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Hole-doped high-temperature cuprate superconductors below optimum doping have electronlike Fermi surfaces occupying a small fraction of the Brillouin zone. There is strong evidence that this is linked to charge density wave (CDW) order, which reconstructs the large holelike Fermi surfaces predicted by band structure calculations. Recent experiments have revealed the structure of the two CDW components in the benchmark bilayer material YBa2Cu3O7−x in high field where quantum oscillation (QO) measurements are performed. We have combined these results with a tight-binding description of the bands in a single bilayer to give a minimal model revealing the essential physics of the situation. Here we show that this approach, combined with the effects of spin-orbit interactions and the pseudogap, gives a good qualitative description of the multiple frequencies seen in the QO observations in this material. Magnetic breakdown through weak CDW splitting of the bands will lead to a field dependence of the QO spectrum and to the observed fourfold symmetry of the results in tilted fields.