A mapping or a function is a rule that assigns a unique entry y for a given argument x, for example y = Sin x. This paper takes a holistic approach to this classical mathematical paradigm whereby the efficacy of mapping is discovered in the periphery of musical control, ranging from interactive musical systems to digital instruments.

Three different viewpoints on mapping are identified: a systems view that focuses on the association between parameters; a functional view that relies on building parameter spaces (this is the holistic approach); and a perceptual view that concerns perceived intentionality and expression.

The authors stress the second aspect, formalizing it “with a geometric interpretation” and provide a framework for its analysis. Finally, they present “examples of mapping control structures for … natural feel and subtle articulation possibilities,” using what they claim as “a fairly limited input control device.” According to the authors, this holistic approach, which changes “the geometric and topological structure of the mapping” with an objective of making the control-to-sound coupling dynamic, “illustrates the way that the desire to create certain control or sonic gestures is built into the mapping control structure itself.”

The paper is no doubt interesting and should be of interest to music researchers and software professionals specializing in music system designs.