HARMONY IN MUSIC. 67 



voices, singing the vowel oo in too, in the middle positions of their 

 register, appears not to differ materially from this form of wave. 

 We also know the laws of the motion of strings with suffi- 

 cient accuracy to assign in some cases the form of motion which 

 they impart to the air. Thus Fig. 4 represents the forms suc- 

 cessively assumed by a string struck, as in the German Zither, 

 by a pointed style [the plectrum of the ancient lyra, or the quill 

 of the old harpsichord, which may be easily imitated on a 

 guitar]. A a represents the form assumed by the string at the 

 moment of percussion. Then, at equal intervals of time, follow 

 the forms B, C, D, E, F, G ; and then, in inverse order, F, E, D, 

 C, B, A, and so on in perpetual repetition. The form of motion 

 which such a string, by means of an attached sounding-board, 

 imparts to the surrounding air, probably corresponds to the 

 broken line in Fig. 5, where h h indicates the position of equili- 

 brium, and the letters a b c d e f g show the line of the wave 

 which is produced by the action of several forms of string 

 marked by the corresponding capital letters in Fig. 4. It is 

 easily seen how greatly this form of wave (which of course 



FIG. 5. 



could not occur in water) differs from that of Fig. 3 (inde- 

 pendently of magnitude), as the string only imparts to the air a 

 series of short impulses, alternately directed to opposite sides. 1 

 The waves of air produced by the tone of a violin would, on 



FIG. 6. 



the same principle, be represented by Fig. 6. During each 



1 It is here assumed that the sounding-board and air in contact with it 

 immediately ohey the impulse given by the end of the string without exercising 

 a perceptible reaction on the motion of the string. 



F2 



