134 THE STUDY OF SPEECH CURVES. 



can not be distingiiislied from vocal curves; indeed, it can be expected to 

 counterfeit every curve of a vowel or a musical instrument blown by 

 the lips. 



The results from the pendulum apparatus make clear from the start 

 that — as the construction of the apparatus indicates — the vibrations are 

 interdependent. When the pendulums are fastened together by clamps 

 at the bottom, they all trace the same curve. When they are allowed 

 to swing freely, the bottom of the longest pendulum does not trace a sinu- 

 soid, but a curve depending on the vibrations of the other pendulums; 

 this curve thus depends essentially not only on the length of the longest 

 pendulum, but also on the lengths, weights, and periods of the smaller 

 ones and on the degree of friction. Applied to the voice, this indicates 

 that the vibrations of the largest element of the vocal cavity are deter- 

 mined not only by its size, its openings, and its internal friction, but also 

 by the sizes, openings, and friction of the connecting cavities; moreover, 

 not only the form of the vibration but its ver>' period are thus dependent. 

 We can reject as absolutely worthless a long EngUsh investigation in which 

 the tones of the vowels are calculated merely from the size of one large 

 cavity, because the tone of any one cavity depends on all the others and 

 on the openings. 



Another line of work closely connected with these experiments is the 

 computing and plotting of compound curves. Curves are calculated and 

 plotted on different assumptions until those are found which resemble the 

 curves obtained in the speech tracings. 



This method has the advantage that each factor is accurately known 

 from the start. It has the disadvantage that until the leading principles 

 are discovered, the work requires an incredible amount of time. The 

 method, however, is the only one that leads to a solution of some of the 

 vowel problems. 



The work was conducted on the following plan. A table was computed 

 for a set of " simple sinusoids," 



y=a.sm—t, 



for a=100, r=360, 180, 120, ... 36, and t = 5, 10, 15, ... 360. 

 The values of the elements depending on friction e~" for £ = 0.001, 

 0.002, 0.050, ... f = 5, 10, 15, . . . 360 were then computed, each 

 set of £ being written on a separate "friction shp." A friction shp was 

 then laid beside each of the "simple sinusoids" in succession and a table 

 for the " frictional sinusoids" 



y=a.e ".sin— :^ 



