Abstract: A system for updating a control coefficient to a target value during a prescribed number of periodic incremental update increments. The system divides the desired change in the value of the coefficient by the number of update increments. Specifically, the number of increments by the number of increments is limited to powers of two, so that the division can be accomplished simply by demarking the change in value according to the portion of number of increments, thereby separating the change into a quotient and a remainder. The value of each update increment is nominally equal to the quotient, with the remainder being distributed relatively evenly by adding one to selected updates.

Abstract: An oscillator for digital music synthesis that provides a smooth waveform that is rich in harmonic content and whose shape is continuously and dynamically variable over a wide range of harmonically rich shapes. The oscillator is efficient in that it generates the shapes in a time consonant with sampling rates commonly used in music synthesis, and is generally free of discontinuities which would otherwise create audible alias components on subsequent signal processing.