Three Essays on the Fundamentals of Piano-Playing


In 1937, Cambridge University Press published a book, Science & Music, by the noted physicist, Sir James Jeans, in which he presented in lay terms the known mathematical and physical foundations of music. Among other things, he denied the claim of the pianist that the quality of sound can be affected by the way the key is depressed.

"In reply, the untemperamental scientist points out that, in striking a single note, the pianist has only one variable at his disposal - the force with which he strikes the key; this determines the velocity with which the hammer hits the wires and once this is settled all the rest follows automatically." (p.98)

"To put the matter beyond doubt, three American scientists, Hart, Fuller and Lusby, have recently made records of the sound curves of single notes played by well-known virtuosi, and also of the same note played by letting a weight fall on the keys. Two pairs of such curves are shewn in Plate IV. In each case the upper curve records the note played by the professional, the lower curve that played by the falling weight. No visible difference can be detected." (p.99) Because of the widespread readership of the book and the prestige of Sir James, this conclusion appears to have been accepted as gospel by physicists and others, - even a few musicians, including Paderewski, - up to the present day.

In the April, 1979, issue of Scientific American, the physicist, G. Weinreich, replied to a letter to the editor about his recent article on the acoustics of the piano. He stated flatly that Hart, Fuller and Lusby had 'proved' that the pianist had no control of tone. As recently as 1996, in a letter of rejection from the American music magazine, Clavier, the editors stated that the manuscript "does not reflect the publication's outlook regarding tone, i.e., that tone cannot be changed." The perpetuation of this belief is, of course, in the interests of manufacturers of electronic pianos in which dynamic level, but not tone can be controlled. They can thus claim that their product is as good as the real thing.

In spite of all this, musicians can clearly hear the variation in tone quality on an acoustic piano. Even laymen will say that they prefer the 'touch' - meaning tone - of one pianist to that of another. It is true that some pianists have made extravagant claims about their ability to express various emotions with a single note. Liszt occasionally wrote "vibrato" on his piano pieces. Apparently he believed, as have others, that rocking the finger on the key, as a violinist rocks his finger on a string, will produce such an effect. Since, after the string is struck, the only connection between key and either string or soundboard is via the massive frame, it would be difficult to explain such an effect. It is more likely that the performer's ear would be affected. Perhaps Liszt was sufficiently acute psychologically to realize that the sight of a rocking finger would convince some listeners that they were hearing a vibrato.

But what about the 1934 paper in the Journal of the Acoustical Society of America by Hart, Fuller and Lusby? It is said to have proved by experiment that the only variable under the pianist's control is hammer velocity, and that the apparent control of tone is an illusion. The question is easily resolved by a careful reading of the paper. They proved no such thing! Almost all their data were obtained with a mechanical device that struck the key with controlled velocity and acceleration. The resulting sound curves on an oscilloscope were only affected by the velocity of the striker but not by its acceleration. While this conclusion appears to be quite justified, a mechanical device is not a pianist. So they supplemented these results.

Each of two pianists, Abram Chasins and Helene Dietrichs, played single notes at the two extremes of touch, percussive and non-percussive. For each of them, the tone quality of the two touches, as evidenced by the sound curves, was quite different. This seems to be direct proof that the pianist can control tone, but Hart et al. proceeded to claim the contrary! They stated that they could duplicate the pianists' sound curves with their device, and presented the following argument:

1. Acceleration of the striker has no effect on the sound curve, only velocity.
2. The striker can duplicate the sound curves of the pianist.
3. Since striker and pianist are equivalent, conclusions obtained from the striker apply to the pianist.

Even if one accepts such questionable logic, there are other problems. At one point, to demonstrate the consistency of the striker, they present two sound curves at the same setting of the striker. They are very similar but do show visible differences. Hence, one wonders about the perfect matches in the striker-pianist comparisons. In view of this reproducibility, the following statement in their paper, quoted verbatim, is incomprehensible.

"It is significant that whereas Mr.Chasins struck these two notes with what he termed the extremes of difference in striking, the writers succeeded in matching them, not only with the mechanical striker but with the instrument set for the same type of striking on both occasions." They say that the setting was chosen at random from among the nine available. (My italics.)

To my knowledge, their experiment has never been duplicated.

How is it that such obvious flaws in their arguments were missed not only by the referees who recommended publication of the paper, but also by other physicists such as Sir James Jeans and G. Weinreich? To present-day paleoanthropologists Piltdown man was an obvious fraud. But at the time, and for many years thereafter, it was accepted as genuine, simply because it supported current theories of human evolution. I suspect a similar situation here. A violinist can control tone because he is in direct physical contact with the string, through finger and bow, as long as the note sounds. A pianist is never in such direct contact. The physical connection between finger and hammer is broken when the hammer flies free, a fraction of a second before its impact on the string. And no one could imagine how, in such circumstances, tone could be controlled.

The overly simple theoretical model which implicitly underlies the argument for no tone control, assumes that

(a) the hammer and its supporting arm act as a rigid body, and/or
(b) the contact between hammer and string is instantaneous.

Neither is true. The long wooden dowel supporting the hammer is relatively flexible, and, according to Weinreich's article in Scientific American, the hammer is in contact with the string for 6 or 7 milliseconds, independent of the displacement of the string.

The sound curve recorded by an oscilloscope shows how the dynamic level of the note varies with time. The curve oscillates rapidly. The amplitude of the oscillations, and hence the loudness of the sound, increases sharply for 6 or 7 milliseconds to a peak and then drops quickly to a lower level. The initial burst is known as the 'prompt' sound. The amplitude may, or may not, then increase very slightly before slowly decreasing to zero. This portion is known as the 'after' sound.

A string prefers to vibrate at its own natural frequencies, or harmonics, which are determined by the length, weight and tension of the string. When vibrating at these frequencies, the energy is dissipated very slowly and the sound lasts a long time. If other frequencies are imposed on the string, however, the energy in those frequencies disappears quickly as soon as the driving force is removed.

We have here the explanation of the shape of the sound curve. When a piano key is depressed, the energy is transmitted to hammer-and-arm and then, when the string is struck, from hammer to string. The flaw in the simplistic model is the assumption that all the energy in the hammer is the kinetic energy of its forward motion. This would only be true if hammer-and-arm were a rigid body. But because it is quite flexible, depression of the key not only throws the hammer forward, but causes it to vibrate. And the vibrations are at the natural frequencies of hammer-and-arm, which differ from those of the string. When the hammer strikes the string, two things happen: the kinetic energy of the forward movement is translated into the natural frequencies of the string; the vibrating hammer imposes its own extraneous frequencies on the string for the 6 or 7 milliseconds of contact. Hence the prompt sound consists of both natural and imposed frequencies: as soon as contact is broken, the latter quickly disappear and only the former remain. The prompt sound, which lasts for the first one or two hundredths of a second, contains the harsh dissonant frequencies; the after sound consists only of the natural string frequencies.

A sound is pleasing and musical when it is dominated by the lower harmonics of the note and discordant frequencies are weak. Thus the pianist wants to maximize the energy in the natural frequencies, i.e. the kinetic energy of the forward motion, and minimize the vibrational energy that produces the discordant frequencies in the prompt sound. The relative strengths of the natural frequencies are determined by the structure of the piano. But the division of energy between forward motion and hammer vibration can be controlled by the pianist. A key that is hit from above will jar hammer-and-arm into strong vibrations but, if the key is accelerated smoothly, vibrations are minimal, and so are the discordant frequencies in the prompt sound. The key to tone control thus lies in the way the key is depressed and the hammer is accelerated.2

The above theory explains the effect of the mis-named soft pedal, which primarily affects tone rather than loudness. Except in the bottom octave, each note has two or three strings. When the action is shifted by the soft pedal, one of the strings is not contacted by the hammer. The hammer imposes its own frequencies on one or two, but not all of the strings and less prompt sound is produced. The unstruck string vibrates sympathetically only at its natural frequencies, reinforcing the after sound. Less prompt sound, more after sound, sweeter tone.

The theory provides a plausible explanation of how tone can be affected by the pianist, but has not been fully verified experimentally. No one, to my knowledge, has recorded the vibrations of the hammer. However, Hart et al. provides strong supporting evidence. They not only recorded sound curves, but used an optical device to obtain a plot of hammer position against time. From this they could infer how it was accelerated. The results are revealing. When the key was played in a percussive manner by the pianist, the hammer was sharply accelerated at the beginning of its flight and then continued under its own momentum. In the non-percussive case, the hammer was accelerated continuously throughout its flight until its final release. It seems reasonable to assume that the percussive case generates much more vibration of hammer-and-arm than the non-percussive and, in consequence, much more prompt sound and less after sound. One's perception of tone quality is strongly associated with the relative strength of prompt sound and after sound. This is the major, if not the only component of sound quality on the piano. For a fixed energy input, a strong prompt sound leads to a weak after sound, and conversely.

Anyone can test this himself. Hold down the pedal so that the dampers are off the strings, then hit a key from above with a stiff finger, just as the piano-tuner does. Acute listening may detect the harsh attack of the prompt sound, even though it only lasts for less than two hundredths of a second. It is much easier to observe the relative weakness and quick fading of the after sound. For comparison, again with the pedal down, starting with the fingertip on the key surface, depress the key smoothly with a strong steady pulling movement of the finger. No initial attack is heard, the after sound is stronger and lasts a long time. This is the 'singing tone' so admired by the Romantics.

One wants to reduce the prompt sound, but it is neither possible nor desirable to eliminate it completely; its presence contributes to the unique sound of the piano. There is a wide range of touch between the hard percussive tone and the warm sustained tone. The latter is used for legato playing. This is more than just the connection of successive notes into a continuous sound; the touch minimizes the prompt sound 'bump' at the beginning of each note making the melodic line smoother. Sometimes the strict continuity of sound required for legato is not possible because of an awkward configuration of notes. Such a necessary break can be partially covered by the pedal but, in addition, legato touch which reduces the prompt sound bump at the beginning of the second note helps the illusion of legato.

Whereas in legato the key is depressed with a constant or increasing force, in staccato the key is given an initial sharp impulse, - starting at the key surface to avoid too percussive a sound, - followed by a decreasing force. In staccato, one wants a bright attack and has no use for a sustained after sound. A good ear can easily distinguish staccato from legato even when the pedal is down and the dampers are off the keys. The pianist, of course, does not normally think in terms of force or acceleration but rather of legato or staccato touch, of warm or brilliant tone.

Two other types of touch should be mentioned, detached and portamento. The main characteristic of the former is the break in the continuity of sound so that it is non-legato. It differs from staccato, however, in that not only are the breaks shorter, but the notes are normally played with the smooth acceleration of the legato touch and minimal prompt sound. Portamento, on the other hand, is played with the sharp initial impulse of the staccato touch, but the note is held.

The pianist is not limited to either a staccato or legato touch. A sensitive pianist can exploit the continuous range in between or even, for a special effect, deliberately use the percussive touch outside that range. It is simply a matter of how key and hammer are accelerated.

This theory of tone control has numerous implications for piano technique. It is perhaps some confirmation of the theory that the implied techniques coincide with those used by some of the very best pianists.





Published by Sandstone ePress