82 
Proceedings of Royal Society of Edinburgh. [sess. 
most accurate method of obtaining curves from the wax cylinder 
of the phonograph, but he has applied the Fourierian analysis with 
striking results in general support of the fixed pitch theory.* 
The method consists in measuring microscopically the transverse 
diameter of the impressions on the surface of the phonograph 
cylinder, on different (generally equidistant) parts of the period, 
and in inferring from these measurements the depth of the im- 
pressions on the same spot, or, in other words, deriving from them 
the curve of the tone which produced the impression. 
[Dr M'Kendrick here alluded to Dr Boeke’s paper, describing 
his method, in the Proceedings of the Royal Society of Edinburgh , 
1898.] 
Curves of the vowel-tones may also he obtained on a larger 
scale by M‘Kendrick’s t phonograph recorder. 
The following analyses, supplied by Boeke, are very instructive. 
The first is the analysis of the tones of a cornet. Observe how the 
intensity of the partials gradually diminishes : — 
Tone. 1 2 
/ =170 v.d., 1 1*05 
c' =256 „ 1 0-92 
g' =384 ,, 1 0*76 
c' = 512 „ 1 0*92 (?; 
3 4 5 
1-22 1*15 0-01 
0-81 0-53 0-39 
0-46 0*14 0 09 
0-30 0-14 0-15 
6 7 8 
0*80 0*53 0-28 
0-20 0-07 0*04 
0-06 0-07 0-02 
0*09 0*07 0-06 
9 10 Partials. 
0-13 0-10 „ 
0*06 0-04 ,, 
0-01 001 ,, 
0*03 0*02 „ 
Contrast this analysis with that of the vowel a, sung by Boeke 
(aged 50) on the notes / and c', and the same vowel on the notes 
of g' and c", sung by his son, aged 12, both like the vowel in the 
word “ heart.” It will be seen, from the analytical numbers, that 
the formant of the son’s vowel a was almost the same as that of 
the father, although the pitch of his voice was exactly an octave 
higher. 
Man, aged 50, singing aa — 
Pitch. 12 3 4 5 6 7 8 9 10 Partials. 
/ 170|? v.d., 1 0-86 0-46 V'U 1'90 1*55 0*51 0*54 0*43 0'44 „ 
c' 256 „ 1 0-49 1-96 V25 0‘60 0’56 0*23 0*05 0*06 0*10 ,, 
* I have to thank Dr Boeke for unpublished notes on the subject, and also 
for many interesting analyses. 
t M ‘Kendrick, “ Observations on the Phonograph,” Trans. Boy. Soc. Edin., 
vol. xxxviii. part iv. No. 22 ; also Proc. Roy. Soc.. Edin., 1896-97, “ Opening 
Address”; also Sound and Speech Waves as revealed by the Phonograph , 
London, 1897. 
