Biological oscillators adapt to environmental changes with widely tunable frequencies, a property theoretical studies attributed to positive feedbacks. However, no experiments have tested this theory. Here, we created synthetic cells to independently tune the frequency and feedback strength of a cell-cycle oscillator, enabling continuous mapping of period landscape in response to network perturbations. We found that although inhibiting positive feedback of cyclin-dependent kinase (Cdk1) reduces the tunability, the reduction is not as significant as theoretically...