August 8, 1878] 



NATURE 



395 



sung by one voice : that numbered 5 in our previous com- 

 munication. 



Table V, gives the amplitudes of the first six harmonic partial 

 tones for this series ; and Table VI. gives the same constituents 

 of another series of u's, sung by the voice formerly numbered i. 



Comparatively few curves have been transcribed for the sound 

 u, because the groups of constituents in this letter are much 

 simpler than those in o. Moreover, although the curves for 

 only two voices have been analysed, we have by numerous 

 examples satisfied ourselves that the selected examples represent 



with sufficient accuracy results produced by several other 

 voices. 



In examining Fig. 2 it must be borne in mind that the phono- 

 graph was turned in al 1 cases at approximately the same speed, 

 as accurately as this could be done by aid of a metronome. The 

 length of the period in the curve corresponds, therefore, to the 

 duration of the vibration which the voice produced on each 

 note. On the upper path of the scale the wave-forms are 

 almost exactly simple harmonic curves, but from ^ down to d 

 the period is composed of two halves each closely resembling 



T.'VBLE V. — Harmonic Constituents ofn Sung at Various Pitches by Voice N'o. 5. 



13-6 0-6 0-2 0-4- 



3-3- 



•lU-7- 



■ 1-4 0-4 0-3 



3-1- 



7-4 ■ 



■4-1 



1-8- 



•5-0- 



■2-8- 



0-4 0-6 0-3 



-0-3— -^-^0- 5-^—^0-1 ; 



Table VI. — Harmonic Constituents 0/ n Sung at Various Pilches by Voice No. l. 



9-4 0-7 0*2 0-3 0-2 



2-2- 



•18-9 



1-3 ■ 



•12-0 



2-2- 



■13-6- 



■0-6- 



-1-6- 



-0-3- 



2-1- 



2-7- 



-12-7- 



■VI- 



-1-4- 



-0-2 0-2 



' fhs 



r^r V 'Y^ '^'^¥r'^ ^'^'Y'v^''yyv'Y'''v^wy 



a simple harmonic cui-ve, so that the form on e, for example, is 

 not readily distinguished by eye from that on /, an octave higher. 

 Below d the curve breaks up into a somewhat irregular triplet. 



We will call the curves for the notes above b\} sunple u curves, 

 and those from ^downwards duplex it cmwQs. The analysis of 

 the duplex curves shows that they consist of a very weak prime 

 tone \\ith an immensely strong second partial. The figures and 

 tables might easily be extended above e', but it is unnecessary to 

 continue them, for the higher notes all give the same close 

 approximation to the simple harmonic wave. We cannot say 

 that we have obtained a good w below d from any voice. The 



marks on the tinfoil were always feeble, and the sound ai 

 repeated by the phonograph was little more than an inarticulate 

 groan. It will be observed that the note a is wanting in the 

 tables and in the figure. It has been omitted because we had 

 difficulty in getting a good it back from the phonograph when 

 the vowel was sung on this note. We have no doubt a good u 

 can be pronounced at this pitch, but we observed a constant 

 tendency towards the o character both in the curves and in the 

 sound ; that is to say, there was a tendency to give the two 

 lowest partials instead of a simple prime, or a strong second and 

 very weak prime. Moreover, the curves would vary in character 



