Charts and formulas are presented for the calculation of the loudness of noises having approximately continuous spectra. By means of direct loudness matches it is shown that the loudnesses in octave bands can be combined according to the formula St = Sm+0.3(ΣS − Sm), where St is the loudness (in sones) of the total noise, Sm is the loudness of the loudest band, and ΣS is the sum of the loudnesses of all the bands. The loudnesses of the octave bands can be determined from measurements of their sound pressure levels by means of a chart based upon a new determination of the equal loudness contours for bands of noise. Other charts and formulas are presented for half- and third-octave band widths. Measurements were also made of the dependence of loudness on such factors as (a) separation between noncontiguous bands, (b) width of very narrow bands, and (c) rate and level of square wave modulation.
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S. S. Stevens (1956) studied this question.