98 THE STUDY OF SPEECH CURVES. 



When the vibration has several harmonic and inharmonic elements, 

 the harmonic analysis does not give the components. As indicated above, 

 the curve that furnishes the harmonic plot in fif::ure 81 may have been 

 produced by a set of simple sinusoids whose amphtudes are given in figure 

 80, or by a set with the amphtudes given in figure 81; in the former 

 five harmonics and one inharmonic were used; in the latter, only five 

 harmonics. The same curve could be just as well produced by any other 

 inharmonic below 5 in connection with 5 harmonics, the amplitudes being 

 appropriately selected. In every case the harmonic analysis would give 

 the result in figure 81. 



No matter how a curve was produced, the harmonic analysis will 

 always give the same result. When the possibility of the presence of 

 inharmonic components is admitted, the harmonic analysis of the curve 

 gives no conclusion, and the problem of its composition becomes inde- 

 terminate unless some hmiting suppositions are made. If we assume that 

 the vowel curs^e had as many chief components as there are maxima in 

 the harmonic plot, we can proceed to calculate these components as 

 indicated above (p. 79). 



