A set of orthonormal color matching functions is developed, in which the first is an all-positive achromatic function, the second is redgreen, and the third can be loosely described as blueyellow. The achromatic function, proportional to the familiar $ \bar y $, is a sum of red and green cones. The redgreen function uses the same cone sensitivities, but subtracted, with coefficients so that it is orthogonal to the achromatic one. The third function involves all three cones, but is primarily a blue sensitivity. Using this basis to compute the tristimulus vectors of narrow-band lights at unit power gives Jozef Cohen's locus of unit monochromats, (LUM) an invariant shape now graphed in a space where the axes have intuitive meaning. The extreme points of the LUM reveal the wavelengths that act most strongly in mixtures, a close approximation to William Thornton's Prime Colors. In effect, decades of research converge in three functions and a vectorial schema, demystifying such issues as color rendering and the selection of additive primaries. (c) 2011 Wiley Periodicals, Inc. Col Res Appl, 2011.