THE 



PHILOSOPHICAL MAGAZINE. 



I. On the two Systems of Musical Temperament recorn- 

 jnended hy Earl Stanhope, — Mr, Hatvkes's System, &c. 

 By Mr, John Farey. 



To Mr, Tilloch. 



TT ''''' 



XIaving bestowed some pains to illustrate the System of 



Musical Temperament described by Earl Stanhope in your 

 xxvth volume, as applicable to keyed Instruments, by the 

 help of a Monochord, whose divisions are according to 

 geometric mea?i proportionals, I beg now to present to your 

 readers, the notes of the other System, described by his 

 Lordship in the same Essay, to be effected by making three 

 successive tempered Fifths, and two successive major Thirds^ 

 in <iifferent parts of the scale, beat equally quick respec- 

 tively. 



The table accompanying}; this, is divided into 10 columns, 

 entitled at the bottom, as has usually been done. 



Column 4 contains the number of complete vibrations 

 made by a musical string or other sounding body in one 

 second of time, when the intervals are agreeable to Earl 

 Stanhope's Monochord System 'j whose logarithms, lengths 

 of strings, and other particulars for comparison herewith, 

 will be found vol. xxvii. p. 195*, and vol. xxviii. p. 141. / 



* I beg here to correct an unfortunate error In the length of string which 

 I have in this page assigned to Lord Stanhope's 6th, owing to my having 

 taken out the number answering to the logarithm •8100S00 (instead of 

 •8010300) viz. '6456987 instead of '6324554; for which correction I wish tq 

 acknowledge rny obligation to Mr. J. Barraud, a gentleman engaged in these 

 inquiries, who has verified th^ numbers in this column, except insoijie of their 

 last places, independent of thelogarithms in the preceding column. 



Vol. 30. No. 117. Feb, 1808. A 2 Columns 



