[ 414 ) 



LXr. "FurtTier 'Remarks on the Rev. Mr. Piston's "^ssai/ 



on peri fit Intonation:" end kis Scale with 5^ Nates in 



the Octave ; and on other Scales {perfect and temoered) 



for 12, 14, 16. 17, 19, 21, 22, and -24: Notes in the 



Octave respectively, b'c. JSij Mr. John Farey Senior. 



To Mr. Tilloch. 



Sir, JLn my last communication, respecting; Mr. Liston's 

 Euharmonic Organs at Flight's in St. Martin's Lane, two 

 errors have escai^ed correction in p. 3 75, viz. line 9 from 

 the bottom of the note, for 7T read 7L, and line 2 fronj 

 bottom, after each, insert, «« and. 



It is perhaps not generally understood, that the Douzeave 

 or Scale of 12 notes, wherein the intervals above C are all 

 diatonic, major and minor, has no sharpened notes, but all 

 of the five interposed or chromatic notes, are flats (as I 

 used to denote them, in my early papers in your Magazine), 

 thus : 



I 2 II 3 iir 4 5 V 6 VI 7 VII vm 



C Db D Eb E F Gb G Ab A Bb B c 



S h* Sj*SSs>S^S^S 



A \ i JL*A »4»BS S 9 S 1 



T TT T T T V TT T T "5" TT TT T 



LlLiLI<|L!LlL 



The fir.^t of the above lines, marks the Intervals major 

 and minor; the second, the letters or notes; the third, 

 placed inlermediary, show the intervals between the adja- 

 cent notes to be of three diflferent values, viz. the major 

 Semitone S, the Tiiedius Semitone S, and the minor Semi- 

 tone .-, , the octave consisting of 7S + 31^ + 2); and 

 wherein it is easy, to count pp any other intervals in S, ^ 

 and ; (v\hich may be called the Chromatic Elements)^ 

 thus, sS + &) -f a is the Major Third, and 4 S + 23 + 

 $3 the Fifth, &c. The fourth line shows the ratios of the 

 above If^tervals in this chromatic scale ; and the fifth 

 show.-, by the leltt rs L and 1, placed inlermediarv, the major 

 and minor Liniinas, of a regularly tempeied scale; m 

 vhich it will be perceived, that in three iqstanpes the I or 

 6at is substituted for >, and in two inst£^nces for tf. 

 Jhough the five flats wotild seem tp indipate D, as the 

 I 



• For the convenience of printing, I have taken the liberty of substituting 

 the old English capital ( ^ ) for the S with curved points for the Semi- 

 tone meciius — '.7X + f + 4m in our 5th plate in vol. xnviii and wass.a 

 written in the copy ; and the old English small ( tf ) for the scrip capital S 

 or the Semitone minor ^ 36S + f + 3m in the Table, and i^^thc copy.-^ 



Key 



