Arduino Tone Library at Low Clock Speeds

pert:
If you use an active piezo buzzer, it has the circuitry to generate an audible frequency built in to the buzzer so all you need to do to get a beep is set the output pin HIGH. Most of the piezo buzzers that are in an enclosure (rather than just the bare piezo discs) are active.

I need to generate the tone on the chip, to send the tone to another device.

I understand a slower clock speed may limit the range of frequencies that can be generated, but as long as I can get some good audible tones it's fine.