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)]\gevcc.
The measured ratio is alternatively employed to test the flavour independence of the strong coupling constant for b and light quarks.