A gas burner system has a gas burner with a conduit through which an air-gas mixture is conducted; a variable-speed forced-air device that forces air through the conduit; a control valve that controls a supply of gas for mixture with the air to thereby form the air-gas mixture; and an electrode configured to ignite the air-gas mixture so as to produce a flame. The electrode is further configured to measure a flame ionization current associated with the flame. A controller is configured to actively control the variable-speed forced-air device based on the flame ionization current measured by the electrode so as to automatically avoid a flame harmonic mode of the gas burner. Corresponding methods are provided.