Hadronic Z decay data taken with the ALEPH detector at LEP1 are used to mea
sure 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 i
nclusive 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 inclu
ding mass effects. Taking the first moment of the y(3) distribution, which
is the observable with the smallest hadronization corrections and systemati
c uncertainties, the result is
m(b)(M-z) = [3.27 +/- 0.22(stat) +/- 0.22(exp) +/- 0.38(had) +/- 0.16(theo)
] GeV/c(2) .
The measured ratio is alternatively employed to test the flavour independen
ce of the strong coupling constant for b and light quarks.