HARMONICS, ACUTE, are phenomena attending a sounding string or pipe, &c. which were first noticed by Galileo, and subsequently by Peter Marsenne, M. Sauveur, M. Tartini, &c. : but Daniel Bernoulli first dis covered the reason, and explained the theory of the acute harmonics, by sliming, that a sounding string, at the same time that its whole length vibrated a given note, might maintain subordinate vibrations of its half, its third part, its fourth, and its fifth parts in length ; each of such vibrating parts impressing on the surrounding air independent pulses, the times of whose single vibrations are in the ratios 1, i,1,1-,3; and by which the original sound, or generator, would be accompanied by its octave or VIII, its major twelfth or XII, is double octave or XV, and by its major seventeenth or XVII ; although only the XlItti and XVIlth,or octave of the fifth and double octave of the major third, had yet been described, among the acute harmonics attending a sound. And this great mathematician, although unable to contrive any'ex periment, by which the vi brations of the 1 and ith part of the string might be evidently shewn to subsist along with the whole vibrations, yet he shew ed, from the nature of the Taylorean or harmonica! c urve, that these subdivisions of a sounding string were not only alike possible, and even more probable to happen than those of -1-d, and -1-th ; but that theory and probability were not against the happening of even more minute vibrating divisions of the wnole string, as 1-th, +th, 1-th, 1th, &c.: and that in the use of the trumpet, horn, and other sounding tubes or pipes, all these subdivisions of the whole vibrating column of air might be made, separated by nodes or points in the axis of the tube, in a comparative state of rest with regard to these inferior or harmonica! vibrations, although moving to and fro with the velocity peculiar to the sound of the whole tube : and he inferred, with great seeming proba bility, that the parts of bells, and most other bodies yield ing musical sounds, were in the same manner capable of subordinate or acute harmonic vibrations, along with those of their principal or gravest sound.
It was probably not until about the year 1765, after the very ingenious Mr James Watt of Birmingham had con trived his wheel monochord, that the acute harmonics of a vibrating string were produced in experiment, and some of them actually rendered visible to the eye ; as is related by the late Dr Robinson, who, several years after, made a more extended and complete set of experiments on the same instrument which Mr Watt had before used ; thereby fully confirming all that D. Bernoulli had theore
tically advanced.
Some years after this, Mr John Isaac Hawkins of London, the ingenious inventor of the piano-forte with spirally coiled strings, and of the claviole, or finger-keyed viol, contrived an experiment, which seems to leave nothing to wish with regard to this very curious and interesting sub ject. A spirally coiled string, many feet in length, was prepared by winding a brass piano-forte bass wire closely round a steel wire about the size of a crow quill, and when removed therefrom, pulling it out, so that its spirals be came considerably more open, comparatively, than those of a common cork screw, or the string was nearly in the state of being a cockled," as tuners call it, at equal dis tances, throughout its whole length. Along the side of a large wainscoated room, this spirally coiled string was stretched, over two bridges, near its extremities, and brought to such a degree of tension, as not to yield a sound, but leave its vibrations, when strongly twitched, plainly visible to the eye. The space between the bridges had previously been carefully divided, on the wainscoat, into numerous equal parts, and marked 1 ; 1,1 ; 1, (1), n 1, 4, 3, a, (n, (s), (a), s, &c. ; and if, wnen tne whole string was vibrating, a slight obstacle was opposed to the vibrations of the string, opposite to any one of these di visions, like the edge of the feathers of a quill, held to touch it very lightly, or even if a sudden blast of air from the mouth were made on the string, opposite a division, the string instantly assumed all the subordinate vibrations proper to the aliquot division against which the obstacle or impulse was directed ; and the eye and ear too, in many of the instances, could be gratified, by seeing these very compound vibrations simultaneously carried on by the whole string, and by its several aliquot parts, during se veral minutes, under favourable circumstances, many of the vibrations being slow enough to be counted, and their number in a given time ascertained and compared, by which every point of the theory of D. Bernoulli is in the fullest manner confirmed.