626 BELL SYSTEM TECHNICAL JOURNAL 



differences are small and the judgments are greatly affected by particu- 

 lar instruments. Clearly the quality rises rapidly as the cut-off is 

 extended upwards to 8000 cycles, or downward to 80 cycles, but out- 

 side these limits the results are inconclusive. Out of 370 ratings re- 

 corded, only a scattered 13 were greater than 1.0. In general, there- 

 fore, it must be concluded that reproduction of the full audible range 

 was preferred. 



The curves of Fig. 6 do not define acceptable frequency ranges 

 directly, but the method with slight changes would give them. The 

 observers would be instructed to judge whether for any particular ap- 

 plication the range being heard would be satisfactory. However, these 

 curves, coupled with the general experience of engineers and musicians 

 should aid in determining acceptable ranges where direct tests are im- 

 practicable. 



Conclusion 



The author is not familiar with any published results of comprehen- 

 sive listening tests that can be compared directly to these data. How- 

 ever, the audible ranges here presented have been compared with 

 physical measurements ^ of peak sound output of a number of the in- 

 struments. The physical measurements give the peak amplitudes in 

 octave ranges below 500 cycles, and in half octave ranges above this 

 point, whereas interpolation between these limits was possible in 

 selecting the audible ranges. On the other hand, auditory masking 

 must play a part in determining the audible cut-off points. Consider- 

 ing these limitations to comparison, the two sets of data are consistent 

 on every instrument tested in common. 



The more important results of the tests are considered to be as 

 follows : 



1. The piano was alone in producing tones with inaudible funda- 

 mentals. 



2. Audible frequencies down to 40 cycles were produced by the 

 musical instruments, but reproduction only to 60 cycles was con- 

 sidered almost as satisfactory. 



3. It was found that transmission of the highest audible frequencies 

 was needed for perfect reproduction of musical instruments, mainly 

 because of the noises accompanying the musical tones. A 10,000 cycle 

 upper cut-off had slight effect upon the tone quality of most instru- 

 ments, but a 5000 cycle cut-off had an appreciable effect upon all except 

 the large drums. 



1 "Absolute Amplitudes and Spectra of Certain Musical Instruments and Orches- 

 tras" by L. J. Sivian, Ji. K. Dunn and S. D. White, Jour. Acous. Soc. of Afnerica, 

 January, 1931. 



