Disformal invariance of continuous media with linear equation of state

We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form $p=w\rho$ is invariant under a 1-parameter family of continuous disformal transformations. In the special case of $w=1\mathrm{/}3$ (ultrarelativistic gas), such a family reduces to conformal transformations. As examples, perfect fluids, homogeneous and isotropic solids are discussed.