110 
Proceedings of Poyal Society of Edinburgh. [sess. 
The resonance is now, of course, spread out over a wider range of 
partials, and is easily seen to consist of two resonances, about half 
an octave apart. 
Next let us examine the series of nineteen analyses of Dutch aa t 
given by Dr Boeke in Pfliiger’s Archiv ., vol. i. pp. 312, 313. The 
analysis already shown in fig. 3 is No. 10 in that series. It is 
best to consider the series in two parts, viz., Nos. 1 to 9, which are 
sung by Herr von Duinen to a rising scale of notes, from c, 132 v.d., 
to d\ 297 v.d.; and Nos. 10 to 20 (No. 11 is missing), which were 
spoken by Dr Boeke at various (undesigned) pitches, from 175 to 
214*5 v.d. The unit of amplitude in the table is, in each case, the 
amplitude of the first partial, or fundamental. 
Herr von Duinen’s sung aa. 
v.d. 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
132, 
1 
0*63 
0*36 
0*40 
0*81 
0*36 
0*67 
0*23 
1.07 
016 
1*06 
0*67 
148*5, 
1 
2*10 
2-50 
1*54 
4*40 
0*00 
1*72 
219 
1*50 
1*20 
0*65 
0*76 
165, 
1 
0*81 
0*88 
1*30 
2*26 
1*14 
1*00 
1-32 
0*61 
0*16 
0*05 
0*13 
176, 
1 
0*95 
0*39 
1-22 
0-87 
0-83 
1*18 
0*68 
0*39 
0-21 
0*14 
0*33 
198, 
1 
0*19 
0-46 
0*93 
0*26 
0*46 
0*75 
0*23 
0*15 
0*09 
0*04 
0*03 
220, 
1 
0*36 
0*56 
1*09 
0*67 
0-95 
0*17 
0*36 
0*15 
0*17 
0*12 
0*13 
247*5, 
1 
0*41 
4*12 
0*79 
1*10 
0*64 
0*29 
0*28 
0*21 
0*17 
0*23 
0-29 
264, 
1 
1*13 
1*44 
1-19 
0*41 
0*22 
0-16 
0-13 
0*18 
0*20 
0-12 
0*20 
297, 
1 
2-68 
2*96 
6*50 
1*20 
0*56 
0*38 
0*36 
0*03 
0*24 
0*37 
0-24 ! 
| 
On inspecting these nine series of partials, it is easy to discern in 
the first seven of them the presence of both of the resonances which 
made themselves felt in the analysis of Dr Boeke’s aa , fig. 3. 
Proceeding to analyse these seven on the principle above recom- 
mended, we get the following table : — 
a- and ^-Resonances of Herr von Duinen’s sung aa. 
Y.D. 
Partials Reinforced. 
Mean Resonances. 
Radical 
Ratio. 
a 
/3 
a 
£ 
132, 
4-6 
8-10 
663 
1184 
1*785 
148-5, . 
4-6 
7-9 
707 
1204 
1*703 
165, 
4-6 
7-9 
828 
1304 
1-574 
176, 
3-5 
6-8 
748 
1229 
1-643 
198, 
3-5 
6-8 
779 
1361 
1*747 
220, 
2-5 
5-7 
860 
1266 
1*473 
247*5, . 
2-4 
4-7 
769 
1297 
1*686 
