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veral other sounds 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 the third major above the double octave. 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.

If the bow of a violoncello be strongly rubbed against one of its large strings, or the string of a trumpet marine, you will perceive the same effect. In a word, 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. Rameau confirmed the truth of this phenomenon by the help of several organpipes.

This experiment respecting the resonance of sonorous bodies, is not new. It was known to Dr. Wallis and to Mersesne, 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 the use of it, in deducing 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 thorough bass; a system which has been opposed with much declamation, but which, however, most musicians seem at present to have adopted.

All his harmony, therefore, is multiple, and composed of sounds which would give the aliquot parts of the sonorous body, 1, 1, 1, †, %, 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 octave 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.

EXPERIMENT II.

If you adjust several strings to the octave, the twelfth, and the seventeenth, of the determinate sound emitted by another string, both ascending and descending; as often as you make that which gives the determinate sound to resound strongly, 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 you take care to damp suddenly, by means of a soft body, the sound of the former.

Most people have heard the glasses on a table emit a 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.

In a manner somewhat similar, the diversity of tones agitates, in various ways, the fibres of our bodies, excites the passions, and produces in the soul sensations so different.

On the harmonical sounds heard with the principal sound: whether they have their source immediately in the sonorous body, or exist 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. Philosophers of eminence have endeavoured to discover whether independently of the total vibrations made by a body, there are 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?

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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 such a determinate sound has the property of putting into a state of vibration bodies disposed to give its octave, its twelfth, &c. we must allow that this sound may put in motion the particles of the air, susceptible of vibrations of double, triple, quadruple, and quintuple velocity. What, however, appears most probable in this respect is, that these vibrations exist only in the ear: it seems indeed to be proved by the anatomy of this organ, that sound is transmitted to the soul only by the vibrations of those nervous fibres which cover the interior part of the ear; and as they are of different lengths, there are always some of them which perform their vibrations isochronous to those of a given sound. But, at the same time, and in consequence of the property above mentioned, this sound must put in motion those fibres susceptible of isochronous vibrations, and even those which can make vibrations of double, triple, quadruple, &c. velocity. Such, in our opinion, is the most probable explanation that can be given of this singular phenomenon.

Of the modern music.

Every one knows that the gamut, or diatonic scale, is represented by the sounds ut, re, mi, fa, sol, la, si, ut, which complete the whole extent of the octave; and it appears, from the generation of it, as explained by Rameau, that from ut to re there is a tone major; from re to mi a tone minor; from mi to fa a semi-tone major; from fa to sol a tone major, as well as from sol to la; and in the last place, that from la to si there is a tone minor, and from si to ut a semi-tone major.

It is thence concluded, that in this scale there are three intervals which are not entirely just: these are,

1st. The third minor, from re to fa, which, being composed of a tone minor and a semi-tone major, is only in the ratio of 27 to 32; but this ratio is somewhat less than that of 5 to 6, which expresses exactly the third minor.

2nd. The third major, from fa to la, is too high, being composed of two tones major; whereas, to be exactly in the ratio of 4 to 5, it ought to consist of a tone major and a tone minor.

3rd. The third minor, from la to ut, is as far from being just as that of from re to fa, and for the same

reason.

On the cause of the pleasure arising from music.-The effects of harmony on man and on animals.

It has often been asked, why two sounds, which form together, the fifth and the third, excite pleasure, while the ear experiences a disagreeable sensation, by hearing sounds which are no more than a tone or a semi-tone distant from each other. Though it is difficult to answer this question, the following observations may tend to throw some light upon it.

Pleasure, we are told, arises from the perception of relations, as may be proved by various examples taken from the arts. The pleasure, therefore, derived from music, consists in the perception of the relations of sounds. But are these relations sufficiently simple for

the soul to perceive and distinguish their order? Sounds will please when heard together in a certain order; but, on the other hand, they will displease if their relations are too complex, or if they are absolutely destitute of order.

This reasoning will be sufficiently proved by an enumeration of the known concords and discords. In unison, the vibrations of two sounds continually coincide, throughout the whole time of their duration; this is the simplest kind of relation. Unison also is the first concord in the octave; the two sounds of which it is composed perform their vibrations in such a manner, that two of the one are completed in the same time as one of the other: thus the unison is succeeded by the octave. It is so natural to man, that he, who through some defect in his voice, cannot reach a sound too grave or too acute, falls into the higher or lower octave.

When the vibrations of two sounds are performed in such a manner, that three of the one correspond to one of the other, these give the simplest relation next to those above mentioned. Who does not know, that the concord most agreeable to the ear is the twelfth, or the octave of the fifth? In that respect it even surpasses the fifth.

Next to the fifth, is the double octave of the fifth, or the seventeenth major, which is expressed by the ratio of 1 to 3. This concord, next to the twelfth, is the most agreeable.

The fourth, expressed by, the third minor, expressed by, and the sixths, both major and minor, expressed by and, are concords, for the same

reason.

But it appears that all the other sounds, after these relations, are too complex for the soul to perceive their order.

The following very strong objection, however, may be made to this reasoning. How can the pleasure arising from concords consist in the perception of them, since the soul often does not know whether such relations exist between the sounds? The most ignorant