308 K W. Scripture — Nature of Vowels. 



of the impressed force. If the variations of the acting force 

 are of the nature of a sum of harmonics, the period impressed 

 will be that of one of them. If the cords acted like most 

 musical instruments, their vibrations could be properly treated 

 as the sum of a series of harmonics and the mouth tone would 

 necessarily be one of them. " The forced vibrations of the 

 mouth cavity can include only harmonic partials of the larynx 

 note." * 



It has been shown above that the mouth tone is inharmonic 

 to the cord tone and that it is &free vibration. It follows that 

 the cord vibrations are not of the nature of the sum of a 

 series of harmonics. Hermann draws the conclusion that the 

 vibrations of the cords must be of an explosive nature, to 

 which a harmonic analysis is not applicable. To this it has 

 been answered that when the mouth tone is high in relation to 

 the cord tone, the treatment by analysis into a series of har- 

 monics may not be applicable and that this may not disturb 

 the usual views of resonance, but that, when the natural period 

 of the mouth cavity is not distant from the cord period, the 

 cavity must vibrate- with a period that is harmonic to the cord 

 period, f Rayleigh apparently does not regard the deductions 

 of Hermann as conclusive. The issue seems clearly presented 

 in the curves of the nature of those in tig. 1. In the first part 

 of the vowel a in 1 the cord tone rises steadily till it is only 

 about a duodecime below the mouth tone, and yet the mouth 

 tone remains constant with no attempt at becoming one of the 

 harmonics of the cord tone. Continuing along the curve, we 

 find that beyond the middle the period of the mouth vibration 

 is somewhat lengthened while that of the cord vibration con- 

 tinues to become shorter. In the latter third of the curve the 

 vibrations are clearly in groups of twos, alternate ones being 

 stronger. As the change from the a portion to the i portion 

 is continuous without anything like a break that might indicate 

 a sudden readjustment of the cords, each pair of waves in the 

 i. portion must belong to one cord vibration and each single 

 wave must represent a mouth vibration. The mouth period is 

 slightly less than half the cord period. Thus even when the 

 two tones used in forming the vowel i are nearly in the relation 

 of a simple musical interval, there is no accommodation of one 

 to the other. It is to be noticed that the first vibration of 

 each pair in the i is stronger than the second, just as in the a 

 portion the first vibration is stronger than the following ones. 

 It is worthy of remark that the relative strengths are not the 

 same in the two cases and that the character of the explosion 

 from the cords must differ to some extent in the two halves of 

 ai. Similar conditions are found in the other vowels. 



* Rayleigh, Theory of Sound, § 397. f Rayleigh, § 397. 



