By the application of the principle of regeneration to certain modulation systems, a generator of submultiple or other fractional frequency ratio may be obtained. A simple example is obtained by considering a second-order modulator whose output is connected back to a conjugate input by means of a feedback loop including an amplifier and a selective network. If an inputfrequencyfo is applied, it is found that afrequency component f0/2 appearing in the feedback path will modulate with the applied frequency to produce sidebands of f0/2 and 3f0/2. The network and amplifier, being especially efficient for the frequency f0/2 and having a gain higher than the modulator loss, will reinforce this component causing it to build up to some steady-state value. Similar processes are possible by which greater submultiple ratios may be obtained. Since the output wave is obtained by a modulation process involving the input wave, it will appear only when an input is applied and then bears a fixed frequency ratio with respect to it. Experiments show that the ability of the generator to produce a fractional frequency is independent of phase shift in the feedback path. Circuits are possible in which the amplitude of the fractional-frequency wave will bear a linear relation to the input wave over a reasonable range and at the same time maintain a constant phase angle between the two waves. Typical circuits are discussed which make use of copper oxide as the modulator elements.