Sones, Spectra, and Summation

Abstract

The current assumption that the loudness in sones of a noise is the sum of the loudnesses in the separate octave bands is shown under direct test to be grossly wrong. These tests show that the loudnesses in octave bands can be combined according to the formula St = Sm + F(ΣS − Sm) where St is the loudness (in sones) of the total noise, Sm is the loudness of the loudest band, ΣS is the sum of the loudnesses of all the bands, and F is a factor that may vary between zero and one. It turns out that under a wide variety of conditions the factor F has the value of 0.27. Consequently, the rule for combining the loudnesses in octave bands is simply this: to the loudness in sones of the loudest band add 0.27 times the sum of the sones in the remaining bands. In order to facilitate the determination of the loudness level (in phons) of the octave bands, equal loudness contours for octave bands were measured in a diffuse sound field. These contours differ markedly from the well-known contours for pure tones. Since loudness in sones S is related to loudness level in phons P by the relation, log S = 0.03P − 1.2, a chart can be constructed from which the loudness of a noise can be computed under the foregoing rule of summation.