The Horizontal Spacing of Graphical Notation

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Abstract

While several articles have explored the automated spacing of a line of music, little attention has been paid to the automated spacing of graphical notation in the horizontal domain. This article proposes an algorithm to stretch and compress images so that they are able to be integrated into a traditional horizontal spacing model while still attaining certain “target points” in a score. This is done via a linear program that distributes stretching error over the graphical object. The linear program is described through a presentation of its constituent matrices along with several musical examples that demonstrate its functionality. The article concludes with ideas regarding the program’s broader applicability to the domain of graphical notation.