We report intermediate resolution Hα spectroscopy of the black hole candidate Nova Muscae 1991 during quiescence. We classify the companion star as a K3-K4V which contributes 85±6 percent to the total flux from the binary. The photospheric absorption lines are broadened by 106±13 kms-1 with respect to template field stars, leading to a system mass ratio of q = M1/M2 = 7.8+3.4-2.0. Doppler imaging of the Hα line shows strong emission coming from the secondary star (EW = 3.1±0.6Å) which we associate with chromospheric activity. However, the hot-spot is not detected and this may indicate a lower mass transfer rate than in other X-ray transients of comparable orbital periods. The surface brightness distribution of the accretion disk in Hα follows a relation I∞R-1.1, less steep than typically observed in cataclysmic variables. Updated system parameters are also presented.