A method and apparatus for producing a tone (e.g. for music) without use of a waveform memory and using a feedback loop. The feedback loop includes a waveform generator which calculates, in real time, a parabolic approximation to a sine wave. The feedback loop includes a delay phase differencer to eliminate hunting. The output waveform from the feedback loop is provided to a sine function generator which approximates a sine value using a third order polynomial, to provide the output tone.