1^0 Exper'nnetit: and Jfiqii'irus nfpeBing Sound and Light. 



Phte'v. 



Figs. 4 1 and 42. Two different pofitions of a major third, compofed of fimllar vlbrir 

 tlons, as reprefented by figures of fines. 



F'g* 43- ■^ contracted reprefentation of a feries of vibrations. A, a fimple uniform 

 found. B, the beating of two equal founds nearly in unifon, a;s derived from redilinear 

 figures. C, the teats of two equal founds, derived from figures of fines. D, a mufical 

 confonance, making by its frequent beats a fundamental harmonic. E, the imperfeft 

 beats of two unequal founds. 



Fig. 44. Various forms of the oibit of a mufical chord, when infleded, and when 

 ftruck. 



Fig. 45v Forms of the orbit, when the found is produced by means of a bow. 

 . Fig. 46. Epitrochoidal curves, formed by combining a fimple rotation or vibration with 

 Other fubordinate rotations or vibrations. 



Figs. 47 and 48. (in Plate VI.) The fuccefl'ive forms of a tended chord, when in- 

 flected and let go, according to the conftruftion of De la Grange and Euler. 



Figs. 49. The appearance of a vibrating chord which had been infleded in the middle, 

 the ftrongeft lines reprefcnting the mod luminous parts. 



Fig. 50. The appearance of a vibrating chord, when infleded at any other point thaa 

 the middle. 



Plate VI. 



Fig. 51. The appearance of a chord, when put in motion by a how applied nearly at 

 ene third of the length from its end. 



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



Fig. 53. A comparative view of different fyftems of temperament. The whole circum- 

 ference reprefenrs an odave. The inner circle L is divided into 3O1O3 parts, correfpond- 

 ing with the logarithmical parts of an odave. The next circle R (hows the magnitude of 

 the fimpleft mufical and other ratios. Q_ is divided into twelve equal parts, reprefenting 

 the femitones of the equal temperament defcribed by Zarlino, differing but little from the 

 fyftem of Ariftoxenus, and warmly recommended by Marpurg and other late writers. Y 

 exhibits the fyftem propofed in this paper as the moftdefirable; and P the pradical method 

 nearly approaching to it, which correfponds with the eleventh method in Marpurg"? enu-- 

 meration, except that, by beginning with C inftead of B, the pradical effed of the 

 temperament is precifely inverted. K is the fyftem of Kirnberger andSulzer; which is 

 derived from one perfed third, ten perfed and two equally imperfed fifths. M is the 

 ^ftem of mean tones, the JiJIema partkipato of the old Italian writers, ftill frequently ufed 

 in tuning organs, approved alfo by Dr. Smith for common ufe. S fliows the refult of alL 

 the calculations in Dr. Smith's harmonics, the fyftem propofed for his changeable harp- 

 (shord, but neither ia that not any other form capable of ^radical application. 



