(10) 



842 BELL SYSTEM TECHNICAL JOURNAL 



to deal with the average value for each of the five groups. The 

 average for the first group is designated Vi, signifying long-vowel 

 index; for the second group Vs, signifying short-vowel index; for the 

 third group C„, signifying nasalized-consonant index; for the fourth 

 group Cs, signifying stop-consonant index; for the fifth group C/, 

 signifying fricative-consonant index. If the articulation obtained from 

 any test for each sound be designated by the phonetic symbol for 

 that sound, then, 



Vi = .19 a + .27 e + .15 6 + .08 u + .14 o' + .17 a 



Vs = .30 i + .13 o + .10 a' + .04 u + -31 e + .02 y + .10 w 



Cn = .25 r + .24 I -f .08 ng + .26 n + .17 m 



Cs = .14 d + .31 t + .08 b + .10 p + .09 g + .18 k + .03 j 



+ .03 ch + .04 p 



Cf = .10 z + .32 s -f .10 V + .15 f + .02 zh + .11 sh 



+ .06 th' + .07 th + .07 st.. 



The sound index is related to these values by 



i = .162 Vi + .196 Vs + .255 C„ + .252 C. + .135 Cf. (11) 



For obtaining the most representative single value for the syllable 

 index /, the equation given below is used. 



/ = .5 r- + .5 i\ (12) 



This equation is based upon the frequenc}^ of occurrence of the syllable 

 forms in English speech. As pointed out before, if the compound 

 consonants be considered as simple sounds, then there are less than 

 10 per cent of syllable forms other than the two- and three-sound type. 

 The frequency of occurrence of these two types is approximately 

 equal. 



Similar formulae to the above may be used to relate articulation 

 results in English to articulation results in a different language. To 

 do this it is necessary to select the fundamental sounds of the different 

 languages that correspond to the 36 fundamental sounds of English, 

 where the correspondence is based on similar phonetic characteristics 

 and similar positions of the vocal organs in producing the sounds. 

 When this is done, the coefficients in Eqs. 10, 11 and 12, must be 

 modified to correspond with the frequencies of occurrence of the 

 sounds and syllables in the language. 



Observed values of individual sound articulation are thus reduced 



