In a sound waveform synthesizer, a waveform data supplying section reads the waveform data from a storage medium for supplying the waveform data to a waveform buffer in response to a first transfer request. A waveform data processing section retrieves the waveform data from the waveform buffer in response to a second transfer request. The waveform data processing section performs sound waveform synthesis based on the retrieved waveform data and given control parameters, while notifying a state and progress of the sound waveform synthesis to a control data processing section. The control data processing section issues the first transfer request based on the notified progress of the sound waveform synthesis. The control data processing section receives waveform control information from an outside and creates the control parameters based on the waveform control information and the notified state of the sound waveform synthesis. The control data processing section issues the second transfer request corresponding to the first transfer request together with the created control parameters to the waveform data processing section.