The ash-fall and outflow sheets of the 0.7-m.y.-old Bishop Tuff represent >170 km3 of compositionally zoned rhyolitic magma emplaced during collapse of the Long Valley caldera, California. Field, mineralogic, and chemical evidence agree that tapping of the thermally and chemically zoned chamber was continuous, without interruptions sufficient to permit mixing or phase re-equilibration. Fe-Ti oxide temperatures for 68 glassy samples increase systematically with eruptive progress from 720 to 790 °C; this increase corresponds well with the stratigraphic sequence, but the temperatures in no way correspond to the degree of welding. Ubiquitous quartz, sanidine, oligoclase, biotite, ilmenite, titanomagnetite, zircon, and apatite change composition progressively with temperature. The uniformity within every sample of each mineral species (irrespective of size and whether discrete or as inclusions) is not compatible with protracted crystal settling. Euhedral allanite (ρ > 4, La + Ce > 16% by weight) occurs in all early-erupted samples (720 to 763 °C) but in none erupted later. Despite this, whole-rock La + Ce values increased threefold during the eruption. Pyrrhotite, hypersthene, and augite appear abruptly at 737 °C and occur in all later samples. These sharp isothermal interfaces indicate lack of any extensive history of crystal settling. Whole-rock major-element gradients were modest, but many trace-element concentration gradients were very steep despite a drop of only ∼2% by weight SiO2 within the magma volume erupted. Enrichment factors (the ratio of the value in the early-erupted samples to the value in the late-erupted samples) are Ba, 0.02; Sr, 2.5; Cs, 3.8; Nb, >5; Rb/Sr, 22; Mg/Fe, 0.1; Ce/Yb 0.2; Eu/Eu*, 0.07; Zr/Hf, 0.65; Ba/K, 0.02; and Ba/Rb, 0.01. These can neither have been established by transfer of any reasonable combination of phenocrysts nor inherited from progressive partial melting. Abundant bulk and phenocrystic data further exclude large-scale assimilation, liquid immiscibility, and contamination by underplating mafic magma. The compositional and thermal gradients existed in the liquid prior to phenocryst precipitation and developed largely independently of crystal-liquid equilibria. Within water- and halogen-enriched high-silica roof zones of large magma chambers, chemical separations take place through the combined effects of convective circulation, internal diffusion, complexation, and wall-rock exchange to develop compositional gradients, which are linked to gradients in the structure of the melt and are controlled by the thermal and gravitational fields of the magma chamber itself. Liquid-state differentiation through processes of convection-driven thermogravitational diffusion probably requires progressive establishment of a stable density gradient in order to retard convective re-mixing of the zoned upper part of the system. These processes evidently produce differentiated tops on magma bodies that represent a wide range in initial bulk composition. The degree of enrichment within a given chamber probably reflects the repose time between eruptions, the volatile flux, and the rate of energy transfer from the mantle more than it does the bulk composition of the unerupted dominant volume. Dikes and stocks injected above such a system will be either barren of or enriched in elements susceptible to subsequent hydrothermal concentration to ore grades; enrichment or barrenness depends on the timing of emplacement relative to cycles of enrichment and eruption. Crystal-liquid equilibria probably predominate during initial generation of the dominant magma volume as well as during its ultimate plutonic consolidation. Thermogravitationally generated, strongly differentiated capping magmas commonly erupt, but some crystallize as alaskites, leucogranites, and granite porphyries, and some may be resorbed by the dominant volume during the waning stages of a pluton’s magmatic lifetime.