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Five kinds of loudness functions were examined to determine a suitable function for drawing equal-loudness-level contours based on experimental data. First, equal-loudness relations were measured between 125-Hz and 1-kHz pure tones from 70 phons down to 5 phons and thresholds of hearing were measured at both frequencies. Then, five model equations expressing the equal-loudness relation were derived from the five loudness functions, and these equations were fitted to the data. The results showed that three of them could well explain the equal-loudness relation down to 5 phons. Among the three functions, the loudness function proposed by Zwislocki and Hellman [J. Acoust. Soc. Am., 32, 924 (1960)] and Lochner and Burger [J. Acoust. Soc. Am., 33, 1705–1707 (1961)] was regarded as the most appropriate function for drawing equal-loudness-level contours, because the number of parameters of the function was fewer than that in the other two and the threshold of hearing could be used for the fitting as a datum of the equal-loudness relation, resulting in a more stable estimation of the parameters of the model equation.

Comparison of loudness functions suitable for drawing equal-loudness-level contours.