Nested modulator and feedback FM matching of instrument tones

Most previous work with nested and feedback frequency modulation (FM) has matched harmonic musical instrument tones with only a single carrier. This paper introduces a genetic algorithm technique for optimizing parameters for several carriers. We give results using the method to match a trumpet, tenor voice and Chinese pipa. The results show that feedback FM often gives the best matches when we compare the techniques against the same number of table lookups, indicating that feedback FM is a good choice for software synthesis. Double- or triple-nested modulator FM gives the best results for the same number of carriers, making them the best choices if nested FM hardware is available.