The spectral power values representing Thornton's "alternative primary" PC, NP, and AP colour matching functions (CMF) are compared with the power values representing the 49-observer Stiles-Burch average definition. The Thornton measurements are first converted by matrix transformation into a data set expressed in terms of spectral power at the Stiles-Burch primary wavelengths. Graphs and power ratios are used to compare the definitions for two alternative matches to the same visual stimulus. A triplet of n:n spectral-power ratios (one in each dimension, R, G, and B) is used to quantify the differences between the alternative matches. The relationship between the Thornton PC and Stiles-Burch match-definitions is then found to deviate from the expected power-ratio of 1:1 after matrix transformation. The revealed relationship is an internally consistent and smooth function of matched wavelength, which has a different nonlinear characteristic in each R, G, and B dimension relative to the Stiles-Burch reference model. The "Thornton bow-tie" phenomenon is also demonstrated between a pair of maximum saturation CMF definitions made with alternative primaries. The implicit differences in neutral axis definition represented by the bow-tie diagram are linked to differences in trichromatic unit (T-unit) definition. In this case, the conventional CMF normalization process is postulated to be inaccurate at the wavelengths concerned, resulting in incompatibility between the T-unit definitions of the two primary sets being compared. The conventional N --> 3 T-unit definition of visual neutrality equating Illuminant S, to a single R:G:B power ratio is extended, by adding an extra N --> N mapping to the definition. The resulting N --> N --> 3 mapping is in principle a fully determined redefinition of three-dimensional T-unit equivalence, in which many R:G:B ratios for a comprehensive set of visually neutral metamers can be mapped by N --> N transformation onto the conventional single ratio. The effect of N --> N mapping is to transform spectral power distributions (SPDs) into spectral effect distributions (SEDs) expressed in T-units. The SPD/SED transform, thus defined, is proposed as a method for unifying CMF determinations made with alternative primaries. The expected outcome is that after transforming SPDs by N --> N mapping into SEDs the definitions for all visually matching metamers will be demonstrably interconvertible by matrix product. (C) 2004 Wiley Periodicals, Inc.