Abstract: A waveform of arbitrary complexity may be generated using a minimal number of circuit elements and minimal complexity by generating a frequency domain from a minimum set of base frequencies by storing lower octave frequencies of the minimal base set within a note memory. Selected octave and pitch, or note may be read from the note memory according to a list of notes to be thusly read as stored within a note list memory. Each of the instantaneous values of the base frequencies read from the note memory is then added in an accumulator to represent the instantaneous value of the sum of notes or tones comprising the complex frequency at that time. The application of process time periods will replicate an arbitrary complex waveform. Such a frequency generator can find wide application within electronic musical devices, tests and analysis instrumentation, communications and many other fields.