EXAMPLES OF VOWEL ANALYSIS. 



155 



The new ordinates are multiplied by the cosines as usual; the results 

 are given in the table on p. 154. 



The results of applying the schedules to the table are the values given 

 as a and b in the table of results of frictional analysis. The values a and 

 h are here the amplitudes of the cosine and sine series; the values of 

 f. = , ^r^s are the amplitudes of the single sine series. In the same way 

 as above (p. 139) q and r are computed. The plot of results is given in 



figure 136. 



We now have to calculate the inharmonic components from the table 

 of results. We find the ordinal numbers of the inharmonics for the curve 

 without friction, figure 135, from the values in column c. The groups of 

 ordinates are clearly marked off by minima at 0.24, 0.26, 0.09, 0.08, 0.05, 

 and 0.08. Dividing each of these in the ratio of its neighbors we have 

 for the highest component 



(14 X 0.03) + (15 X 0.15) + (16 X 0.35) + (17 X 0.21) + (18 X 0.08) _ jg g 

 0.03 + 0.05 + 0.35 +"0.21 + 0.08 



For the next highest component we have 



(11 X 0.04) + (12 X 0.11) + (13 X 0.13) + (14 X 0.02) ^ ^34 

 0.04 + 0.11 + 0.13 + 0.02 



Proceeding in this way we get the entire series of components above 

 the fundamental: 3.0, 5.3, 9.5, 12.4, 16.2. The fundamental we know 

 to be always present; it must therefore be added to the set. As approxi- 



