
HARMONIC ANALYSIS OF CERTAIN VOWEL SOUNDS. 751 
value of y, having used them before in another investigation, and we have 
verified them independently. They are given below :— 
1 
Av=55 ( Nn +HY2t Ys +44 +Y5+ Yc +Y; +Ys+ Yo Yt In +42) 
1 $e 
ap { 241 + Y3— Ys — 2Y1 -Yo FY + J3( to-go s+ Yx).} 
1 
Ar=75 ( 241+ Y2—Ys—2Ys— Ys + Yor 2 + Ys—Yo— 2Yro— Yu +n) 
1 
A;= fa (n-ys +Ys—- Yi +9) 
1 
M=B ( 291 —Yo— Yo 2Ys—Ys— Yo + 2Yi —Ys— Yo + 2Ys0 — Yr — 2 ) 
1 — ‘) 
Ao i5 2, + Y3—Ys— 2Y1 — Yo eel J/3(%2.—-Ys—-Ys +41) i 
il 
ei (1-Yt I —UtYs—Yet Ys —Yot Yo— oo + Jn—Yu) 
1 as 
1B =F | e+ 20+ YoYo 20 Yr + J/3(Y3+Ys—Y9— Yu) ; 
B, al Yat Y¥3— Ys— Yer Ys t+ Yo— Of ira) 
i 
Sa (Yt Yo-Yo+ Jw) 
bg= rar 3B ( Yo Ys t+ Ys—YotYs—Yo +91) 
1 A 
B= { ot 2st Yo-Yo var n/ dys +Y5—Ys—Yu) } 
The process of measurement and calculation indicated above has been 
applied to more than a hundred curves. It extended only to the sixth partial 
tone, and, already laborious, would have been far more so if an attempt had 
been made to carry it further. To do so, however, seemed to be unnecessary ; 
the results of the analysis showed that the curves were constituted essentially 
of low lying partials, and, independently of that, we knew beforehand that our 
phonograph was incapable of registering tones of very high pitch. A shrill 
whistle, however loud, made no impression on the tinfoil. No doubt, this 
accounts for the fact that the phonograph fails to reproduce certain vowels well, 
notably the sound 7 (as in machine), and the French or German #. It shows, 
however, that those vowels which the phonograph does speak well have their 
essential characteristics determined by comparatively low partial tones; and 
our investigation has been confined to vowels of this class. Several of the 
