Musical Temperament of Keyed Instnimenis, 303 



the one with flats, the other with sharps, be adopted. The 

 method that I chose in my publication on teniperainent, 

 1805, (with submission to the learned Dr. Bradley, whom 

 1 have not the honour of" knowing) was upon the principle 

 of a specific division of the major tones of the scale, which 

 must occaiionally serve as minor tones, and is effected by 

 subtracting one-fifth of a comma from a certain number of, 

 perfect fifths, in order to temper those tones which in every 

 additional flat or sharp consequent to a new key require a 

 tone a comm.a hitrher or lower; and to tune perfect, or in a 

 small degree sharper, some of the fifths to meet such tones 

 as are substitutes for real ones. This seems to nie to be the 

 best principle for tempering our present scale; and any at- 

 tempt to reduce the anomalous tone B *, the result of the 

 twelfth quint, or fifth, is much easier understood than ac- 

 complished. To some theorists it is known, that by tuning 

 all the fifths one-eleventh part of a comma flat with respect 

 to that tone, it will be reduced so near to the original, C, as 

 to be an imperceptible difference to the ear. But what theii 

 will becon)e of the major thirds, and their replicates ? The 

 answer is ready : not one of them will be tolerably in "tune; 

 every one of them nearly a comma too sharp : shocking to 

 a musical ear. Chords, too, that most frequently occur in 

 duets and trios, the semi-tones major will be also nearly a 

 comma too flat, and all the harmonics disgusting. 



With respect to Mr. Farey'S observations on modulation, 

 I can only say, that, since abrupt cadences are so frequent 

 in modern music, it would be difficult to ascertain by any 

 calculation what keys are more or less used by the moderns; 

 consequently, their times of occurrence cannot, with any 

 degree of certainty, be known. Modulation often extend- 

 ing to the 7ih sharp and 7th flat, i much wish to know 

 what temperament can reach the one or the other, without 

 producing a worse scale than the present * ; for the power 

 (or refutation of the filth) which reduces the excess of one 

 (viz. the I'Jtli quint), gives neaily a two-fold excess to the 



* Doe» the autlur here mean his own system, or what particular systeru 

 docs he mean ? — Edit- 



Vol. 28. No. 1 12. Sept. 1807- U other 



