The Paradigmatic Discourse on presto®

The presto® composition software was developed as a commercial implementation and operationalization of mathematical music theory. Several large compositions have been successfully realized on this software [101, 103, 680]. One of them will be discussed in chapter 51. We describe the overall architecture and functionality of presto®. This is mainly driven by a local/global paradigmatic perspective. The paradigmata of transformation and deformation are realized on (1) the level of modular affine transformations in the four-dimensional space of onset, pitch, duration, and loudness, and (2) the level of variational deformations. Both paradigmata are discussed and exemplified. We conclude the chapter with a remark on the problem of abstraction in paradigmatic composition, since composers tend to have major difficulties to get familiar with abstract paradigmatic structures.