It’s a bit more complicated than this. A lot of big generators are induction generators, and the associated electronics can make a tradeoff of voltage and frequency. In a grid setting, the frequency will be maintained at 60 Hz plus or minus not very much. Everything is, hopefully, arranged to maintain the correct voltage and frequency. The actual mechanism behind this have always struck me as arcane and somewhat fragile, especially in light of modern loads that don’t act at all like resistors under varying voltage conditions.