EXAMPLES OF VOWEL ANALYSIS. 



145 



but fails to continue the rapid fall for the first partial. We may suspect 

 that the first partial is also present. We have no means" of treating it as a 

 minimum, but we can continue the fall proportionately from 54.9 to 24.6 

 and then to 1 1 .0. We then assume a first coiiiponent with the wave- 

 length 360 and the amplitude 18.4— 11.0 = 7. 4mm. The large component 

 must now be recalculated. We have 



(1 X 11.0) + (2 X 24.6) + (3 X 54.9) + (4 X 68.5) + (5X 14.1 ) _ „ „q 

 11.0 + 24.6 + 54.9 + 68.5+14.1 



with the wave-length 106.2mm. and the amphtude91.4 

 monies is given in figure 125. 



We are now in position to discuss the accuracy of the results, 

 curve in figure 121 was obtained by adding the three curves 



The plot of inhar- 

 The 



y' = lo.e ^<">^^:sm^^t, y"= lOO.e -««"'. sin ^t, 



n — I, 

 360' 



271 



2/"'=10.e-°'^^sin ~t. 



100 



90 



80 



70 



60 



SO 



40 



30 



20 



10 



The curves themselves are given in figure 127; the 



true plot — or plot of components — is given in figure 128. 



The first maximum of the compound curves lay at 



102 above the axis; the true axis is therefore at 102 



below the tangential line and not 100, as found by 



the calculation on p. 141. The coefficient of friction 



was 0.0030, instead of 0.0028, as found on p. 141. The 



difference between these two values does not arise 



from the limited number of decimal places, but from 



the difficulty of obtaining the necessar}^ data from the 



curve. The results of the various methods of analysis 



are given in the "comparative table 



of results." It is at once evident 



that the only method that approaches 



the truth is the frictional analysis 



with the subsequent deduction of the 



inharmonics. 



Purely as a matter of curve analysis, without any consideration of 

 the processes in the vocal organs, we are forced to conclude that the simple 

 harmonic analysis — into harmonics or inharmonics — does not give even 

 an inkUng of the true composition of such a curve as that in figure 121. 

 As explained above (p. 77) the curve in figure 121 may be represented 

 by the results of the simple harmonic analysis, but that may just as truly 

 be done bj' any other analysis. A mere representation of the curve, hov.'- 



I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 IS 17 IS 



Fig. 128.- 



-Plot of actual components of 

 figiire 121. 



