03. Such calculations are applicable to many pracVcal purposes in music. They enable us to estimate the results of any series of the intervals taken truly, or the effect of such alterations of them, as may be necessary in tuning some in struments. They furnish the principles on which musical instruments must be formed, or by which the imperfections of instruments may be remedied. But we should very much mistake the matter, should we suppose, that from the consi deration of these proportions, WC SlIOUld be able to deduce the rules that are to guide the musician in the use of musical intervals. Such an attempt has been frequently made, but has always proved abortive. Speculative inquirers may please themselves, by finding a physical cause of the plea sure given to the ear, by certain combinations, in the coin cidences of their v ibrations; but they could never derive from such speculations, one practical rule to guide the com poser. If, for instance, they find that a fifth or octave is pleasing, because of the frequent coincidence of the vibra tions, they could never have foretold that such intervals taken successively, between the same parts, in similar mo tion, would be offensive, but agreeable in contrary motion. Nor when experience has found the rule, can they assign any teason for it. The truth is, our knowledge of the causes of our sensations is imperfect and uncertain ; the sensations themselves are immediately subjected to our observation and reflection : the direct appeal to them is, therefore, the only rational one. The rules of music, like the common law, are to be sought for in the collected decisions of competent judges, \SIM, ill the course of time, have successively pointed out what combinations and progressions are good, and what displeasing, and have thus gradually refined and improved the art. .Musie is a language; and there is a striking ana logy between this science and grammar. Whoever would understand any language, or acquire its use, must apply to the rules of grammar, founded on the practice of those who speak or yvrite it : and he would be very ill advised, who should forsake these common rules for the metaphysical speculations of Ilarris or IIorne Tooke.
64. M. D'Alembert has very successfully exposed the mistake of those who seek the foundations of musical sci ence in geometrical, arithmetical, and harmonica] progres sions, or in metaphysical speculations. Yet he seems to have exposed himself to a similar censure, in endeavouring afier Ramealt, to found it on one experiment. The desire to reduce every science, or branch of human knowledge, to some one principle, and thence to deduce the whole theory, has long prevailed among philosophers. This we cannot
help thinking a very mistaken aim. It seems to us to re semble the conduct of an architect, who, to show his art, should prefer placing, a pyramid on its small end, rather than on that broad basis on which it vvould firmly rest. he ex periment on which Bameau, and after him D'Alembert, setk to build the whole science of music, is this. When a sono rous body is struck till it gives a sound, the ear, besides the principal sound and its octave, perceives two other sounds, very high. of which one is the twelfth above the principal sound, that is to say, the octave to the filth of that sound ; and the other the seventeenth major above the same sound, that is to say, the double octave of its third major. This expel iment is certainly very curious. But there is another experiment which 'M. D'Alembert has not noticed, which, as we think, involves the true principle of the science, viz. that these sounds, or their octaves, heard simultaneously or successively, are extremely agreeable to the ear. When in stead of this experiment; lie tells us, that these sounds please, because they are the immediate production of nature, he appears to us to be more wide of the mark than those who incurred his censure, in seeking to account for the pleasure given by consonances, from the coincidence of the vibrations. Yet AI. D'Alembert tells us, that for want of knowing this experiment, preceding artists had been obliged to grope in the dark ; as if major thirds and perfect fifths, had been con cealed from the musical world, till this experiment discovered them ; or as if this experiment had thrown any light what ever on the fact, that these are agreeable to the ear. In truth, Al. D'Alembert, with all his ingenuity, has found dif ficulty to tack to this expet iment the rules of composition ; and so far front throwing any light on the science, the en deavour serves only to render dark and perplexed, what is very plain when laid down as a practical rttle. If Al. Ra mean has contributed something to the arrangement of the rules of harmony, by turning the.attention of musicians to the method of fundamental basses, that advantage rises out of the method itself, and not in the most distant manner from the experiment with which he endeavours to connect it.* 65. The rules of harmony may be regarded in various lights, and variously arranged, and one arrangement may be more luminous than another, or lead more easily to a knowledge of the doctrine to he taught. But so long as the doctrine is the sante that is put in practice by the best mos