HARMONIC ANALYSIS. 



83 



another? Do these differences lie in the presence of certain tones of 

 definite pitch (Helmholtz, Hermann)? If so, are these tones overtones of 

 the glottal tone (Helmholtz), or inharmonic to it (Hermann)? Do the 

 differences he in the relations of the cavity tones to one another? On 

 any of these principles what distinguishes [a] from [o], etc.? It is evident 

 that a theory of the vowels is involved; whether the simple inharmonic 

 analysis can give results reliable enough to furnish a decision is a matter 

 for investigation. In the following chapters some modifications of this 



5.00 

 4.50 

 4.00 

 3.50 

 300 

 2.50 

 2.00 



uo 



1.00 



0.50 



piG. 8.5. — Wave from 

 [a] in"caUed." 



6.S0 

 6X30 

 S.50 

 5.00 

 ^4^50 

 4.00 

 3.S0 

 3JM 



a.oo 



1.50 



ijoo 



n.50 



I I I I I I I I ■ ■ ■ 



1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 O 20 



Fia. 86. — Harmonic plot to figure 85. 



J L 



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



Fig. 87.— Component plot from figure 86. 



method will be considered, after which will follow a discussion of the 

 applicability of the different procedures. 



We will now turn to a detailed treatment of the method of harmonic 

 analysis; the reader who does not wish to follow it can proceed to the 

 following chapter without interruption of the train of thought. 



In a " simple sinusoid" function of the form 



y = a.sin(^t-q) 



(1) 



y is the elongation at the moment /, a is the amplitude or the maximum 

 value of y, T is the period, or the time of one complete cycle. The phase q 

 depends on the moment from which t is calculated ; if i is taken from the 



