Smoothness under parameter changes: derivatives and total variation

Abstract

Apart from the sounds they make, synthesis models are distinguished by how the sound is controlled by synthesis parameters. Smoothness under parameter changes is often a desirable aspect of a synthesis model. The concept of smoothness can be made more accurate by regarding the synthesis model as a function that maps points in parameter space to points in a perceptual feature space. We introduce new conceptual tools for analyzing the smoothness related to the derivative and total variation of a function and apply them to FM synthesis and an ordinary differential equation. The proposed methods can be used to find well behaved regions in parameter space.

Proceedings of the 10th Sound and Music Computing Conference, Stockholm, Sweden (2013)