The main optical and electrical properties of the new, fast, and low-gain six-stage hemispherical photomultiplier tubes (PMTs) 9116A and 9117A from Electron Tubes Inc. have been studied in detail for their use in the air Cherenkov telescope MAGIC, a 17-m telescope to be installed in 2001 on the Canary Island of La Palma. Special emphasis is put on the discussion of the detection efficiency and the factors contributing to its absolute value and its uniformity over the photocathode. In particular, the photoelectron collection efficiency and its dependence on the voltage between the photocathode and first dynode have been measured. Also, the influence of the first dynode multiplication uniformity on the overall uniformity of the PMT response is discussed. The hemispherical cathode together with a specially shaped light concentrator allows increase of the effective quantum efficiency. This improvement has been measured as a function of wavelength. Aging and afterpulsing rate studies have been carried out at a PMT gain of 2 x 10(4).