  Hadronic Z decay data taken with the ALEPH detector at LEP1 are used to
measure the three-jet rate as well as moments of various event-shape variables.
The ratios of the observables obtained from b-tagged events and from an
inclusive sample are determined. The mass of the b quark is extracted from a
fit to the measured ratios using a next-to-leading order prediction including
mass effects. Taking the first moment of the y3 distribution, which is the
observable with the smallest hadronization corrections and systematic
uncertainties, the result is: mb(MZ) = [3.27+-0.22(stat)
+-0.22(exp)+-0.38(had)+-0.16(theo)] GeV/c2. The measured ratio is alternatively
employed to test the flavour independence of the strong coupling constant for b
and light quarks.
