Regular Expressions as Violin Bowing Patterns

String players spend a significant amount of practice time creating and learning bowings. These may be indicated in the music using up-bow and down-bow symbols, but those traditional notations do not capture the complex bowing patterns that are latent within the music. Regular expressions, a mathematical notation for a simple class of formal languages, can describe precisely the bowing patterns that commonly arise in string music. A software tool based on regular expressions enables performers to search for passages that can be handled with similar bowings, and to edit them consistently. A computer-based music editor incorporating bowing patterns has been implemented, using Lilypond to typeset the music. Our approach has been evaluated by using the editor to study ten movements from six violin sonatas by W. A. Mozart. Our experience shows that the editor is successful at finding passages and inserting bowings; that relatively complex patterns occur a number of times; and that the bowings can be inserted automatically and consistently. A significant challenge faced by a string player learning a new piece is deciding on the bowings to be used. String players spend a significant amount of practice time creating and learning bowings. For this reason, teachers generally provide bowings for students until they are experienced enough to create their own. These may be indicated in the music using up-bow and down-bow symbols, but those traditional notations do not capture the complex bowing patterns that are latent within the music. Orchestral players also create bowings, agreed upon by the concertmaster and conductor, yet these may vanish when a rented orchestral part is cleaned up. String musicians know a great deal about bowings, but much of their knowledge is ephemeral and not permanently integrated into our musical heritage. Many music-editing software tools offer little help with bowings. They accept individual slurs, ties, and up-bow and down-bow symbols sprinkled throughout the text, but do not treat a complete bowing pattern as an object in its own right. This limits what the musician can do. For example, it is impossible to search for a specific bowing, or to look for passages where a similar approach would be suitable. In this article, we introduce explicit notation for bowing patterns, as well as a software tool that uses the patterns to give practical support to string players. Patterns can be used to define a class of passages that can be bowed in a particular way, and Computer Music Journal, 36:2, pp. 74–84, Summer 2012 c © 2012 Massachusetts Institute of Technology. they can also specify the bowings to be applied in matching passages. Bowing patterns help a string player to bow similar passages consistently. Patterns allow bowings to be treated as entities so that they can be defined, searched for, applied to music, stored in a database, and analyzed. Patterns are defined using regular expressions, a mathematical method for precisely defining the structure of a class of strings. This mathematical precision leads to clarity for the musician, and it provides a foundation for algorithms that operate on bowings. We write these patterns in both regular expression notation and using traditional music score notation. The score notation could be used directly by musicians without requiring that they learn how to write regular expressions, e. g., when editing orchestral parts on an electronic music stand. The patterns can be used both to search for suitable passages of music and to insert a bowing into the matching positions. This enables software to edit parts for different string sections in an ensemble so that their bowings are compatible, as well as to archive bowings in a database. To demonstrate the feasibility of this approach, we have implemented a prototype software music editor that implements bowing patterns. The music is entered in Lilypond notation (Lilypond is free software for typesetting music), and the regular expression bowing patterns are entered as character strings. The system can search the music for occurrences of a pattern, and it can insert bowings consistently. The software annotates the Lilypond notation accordingly, and uses Lilypond 74 Computer Music Journal to typeset the music with the bowing symbols inserted. Our approach has been evaluated by using the editor to study ten movements from six violin sonatas by W. A. Mozart. Our experience shows that the editor is successful at finding passages and inserting the bowings; that relatively complex patterns occur a number of times; and that the bowings can be inserted automatically and consistently.