One of the primary science goals of the next generation of hard X-ray timing instruments is to determine the equation of state of the matter at supranuclear densities inside neutron stars, by measuring the radius of neutron stars with different masses to accuracies of a few percent. Three main techniques can be used to achieve this goal. The first involves waveform modelling. The flux we observe from a hotspot on the neutron star surface offset from the rotational pole will be modulated by the star's rotation, and this periodic modulation at the spin frequency is called a pulsation. As the photons propagate through the curved space-time of the star, information about mass and radius is encoded into the shape of the waveform (pulse profile) via special and general relativistic effects. Using pulsations from known sources (which have hotspots that develop either during thermonuclear bursts or due to channelled accretion) it is possible to obtain tight constraints on mass and radius. The second technique involves characterising the spin distribution of accreting neutron stars. A large collecting area enables highly sensitive searches for weak or intermittent pulsations (which yield spin) from the many accreting neutron stars whose spin rates are not yet known. The most rapidly rotating stars provide a very clean constraint, since the limiting spin rate where the equatorial surface velocity is comparable to the local orbital velocity, at which mass-shedding occurs, is a function of mass and radius. However the overall spin distribution also provides a guide to the torque mechanisms in operation and the moment of inertia, both of which can depend sensitively on dense matter physics. The third technique is to search for quasiperiodic oscillations in X-ray flux associated with global seismic vibrations of magnetars (the most highly magnetized neutron stars), triggered by magnetic explosions. The vibrational frequencies depend on stellar parameters including the dense matter equation of state, and large area X-ray timing instruments would provide much improved detection capability. We illustrate how these complementary X-ray timing techniques can be used to constrain the dense matter equation of state, and discuss the results that might be expected from a 10m 2 instrument. We also discuss how the results from such a facility would compare to other astronomical investigations of neutron star properties.