The Bell System Technical Journal 



October, 1933 



Loudness, Its Definition, Measurement and Calculation* 



By HARVEY FLETCHER and W. A. MUNSON 



An empirical formula for calculating the loudness of any steady sound 

 from an analysis of the intensity and frequency of its components is devel- 

 oped in this article. The development is based on fundamental properties 

 of the hearing mechanism in such a way that a scale of loudness values 

 results. In order to determine the form of the function representing this 

 loudness scale and of the other factors entering into the loudness formula, 

 measurements were made of the loudness levels of many sounds, both of pure 

 tones and of complex wave forms. These tests are described and the method 

 of measuring loudness levels is discussed in detail. Definitions are given 

 endeavoring to clarify the terms used and the measurement of the physical 

 quantities which determine the characteristics of a sound wave stimulating 

 the auditory mechanism. 



Introduction 



LOUDNESS is a psychological term used to describe the magnitude 

 of an auditory sensation. Although we use the terms "very 

 loud," "loud," "moderately loud," "soft" and "very soft," corre- 

 sponding to the musical notations ff, f, mf, p, and pp, to define the 

 magnitude, it is evident that these terms are not at all precise and 

 depend upon the experience, the auditory acuity, and the customs of 

 the persons using them. If loudness depended only upon the intensity 

 of the sound wave producing the loudness, then measurements of the 

 physical intensity would definitely determine the loudness as sensed 

 by a typical individual and therefore could be used as a precise means 

 of defining it. However, no such simple relation exists. 



The magnitude of an auditory sensation, that is, the loudness of the 

 sound, is probably dependent upon the total number of nerve impulses 

 that reach the brain per second along the auditory tract. It is evident 

 that these auditory phenomena are dependent not alone upon the in- 

 tensity of the sound but also upon their physical composition. For 

 example, if a person listened to a flute and then to a bass drum placed 

 at such distances that the sounds coming from the two instruments 

 are judged to be equally loud, then the intensity of the sound at the ear 

 produced by the bass drum would be many times that produced by 

 the flute. 



If the composition of the sound, that is, its wave form, is held con- 

 stant, but its intensity at the ear of the listener varied, then the loud- 



* Jour. Acous. Soc. Amer., October, 1933. 



377 



