Optimal Positioning in low-Dimensional control Spaces using Convex Optimization

A music analysis and control system for use in live performance is presented and demonstrated. Musical features, such as harmony, rhythmic patterning, or melodic structure, are extracted and automatically placed at appropriate locations in a control space. The control space is of low dimensionality, usually only two dimensions, wherein perceptual dissimilarity is represented as distance. The system can be viewed as a listening assistant that aids a performing computer musician with usable information about the evolving musical context so that the material under control can be adjusted to respond in interesting ways to that context. The method developed to position the points is based on a semidefinite programming relaxation of a nonconvex positioning problem and is both novel and elegant. Another novel feature of our work is an interprocess communication implementation that provides for two-way traffic between Max/MSP and MATLAB in realtime. We demonstrate the system with a harmony space and a melodic process space. The method is robust, rapid, and not plagued by problems with local minima. This successful use of convex optimization suggests that semidefinite programming may have broad application in the computer music field.