HARMONY IN MUSIC. 65 



You perceive that the pitch of the tone corresponds to the 

 length of the wave. To this we should add that the height of 

 the ridges, or, transferred to air, the degree of alternate con- 

 densation and rarefaction, corresponds to the loudness and 

 intensity of the tone. But waves of the same height may 

 have different forms. The crest of the ridge, for example, may 

 be rounded off or pointed. Corresponding varieties also occur 

 in waves of sound of the same pitch and loudness. The so- 

 called timbre or quality of tone is what corresponds to the form 

 of the waves of water. The conception of form is transferred 

 from waves of water to waves of sound. Supposing waves of 

 water of different forms to be pressed flat as before, the surface, 

 having been levelled, will of course display no differences of 

 form, but, in the interior of the mass of water, we shall have 

 different distributions of pressure, and hence of density, which 

 exactly correspond to the differences of form in the still uncom- 

 pressed surface. In this sense then we can continue to speak of 



FIG. 3. 



the form of waves of sound, and can represent it geometrically. 

 We make the curve rise where the pressure, and hence density, 

 increases, and fall where it diminishes just as if we had a 

 compressed fluid beneath the curve, which would expand to 

 the height of the curve in order to regain its natural density. 



Unfortunately, the form of waves of sound, on which de- 

 pends the quality of the tones produced by various sounding 

 bodies, can at present be assigned in only a very few cases. 



Among the forms of waves of sound which we are able to 

 determine with more exactness is one of great importance, here 

 termed the simple or pure wave-form, and represented in Fig. 3. 



this differs in different countries. Hence the figures of the author have 

 been left unreduced. They are sufficiently near to those usually adopted in 

 England, to occasion no difficulty to the reader in these general remarks. TK 

 I. P 



