# A simple grammar for music notation

A few years ago, I became interested in the prospect of using GNU Lilypond as a way to typeset musical scores. I knew about Lilypond and its Python API abjad through a fairly nifty hacker called Piaras Hoban, who was doing a doctorate at UCC at the same time I was skulking about as an undergraduate. This was back in 20082009. Actually, looking back on it, the environment in Cork was really conducive to cooperation between students and there was very little emphasis on making any really painful distinctions between grad and undergrad students. I mention this as a side note or preamble to what exactly this post is about.

Lilypond lets you express musical ideas in a very succinct form. It’s a powerful language and lets you do pretty much anything you want in terms of typesetting music but if you look at the very core of its syntax for expressing musical content, it’s very elegant.

For example, the phrase:


c''2 d''2 f''2. e''4 fs''1



Can be explained in terms of a grammar where:

{phrase}             := {complex tone} | {complex tone} {phrase}
{complex tone}       := {pitch}{complex rhythm}
{complex rhyhthm}    := {rhythm} | {rhythm}{augmentation}
{pitch}              := {pitchclass}{octave} | {pitch_regex}{accidental}{octave}
{rhythm}             := {rhythm_regex} | {rhythm_regex}{augmentation_regex}
{pitchclass}         := {pc_regex}
{octave}             := {oct_regex}
{oct_regex}          := /\'*|\,*/
{pc_regex}           := /[A-Ga-g]|[Rr]/
{accidental_regex}   := /|[f]*|(qf)?|(qs)?|[s]*|t?q?[fs]/
{rhythm_regex}       := /\d+/
{augmentation_regex} := /[.]+/


This is kind of a quick and dirty explanation that goes for the root of what is going on in terms of information within a string containing a musical phrase written in lilypond. Regular expressions (regex above) are a useful way to manipulate musical information within a score when you are editing lilypond with an editor like Frescobaldi. Actually, they are useful for editing any language in any editor.

What took me longer to realise was that regular expressions are also very useful if you want to write something that is accepted by a finite state machine. Languages contained within the Chomsky Hierarchy are one of the core building blocks in computer science. Unfortunately they are not yet teaching composers about regular languages at music university…so we have to somehow figure it out ourselves.

What basically attracted me to working with Lilypond a few years back, was that it seemed to open up some interesting possibilities for representing musical ideas in different ways. I’ve been interested in the music of Morton Feldman for a long time, where very subtle differences in notation are a central feature of the style.

abjad is an API for “Formalized Score Control” and it is very handy for manipulating lilypond strings. If you’re patient it’s also a pretty good way to manage scores. If longterm maintainability is your thing, you may want to consider either using a more minimal setup, or building your own interface library for abjad as the codebase gets refactored frequently.

Anyway, the point being that tools like abjad make it very easy to control aspects of a music score at a high level. This got me thinking about the idea of possibly trying to write a sort of notated [generative music]

So this year, Thomas Grill and I have been working together as part of the rotting sounds rotting sounds project. The project is largely focused on obsolesence and decay of digital audio. We spent a few months working on a score for ensemble and created an automated build process that exposed the compiled binary data to erosion each time a build is run, generating variations on the original score. The source code for the project is up on github under rill.