The theory of statistical fluctuations has been applied to fitting Munsell data for nearly neutral specimens. This leads to a form of hyperbolic cosine law for lightness value expressed as a function of luminous reflectance. An inverse relationship can be readily obtained in terms of standard mathematical functions. Account is taken of the effects of adaptation.
H. W. Holdaway, "Fluctuation theory of luminance applied to the Munsell scale of lightness," J. Opt. Soc. Am. 63, 1613-1615 (1973)