ARTICLE VII.

Of the resonance of sonorous bodies; the fundamental principle of harmony and melody; with some other harmonical phenomena.

EXPERIMENT 1.

If you listen to the sound of a bell, especially when very grave, however indifferent your ear may be, you will easily distinguish, besides the principal sound, several others more acute; but if you have an ear accustomed to appreciate the musical intervals, you will perceive that one of these sounds is the twelfth or fifth above the octave, and another the seventeenth major, or third major above the double octave. If your ear be exceedingly delicate, you will distinguish also its octave, its double, and even its triple octave the latter indeed are somewhat more difficult to be heard, because the octaves are almost confounded with the fundamental sound, in consequence of that natural sensation which makes us confound the octave with unison.

The same effect will be perceived if the bow of a violoncello be strongly rubbed against one of its large strings, or the string of a trumpet-marine.

In short, if you have an experienced ear, you will be able to distinguish these different sounds, either in the resonance of a string, or in that of any other sonorous body, and even in the voice.

Another method of making this experiment.

Suspend a pair of tongs by a woollen or cotton

cord, or any other kind of small string, and twisting the extremities of it around the fore finger of each hand, put these two fingers into your ears. If the lower part of the tongs be then struck, you will first hear a loud and grave sound, like that of a large bell at a distance; and this tone will be accompanied by several others more acute; among which, when they begin to die away, you will distinguish the twelfth and the seventeenth of the lowest tone.

The truth of this phenomenon, in regard to the multiplicity of sounds, is confirmed by another experiment, mentioned by Rameau, in his Harmonisal generation. If you take, says he, those stops of the organ called bourdon, prestant or flute, nazard and tierce, which form the octave, the twelfth and seventeenth major of the bourdon, and if you draw out in succession each of the other stops, while the bourdon alone is sounding, you will hear their sounds -successively mixed with each other; you may even distinguish them while they are all sounding toge ther; but if you prelude for a moment, by way of amusement, on the same set of keys,, and then return to the single key first touched, you will think you hear only one tone, that of the bourdon, the gravect of all which corresponds to the sound of the whole system.

REMARK.

This experiment, respecting the resonance of sonorous bodies, is not new. It was known to Dr. Wallis, and to Mersenne, who speak of it in their works; but it appeared to them a simple phenomenon, with the consequences of which they were entirely unacquainted. Rameau first discovered its

use in deducing from it all the rules of musical composition, which before had been founded on mere sentiment, and on experience, incapable of serving as a guide in all cases, and of accounting for every effect. It forms the basis of his theory of fundamental bass, a system which has been opposed with much declamation, but which however most musicians seem at present to have adopted.

All his harmony then is multiple, and composed. of sounds which would be produced by the aliquot parts of the sonorous body,,,,, and we might add,, &c. But the weakness of these sounds, which go on always decreasing in strength, renders it difficult to distinguish them. Rameau however says that he could distinguish very plainly the sound expressed by, which is the double oc tave of a sound divided nearly into two equal parts, being the interval between la and si flat below the first octave: he calls it a lost sound, and totally excludes it from harmony. It would indeed be singu larly discordant with all the other sounds given by the fundamental tone.

We must however observe that the celebrated Tartini, in regard to this sound, was not of the same opinion as Rameau. Instead of calling it a lost sound, he maintains that it may be employed in melody as well as harmony; he distinguishes it by the name of the seventh consonant. But we shall leave it to musicians to appreciate this idea of Tartini, whose celebrity in composition, as well as execution, required a refutation of a different kind, from that to be found at the end of a work printed in 1767, entitled Histoire de la Musique.

EXPERIMENT II.

If you tune several strings to the octave, to the twelfth, and to the seventeenth major, of the deter minate sound emitted by another string, both ascending and descending; as often as you make that which gives the determinate sound to resound strongly, and with continuance, you will immediately see all the rest put themselves in a state of vibration you will even hear those sound which are tuned lower, if care be taken to damp suddenly, by means of a soft body, the sound of the former.

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Most persons have heard the glasses on a table sound, when a person near them has been singing with a strong and a loud voice. The strings of an instrument, though not touched, are often heard to sound, in consequence of the same cause, especially after swelling notes long continued.

This phenomenon arises, no doubt, from the vibrations of the air being communicated to the string, or to the sonorous body, elevated to the above tones for it may be easily conceived that the vibrations of strings, tuned to unison or to the octave, or to the twelfth, &c, of that put in motion, are disposed to recommence regularly, and at the same time as those of that string, one vibration corresponding to another, in the case of unison; two to one, in the case of the octave; or three to one in that of the twelfth the small impulsions therefore of the vibrating air, produced by the string put in motion, will always concur to increase those movements, at first insensible, which they have occasioned in the other strings; because they will take place in the same direction, and will at length

render them sensible. Thus a gentle breadth of air, continued always in the same direction, is at length able to elevate the waters of the ocean. But when the strings in question are stretched in such a manner, that their vibrations can have no correspondence with those of the string which is struck, they will in this case be sometimes assisted and sometimes opposed, and the small movement which can be communicated to them, will be annihilated as soon as produced, consequently they will remain at rest.

QUESTION.

Do the sounds heard with the principal sound derive their source immediately from the sonorous body, or do they reside only in the air or the organ?

It is very probable that the principal sound is the only one that derives its origin immediately from the vibrations of the sonorous body. Philo sophers of eminence have endeavoured to discover whether, independently of the total vibrations made by the body, there are not also partial vibrations; but hitherto they have been able to observe only simple vibrations. Besides, how can it be conceived that the whole of a string should be in vibration, and that during its motion it should divide itself into two or three parts that perform also their distinct vibrations?

It must then be said that these harmonical sounds of octave, twelfth, seventeenth, &c, are in the air or the organ both suppositions are probable; for since a determinate sound has the property of putting into a state of vibration bodies disposed to