LETTER RESPECTING SOUND AND LIOIIT. 



6U 



tciied major thirds as of no value, not 

 wiih regard to its intrinsic merits, but be- 

 cause it was not intended for any instrument 

 in common use ; since, in these instruments, 

 the difficulty is not so much how to divide 

 the imptrtection among the thirds and fii"ths 

 of the same scale, as to profiortion properly 

 the impeffections of the thirds of different 

 keys. Yet 1 do not mean it to be under- 

 stood, that I can agree to the solidity of those 

 foundations on which Dr. Smith lias built his 

 system for a single scale : although to Stan- 

 ley and foDoria it might be pleasing, because 

 its imperfections are far too small to offend 

 the ear. Professor llobison justly observes, 

 that different persons differ exceedingly in 

 their estimation of the effect of the same 

 temperament on different concords, and that 

 much of this arises from their different dis- 

 positions ; it appears, therefore, that Dr. 

 Smith was too precipitate in laying down his 

 principle for the comparison of the effects of 

 temperament. 



With respect to the system which I have 

 proposed. Professor Robison thinks, that the 

 temperanrents of several of the thirds which 

 occm- frequently are much too great. If we 

 wish to form a judgment of any system of 

 temperament, it must be by comparison with 

 some other. It does not appear with what 

 system Professor Robison would wish the 

 comparison to be made, but he rather seems 

 to incline to the equal temperament, al- 

 though he gives directions for tuning by an- 

 other. At any rate, no temperament of an 

 interval can be said to be much too great, 

 unless it be greater than that of the same in- 

 terval in the system of equal temperament ; 

 for, if any interval be made more perfect 

 than this, some other similar interval must 



be as much less perfect. In my system, the 

 only thirds perceptilily greater than those of 

 the equal tempeiaaient, are the major third* 

 on E, Acs, 13, C sharp, or Cis, and Fia, 

 and the minor on C, Cis, F, Gis, Besi 

 and F,es. Of these none can be said to oc- 

 cur frequently, except the major third on E, 

 and the minor on C. The sixths require no 

 separate consideration. Now, since the mi- 

 nor chord is intended to be less completely 

 harmonious than the major, its character will 

 be by no means materially impaired by this 

 imperfection, which it would be somewhat 

 difficult to remove. The third on E is noi 

 sharp enough to be very offensive, but in- 

 compliance with the usual practice of malc'- 

 ing this third somewhat more perfect than 

 the intervals of Aes and C, I have, in the 

 method recommended for common use, 

 made it equal to the third of the equal tem- 

 perament. The directions given for tuning, 

 in§ (is. and in § 80, of the article, are liable 

 to far greater objections. For instance, the 

 temperament of the lllds on Aes and Fis, 

 in the latter, is about .00880, or more than a 

 comma and a half; which Professor Robi- 

 son will readily allow to be " much too great" 

 for any thirds ; since he has asserted, • witli 

 Dr. Smith and others, that the error of a 

 comma would be intolerable. Mr. Maxwell 

 has, however, very decidedly proved, in his 

 Essay on Tune, that the greatest harmonists, 

 Corelli, Tartini, and Giardini, have admitted 

 very frequently the error of a comma, in 

 their most refined compositions. And I 

 have the authority of sev<;ral celebrated per- 

 formers on stringed and wind instruments, 

 for asserting, that they take of choice the 

 characteristic semitone, leading into the key 

 note, considerably sharper than the same 



