80 



THE STUDY OF SPEECH CURVES. 



When we consider how an inharmonic appears in a harmonic analysis 

 (figure 76), the conclusion seems unavoidable that the members taken for 

 the weighted mean should not be broken oS so arbitrarily. In the example 

 just given the results are cut off at the 10th harmonic; 

 the strength of this harmonic makes it evident that at it 

 or just above it another strong tone must be present. The 

 amplitude of the 9th harmonic is due not only to the strong 

 tone between the 7th and 8th but also to that at or above 

 the 10th. |Since the amplitude for the 9th arose from at 



least two tones, one above and 

 one below, it might, therefore, 

 properly be divided between them. 

 Divided in the ratio of the neigh- 

 boring tones (50.2 : 14.6) the ampli- 

 tude 13.6 gives 10.5 and 3. 1. The 

 amplitude 2.2 of the 5th harmonic 

 might Ukewise be divided in the 

 ratio of the two neighboring tones 

 (13.9:7.3) giving 1.4 and 0.8. 

 For calculating the inharmonic between the 7 th and the 8th, we may 

 then use the neighboring parts of the 9th and 5th, giving 



AX)0 



3.50 



2.50 



2.00 



1.50 



1.00 



0.50 



Fig. 82.- 

 [a] in " 



-W.ave from 

 MarshaU." 



li.li.ll.ll 



u 



I 2 3 4 5 6 7 8 9 10 II 12 13 14 IS 16 17 18 19 20 



Fig. 83. — Harmonic plot to figure 82. 



Ig 



(1.4 



6.00 



5.50 



5.00 



1.50 



4.00 



3.50 



3J30 



2.50 



2.00 



1.50 



1.00 



050 



X5) + (13.9X 6) +(44.7x 7 ) + (50.2 X 8) + (10.5x 9 )_ ^ ^^ 

 1.4+13.9 + 44.7 + 50.2+10.5. 



The frequency of the inharmonic is thus 7.45 

 times 98, or 730 vibrations. 



The last calculation indicates the fundamen- 

 tal idea of the method I have adopted. In each 

 case it is assumed that there were present as 

 many component tones as there are prominent 

 harmonics in the harmonic plot; then every ampU- 

 tude that is smaller than both its neighbors is 

 divided into two parts proportional to their sizes; 

 the weighted mean is then calculated for each 

 group of ampUtudes around a maximum, the cal- 

 culation being extended to 

 the parts of the minimum 

 amplitudes. The following 

 examples will illustrate how 

 the component tones are ob- 

 tained from the results of a 

 harmonic analysis. 



3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 



I 2 



Fig. 84. — Component plot from figure 83 



