378 BELL SYSTEM TECHNICAL JOURNAL 



ness produced will be the same for the same intensity only if the same 

 or an equivalent ear is receiving the sound and also only if the listener 

 is in the same psychological and physiological conditions, with reference 

 to fatigue, attention, alertness, etc. Therefore, in order to determine 

 the loudness produced, it is necessary to define the intensity of the 

 sound, its physical composition, the kind of ear receiving it, and the 

 physiological and psychological conditions of the listener. In most 

 engineering problems we are interested mainly in the effect upon a 

 typical observer who is in a typical condition for listening. 



In a paper during 1921 one of us suggested using the number of 

 decibels above threshold as a measure of loudness and some experi- 

 mental data were presented on this basis. As more data were accumu- 

 lated it was evident that such a basis for defining loudness must be 

 abandoned. 



In 1924 in a paper by Steinberg and Fletcher ^ some data were 

 given which showed the effects of eliminating certain frequency bands 

 upon the loudness of the sound. By using such data as a basis, a 

 mathematical formula was given for calculating the loudness losses of 

 a sound being transmitted to the ear, due to changes in the trans- 

 mission system. The formula was limited in its application to the 

 particular sounds studied, namely, speech and a sound which was 

 generated by an electrical buzzer and called the test tone. 



In 1925 Steinberg ^ developed a formula for calculating the loudness 

 of any complex sound. The results computed by this formula agreed 

 with the data which were then available. However, as more data 

 have accumulated it has been found to be inadequate. Since that 

 time considerably more information concerning the mechanism of 

 hearing has been discovered and the technique in making loudness 

 measurements has advanced. Also more powerful methods for pro- 

 ducing complex tones of any known composition are now available. 

 For these reasons and because of the demand for a loudness formula of 

 general application, especially in connection with noise measurements, 

 the whole subject was reviewed by the Bell Telephone Laboratories and 

 the work reported in the present paper undertaken. This work has 

 resulted in better experimental methods for determining the loudness 

 level of any sustained complex sound and a formula which gives 

 calculated results in agreement with the great variety of loudness data 

 which are now available. 



' H. Fletcher and J. C. Steinberg, "Loudness of a Complex Sound," Phvs, Rev. 24, 

 306(1924). 



2 J. C. Steinberg, "The Loudness of a Sound and Its Physical Stimulus," Pliys. Rev. 

 26, 507 (1925). 



