128 



THE STUDY OF SPEECH CURVES. 



impression of a tone whose pitch is the mean for the group, and whose 

 timbre is the result of the distribution of the stimulation within the group. 

 For example, let us suppose that a tuning-fork of 100 vibrations per second 

 arouses a set of fibers with the relative strengths shown in figure 113; 

 the mental response is a tone of a certain pitch with the tuning-fork timbre. 

 We will suppose likewise a set of siren puffs to arouse fibers in the rela- 

 tions shown in figure 114; the mental response will be a tone of the same 

 pitch as the fork, but with the puff timbre. 



These facts I would account for on the centroid principle. The com- 

 plex of nerve currents produces mental results which are fused into a 

 single tone, whose period is the mean of the lot. The mode of distribu- 

 tion of the mental impression around the mean is what we feel as the 

 timbre of the tone. 



The term "mean" is purposely used. Although we have at present 

 no method for measuring the amplitudes of the vibrations of the fibers in 

 the ear or the intensities of the mental elements composing the impression, 

 it is presumably true that the pitch of the tone as perceived is a mean 



of the group. Whether it 

 is a simple average, or the 

 weighted mean, or some 

 other mean, must be left 

 for the future to decide. 



WTien two vibrations 

 stimulate overlapping 

 groups of fibers, some of 

 them must respond to the 

 sum of the impulses, and their nerves must likewise carry greater currents 

 than for each case separately. We must assume that the mental effect 

 is similarly composed of the overlapping impressions, and that the two 

 centroids with their timbres are resolved out of the group. Figure 115 

 illustrates the stimulation of the fibers of three tones singly, and, in the 

 lowest hne, by the same three simultaneously; the complex stimulation 

 in the last case produces the mental impression of three tones. 



A detailed treatment would need to consider the natural tone of each 

 fiber. As explained previously (p. 120) a vibration reaching a resonator 

 arouses two responses, one with the period of the vibration itself and one 

 with the period of the resonator. Each fiber of the ear must therefore 

 perform — like every other resonator at the first instant — the sum of two 

 vibrations, one with the period of the impressed force and one with its 

 own period. For musical tones where the same vibration is maintained, 

 the first component is of no importance because it rapidly disappears, 



Ail 



liii. 



Figs. 113,114. — Relative stimulations of acoustic fibers, 

 first and second cases. 



