34 



SCIENCE 



[N. S. Vol. XLIV. No. 1123 



a complete corps of efficient lecturers who 

 could answer the call to some local organiza- 

 tion. 



There are many individuals who are look- 

 ing for a field in which they can utilize their 

 executive powers in a worthy way. There are 

 many wealthy people who are ready and even 

 anxious to donate funds to a worthy cause. 

 We believe a no more worthy cause exists than 

 the one just suggested. 



Much work has already been accomplished 

 by organization such as the T. M. C. A. to en- 

 courage right living among young men, but 

 little of it touches the group of busy individ- 

 uals who are the victims as well as the causes 

 of the Period of Retrogression. 



C. H. Forsyth 



Ann Arbok, Mich. 



SPECIAL ARTICLES 



A METHOD OF PLOTTING THE INFLECTIONS 

 OF THE VOICE 



Some time ago, while the writer was en- 

 gaged in the study of the " tones " of certain 

 oriental languages, it became desirable to rep- 

 resent visually the tonal movements or figures 

 executed by the voice in actual speech. 

 Records of native speech were taken by the 

 Rousselot apparatus, and the wave-lengths in 

 each tracing were measured throughout, re- 

 sulting in a series of numbers for each utter- 

 ance — which series we may for the moment 

 suppose as included within the compass of two 

 octaves, from 10 to 40 of our scheme. 



In default of any record of previous at- 

 tempts of this kind, the following scheme was 

 first tried as the most obvious and simple. 

 Beginning at the top, the unit lines of the co- 

 ordinate paper were numbered in succession 

 downward from 10 to 40. Then beginning at 

 the left-hand margin the measured numbers 

 from the record were plotted in order, each 

 upon its numbered line, but each advanced be- 

 yond its predecessor by a constant interval 

 chosen after experiment as best suited to bring 

 out the features of the voice-inflection. A 

 continuous line drawn through the series of 

 plotted points would then represent the move- 

 ment of voice as regards pitch. Finally the 



whole was brought into relation with concert 

 pitch by measuring the wave-length of the 

 record of a C-fork and marking its place 

 among the numbered lines, and computing the 

 positions of the other notes of the scale ac- 

 cording to the well-known ratios of the dia- 

 tonic scale. 



The results seemed convincing; but a study 

 of them revealed a certain distortion of ver- 

 tical values similar in kind to the horizontal 

 distortion of Mercator's maps. This was due 

 to the fact that the number-intervals were 

 equally spaced, whereas to our thought and 

 visual imagination the semitone intervals are 

 equal. The first step toward remedying the 

 difficulty was obvious and easy. The letters 

 of the twelve semitones took the places of the 

 integers on the unit-lines of the chart. The 

 next step — to find the new places of these 

 integers — was not so easy. After some fum- 

 bling and groping the following points be- 

 came clear. 



1. Each semitone of the series brings with 

 it to its new place the same numerical value 

 which it had in its former position as a defi- 

 nite term of a geometrical progression of 

 twenty-four terms between 10 and 40, with 

 s -v(2 for the common ratio. In Table I. below 



are given these values for the upper octave. 

 Those for the lower octave are simply twice 

 these. These numbers were entered on the 

 chart against their respective semitones. 



2. The integral numbers must next be as- 

 signed to their proper stations within this 

 decimal series. Indeed 10, 20 and 40 already 

 appear in that series, and so are assigned to 

 position; while 15 and 30 are. so close to semi- 

 tone positions as to be practically coincident 

 with them. A rough determination of the 

 other positions might be made by the method 

 of proportional parts, but the only real deter- 

 mination is by solving the equation of the 

 geometrical progression just described. That 

 equation is y =■ a x , in which y and x are vari- 

 ables, and a is constant, namely the common 

 ratio 12 ->/2. The values of y are the integral 

 numbers from 10 to 40. By applying these 

 values in succession to the equation, the corre- 

 sponding values of x are obtained, that is the 



