222 A HISTORY OF 



.hem And, if this be so, those philosophers who make the tone ol a 

 sonorous body, of a bell, or the string of a harpsichord, for instance, 

 to depend upon the number only of its vibrations, and not the force, 

 have mistaken what is only an effect for a cause. A bell, or an elastic 

 string, can only be considered as a drum beaten ; and the frequency 

 of the blows can make no alteration whatever in the tone. The largest 

 bells, and the longest and thickest strings, have the most forceful vi- 

 brations ; and, therefore, their tones are the most loud and the most 

 grave. 



To know the manner in which sounds thus produced become pleas- 

 ing, it must be observed, no one continuing tone, how loud and swel- 

 ling soever, can give us satisfaction ; we must have a succession of 

 them, and those in the most pleasing proportion. The nature of this 

 proportion may be thus conceived. If we strike a body incapable of 

 vibration with a double force, or, what amounts to the same thing, 

 with a double mass of matter, it will produce a sound that will be 

 doubly grave. Music has been said, by the ancients, to have been 

 first invented from the blows of different hammers on an anvil. Sup- 

 pose then we strike an anvil with a hammer of one pound weight, and 

 again with a hammer of two pounds, it is plain that the two pound 

 hammer will produce a sound twice as grave as the former. But if 

 we strike with a two pound hammer, and then with a three pound, it 

 is evident that the latter will produce a sound one third more grave 

 than the former. If we strike the anvil with a three pound hammer, 

 and then with a four pound, it will likewise follow that the latter will 

 be a quarter part more grave than the former. Now, in the compa- 

 ring between all those sounds, it is obvious that the difference between 

 one and two is more easily perceived, than between two aud three, 

 three and four, or any numbers succeeding in the same proportion. 

 The succession of sounds will be, therefore, pleasing in proportion to 

 the ease with which they may be distinguished. That sound which 

 is double the former, or, in other words, the octave to the preceding 

 tone, will, of all others, be the most pleasing harmony. The next to 

 that, which is as two to three, or, in other words, the third, will be 

 most agreeable. And thus, universally, those sounds whose difference 

 may be most easily compared, are the most agreeable. 



" Musicians, therefore, have contented themselves with seven dif- 

 ferent proportions of sound, which are called notes, and which suffi 

 ciently answer all the purposes of pleasure. Not but that they might 

 adopt a greater diversity of proportions; and some have actually done 

 so; but, in these, the differences of the proportion are so impercepti- 

 ble, that the ear is rather fatigued than pleased in making the distinc- 

 tion. In order, however, to give variety, they have admitted half 

 tones; but in all the countries where music is yet in its infancy, they 

 have rejected such; ana they can find music in none but the obvious 

 ones. The Chinese, for instance, have neither flats nor sharps in their 

 music ; but the intervals between their other notes, are in the same 

 proportion with ours. 



"Many more barbarous nations have their peculiar instruments of 

 music ; and what is remarkable, the proportion between their notes is 

 in all the same ^s in ours. This is not the place for entering "ito tho 



