76 



THE STUDY OF SPEECH CURVES. 



are multiplied by certain numbers and the results are ■written in a table. 

 Special patterns with perforations marked + and — are laid over this 

 table and the additions and subtractions are made as indicated by each 

 pattern. There are as many patterns as there are ordinates; the designs 

 for the patterns for 12, 24, 36, and 72 ordinates are given at the end of the 



volume. From the results for each pair of patterns 

 we obtain the amplitude of one of the simple har- 

 monics; thus with 12 ordinates we obtain the first 

 six harmonics, with 24 ordinates the first twelve, 

 etc. A detailed account of this method of analj^sis 

 is given in the latter part of this chapter; complete 

 examples are given in Chapter XI. 





Fig. 67. — Simple sinusoid. 



Fio. 68. — Sinusoids of different 

 amplitudes. 



Fig. 69.^ — Sinusoid a quarter period 

 ahead of that in figure 67. 



The wave in the top line of figure 71, when 

 analyzed, gives the simple sinusoids indicated below 

 it. A plot showing the relations of amplitude among 

 the harmonics is termed a " harmonic plot " ; that 

 for figure 71 is given in figure 72. The figures along 

 the X-axis give the ordinal numbers of the harmonics. 

 An ordinate is erected for each harmonic whose height 

 is 10 times the amplitude of the harmonic. The 

 accuracy of a harmonic analysis can be tested by combining the sinusoids 

 and comparing the resulting curve with the original. The three simple sinu- 

 soids of fig. 71, when added, give the original curve in the top line exactly. 

 The irregular curve (figure 73) requires a large number of harmonic 

 sinusoids to represent it with any approach to accuracy; if we are content 

 with the accuracy obtained by an analysis into 12 harmonics, the result 



Fig. 70. — Harmonic series of 

 simple sinusoids. 



