A circuit locks onto a frequency of data encoded on a medium, taking frequency variations in the physical travel of the medium into account. The circuit includes a disk locked clock (DLC) circuit having a synthesizer operating under digital control based on a feedback signal to produce a servo reference clock and a read reference clock that track frequency variations in the physical travel of the medium. A recovered clock signal is produced based on the servo reference clock and the read reference clock. A digital phase locked loop maintains a frequency lock of the recovered clock signal. An error measurement circuit is connected to the digital phase locked loop. The error measurement circuit produces the feedback signal for digitally controlling the digital logic circuit synthesizer to produce the servo reference clock and the read reference clock that track frequency variations in the physical travel of the medium.