Abstract: A frequency synthesizer, responsive to a reference signal having a frequency f.sub.r, for supplying an output signal at a frequency selectable from M times N signal frequencies (where M and N are preselected integers) is disclosed. In each disclosed arrangement, a set of M signals that are each harmonically related to f.sub.r is derived by a cascade connected harmonic generator and comb filter, and a set of M signals that are each harmonically related to f.sub.r /M is derived from the reference signal by a cascaded frequency divider, harmonic generator and comb filter. Each of these signal frequencies within the two sets of signals can be selectively coupled to the input ports of signal mixing apparatus and bandpass filtering is employed to couple either the mixer sum or difference frequency to the synthesizer output terminal. In some situations, a single mixer circuit and bandpass filter is employed.