Title
Non-linear systems in the spacing of musical scores

Abstract
Currently, an extension of Donald Knuth’s “Box and Glue” spacing algorithm called the “Spring and Rods” algorithm is used for the horizontal and vertical spacing of musical notation in three major open source music typesetting projects (LilyPond, MuseScore and Guido).  All of these programs treat spacing along the two axes as separate problems, using heuristics to resolve issues that arise when an object’s horizontal position depends on its vertical position and vice versa.  The present study attempts to formalize this problem by expressing circular spacing dependencies as non-linear dynamic systems.  Several methods, including convex optimization, machine learning and multi-pass algorithms are proposed to resolve these spacing problems.

About the presenter
Mike Solomon (www.mikesolomon.org) is currently a researcher with the Grame in Lyon, France and the artistic director of the Ensemble 101.  The recipient of several awards in music composition, theory and technology, his research centers on animated musical scores, musical notation spacing algorithms and participative musical engraving.