'268 PHILOSOPHICAL TRANSACTIONS. [aNNO 17 46. 



equal to the greatest elongation of its orbit, from the same colure in the adverse 

 part, and to the distance of the poles of the orbit from the equinoctial points. 



Of tlie various Genera and Species of Music among the Ancients, with some Ob- 

 servations concerning their Scale. By John Chrtstoph. Pepusch,* Music. D., 

 andF.R.S. N" 481, p. 266. ,, 



In compliance with your request, I here send you some of my thoughts on the 

 various genera and species of the Greek, music. What were these, and how far 

 the doctrine of the ancients in this respect is reconcileable with the true nature 

 of musical sounds, are questions which have not a little perplexed the learned. 

 That musical intervals are founded on certain ratios expressible in numbers, is an 

 old discovery. It is well known that all musical ratios may be analysed into the 

 prime numbers 2, 3, and 5 ; and that all intervals may be found from the octave, 

 5th and 3d major; which respectively correspond to those numbers. These are 

 the musician's elements, from the various combinations of which, all the agree- 

 able variety of relations of sounds result. This system is so well founded on ex- 

 perience, that we may look upon it as the standard of truth. Every interval that 

 occurs in music is good or bad, as it approaches to, or deviates from, what it 

 ought to be on these principles. 



The doctrine of some of the ancients seems different. Whoever looks into 

 the numbers given by Ptolemy, will not only find th primes 2, 3, and 5, but 

 7, 1 1, &c. introduced. Nay he seems to think all 4ths good, provided their com- 

 ponent intervals may be expressed by superparticular ratios. But these are justly 

 exploded conceits ; and it seems not improbable that the contradictions of 

 different numerical hypotheses, even in the age of Aristoxenus, and their incon- 

 sistency with experience, might lead him to reject numbers altogether. It is 

 pity he did : had he made a proper use of them, we should have had a clearer in- 

 sight into the music of his times. However, what remains of the writings of 

 this great musician, joined to observation and experience, has enabled Dr. P. to 

 throw some light on the obscure subject of the ancient species of music. 



By the manner in which Euclid and others find the notes of their scale, it 



' • Dr. Pepusch was one of the greatest theoretic or scientific musicians among the modems. He 

 was a Prussian by birth ; and in 168O, when not quite 15 years of age, he was chosen to teach music 

 to the Prince Royal of Prussia. He afterwards came to England, and was engaged at Drury-lane 

 theatre ; though the popularity of Handel kept Pepusch in the 2d rank ; yet his talents and judgment 

 were so much respected, that he taught music to professors of music themselves. The university of 

 Oxford honoured Dr. P. with the degree of Dr. of music, and the R. S. elected him one of their 

 members. He married a Tuscan lady, an eminent opera singer, who had acquired by her profession 

 a fortune of «^10,000. Dr. P. died in 1752, being 85 years of age. and was buried in the Charter- 

 house. 



