100 THE STUDY OF SPEECH CURVES. 



then schedules for 432. For V = 3T, just half as many would be 

 required in each case; for V = m.T, then m times as many. If r is the 

 number of ordinates measured and V = mT the form of the analysis, the 

 number of the schedules will be mr. 



The method is evidently of some importance. Thus a curve consist- 

 ing of an inharmonic with the period ^T = i^T— which was used as an 

 example to show the application of the harmonic analysis to an inharmonic 

 (p 77) — would be found at once with its exact period and amphtude by 

 an inharmonic analysis where V=2T; the labor required would not be 

 greater than that involved in the harmonic analysis with the subsequent 

 calculations (p. 79) . To obtain the higher inharmonics the analysis must be 

 more extended and a considerable number of ordinates must be measured. 



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FiQ. 89.— Clarionet. 



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Fig. 90.— Cornet. 



Fig. 91. — Saxophone. 



This method is applicable only when the vibration is maintained 

 unchanged for several waves. Such is undoubtedly the case in many 

 musical instruments, for example, the clarionet (figure 89), the cornet (figure 

 90), and the saxophone (figure 91) ; it is sometimes approximated in singing. 

 It is never the case in speech ; not only does the wave-length (period of the 

 tone from the glottis) change at every wave (it always rises, falls, or wavers, 

 p. 40), but the adjustments of the mouth and other vocal cavities also 

 change at every instant (p. 41). The conditions in two successive waves 

 are therefore different, and each wave must be treated by itself. It will 

 not do to simply repeat the ordinates of a single wave in order to obtain a 

 multiple one. This breaks the inharmonics off at odd points and begins 

 them at the same point for each wave; the results of repeating the ordi- 

 nates and then analyzing such a multiple wave are identical with those 

 furnished by the analysis of a single wave. 



