5J2 



EXPERIMENTS AND INQUIRIES 



comma, which will not offend the nicest ear; 

 E : C*, and A* : C, equal; F« : A« too 

 eharp by a comma ; and the major thirds of 

 all the intermediate keys more or less per- 

 fect, as they approach more or less to C in 

 the order of modulation. The fifths are per- 

 fect enough in every system. The results of 

 this method are shown in Table xii. In 

 practice, nearly the same effect may be very 

 simply produce«l, by tuning from C, to F, 

 Bi, E*, G«, C*, F«, six perfect fourths; 

 and C, G, D, A, E, B, F*, six equally im- 



perfect fifths. (Plate 5. Fig. 55.) If the un- 

 avoidable imperfections of the fourths be 

 such as to incline them to sharpness, the 

 temperament will approach more nearly to 

 equality, which is preferable to an inaccu- 

 racy on the other side. An easy method of 

 comparing different systems of temperament 

 is exhibited in Plate fi. Fig. 56, which may 

 readily be extended to all the systems that 

 have ever been invented. For the guitar, 

 the frets can scarcely be better fixed thaa 

 according to the equal temperament. 



Table xTi. 



A shows the division of a monochord corresponding to each note, in the system proposed; 

 B, the logarithm of the temperament of each of the major thirds; C, of the minor thirds ; 

 D, of the fifths ; C and D being both negative. 



Thus, Sir, I have endeavoured to advance 

 a few steps only, in the investigation of some 

 very obscure but interesting subjects. As far 

 as I know, most of these observations are 

 new ; but, if they should be found to have 

 been already made b} any other person, 

 their repetition in a connected chain of 

 inference may still be excusable. I am per- 

 suaded also, that at least some of the posi- 

 tions maintained are incontrovertibly con- 

 fiisteat with truth and nature; but, should 



further experiments tend to confute any opi- 

 nions that 1 have suggested, I shall relin- 

 quish them with as much readiness, as I have 

 long since abandoned the hypothesis, which 

 I once took the liberty of submitting to the 

 Royal Society, on the functions of the crys- 

 talline lens. 



I am, &c. 



Emanuel College, Cam- 

 bridge, SthJuly, 1709- 



THOMAS YOUNG. 



