112 BELL SYSTEM TECHNICAL JOURNAL 



assume maximum coupling, i.e., ii = 1.75, we get Vi — 98 cu. cm. and 

 F2 = 62 cu. cm., which seems absurd; if we assumed for er a system of 

 only two degrees of freedom, the most reasonable course would be to 

 give ju a smaller value (say, unity) and solve on the basis that F2 > Vi 

 which would give (if Ki = 1.5) Vi = 45 cu. cm., V2 = 73 cu. cm., and 

 K2 = i-5 cm. These data are entered (very tentatively) in Fig. 5; 

 here again we revise the previous order, and place er between short a 

 and short e. 



It is not at all certain, however, from the spectra of the er sound 

 (see chart. Fig. 13, in the paper "The Sounds of Speech") that it is 

 produced by a system of only two degrees of freedom ; the analyses of 

 the female voices gave 3 definite peaks, and we note that when the tip 

 of the tongue is raised, for this sound, there is a third cavity betewen 

 the tongue and the lips which is doubtless significant. There will be 

 noted, with a question mark, a third line (of frequency about 700, for the 

 male voices) in the spectrum of er shown in Fig. 4. I have attempted, 

 from the three lines shown in Fig. 4, and some simple assump- 

 tions regarding the volumes and conductivities, to obtain a rough 

 solution, using 3 degrees of freedom for this sound; but none of these 

 results are entered in the chart, because they appear to be unreason- 

 able.^ 



No attempt has been made to subject the semi-vowel sounds 

 (/, wg, n, m) to dynamical calculations. It is evident from their 

 spectra (cf. "The Sounds of Speech") that they are produced by 

 systems of three or four degrees of freedom, which is to be expected, 

 if, in addition to mouth and pharynx, the tongue, naso-pharynx, or 



8 By trial and error it was hoped that some triply-resonant system could be found 

 which would give the spectrum of er, as shown in Fig. 4. After solving more than a 

 dozen of these systems, the best fit was one in which Vi =31, F2 = 63, V3 =31 cu. 

 cm.; Ki = Ki = \ cm., Kz = h cm. The calculated frequencies for this system are 

 445, 890, and 1,520 cycles. The trouble with this solution is that the middle cavity 

 ( V2, between the tongue and the roof of the mouth in this case) is the largest of the 

 three, which does not seem reasonable. A model made to these specifications, and 

 tried by the method described later, gave a sound something like er but not so satis- 

 factorily that one could accept this as a solution. Consequently it is not entered in 

 Fig. 5. 



At first, in a number of these attempted solutions, the innermost chamber, F3, 

 was taken as the largest of the three. These all led to too great a separation of the 

 two lower resonant frequencies to be acceptable. 



The sound er, in addition to the three resonances about as shown in the chart, may 

 contain a component of higher frequency; or it may be due to a progressive variation 

 or modulation of the two principal frequencies shown in the chart. Some of Paget's 

 results suggest this; and if this is so, it would be a most difficult vowel to imitate with 

 a. fixed resonator. It is possible that X-ray pictures may reveal some point hitherto 

 overlooked in the mouth adjustment for this sound. 



