Undulosity in quartz from low rank metamorphic rocks, as studied with a universal stage, is sufficiently different from that in pluton-derived quartz to be useful in provenance interpretation. Subdivision of monocrystalline quartz of medium sand-size into two populations, one with <=s 5 degrees undulosity and one with > 5 degrees undulosity, enables efficient and reliable interpretation. Geometrical and empirical analyses of the relation between true angles of undulosity and corresponding apparent values determined on a conventional flat stage indicate that apparent values approach real values closely enough to obviate use of the universal stage for recognition of the two quartz undulosity populations in routine petrographic analysis. The amount of polycrystalline quartz and the number of crystals per grain of polycrystalline quartz in medium-sized Holocene sand also assist in provenance interpretation. Thirteen percent of the total quartz derived from plutonic rocks is polycrystalline. This compares with 29% in sand from middle and upper-rank metamorphic rocks and 53% in sand from low-rank metamorphic rocks. Greater than 75% of the polycrystalline quartz grains from plutonic and high-rank metamorphic sources contain 2-3 crystal units per grain; less than 75% of the quartz grains from low-rank metamorphic rocks contain 2-3 crystal units. Plotting of four variables, relative percentage of (1) undulose, (2) non-undulose and (3) polycrystalline quartz, and (4) number of crystal units per polycrystalline grain, on a single diamond diagram enables one to discriminate sands of plutonic, low-rank and high-rank metamorphic parentage, both for Recent and ancient sands.