We report intermediate resolution H alpha spectroscopy of the black hole candidate Nova Muscae 1991 during quiescence. We classify the companion star as a K3-K4V which contributes 85 plusmn 6 percent to the total flux from the binary. The photospheric absorption lines are broadened by 106 plusmn 13 km s^-1 with respect to template field stars, leading to a system mass ratio of q = M_1/M_2 = 7.8^+3.4_-2.0. Doppler imaging of the H alpha line shows strong emission coming from the secondary star (EW = 3.1 plusmn 0.6 Angstrom) 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 H alpha follows a relation I propto R^-1.1, less steep than typically observed in cataclysmic variables. Updated system parameters are also presented.