradually pared down in a graceful
curve until at the actual edge the thickness is no more than about
one-thirty-second of an inch. According to the most approved modern
practice it is found advisable to pocket these ribs into the wooden
framing of the instrument, by continuing them past the edge of the
sound board and making suitable apertures in the framing, into which
the extensions are adjusted and fastened. This has the effect of
holding the board more firmly in its fastenings and also of preventing
the early loosening of the ribs from their places; an occurrence which
causes much rattling, and complete impairment of tonal quality. It is
usual to have twelve ribs upon the surface of the board, but the number
may be varied whenever it is considered necessary. If it is required to
give specially ample support to the board on account of unusually great
strain, or for any other reason, the number may be increased, but such
procedure must be taken with caution, as too many ribs weight the board
to such an extent as to deaden its power of molecular and undulatory
vibration. This must at all costs be avoided.
It is usual to glue the ribs upon the surface of the board first--that
is before the bridges--and good practice dictates that the surface
of the board be dried out in a hot-box for at least 24 hours before
either of these processes take place. If this be carried out properly,
the resultant shrinking of the wood will be taken up after the board
has become thoroughly cooled, and if the process is repeated when the
board is glued into the framing of the instrument, the result will be
to endow it with a natural “crown,” or arch, caused by the re-active
swelling that takes place after the artificially induced shrinking.
Although the above methods of ribbing are to be considered the best and
as representing the most advanced practice, yet it will be found that
some makers dispose the ribs in a fan-like manner, having the diverging
points of the fan at the upper end of the board, while others adopt an
oblique disposition and arrange them as before described. Also, we find
a straight up-and-down arrangement whereby the ribs are glued parallel
to the plane of the treble strings. We term these three styles the fan
form, the oblique form, and the vertical form respectively.
As for the comparative advantages of the three types of construction
thus described, it may be said that they all represent individual
features that are more or less beneficial. For example, the fan-like
disposition gives a greater number of long ribs, while the oblique form
provides more of separate units. The vertical system may be considered
as a mean between the other two.
In general, we shall be well advised in remembering that the prime
function of ribbing is to increase the tension of the board and its
elasticity, and thus to promote the power of resonance. A secondary
function is that of providing extra resisting power. Now it is obvious
that both of these duties can be better performed by a multiplicity
of ribs, and consequently a system is to be recommended that permits
the employment of the largest total area of ribbing. At the same time
unduly long ribs are not good, for they have a greater tendency to
become loose and to spring up from the surface of the board, with
dire results to tone and durability. It would therefore seem that the
oblique disposition has more to recommend it than the others, since it
provides enough total ribbing area without imposing inconveniently long
ribbing units upon the surface of the board.
When the ribbing of the sound-board and the fixing of the bridges has
been accomplished, it remains to adjust the completed structure within
the wooden back-framing of the instrument. It is necessary that the
board be so secured that it shall acquire a position analogous to that
of a stretched membrane--at least as far as concerns the rigidity with
which its edges are fixed to the framing. There are several methods for
obtaining the required rigidity of the edges of the board. The natural
or artificial crowning of the board’s surface is best attained through
the medium of particularly rigid edge fastening; and the adoption of a
continuous closing rim for the board, as in certain grand pianofortes,
together with the use of a system of screw compression, alike indicate
the various directions in which the ideas of experimenters have led
them. The underlying notion in all these devices is to endow the
vibrating surface with both elasticity and durability to an extent that
could not be attained with the unaided wood.
The gluing of the sound-board to the framing is a process that demands
the greatest skill and care. It is essential that the board be warmed,
and that the glue which is used be in just the proper condition;
neither too thick nor too thin, and, above all, boiling hot. If the
fastening be done when the board is in the shrunken condition described
above, and with the required skill and care, it will be found that
the fibres of the wood have been squeezed together so as to raise
the center part of the board somewhat above the level of the edges.
This gives what we have denominated the “crown,” and is important as
affecting the durability and resisting power of the entire board. It
must be remembered that by relieving the sound-board of as much as
possible of the strain imposed by the strings, we are able to increase
its durability and to preserve its tone-producing quality more surely
than is otherwise possible. Boards that are not so protected must
inevitably become entirely flattened out in the course of a few years.
When this happens the level of the belly-bridge sinks and the bearing
of the strings upon the latter is destroyed. Hence an immediate and
inevitable deterioration of tone quality. For the altering of the
level in this manner affects the impression of the vibrations of the
strings upon the bridges and hence upon the board itself. If the
height of the bridges be too great, the bearing of the strings upon
them will likewise be excessive, and the board will be crushed down in
the same manner. If, however, the directions as to bridging, ribbing
and adjustment that have been given are followed with discretion, the
troubles outlined here are likely at least to be minimized.
Of course, the later care of the pianoforte after it is sold has much
to do with the manifold troubles that occur within the entire resonance
apparatus. These things cannot be foreseen, and it is, therefore,
most essential to guard against them as much as possible by careful
attention to the details of construction and adjustment.
Lastly, we may observe that the practice of screwing the bridges down
on to the board by screws driven in from the rear is to be condemned.
While it is undoubtedly advantageous to take some measure to increase
the permanency of the fastening, it will be found that it is far
better, acoustically, to provide the bridge with wooden dowels and glue
these into suitable holes in the board. Thus the conducting power of
the bridge is increased and the vibrating surface of the sound-board is
not broken up by the insertion of foreign metallic substances. Another
and concomitant advantage is the absence of the wooden washers under
the heads of these bridge-screws. Such devices are too often, as they
become loose, a source of rattling and jingling.
It is well to be rid of them, as of all possible things that are
likely to be similarly affected by wear or atmospheric conditions.