On the Nomenclature of Musical Intervals. 367 



Hitermediate ones, P(58), and L(46), which are left with their 

 former simple names, Apotome and Limma, for want of more 

 prefixes than are above enumerated. 



But there is in the Tables another family of smaller Semitones, 

 which for convenience are named Hyperoche, of which there is 

 the major TT (15), the medius D (14), and the minor tp (10). 



And a family of still smaller such Semitones, named Residual, 

 having no m, with the several prefixes, greater ]f^ (5 ?) *, major 

 r(5), Liston's C(4), medins ;)<;; (3), minor r(2), and submi- 

 iiimum f(0) : and to which the Minimum i:(l) would have 

 been added, but from my desire, to avoid loading this very im- 

 portant interval, witli compound names, which is already so well 

 known by the simple name of Schisma. 



A principle, on which all the numerous family of Residuals 

 (of the class of Semitones, but m which no n\'s enter) seems to be 

 deducible, from considering certain of the larger of the Commas 

 and smaller of the Diesises, as quarter Tones ; and two of these 

 to be equivalent, to one of certain of the Semitones respectively : 

 analogouslv to the modes in which I have shewn in p. 366, that 

 Commas may be derived from Semitones and Tones; but this is 

 a subject on which I must not at present enlarge, except to give 

 such Equations, for the several Residuals in the Tables, viz. 

 5L-43-2£ = f, S-L = 2, 3L-2 ^--2 ==:r, 2L-S) 

 -2£=;^, L-2e = r, fe.-2e = r, and5L-3 5?-4£ = ]J^. 



It remains nov/ to mention, only one other class of Intervals, 

 in mv Tables, and which are called Fuactions, ivherem f is 

 negative. Three of these have the prefixes, medius d (1 ?), 

 greater F (1 ?) and major R (6). 



I have never found leisure, and probably never may, for de- 

 ducing any general j)rinciple, on which these and the numerous 

 other Fractions in mv large MS. Tables of Intervals, may all be 

 derived. My Table of Mr. Liston's 220 Intervals (which I hope 

 at some time to be able to puluish) contains no example of this 

 class of Intervals called Fractions, which occasions them to be of 

 far less consequence, in mv estimation. 



I am, sir, your obedient servant, 

 Westminster, Nov. 29, 101 J. JoHN FaREY, Sen. 



* The reason of the expression R C5?) being used, is, tliat thia is one ol' 

 the few Intervals, which my artificiiil Commas will not defiitiiive/y expresc, 

 wit!io(it the use of f and ni, or one of them. 



%' Mr. J'am/,when he very lately sent nie this Communication, explained 

 the reason of the Ion;; »lciiiy since it was written, to have arisen, from send- 

 ing his MS. some time after it was completed, to a musical Friend, who 

 he conceived was much interested in the suhjoct it treats of, and of whom 

 Le requested the favom- to revise it, and mark any suj;i;estloi)s for its im- 

 provement which miuht occur to isim ; but this was never done, or the Paper 

 returned to Mr. !•'. until lately, without comment, in the state it went, and 

 now appears. — Editor. 



LXXXVI. Sum- 



