How to make a variable frequency circuit
This is called a VCO or resistor tuned oscillator.  The easiest are Realaxation OScillators with CMOS Schmitt Trigger, feedback pot (1M) and input shunt cap. For sine waves, A VCO is used with linear output or a BPF to make it a sine wave.

Define inputs and outputs for f , harmonics and voltage first. then look for hundreds of suitable solutions that exist for VCO, RF Tx etc.  Varicaps were once common for FM and used in VCXO's as well VC tuneable oscillators.  Define your sensitivity in Hz/V or KHz/V or MHz/V or kHz/Ohm in a relaxation oscillator with a fixed R and variable R as a % of total R or Voltage controlled Varicap for fine tuning.  

Basically you must DEFINE SPECS before starting ANY design.

But VCO's come in a wide range of solutions from very unstable but sensitive to wide tuining range, or very stable and precice control for small FM or PM modulation using VCXO.