150 Dr. Young's Experiments and Inquiries, &c. 



Fig. 51. The appearance of a chord, when put in motion by 

 a bow applied nearly at one third of the length from its end.. 

 Fig. 52. The method of tuning recommended for common use. 



Plate VII. 



Fig. 5%. A comparative view of different systems of tem- 

 perament. The whole circumference represents an octave. The 

 inner circle L is divided into 30103 parts, corresponding with 

 the logarithmical parts of an octave. The next circle R shows 

 the magnitude of the simplest musical and other ratios. Q is di- 

 vided into twelve equal parts, representing the semitones of the 

 equal temperament described by Zarlino, differing but little 

 from the system of Aristoxenus, and warmly recommended by 

 Marpurg and other late writers. Y exhibits the system pro- 

 posed in this paper as the most desirable ; and P the practical 

 method nearly approaching to it, which corresponds with the 

 eleventh method in Marpurg's enumeration, except that, by 

 beginning with C instead of B, the practical effect of the tem- 

 perament is precisely inverted. K is the system of Kirnberger 

 and Sulzer ; which is derived from one perfect third, ten per- 

 fect and two equally imperfect fifths. M is the system of mean 

 tones, the sistema participate) of the old Italian writers, still fre- 

 quently used in tuning organs, approved also by Dr. Smith for 

 common use. S shows the result of all the calculations in Dr. 

 Smith's harmonics, the system proposed for his changeable 

 harpsichord, but neither in that nor any other form capable of 

 practical application. 



