2014 May 19
So wrote Leonardo da Vinci [ Notebooks, F.61]. That he noticed the presence of convective motion in the dust -- hardly an obvious phenomenon -- testifies eloquently to Leonardo's famous skill as an observer ; that he seems to have done no further work on the subject, leaving it among the innumerable "queries" or rather self-admonitions ("observe the manner ...") in his notebooks testifies likewise to the directionlessmess which prevented him from launching the scientific revolution a century in advance.
Galileo, a more focused genius, also considered the vibrations of a plate [Two New Sciences I, 144] while attempting to modernise the ancient Greek theory of music:
SAGREDO: Since it is impossible to count the vibrations of a sounding string on account of its high frequency, I should still have been in doubt as to whether a string, emitting the upper octave, made twice as many vibrations in the same time as one giving the fundamental, had it not been for the following fact, namely, that at the instant when the tone jumps to the octave, the waves which constantly accompany the vibrating glass divide up into smaller ones which are precisely half as long as the former.
SALVIATI: This is a beautiful experiment enabling us to distinguish individually the waves which are produced by the vibrations of a sonorous body, which spread through the air, bringing to the tympanum of the ear a stimulus which the mind translates into sound. But since these waves in the water last only so long as the friction of the finger continues and are, even then, not constant but are always forming and disappearing, would it not be a fine thing if one had the ability to produce waves which would persist for a long while, even months and years, so as to easily measure and count them?
SAGREDO: Such an invention would, I assure you, command my admiration.
SALVIATI: The device is one which I hit upon by accident; my part consists merely in the observation of it and in the appreciation of its value as a confirmation of something to which I had given profound consideration; and yet the device is, in itself, rather common. As I was scraping a brass plate with a sharp iron chisel in order to remove some spots from it and was running the chisel rather rapidly over it, I once or twice, during many strokes, heard the plate emit a rather strong and clear whistling sound; on looking at the plate more carefully, I noticed a long row of fine streaks parallel and equidistant from one another. Scraping with the chisel over and over again, I noticed that it was only when the plate emitted this hissing noise that any marks were left upon it; when the scraping was not accompanied by this sibilant note there was not the least trace of such marks. Repeating the trick several times and making the stroke, now with greater now with less speed, the whistling followed with a pitch which was correspondingly higher and lower. I noted also that the marks made when the tones were higher were closer together; but when the tones were deeper, they were farther apart. I also observed that when, during a single stroke, the speed increased toward the end the sound became sharper and the streaks grew closer together, but always in such a way as to remain sharply defined and equidistant. Besides whenever the stroke was accompanied by hissing I felt the chisel tremble in my grasp and a sort of shiver run through my hand. In short we see and hear in the case of the chisel precisely that which is seen and heard in the case of a whisper followed by a loud voice; for, when the breath is emitted without the production of a tone, one does not feel either in the throat or mouth any motion to speak of in comparison with that which is felt in the larynx and upper part of the throat when the voice is used, especially when the tones employed are low and strong.
Here is a recreation of Galileo's experiment (from "ToneSpectra.com"):
Like most pioneering experiments, Galileo's Chisel has no self-evident interpretation. Galileo himself sees the marks left behind on the plate as measures of wavelength; although the discussion is necessarily vague, he says that the chisel "trembles", which means that its point is lifting up and down, in and out of contact with the surface, and implies that it does so at a rate comparable to that of a string vibrating at the same pitch. (One is almost surprised that the idea of the phonograph did not occur to him immediately, nor to his successors for over two-hundred years!)
At the same time, he also suggests some kind of resonance effect -- the streaks are produced only when his hand feels "a sort of shiver". This too fits in well with his interest in developing a theory of musical sound as resonant vibration of an instrument.
What Galileo, in contrast to Leonardo, does not investigate, however, is the exact nature of the gouges in the brass plate and their associated debris fields. At the large scale to which he confines himself, the pattern is simple and monotonous: the streaks are "always ... sharply defined and equidistant."
In these two early observers, we see the same dichotomy we have noticed in the papers by Margaret Watts Hughes and Sophie Herrick. Galileo, like Herrick, concentrates on the simplest aspects of the phenomenon, and relates the observed simplicity to straightforward (though in his case not yet fully developed) linear vibration theory. Leonardo, like Watts-Hughes, concentrates on the more difficult, non-linear side, a side which largely defies analysis even today.
As this series continues, we will see how the Romantic natural philosophers of the early 1800s were similarly and unconsciously divided into two camps over the linear versus the non-linear aspects of acoustics, and how this reflected a deeper philosophical divide.
SINGING IN CHLADNI'S GARDEN