Using previously published data and a few new data the compositions of protopyroxene, orthopyroxene, and pigeonite, coexisting with liquid in the system CaO-MgO-SiO2, are reviewed and shown to depend subtly on the number and nature of the coexisting phases such as forsterite, silica, other pyroxene, and liquid. Broadly, protopyroxene contains 0 to 1.0 wt. % CaO, orthopyroxene 1.4 to 2.2%, and pigeonite 3.0 to 6.5%, but pigeonite coexisting with olivine contains up to 1.5 wt. % more CaO than pigeonite coexisting with SiO2 at the same temperature.

In the system CaO-MgO-Al2O3-SiO2 some new analyses and all previously published microprobe analyses of pyroxenes fall into three compositional groups, which are hereafter used to name the pyroxene irrespective of whatever description the original authors gave to their products. For these groups, the compositional subtleties depend on the number and nature of coexisting phases and these are illustrated using sketches of the solid solution polyhedron for each phase, to illustrate, in particular, the decomposition of pigeonite as temperature drops, at 1276°C when forsterite, diopside and liquid coexist, but at other temperatures when other phases coexist. The assemblage orthopyroxene, anorthite, diopside, forsterite is established as the solidus at 1244°C by X-ray diffraction and by new microprobe analyses, and not protopyroxene with anorthite, diopside, and forsterite as was previously accepted. Liquidus surfaces for forsterite and protopyroxene, forsterite and orthopyroxene, and forsterite and pigeonite, are drawn, with temperature data, and several crystallization paths demonstrate the double resorption boundaries, forsterite-protopyroxene-orthopyroxene-liquid and forsterite-orthopyroxene-pigeonite-liquid, and demonstrate crystallization of four pyroxenes, resorption of three of them, and reprecipitation of a second generation of one of them.

No new data are presented for the solidus of the system CaO-MgO-SiO2, but a reinterpretation of the existing data suggests that the solvi of these alumina-free pyroxenes do not show an increase in CaO as temperature decreases. This is contrary to previous interpretations which have mingled data for alumina-bearing and alumina-free pyroxenes. The reinterpretation also favours the reaction protoenstatite + pigeonite ⇌ orthopyroxene at 1375°C and a revision of the previously accepted P-T (Schreinemaker's) net for the pyroxenes is proposed which does not accept orthopyroxene ⇌ protopyroxene + diopside at 1100°C at one bar, which previously has always been accepted by extrapolation from the experimental data at 1 kbar.