140 



THE STUDY OF SPEECH CURVES. 



when the curve is expressed as a sum of cosines and sines (p. 84) ; c gives 

 the ampUtude when the curve is expressed as a series of sines alone. The 

 values q and r are obtained as just explained. The harmonic plot is 

 given in figure 122. 



50 

 40 

 30 



20 

 10 



A. 



50 

 40 

 30 

 20 

 10 



I I I I 



I 2 3 4 5 5 7 8 9 10 II 12 13 14 15 16 17 18 



Fiu. 122. — Simple harmonic plot to figure 121. 



I 2 3 4 5 6 7 8 9 10 II 12 13 14 13 16 1/ 13 



Fio. 12.3— Plot of inharmonic components from 

 figure 122. 



Table op Resutlts of Simple Hahmonic Analysis op Figure 121. 



The simple harmonic analysis has not provided for the possible presence 

 of inharmonics (p. 77). If we suppose that inhannonics are present 

 and assume as manj^ as there are maxima in the harmonic plot we find 

 that there are three. The two minima 2.3 and 0.5 are then divided in 

 the ratios of their neighbors according to the nile given on p. 81. The 

 weighted mean of the first group is thus 



(IX 15.5) + (2x16.2) + (3X36.3)+ (4X44.3)+ (5X11.8) +(6X10.7) + (7X4.9)+ (8X2.8)+ (9X1.2) 

 15.5+16.2 + 36.9 + 44.3+11.8+10.7 + 5.4 + 2.8+1.2 



= 3.6; 



that is, the inharmonic has a wave-length 1/3.6 that of the fundamental, 

 or 100.0mm. The other two inharmonics have wave-lengths 1/10.6 and 



