Abstract: A tone generator (501) for a musical synthesizer has digital waveform generators (602,603) arranged such that a proportion of an output from a waveform generator (602) is supplied to a phase modulating input of a next waveform generator (603), wherein a proportion of the output from the last waveform generator in a chain (603) of serially connected waveform generators is supplied to a phase modulating input of the first waveform generator (602) in said chain, thereby providing a degree of recursion. Outputs from a plurality of waveform generators are supplied to a ring modulator (604) for generating harmonic sums and differences of frequencies produced by said recursion. A variable precision waveform lookup table (803) may be used to select a particular harmonic characteristic of tone and a frequency doubler (1001) may be included in the feedback loop to enable tones containing predominantly odd harmonics to be generated.