316 . LECTURE XXXIV. 



very correct idea of the true nature of the motions of the\^r constituti^ 

 sound. He knew that a pipe or a cord of a double length p"r^du T ;ed > a 

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

 perties of concords depended on the proportions of the times occupied by 

 the vibrations of the separate sounds. It is not indeed improbable that at 

 least as much as this was known to Pythagoras, since he established cor- 

 rectly the numerical ratios between various sounds ; but so little justice has 

 been done to his discoveries 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. t 



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 were 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 called, which owe their improvement to the middle ages. The old 

 ecclesiastical 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 manner they obtained a variety much resembling 

 that of the modes or kinds of music in use among the ancients. Pope 

 Gregory, about the year 600, distinguished the notes by literal characters ; 

 the rules of counterpoint were formed by degrees from the experience 

 of the ecclesiastical musicians ; and early in the eleventh century, Guido 

 of Arezzo, otherwise called Aretin the monk, introduced, together with 

 some improvements in the theory and practice of music, a new method of 

 naming the notes by syllables. 



Some curious experiments on sound may be found in the works of 

 Bacon, but they added very little to the true theory of acustics, and some 

 of them are not perfectly accurate. Galileo* rediscovered what was well 

 known to Aristotle, respecting the nature of sound ; for the words of Ari- 

 stotle had been so much misunderstood and misinterpreted, that he could 

 have profited but little by them. His cotemporaries Mersennet and 

 Kircher^ made a variety of very ingenious experiments and observations, 

 on sound and on sounding bodies, many of them unknown to authors of 

 later date. The theory of the ancient music was very accurately investi- 

 gated, in the middle of the 17th century, by Meibomius : our countryman 

 Wallis, also, besides employing much learning and penetration in the illus- 

 tration of the ancient music, observed some insulated facts in harmonics 

 which were new and interesting. || 



Sir Isaac Newton's propositions^ respecting the velocity of the pro- 

 pagation of sound were the beginning of all the more accurate inves- 



* Op. iii. 58. t Harmonicorum Liber, Par. 1635. 



+ Musurgia, 2vols. fol. Rom. 1650. Phonurgia, fol. 1673. , 



Musicse Antiq. Scrip. Meibomii, 2 vols. 4to, Amst. 1652. 



II Opera, vol. iii. and Cl. Ptolemsei Op. a Wallis, 4 to, Oxf. 1682. 



11 Principia, lib. ii. Prop. 46, &c. 



