Relation of long-term adaptation to the loudness-function slope

The decline in loudness over time, defined as simple loudness adaptation, is modeled by introducing temporal factors into the nonadapted loudness function. This modification generates effective time-dependent intensity and threshold shifts. Model predictions for several frequencies are in accord with recent psychophysical measures [Hellman et al., J. Acoust. Soc. Am. 101, 2176–2185 (1997)]. In contrast to the time constant description of adaptation, the present method produces a direct connection to properties of the loudness function. A consequence of this connection is the demonstration that the increase in loudness adaptation with decreases in SL is linearly related to the loudness-function slope in log–log coordinates. Moreover, the good agreement between the measured and predicted loudness-adaptation data implies a consistency and stability in the use of numbers for loudness judgments.