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With demonstrated applications ranging from metrology to telecommunications, soliton microresonator frequency combs have emerged over the past decade as a remarkable new technology. However, standard implementations only allow for the generation of combs whose repetition rate is tied close to the fundamental resonator free-spectral range (FSR), offering little or no dynamic control over the comb line spacing. Here we propose and experimentally demonstrate harmonic and rational harmonic driving as novel techniques that allow for the robust generation of soliton frequency combs with discretely adjustable frequency spacing. By driving an integrated Kerr microresonator with a periodic train of picosecond pulses whose repetition rate is set close to an integer harmonic of the 3.23 GHz cavity FSR, we deterministically generate soliton frequency combs with frequency spacings discretely adjustable between 3.23 GHz and 19.38 GHz. More remarkably, we also demonstrate that driving the resonator at rational fractions of the FSR allows for the generation of combs whose frequency spacing corresponds to an integer harmonic of the pump repetition rate. By measuring the combs' radio-frequency spectrum, we confirm operation in the low-noise soliton regime with no supermode noise. The novel techniques demonstrated in our work provide new degrees of freedom for the design of synchronously pumped soliton frequency combs.