Saturday, October 14, 2006

Good Vibrations

If Debussy's insistence that you get your piano to sound like it has no hammers is a little bit too taxing an illusion to maintain, maybe it's easier to consider the sweet, flexible nature of those hammers, and the profoundly magical result that comes from their vibrations. R. Wormleighton, Ph.D. writes about tone in his paper "The Fundamentals of Piano-Playing", attempting to disprove the 1934 conclusions of Hart, Fuller (no relation) and Lusby, who claimed that the pianist can control only hammer velocity -- that's it, nothing else -- and that control of tone is an illusion. Their big mistake, he says, lies in the assumption of the rigidity of the hammer.
Wormleighton describes the perceptual importance of the sound and nature of the attack (the "prompt 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.
(my italics)

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 [Hart, Fuller and Lusby's] 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.

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.

Oh, but all the science is blinding, isn't it ... I'll have to assume that somewhere in that paper is talk about all the sympathetic singing and whispering ... all the distancing and shadowing ... all the magic that happens when you put the pedal down ... not to mention when you set the dampers to kissing and teasing the strings ....

Anyway, it's October in New England, and the kitchen window is overcome with blueness and sunlight. And the dry sweet air touches my face in such a way that I'm overcome, too. Autumn always prompts a strange thrill of melancholy.