PITCH FUNCTION 



297 





Numerical Scale of Pitch 



The " mel " is the subjective unit of pitch adopted from the root of the 

 word melody. A pitch of 1000 mels is arbitrarily assigned to a pure 

 1000-cycle tone of 40-db intensity above threshold; to the pitch of a tone 

 sounding half as high as 1000 mels a 

 pitch of 500 mels is assigned. To a 

 tone sounding half as high as 500 

 mels a pitch of 250 mels is assigned, 

 etc. 



On the assumption that it is pos- 

 sible quantitatively to judge that 

 " this pitch is half as high as the for- 

 mer one," a numerical scale of pitch 

 has been constructed by Stevens, 

 Volkmann, and Newman [1937]. The 

 change in pitch was measured by al- 

 lowing the observer to identify alter- 

 nately the pitch of two pure tones 

 maintained at a fixed loudness level. 

 One was maintained at a fixed fre- 

 quency, and the second could be varied 

 in frequency by the observer until its pitch was identified as half the pitch 

 of the fixed-frequency source. Ihe results showed, for instance, that a 

 tone whose pitch sounded half as high as the standard 1000-cycle fre- 

 quency was adjusted by the observer to a frequency of 440 cycles. 

 Figure VII-21 shows how an observer adjusts the frequencies of the 

 variable tones so that they may be experienced as half the pitch of the 

 standard tones. With the aid of this curve the pitch function can be 

 constructed. 



4M 



2M 



1M 



-500 



!200 



u-100 



100 200 500 LM 2M 5M 10M 20M 

 Frequency of standard 



Fig. VII-21. This shows the fre- 

 quency of a tone which sounds half as 

 high in pitch as a standard tone of 

 another frequency (Stevens, Volk- 

 mann, and Newman [1937]). (By 

 courtesy of Stevens and Davis, Hear- 

 ing, John Wiley & Sons, New York.) 



Pitch Function 



To the standard 1000-cycle source sounded at 40 db above threshold 

 was assigned a pitch of 1000 mels. To the 440-cycle source was assigned 

 a pitch of 500 mels, and similarly to all other values of the invariable fre- 

 quencies may be assigned pitches comparable to the experiences of the 

 observer. The relation between frequency and pitch may therefore be 

 obtained by plotting at an assigned loudness level these two quantities 

 in a coordinate system giving the pitch function shown in Fig. VII-22. 



This curve very definitely shows that the frequency-pitch reaction 

 is not a 1-to-l correspondence. Of particular value is the fact that below 

 a frequency of 1000 cycles the rise in the experienced pitch with increased 



