Exptriments and Inquiries refpeB'ing Sound and Light. 127 



made, which refts its chief claim to preference, on the fimilarity of its theory to the aftual 

 praftice of the beft inftrument-makers. However we eftimate the degree of imperfedtion 

 of two tempered concords of the fame nature, it will appear, that the manner of dividing 

 the temperament between them does not materially alter its aggregate fum ; for inftance, 

 the imperfe£tion of a comma in a major-third, occafions it to beat very nearly twice as faft 

 as that of half a comma. If indeed tlie imperfeflion were great it might affe£t an interval 

 fo materially as to deftroy its charader ;, as, in feme methods of temperament, a minor 

 third diminifhed by two commas approaches more nearly to the ratio 6 : 7, than to 5:6; 

 but, with this limitation, the fum of harmony is nearly equal in all fyftems. Hence, if every 

 one of the twelve major and minor thirds occurred equally often in the compofitions which 

 are to be performed on an inllrument, it would be of no great confequcnce, to the fum 

 of the imperfeftions, among which of the thirds they were divided : and, even in this 

 cafe, the opinion of the beft praflical authors is, that the difference of chara£ler produced 

 by a difference of proportions in various keys, would be of confiderable advantage in the 

 general efFe£l of modulation. But, when it is confidered, that upon an average of all the 

 mufic ever compofcd, fome particular keys occur at lead twice as often as others, there 

 feems to be a very ftrong additional reafon for making the harmony the molt perfeft in. 

 thofe keys which are the mod frequently ufed; fmce the aggregate fum of all the imperfec- 

 tions which occur in playing, muft by this means be diminifhed in the greateft poflible 

 degree, and the diverfity of chara£ler at the fame time preferved. Indeed, in praftice, 

 this method, under different modifications, has been almoft univerfal ; for, although many 

 have pretended to aft equal temperament, yet the methods which they have employed to 

 attain it have been evidently defedive. It appears to me, that every purpofc may be 

 anfwered, by makii'g C : E too fliarp by a quarter of a comma, which will not offend the 

 niceft ear } E : G*, and A*:C, equal; F* : A* too fliarp by a comma; and the major 

 thirds of all the intermediate keys more or lefs perfeft, as they approach more or lefs to C 

 jn the order of modulation. The fifths are perfeft enough in every fyftem. The refults of 

 this method are (hown in Table xii. In pra£lice, nearly the fame effeft may be very fimply 

 produced, by tuning from C to F, B*, E^, G*, C*, F* fix perfed fourths ; and C, G, D, 

 A, E, B, F*, fix equally imperte£l fifths, Plate VI. Fig. 52. If the unavoidable imper- 

 fe(ftions of the fourths be fuch as to incline them to (harpnefs, the temperament will 

 approach more nearly to equality, which is preferable to an inaccuracy on the other fide., 

 ^n eafy method of comparing different fyftems of temperament is exhibited in Plate VI.. 

 Fig. 53, which may eafily be extended to all the fyftems that have ever been invented.. 



Table 



