The present study explores the applicability of a three-parameter equation: T-g = phi T-1(g,1) + (1 - phi(1))T-g,T-2 + phi(1)(1 -phi(1))[a(0) + a(1)(2 phi(1) - 1) + a(2)(2 phi(1) - 1)(2)] (where phi(i) and T-g,T-i are, respectively, the weight fraction and the glass transition temperature of the ith neat component), recently proposed for describing the T-g vs. composition dependencies in miscible binary polymer blends and copolymers (Brostow et al. Mater. Lett. 62 (2008) 3152 [16]). Its efficacy is postulated here also for mixtures of polymers with low molecular mass organics (solvent, plasticizer or semicrystalline drug molecule phases) and very strongly/weakly associating polymer blends, including interpolymer complexes. Binary systems where entropic factors overcome the enthalpic ones were also considered. For several complicated (asymmetric or sigmoid) dependencies a description with better accuracy was achieved, compared to the common theoretical or semi-empirical functional forms, some of which require parameters that are not always readily available to the experimentalist or contain a superfluous number of fitting parameters. First-(linear) or second-order(parabolic) polynomial dependencies are established among its prime parameter ao and "interaction terms" of common T-g(phi) functions, which are used as semi-quantitative measures of the strength of intermolecular interactions (e.g., parameter k(GT) of Gordon-Taylor, b of Jenckel-Heusch, and q of Kwei). Changes in the shape of the T-g(phi) plots, and the corresponding a(i) fitting parameter estimates, are discussed in relation to important physicochemical phenomena and properties of the mixtures, such as, the strength of the hetero-contact forces and their composition dependence, irregular excess free-volume effects, as well as nanoscale effects arising from variation of components molecular mass, chains' branching or organization in crystalline phases. (C) 2010 Elsevier B.V. All rights reserved.