Abstract: A new method and apparatus for music synthesis is provided. A chaotic system is driven onto a periodic orbit by a compressed initialization code. A one-dimensional, periodic waveform is then produced from the periodic orbit. A variety of periodic orbits produces a variety of sounds, which sounds approximate the sounds of different musical instruments. By sampling the amplitude of the periodic waveforms over time, a digital version of the sound is produced. The frequency and duration of a note to be synthesized are produced by sampling the periodic waveform at the proper rate to produce the desired frequency and then repeating the waveform to produce a note of the required duration.