This disclosure describes techniques that make use of a waveform fetch unit that operates to retrieve waveform samples on behalf of each of a plurality of hardware processing elements that operate simultaneously to service various audio synthesis parameters generated from one or more audio files, such as musical instrument digital interface (MIDI) files. In one example, a method comprises receiving a request for a waveform sample from an audio processing element, and servicing the request by calculating a waveform sample number for the requested waveform sample based on a phase increment contained in the request and an audio synthesis parameter control word associated with the requested waveform sample, retrieving the waveform sample from a local cache using the waveform sample number, and sending the retrieved waveform sample to the requesting audio processing element.