  We present a number of independent flow observables that can be measured
using multiparticle azimuthal correlations in heavy-ion collisions. Some of
these observables are already well known, such as v2{2} and v2{4}, but most are
new--in particular, joint correlations between v1, v2 and v3. Taken together,
these measurements will allow for a more precise determination of the medium
properties than is currently possible. In particular, by taking ratios of these
observables, we construct quantities which are less sensitive to the
hydrodynamic response of the medium, and thus more directly characterize the
initial-state fluctuations of the event shape, which may constrain models for
early-time, non-equilibrium QCD dynamics. We present predictions for these
ratios using two Monte-Carlo models, and compare to available data.
