Loudness Calculation and Critical Bands

Abstract

The formula St = Sm + F(ΣS − Sm) is a linear approximation expressing total loudness St in terms of the loudness of the loudest band Sm and the sum ΣS of the loudnesses of all other bands. It has been shown that this formula holds when steady noises having reasonably continuous spectra are analyzed in terms of octave bands. The value of F is then 0.3. The purpose here is to apply the formula to half-octave and third-octave bands by a procedure slightly different from the one presented earlier. It is found that a single set of equal loudness contours can be used for all widths of bands, provided the values of F are properly chosen. These values are 0.2 for half-octaves and 0.15 for third octaves. A set of equal loudness contours has been so drawn that they can be used as an overlay with standard plotting papers for octave, half-octave, and third-octave bands. This greatly facilitates the procedure of calculating loudness. If further major improvement is to be made in loudness calculation, it will probably prove necessary to analyze sound spectra in terms of critical band widths instead of in terms of the octave systems. The existence of a critical band width in loudness summation [see Zwicker, Flottorp, and Stevens, J. Acoust. Soc. Am. (to be published)] suggests a “natural” division of the sound spectrum that may eventually prove more useful than the octave systems.