JANUARY 13, 192 ij 



NATURE 



'JO 



was uriginally so produced. Such a deduction 

 has to be made on other grounds. The familiar 

 experiment with a piano string touched lightly in 

 the middle, then at one-third of its length, etc., 

 shows that it vibrates in harmonic parts; an 

 analysis that gives the harmonic components in 

 various amplitudes can be accepted at once as 

 indicating the strength of the components. An 

 analysis, however, that gives all the harmonics 

 as being present to some degree with a bunch of 

 strong ones at one or more points would indicate 

 at once that one or more inharmonics were present. 



.•\ harmonic analysis of the wave in Fig. 4 from 

 the first vowel in " .Marshall " gives the harmonic 

 plot shown in Kig. 5. This merely states that 

 the original wave can be reproduced bv using 

 harmonics in the relations indicated. The deduc- 

 tion concerning how the wave was originally pro- 

 duced is left for the person who interprets the 

 harmonic plot. , 



If such a result were obtained for a wave from 

 :i mii-ical .)r(hc>itr;i. \v<> should h.ive no hc'iif.-ition 



I 2 34 3«'t»K)ltl2l)UiSi6l/)4l920 



Ff&. 5.— Relative amplitudcji of the tinu^ouls found 

 hj harmoofc Analyti*. 



ill concluding that the wave was produced by a 

 summation of vibrations in the harmonic relation. 

 If the wave originated from a single source, we 

 should certainly not be justified in drawing the 

 s.ime conclusion without further evidence. In 

 seeking for further evidence we find, in the first 

 place, that the waves from musical instruments 

 so far as yet studied- the material is extremely 

 limited — do not give harmonic plots like that in 

 Fig. 5, and do give plots having one, two, or 

 three prominent harmonics with the others lack- 

 ing. This would agree with the known fact that 

 most musical instruments vibr;ite in harmoni<-s. 

 If the source of the wave were absolutelv un- 

 known, the most plausible deduction would be 

 that it was some iMxIy or Ixnlies that might vibrate 

 in either harmonics or inharmonics. \Ve should 

 take the weighted means of the groups a( strong 

 harmonics, and should find in this i;ise that the 

 '-omponents were the inharmonics 



». 1:9-3: 115: 176: 19.5. 



1 ii. 1. >uii . .in be expressed in the inharmonic plot 

 in Fig. 6. This conclusion is of vital im[K)rtancc, 

 l>eraHse such results are just those that are always 

 NO. 2672. VOL. [06] 



obtained from careful vowel analyses. The very 

 harmonic analysis itself leads to the conclusion 

 that the vowel tones may be inharmonic. 



In the analyses of vowel waves the fundamental 

 is indicated as weak (as in Fig. 5) or often almost 

 lacking. This fundamental represents the voice 

 tone or the tone from the larynx. We all know 

 that this is the strongest tone of all. We may not 

 be able to hear just what vowel a speaker or 

 singer is producing, but we certainlv know 

 whether he is using a high or a low tone of voice. 

 One writer, observing this peculiarity in the 

 analysis of the waves obtained from a phono- 

 graph, remarked that this instrument must be 

 deaf to the voice tone. He failed to consider that 

 if it was deaf to this tone it could not reproduce 

 it, and that even the most defective phonograph 

 will produce the voice tone so long as it makes 

 any noise at all. The weakness of the funda- 

 mental in l-'ig. 5, therefore, does not show that 



«00 

 550 

 900 

 «W 

 400 

 350 

 MO 

 250 

 200 



• 2 3 4 5 6 7 8 9 K} II I? 15 14 IS i^ 17 16 19 20 



Fn.. 6. - Relative amplitudes of the component inhar- 

 monics a* deduced from Fig. 5. 



the fundamental was lacking in the original 

 vibration. 



I^t us inquire what kind of a strong tone will 

 appear in the harmonic analysis with a weak 

 fundamental. This is the case with a series of 

 sharp puffs. If the period from one puff to the 

 next of a series is subjected to harmonic analysis, 

 the result shows a weak fundament.-U with all 

 the higher harmonics represented in ever-diminish- 

 ing amplitudes. The fundamentals in the vowel 

 curves are therefore not of the nature of sine 

 vibrations, but of series of more or less sharp 

 puffs. 



This is not a new theory of the vowels. In 

 1830 Willis published, in the Transactions of the 

 C.imbridge Philosophical Society, a paper on the 

 tones of the vowels and reed organ-pipes. He 

 .•issertcd that a vowel was composed of a series 

 of puffs with a set of inharmonic overtones. This 

 was rejected in favour of the harmonic theory by 

 Wheatstone, whose conclusions were accepted and 

 jlevclopcd by Helmholtz. For nearly a century 

 the harmonic theory has been universally accepted. 



