Chapter OneTechnology and the Piano
In 1774, the Marquise du Deffand asked the French wit and philosopher Voltaire to contribute some verses for her Christmas entertainment. They were to be sung to the accompaniment of a new instrument called the fortepiano. Voltaire sent some verses he pronounced not very good, "but," he continued, "they are good enough for the fortepiano, which is a tinker's kettle" (instrument de chaudronnier). That Madame du Deffand's aristocratic salon would harbor a fortepiano and not a harpsichord in 1774 is unexpected; some decades would pass in France before the former would fully supplant the latter. But it is of more than passing interest that in the year before Voltaire wrote his poor verses, a seventeen-year-old virtuoso from Salzburg named Wolfgang Amade Mozart wrote the first of the piano concertos (in D major, K. 175) with which he would set in train a musical revolution.
Voltaire's sarcasm reflects the estimate in which he held the tinker's plebeian technology. A chaudronnier made and repaired metal objects for household use-the relation of the word to the English "cauldron," a large kettle, is clear enough. Voltaire, to be sure, actually said "a tinker's instrument," but any instrument that a tinker made was as likely to be a kettle as anything else (hence my somewhat free translation of the phrase). The point is that, the kettle being a product of technology, Voltaire dismissed the piano's worth in technological terms. The piano has come a long distance since 1774, but like the tinker's kettle, it is a product of technology, whether low or high. That fact is the subject of this book. The piano's history has been written in terms of several different approaches: the social history of the instrument; its economic history; the piano as the vehicle for music; and the history of pianists and piano playing, which must refer to the instruments. My purpose is to write a technological history of the piano.
The piano is a machine. That may not be the first word that comes to mind to define the instrument, but it is perhaps the most inclusive, and it is the necessary presupposition of our subject. A machine accomplishes work, that is, it applies energy to some end. The piano's energy produces musical sound vibrations.
All sound is vibration in the air. What differentiates music from other kinds of sound is the regularity of the vibrations. There is a great deal more to the physics of musical sound than this superficial statement, but for our purposes at the moment it is enough. The regularity of vibration implies pitch, the "height" or "depth" of the tone, measured by the rapidity of vibration; timbre, or tone quality, a function of the number and relative strengths of subsidiary vibrations, overtones or harmonics, within the fundamental one; and volume, or loudness, a function of the amount of vibrational energy being applied.
The piano differs from other musical instruments in the way it produces sound. In its simplest essentials, the pressure of the player's finger on the key activates a set of levers that flings a hammer to strike strings. The strings, being stretched tight, respond to the hammer's blow by vibrating. The energy of vibrating strings needs amplification in order to be heard. One end of each string passes across a hardwood bridge, which is glued to a large, thin plate of wood beneath it, the soundboard. The vibrations are transmitted from the string through the bridge to the soundboard, which sympathetically reproduces the vibrations over its own wide surface, setting the air in contact with it into vibration.
The piano has, therefore, three essential parts: a vibrator, which produces the sound vibrations, and which in the piano is the strings; an activator, which causes the vibrator to vibrate, and which in the piano is the hammer and the rest of the mechanism attached to the key (technically, the action); and a resonator, which amplifies the relatively weak vibrations of the vibrator, and which in the piano is the soundboard.
Every musical instrument must have a vibrator and an activator, though not every one needs a resonator. The present standard system of classifying musical instruments, based on the kinds of vibrators used, recognizes four classes of instruments. One is the idiophones (from Greek idios, the thing itself, plus phone, sound), in which the vibrator is the instrument itself, for example, cymbals, rattles, and xylophones. A second class, the membranophones, has as the vibrator a stretched skin or other material that, when struck or otherwise disturbed, gives out a musical tone, for example, drums. In a third class, the aerophones, the vibrator is a column of air enclosed within walls (usually a tube), which vibrates in response to the player's blowing into or across the tube. The aerophones are the wind instruments: clarinets, flutes, tubas, pipe organs, and others.
The fourth class of instruments has as the vibrator stretched strings. These are the chordophones (Greek chorde, string). There are three effective ways, and one ineffective way, to start a string vibrating. The ineffective way is to pass air across it, as in the so-called Aeolian harp. The effective ways are by plucking (guitars, banjos, harpsichords), by friction on the string, usually with a bow (violins and their relatives), and by striking (dulcimers, clavichords, pianos). And there we have placed the piano among musical instruments: it is a struck chordophone.
This book investigates technology in the history of the piano. Before beginning on the history, I shall look in some detail at the machinery of the modern piano. This chapter is intended to exhibit the technological problems of the instrument, to establish the nomenclature of its parts, and to show how the parts are related to each other. The rest of the book will follow those technological problems from the piano's beginnings up to the present.
There are two ways of laying out the strings, the piano's essential vibrators: horizontally and vertically. Theoretically one could hang them at any angle between the two, but no experiments in doing so have lasted. The horizontal configuration is represented in the modern day by the grand piano (pictured from directly above in Figure 1.1), the word "grand" originally meaning simply big. The vertical (Figure 1.2) is generically called the upright piano.
Apart from accommodating the string layout, which carries implications for the design of the action, the case (or rim) of the piano is the box that contains the machine. It has two functions with respect to the instrument's work. The opened lid of the grand piano serves as a reflector, directing sound into the room. When it is closed, the instrument may sound somewhat softer or slightly muffled. But the sound of the grand does not come only from the top; as much comes out the bottom, which is not closed in modern grands (in early ones it was). The raised lid does not modify or enhance the tone, but has to do only with available loudness. One can raise the lid of an upright too, with a similar but lesser effect.
The other function is more subtle. The harder the case material, the more efficiently the case acts as a reflector of vibrations across the soundboard. As the vibrations spread out from the bridge across the board, they meet the case at the edge and are reflected back across the board to enhance the resonance. If the case material is relatively soft, it absorbs some of the vibrating energy and fails to enhance the resonance as much, although one famous maker (Bosendorfer) makes its cases of the same spruce as is used in the soundboard and claims that the case is a resonating extension of the soundboard.
The machine itself may be divided into three distinct but interrelated mechanisms, corresponding to the three acoustic functions discussed above: the vibrator mechanism, the activator mechanism, and the resonator mechanism.
The vibrator is the set of strings and what keeps them in place. In most modern pianos, the lowest eight or so notes have one string to each note (what will hereafter be called single-stringing), a quite thick piece of wire composed of an inner core of steel around which a smaller copper wire is closely wound. About the next eighteen notes also have wound wire, and each note has two strings (double-stringing). The rest of the strings are unwrapped steel, and each note has three strings (triple-stringing). Triple-stringing over most of the range is now nearly universal, and the determination of where to begin the double-stringing and single-stringing and where to use wound wire is an element of design. Thus there may be minor variations from one make and model to another. The strings, as can be observed in Figures 1.1 and 1.2, become shorter as they become higher in pitch, and they are also thinner. Again, the lengths of the strings and the gauges of wire used for various pitches are decided by the designer.
Pitch is determined by the string's rate of vibration. The more vibration cycles in a given time, the higher the pitch. To produce vibrations at rates that a human ear can hear, the string must be stretched relatively tightly. Stretched too tightly, it will break, but too loosely stretched, it will not vibrate fast enough to produce an audible sound. The pitch of any string is determined by the combination of its length, the tension with which it is stretched, and its mass or thickness. The shorter the string, the higher its pitch; the greater the tension on the string, the higher its pitch; the smaller the string's mass, the higher its pitch. Any change of length, mass, or tension will change the pitch.
If two strings are under precisely the same tension and of exactly the same thickness, and one is exactly half as long as the other, the shorter string will vibrate exactly twice as fast as the longer and will sound a pitch exactly an octave higher. The octave has a proportion of two to one in frequency, or the rate of vibration. If the longer string vibrates at 100 vibration cycles per second (100 Hz), and the shorter one is an octave higher, its frequency is 200 Hz.
Here, we run into a problem of design. Suppose that the A above middle C([a.sup.1] in the chart of pitches on p. xxv), which has a frequency of 440 Hz, has a vibrating length (technically, speaking length) of 15 inches. If the A an octave below (a) is of the same gauge wire and at the same tension, it must be 30 inches long, the next one down (A), 60 inches, the next (AA), 120 inches. Still another is the lowest note on the standard modern piano (AAA), and under these conditions it would have a speaking length of 240 inches, or 20 feet! This will not do. Here, too, other factors in the pitch of a string come into play, which explains why the lower strings are not only longer but also thicker than the higher ones. In order to avoid too long a string, you must have a heavier one. The strings become longer as the pitches go lower, but not in the proportions necessary if they did not also become thicker.
The lowest strings are wound in order to be as thick as necessary without excessive stiffness. The amount of stiffness in a piano wire is important, because on it depend the overtones in the sound and therefore the tone quality. A string vibrates not only with a motion over its entire length but also with subsidiary motions along parts of the string. The portions of the string, being shorter than the whole, produce higher but fainter pitches. The diagram in Figure 1.3 shows schematically some of the simultaneous vibrations that go on in this complex pattern. The subsidiary vibrations are called overtones, or, more precisely for the piano, partial tones or partials.
The relative strengths of the fundamental tone and of each of the partials determine the quality of sound. Stiffness in a wire is an impediment to the vibration of partials. Indeed, the very top strings are so short and under so much tension that the wire is extremely stiff and produces few partials. To be sure, the frequencies of those upper partials of the high strings begin very quickly to be higher than the ear can perceive. But the lower strings, which are both longer and under relatively less tension than the upper ones, freely produce partials.
Certain of those weaker but still audible tones vibrate at frequencies that make the string sound harsh and out of tune. There is reason, then, to do away with the harsher higher partials. One wants the mixture of fundamental and partials to produce a full, mellow, round tone with a certain amount of brilliance in it. Brilliance, which can be described as a somewhat hard-edged, sharp sound, is produced by relatively strong higher partials. If there are few higher partials, the tone is somewhat thick and fuzzy, perhaps even a bit hollow. If the relative strength of the higher partials is too great, the sound is strident, very hard, and what has come to be called tinny.
The quality of the wires is a crucial factor in timbre. Evenness and regularity of vibration are possible only if the string has the same mass throughout its length, is perfectly round (any tendency toward an oval shape destroys regularity of vibration), and is completely free of twisting. Impurities in the steel itself, of course, will also hinder proper vibration. Given wires of sufficiently high quality, the timbre depends on the relations among the string's length, mass, tension, and stiffness. The ideal string, the string that acoustic theory assumes, has no stiffness, but there is no such object as an ideal string. Every string is more or less stiff, and the greater the tension on the string, the more the stiffness comes into play. Thus a relatively long string in the high treble must have very high tension, whereas a relatively short string in the bass must have less-than-normal tension. A necessary compromise is involved. Up to a certain point of tension, the string's elasticity is improved, and it produces a tone increasingly rich in partials. Beyond that point, however, the increasing tension brings out stiffness, which damps out partials, and the tone goes dead. By careful increase of the gauge (mass) from top notes to bottom, one may end up in the bass with rather thick but not too stiff wires that are both long enough to give a good sound and short enough to fit inside a case of reasonable proportions. In a very small case, the lowest strings must be relatively short, therefore both quite thick-and correspondingly stiff-and under low tension with a correspondingly low elasticity. The resulting tone is considerably poorer than the optimum. For that reason, a "baby" grand may have a less desirable sound than a large upright. The trade-off in design and materials in pianos produces not perfection, but rather a more or less acceptable, sometimes splendidly successful, compromise.
Timbre also depends on other factors. The material of the activator affects tone quality; the harder it is and the faster the blow, the more upper partials are generated in the sound. The point on the string at which the hammer strikes also affects the tone quality. The diagram of partials (Figure 1.3) shows that, as the string vibrates, certain points along it are relatively at rest, because they mark the points corresponding to the partials. These points of relative but not absolute rest are called nodes. One node occurs at the midpoint of the string, because the second partial divides the string into two equal segments. Another set of nodes is one-third and two-thirds of the way along the string, because the third partial divides the string into three. The partials begin to sound a bit out of tune at about the seventh partial, which sounds a slightly flat minor seventh in the third octave above the fundamental. A hammer blow at one of the nodes tends to damp out partials corresponding to that node. The reason is that a node is a relative point of rest in the string, but the hammer blow moves the string to its widest amplitude of vibration, thus canceling out a point of rest there. If the hammer should strike the string exactly in the middle, all of the even-numbered partials will be damped out, because all of them have a node in the middle of the string. Such a tone would be dull and hollow.