36 HISTORY OF 



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 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 comparing be- 

 tween all those sounds, it is obvious that the dif- 

 ference between one and two is more easily per- 

 ceived, than between two and three, three and 

 four, or any numbers succeeding in the same pro- 

 portion. The succession of sounds will be, there- 

 fore, 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 them- 

 selves with seven different proportions of sound, 

 which are called notes, and which sufficiently 

 answer all the purposes of pleasure. Not but 



