126 THE STUDY OF SPEECH CURVES. 



To this last conclusion we have to object that it is inconsistent with 

 the Helmholtz theory. 



For the sake of completeness let us assume that the ear contains 

 fibers tuned from one vibration per second to 30,000, all being harmonic 

 to the first. That the fibers of the ear may not be tuned exactly as har- 

 monics to the lowest one or that the lowest may have a frequency greater 

 than one per second, are secondary conditions. 



Let a vowel sung on the tone 200 reach the ear. A harmonic analysis 

 of a single wave provides for the tones 200, 400, 600, 800, etc., but it does 

 not provide for the tones 201, 202, 203, etc. Nevertheless these tones 

 are harmonic to the lowest fiber of the ear. The ear, in fact, provides 

 for an inharmonic analysis of the sound on the basis of a very low funda- 

 mental. The simple harmonic analysis with the fundamental 200 can 

 not possibly give the inharmonic tones of the vowel, although the ear 

 will do so. How investigators can have supposed for many decades that 

 the harmonic analysis of a single vibration in any way represents the 

 action in the ear or gives the components as perceived by it on the Helm- 

 holtz theory is absolutely unintelligible. 



It is remarkable that Helmholtz says: "Willis's description of the 

 vibratory movement in the vowels certainly comes close to the reaUty, 

 but it describes only the way in which the vibrations take place in the 

 air and not the reaction of the ear to these vibrations."* In spite of thus 

 admitting the puff theory to be correct, Helmholtz develops a directly 

 opposed one wherein the glottal lips act Uke membranesf and the vocal 

 cavities respond Uke resonators with hard walls. J This he did because 

 he beheved that such a theory was required by his theory of hearing, the 

 thought being first that the ear performs a harmonic analysis of all sounds 

 and then that vowel vibrations must be built up of harmonics. As has just 

 been shown, Helmholtz should have pointed out that the ear provides for 

 an analysis on the basis of a deep fundamental, and the harmonic analysis 

 where the fundamental is the lowest tone of the wave is utterly inadequate 

 to represent the action in the ear. He should then have repeated that 

 the harmonic analysis thus "remains an arbitrary fiction without a real 

 meaning." As explained in a previous chapter, the harmonic analysis can 

 be applied to any curve and gives no indication of the manner in which it 

 was actually produced. 



The usual version of the Helmholtz theory overlooks several import- 

 ant facts of resonance. The fibers of the ear are strongly damped, not 



* Helmholtz, as before, 191. 

 t Helmholtz, as before, 162. 

 } Helmholtz, as before, 186. 



