STKIJJGS 75 



concentrated at a point. If we were to imagine it distributed 

 continuously over a short length of the string this would 

 further increase the relative weight of the lower harmonics 

 (see 38). 



According to a general principle, which is here exemplified, 

 and which will be further referred to in the next chapter, 

 the higher harmonics are excited in greater relative intensity, 

 the more abrupt the character of the originating disturbance. 

 From a musical point of view the harmonics after about the 

 sixth are to be discouraged, since they come sufficiently 

 near to one another in the scale to be mutually discordant. 

 In the pianoforte the hammers are covered with layers of softer 

 material, so that the variation of pressure during the impact 

 is rendered more gradual. 



The point at which the blow is delivered is also a matter 

 of importance. To obtain a note of rich musical quality the 

 lower harmonics should be present in considerable force, and 

 the middle regions of the string are on this account to be 

 avoided. On the other hand, the harmonics of higher order 

 than the sixth are prejudicial, as already stated. Both re- 

 quirements are met by fixing the striking point at a distance 

 of about one-seventh of the length from one end. The partial 

 tones which have nodes at or near this point will then not 

 be excited at all, or only with comparatively feeble intensity. 



27. Vibrations of a Violin String. 



The theory of the vibrations of a string when excited by 

 bowing is somewhat difficult, but the main features have been 

 elucidated by Helmholtz. Since the pitch is found to be that 

 natural to the string, the vibrations are to be regarded as in 

 a sense " free," the function of the bow being to maintain the 

 motion by supplying energy to make up for the losses by 

 dissipation. In the case of the violin &c., where the strings 

 are of light material and pass over a bridge resting on a very 

 sensitive surface (of the resonance cavity), these losses may 

 be relatively considerable. The mode of action of the bow 

 appears to be that it drags the string with it for a time by 

 friction, until at length the latter springs back ; after a further 



