342 Queries respecting Tuning of Musical Instruments. 



flattened Notes, instead of those assumed in my Theorems and 

 Corollaries; which they effect, by stopping in their upward 

 series of consecutive tempered Fifths, with C* ; and continuing 

 their downward series of similar Fifths, one note further than is 

 mentioned above, viz. to Ab. 



The magnitudes and proportions of the several Temperaments 

 and Wolves (although not their places) will still all be truly re- 

 presented by my Theorems or Corollaries, in this new manner 

 of laying the Quint Wolf, or in any other, which the convenience 

 of Musicians, or the fancies of Tuners, may suggest; provided 

 only, that eleven of the Fifths out of the twelve, are precisely 

 equal in magniliide . In either of two particular cases of equally 

 Tempered Fiji lis'^ , my Theorems will still apply, viz. first, in the 

 Isotonic or common equal-temperament Scale, wherein each of 

 the twelve Fifths h flattened the same quantity (or I-12th of the 

 Diaschisma, 12i'+mt); and second, the Scale wherein each of 

 the twelve temperaments of the Fifths are equal, (each I-lOth 

 of the Diaschisma) yet eleven of them are flat, and one sharpy 

 viz. G* Eb, 



I have ventured to call the attention of your Musical Readers 

 to this subject, in order to request to be informed, through the 

 medium of your pages, or otherwise : 



1st. Whether this method of laying the Quint Wolf on C*, 

 rather tha'i on G*, has yet prevailed to'any considerable 

 extent ? 



2nd. Whether, for the general run of Piano- Forte Music, it be 

 really an Improvement to make this change, or otherwise? 



3rd, Whether either of the three Systems oi equal Fifiths, but 

 some of them siiarpened, which are mentioned herein, 

 have been tried? : and if so, how were they approved ? 



I am your obedient servant, 



37, Howland-street, Fitzrov-square, JoHN FarEY Sen. 



Oct. 17, 1820. 



• As the amusement of occasional leisure Hours, I have considered and 

 calculated the Intervals of some other equal Temperaments of the Fifths, to 

 wliich my Theorems above quoted, will not apply ; in one of these, the 

 Fifth Temperament is ^th of the Diaschisnra (or 1'52 + ,\m), tliis beinjj the 

 sharp Temperament of Uvo of the Fifths, viz. C* G* and G* El>, while all 

 the 1 other Fifths are flattened the same quantity. In another of these 

 Systems, ith of the Diaschisma (or 2s + Jm) is the sharp Temperament of 

 three of the Fifths, viz. F* C*, C* G* and G* Eb, while the i) other Fifths 

 are as much flattened. 



t See p. M. vol. xxviii. Plate V. p. 140. 



LIII. On 



