You can adjust the frequency produced by a ring oscillator with three inverters inserting a potentiometer in the feedback network as shown here. The value of the potentiometer can be increased if a wider range of frequencies is needed. The potentiometer can adopt values up to 10 M ohm. With the values shown in the diagram, the signals will be in the audio range. Any CMOS function that can be connected as inverter can be used in this circuit [4011, 4001. 4089, etc].
Variable Oscillator - Three Gates
