404 LECTURE XXXIV. 



with the principal part, yet they had no regular art of counterpoint, or of 

 performing different melodies together ; nor does it appear that they ever 

 employed discords. The tibia of the ancients resembled a hautboy or clari- 

 net, for it had a reed mouth piece, about three inches long; the same per- 

 former generally played on two of these instruments at once. There were, 

 however, several varieties of the tibia; and it is not improbable that some of 

 them may have had the simple mouth piece of the flageolet. 



The first philosophical observer of the phenomena of sound, after Pytha- 

 goras, appears to have been Aristotle; he notices a great variety of curious 

 , facts in harmonics among his mechanical problems; and he entertained a 

 very correct idea of the true nature of the motions of the air constituting 

 sound. He knew that a pipe or a chord of a double length produced a 

 sound of which the vibrations occupied a double time; and that the properties 

 of concords depended on the proportions of the times occupied by the vibra- 

 tions of the separate sounds. It is not indeed improbable that at least as much as 

 this was known to Pythagoras, since he established correctly the numerical 

 ratios between various sounds; but so little justice has been done to his dis- 

 coveries by the imperfect accounts of them which have been preserved, that 

 we cannot expect to be able to ascertain his opinions on any subject with 

 accuracy. 



The invention of the organ, by Ctesibius of Alexandria, about 2000 years 

 ago, forms a remarkable epoch in harmonics. The larger instruments of this 

 kind Avere furnished with hydraulic bellows, the smaller with bellows of 

 leather only ; and they had keys which were depressed, like those of the 

 modern organs, by the fingers of the performer, and which opened valves 

 communicating with the pipes. 



The modern system of music is one of the few sciences, if such it can be 

 Galled, which owe their improvement to the middle ages. The old ecclesi- 

 astical music was probably founded in great measure on that of the Greeks; its 

 peculiar character consisted in the adoption of any note of the scale at pleasure 

 for a key note, without altering materially the other intervals; and in this man- 

 ner they obtained a variety much resembhng that of the modes or kinds of music 

 in use among the ancients. Pope Gregory, about the year 600, distinguished 



