i66 Letter refpeBlng Sound and Light. 



Smith was too precipitate in laying down his principle for the comparifon of the efFeftj 

 of temperament. 



With refpeft to the fyftem which I have propofed, Profeflbr Robifon thinks that 

 the temperaments of feveral of the thirds which occur frequently are much too great. If 

 we wifli to form a judgment of any fyftem of ten.perament, it mud be Ijy comparifon with . 

 fome other. It does' not appear with what fyftem Profeflbr Robifon would wifli the com- 

 parifon to be made, but he rather feems to incline to the equal temperament, although he 

 gives dire£tions for tuning by another. At any rate, no temperament of an interval can be 

 faid to be much too great, unlefs it be greater than that of the fame interval in the fyftem 

 of equal temperament ; for if any interval be madS more perfe£l than this, fome other 

 limilar interval muft be as much lefs perfefV. In my fyftem, the only thirds perceptibly 

 greater than thofe of the equal temptrament, are the major thirds on E, A e s, B, C is, and 

 F i s, and the minor on C, C i s, F, G i s, Be s, and E e s. Of thefe none can be faid to 

 occur frequently, except the major third on E, and the minor on C. The fixths require 

 no feparate confideration. Now fince the minor chord is intended to be lefs completely 

 harmonious than the major, its charafter will be by no. means materially impaired by this 

 imperfeftion, which it would be fompwhat difficult to remove. The third on E is not 

 fharp enough to be very offenfive, but in compliance with the ufual pra£tice of making this 

 third fomewhat more perfe£t than the interval of A e s and C, I have, in the method recom^ 

 mended for common ufe, made it a better third than that of the equal temperament. The 

 dire£lions given for tuning in § 68, ahd in § 80, of the article, are liable to far greater ob- 

 Jeftions. For inftance, the temperament of the Illds on AesandFis, in the latter, is 

 about .00880, or more than a comma and a half ; which Profeflbr Robifon will readily 

 allow to be " much too great" for any thirds; fince he has afl"erted, with Dr. Smith and 

 othersj that the error of a comma would be intolerable. Mr. Maxwell has, however, very 

 decidedly proved, in his Eflay on Tune, that the greateft harmonifts, Corelli, Tartini, and 

 Glardini, have admitted very frequently the error of a comma in their moft refined compo- 

 Ctions. And I have the authority of feveral celebrated performers on ftringed and wind 

 inftruments for aflerting, that they take of choice the chara£leriftic femi-tone, leading into 

 the key note, confiderably fliarper than the fame note is tuned on any keyed inftruments, 

 making an imperfedtion of nearly two commas in the. relation as third of the dominant, 

 which is the fundamental note of the chord : while in the mean time our theorifts have 

 been labouring, by the moft complicated contrivances, to introduce notes into keyed inftru- 

 ments, which fnall have exadlly a contrary efib£t, by making the afcending femi-tone as wide 

 a ftep as poflible. On afking very lately the opinion of a practical mufician of g'-eat emi- 

 nence, and one, who in every refpeft does honour to his profcflion, he decidedly agreed in 

 the fuperiority of fuch a diminiftied femi-tone, and obferved that the key of E derived a 

 very elegant charafter from the ufual method of tuning D i s as E e s, a minor third to C : 

 hence, the Illds £ e s and G being very little tempered, the Illd on the dominant B muft 

 3 be 



