This article explains how to apply time--frequency scattering, a convolutional operator extracting modulations in the time--frequency domain at different rates and scales, to the re-synthesis and manipulation of audio textures. After implementing phase retrieval in the scattering network by gradient backpropagation, we introduce scale--rate DAFx, a class of audio transformations expressed in the domain of time--frequency scattering coefficients. One example of scale--rate DAFx is chirp rate inversion, which causes each sonic event to be locally reversed in time while leaving the arrow of time globally unchanged. Over the past two years, our work has led to the creation of four electroacoustic pieces: ``FAVN''; ``Modulator (Scattering Transform)''; ``Experimental Palimpsest''; ``Inspection''; and a remix of Lorenzo Senni's ``XAllegroX'', released by Warp Records on a vinyl entitled ``The Shape of RemiXXXes to Come''. The source code to reproduce experiments and figures is made freely available at: https://github.com/lostanlen/scattering.m. A companion website containing demos is at: https://lostanlen.com/pubs/dafx2019