The production of coherent radiation at ever-shorter wavelengths has been a long-standing chal- lenge since the invention of lasers[1, 2] and subsequent demonstration of frequency doubling[3]. Modern x-ray free-electron lasers (FELs) use relativistic electrons to produce intense x-ray pulses at few-femtosecond timescales[4-6]. However, the shot noise that seeds the amplification produces pulses with a noisy spectrum and limited temporal coherence. To produce stable transform-limited pulses, a seeding scheme called echo-enabled harmonic generation (EEHG) has been proposed[7, 8] which harnesses the highly nonlinear phase mixing of the celebrated echo phenomenon[9] to generate coherent harmonic density modulations in the electron beam with conventional lasers. Here we report on a demonstration of EEHG up to the 75th harmonic, where 32 nm light is produced from a 2400 nm laser. We also demonstrate that individual harmonic amplitudes are controlled by simple adjustment of the phase mixing. Results show the potential of laser-based manipulations to achieve precise control over the coherent spectrum in future x-ray FELs for new science[10, 11]. Show Partial Abstract