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LXXXV. On the NoiMenolature o/"]VIusical Intervals, and 

 the Advantages of a Set of Sj/mbols or Ckaracters, ly which 

 the mutual Relations of the principal ones can he expressed, in 

 the form of simple Eqiiatiovs :-~with a la hie. 



By Mr. John Farey, Sen, 



To Mr. niloch. 



Sir, — In Plate V of voluine xxviii. of The Philosophical Maga- 

 zine for 1807, the first attempt was made, with which I am ac- 

 quainted, at collecting together in any publication, all the most 

 essential Musical Intervals; accurately (.Icfining these by means 

 of their Ratios and Logarithms, and assigning to each a Symbol 

 or Character, by the help of which their mutual relations might 

 be shown in a great variety of ways, in simple Ecjuations* ; and 

 by means of which Syml)uls the values of all other Musical Inter- 

 vals might in like manner be accurately expressed. 



Since this period, the publication of The Rev. Henry Listen's 

 *' Essay on perfect Intonation," for explaining the principles and 

 use of his Euharmonjc Organ, has served to greatly extend 

 and methodize our knowledge of Intervals ; and my occasional 

 hours of leisure or relaxation, have since been devoted to an in- 

 quiry, into the values of all the Intervals within an Octave, which 

 can arise, in the cJ422 combinations, by pairs, of which Mr. Lis- 

 ten's 59 Notes and their Octaves, are capable. 



The extended and complete Table of Mr. Liston's Intervals 

 thus formed, is found to contain 220 different Notes, two of 

 which are found repeated 52 tiinesf, two others 47 times, two 

 others 45 times, each (all of these being Concords) and others 

 in lesser degrees of repetition, down to 12 other Intervals, which 

 are each found only once, in comparing every two of Mr. Liston's 

 Notes, and their Octaves, as already mentioned. 



In searching for the principles of Nomenclature, by which all 

 these, and even a still greater variety of musical Intervals may be 

 each correctly named, I have found, that fifteen other Intervals, 

 not mentioned in the former engraved Table in your Work, will 

 now be nccesyarv, each to be furnished with \t^Narne and Sym- 

 bol, making in ail 4S tai)ular Intervals : also, that several of the 

 former Symbols, which had been adopted from the late Mr. Over- 

 end's Manuscripts, require now to be altered, iov adapting them 



* Of which lise of tlicsc Symbols, very numerous cxninplos may be seen, 

 imiler tlic names of the vaiious Musical Intervals, ii) Dr. Brewster's "Edin- 

 burgh Encyclo|)a3dia." 



t Each one yf these 59 Listonian Notes, havinj; a true Vth above it and 

 a true 4th below it, cx'-cpt these 7, viz. C'*, (;««, C'«*, D', E'b, F'b, and 

 E'*. And it is somewhat remarkable, that all of these fall in the lower 

 half of the Octave from C to c. 



to 



