8 Phillips, Harmonic Tetrachords of Claudius Ptolemy. 



covered ; it has been shown that the mean and the equal 

 tempered tone can be easily described by means of these 

 tetrachords ; and no other reason for their invention can 

 be assigned. Moreover, from the manner of reasoning of 

 the Pythagoreans it is extremely probable that the 

 calculation of these ratios would present no difficulty to 

 Claudius Ptolemy, did he turn his attention to the matter. 

 Lastly, it is so highly improbable as to be a " moral 

 impossibility" that he should, by chance, hit on the 

 solution of these interesting and important problems. 

 Hence it seems an irresistible conclusion that the equal 

 tempered scale was first invented or perfected by Claudius 

 Ptolemy of Pelusium in the second century, A.D. 



