The band structure of ordered β-brass (β′-CuZn) has been calculated throughout the Brillouin zone by the augmented-plane-wave method. The present band model differs from previous calculations with respect to the position and width of the Cu 3d band. The derived dielectric function ε2(ω) and the photoemission spectra agree well with experiments. We find that the main absorption edge as observed in the ε2 trace has contributions from conduction-band transitions as well as transitions from the Cu d states. The comparison to photoemission results indicates that the calculated Cu d bands are too narrow, but that their position relative to the Fermi level is correct. The derived Fermi-surface model allows a detailed interpretation of the de Hass-van Alphen (dHvA) data. The present model has no open orbit along for B→∥ 〈110〉. This agrees with dHvA as well as magnetoresistance measurements. Four new extremal cross sections have been found and related to previously unexplained dHvA frequencies. In general, the Fermi-surface dimensions agree extremely well with dHvA measurements, and the ratios between the experimental and the calculated cyclotron masses vary between 1.18 and 1.43.