3G0 HISTORY C,F 



succession ot tliein, and those in the most pleasing proportion. 

 The nature of tliis 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. Suppose then we strike an an- 

 vil with a hammer of one pound weight, and again with a ham- 

 mer 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 comparing between all those sounds, it is obvious 

 that the difference between one and two is more easily perceived, 

 than between two and three, three and four, or any numbers suc- 

 ceeding 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 or 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 

 different proportions of sound, which are called notes, and which 

 sufficiently 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 pro- 

 portion are so imperceptible, that the ear is rather fatigued than 

 pleased in making the distinction. In order, however, to give 

 %'ariety, they have admitted half tones ; but in all the countries 

 where music is yet in its infancy, they have rejected such ; and 

 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 propor- 

 tion with ours. 



" Many more barbarous nations have tlieir peculiar instru. 



