THE SOUNDS OV SlTJiCIl 613 



a non-pKriixIio futution, ri-prcscntiHl analytirall\- l)y a Fourier InlcRral, 

 not !)>■ a I'oiiritT St-rics. The continued repetition of the record, 

 however, builds up a peritKlic function consistinjj of a fund.iniental 

 and a series of harmonics. The magnitudes of tliese components hear 

 a simple relation to those of the infinitesimal components of corrcs-, 

 pon<ling fre<iuencies in the Fourier Integral, and it is this series of 

 relati\e amplitudes at different frequencies which is given hy the 

 mechanical analysis of the records. 



It would be possible to present these results as the sound spectra of 

 the vowels, showing their original acoustic pressure amplitudes' but 

 this treatment has been modified for practical reasons to take into 

 account the relative importance of the various pitches in hearing. 

 Using the available data on the relative sensitivity of the ear at 

 different frequencies* the pressure amplitude at each frequency has 

 been multiplied by the corresponding ear sensitivity- factor and the 

 resulting curses are taken as the effective amplitude frequency rela- 

 tions which are most generally characteristic of these sounds. 



The data from the four male records and from the four female 

 records of each sound are separately averaged and the resulting curves 

 are shown in the diagram (Fig. 13). This averaging process was 

 somehwat laborious because the analyses of the separate records were 

 made not with reference to predetermined frequency settings, but 

 rather for those critical frequencies which best determined the shapes 

 of the spectrum curves. The individual curves were therefore plotted 

 on the musical pitch scale and the average ordinates were then read off 

 for small intervals of pitch. These ordinates were then averaged 

 for each group of four analyses. These average ordinates (after being 

 corrected for the calibration of the recording apparatus) were then 

 multiplied by the ear sensitivity factors for the corresponding fre- 

 quencies. Thus the final spectrum diagram shows the relative im- 

 portance of the amplitudes of all the components of each vowel for 

 male and female speakers. 



The amplitude units are entirely arbitrary; it is only the shapes, 



' In Fig. 1, data have liecn given showing the actual distribution of energy in 

 average s()cerh. The tremendous concentration of energy in the lower frequencies 

 is somewhat misleading unless account is also taken of the much reduced sensitivity 

 of the ear in this region. 



♦See Bell System Tech. journal, \'ol. II, No. 4, Octolier, 1923. The paper on 

 Audition, by H. Fletcher, shows a graph of the "Threshold of Audibility" curve 

 from which these data were obtained. The ear sensitivity factors used, of course, 

 relate to the lower intensity levels; but it is thought that no essential inaccuracy 

 is thereby introduced, as the p<jsition of the characteristic frequencies of a given 

 vowel is subject to some variation with different sfx;akers, and moderate variations 

 in the height of these maxima in the energy spectra are not significant, except when 

 taken from cycle to cycle in the case of an individual sound. 



