110 PHYSICAL SCIENCES IN ANCIENT GREECE. 



a Fourth. This observation gave an arithmetical 

 measure of the principal musical intervals, and 

 made Music an arithmetical subject of specula- 

 tion. 



This story, if riot entirely a philosophical fable, 

 is undoubtedly inaccurate; for the musical inter- 

 vals thus spoken of, would not be produced by 

 striking with hammers of the weights there stated. 

 But it is true that the notes of strings have a 

 definite relation to the forces which stretch them ; 

 and this truth is still the groundwork of the theory 

 of musical concords and discords (G). 



It may at first appear that the truth, or even 

 the possibility of this history, by referring the dis- 

 covery to accident, disproves our doctrine, that this, 

 like all other fundamental discoveries, required a 

 distinct and well-pondered Idea as its condition. In 

 this, however, as in all cases of supposed accidental 

 discoveries in science, it will be found, that it was 

 exactly the possession of such an Idea which made 

 the accident possible. 



Pythagoras, assuming the truth of the tradition, 

 must have had an exact and ready apprehension 

 of those relations of musical sounds, which are 

 called respectively an Octave, a Fifth, and a Fourth. 

 If he had not been able to conceive distinctly this 

 relation, the sounds of the anvil would have struck 

 his ears to no more purpose than they did those 

 of the smiths themselves. He must have had, too, 

 a ready familiarity with numerical ratios; and, 





