AUDIBLE FREQUENCY RANGES 



621 



were never less than nine observers, and each had at least six trials on 

 each filter, the minimum number of observations used in computing the 

 percentage of correct judgments on any filter cut-ofif was 54. Several 

 times check tests were made in which the lights were changed, but no 

 filter was inserted. The average scores on these tests always were 

 within the limit 50 =t 4 per cent. 



Data 

 The filter cut-offs producing just noticeable effects upon the sounds 

 were not sharply defined. For every sound there was, between the cut- 

 off recognized every time and the cut-off never recognized, a certain 

 region of appreciable width where the percentage of correct judgments 

 decreased from 100 per cent to 50 per cent. If this percentage is 

 plotted against cut-off frequency a curve such as is shown in Fig. 4 



20 



50 



100 500 1,000 5,000 10,000 



CUT-OFF FREQUENCY IN CYCLES PER SECOND 

 Fig. 4 — Number of times filter condition was correctly perceived as function 

 of cut-off frequency — piano. 



results. Curves of this kind proved useful for interpolation purposes, 

 but their contours were felt to be too dependent upon the individual 

 peculiarities of observers and players to be of general significance. No 

 close correlation existed between the importance of any frequency range 

 and the contours of the curves, for the differences caused by the filters 

 that were recognizable in less than 80 per cent of the tests were very 

 small. In addition, some observers consider that elimination of high 

 frequencies improves the reproduction of certain musical sounds by 

 removing accompanying noises. Therefore it was decided that the 

 useful information from the data could best be presented by straight 

 lines. 



The audible frequency ranges of all the sounds tested have been 

 plotted in this way in Fig. 5. The end points for these lines have been 



