Music, Grammar, and Information Theory
Spurred on by the idea of contour grammar, as explained in a recent post, I have been brainstorming grammar engines a good deal lately. I just finished drawing up a concept I call "unified grammar," which may present a promising method for abstracting units of pitch all the way up to phrases with contextual meaning. Of course, I wish to explore contour grammar a bit more before delving into a new grammar theory.
Thinking, however, has led me to an interesting proposition. I propose that much of the enjoyability of the music to which we listen stems from having a balanced amount of "information" contained within the music. This is not a novel theory, as others have explored it before - namely, Leonard Meyer. It struck me, as I analyzed one of my favorite orchestral pieces using my unified grammar method, that the melody of the piece could be represented, grammatically, by far fewer bytes of information than would be necessary to represent each pitch individually. That is, the melody had a sort of "compressibility" to it - one could compress the melody into several simple strings representing how values of different levels of a grammatical hierarchy change over time. It strikes me that the pieces of music I enjoy the most have some redundancy, but never too much.
Of course, it's obvious that music leans heavily on the concept of repetition, but information theory offers a new perspective in grammar applications. One could, for instance, limit the number of possible values for each level of the grammatical hierarchy, essentially placing an upper bound on the amount of information melodies could contain. This would prevent the piece from becoming too chaotic and uninterpretable. Likewise, one could place a lower bound on the number of values utilized for each level of the hierarchy, preventing the piece from becoming too monotonous. At the pitch level, this would mean that the melody must use between x and y unique pitches; at the word level, it would mean the melody must use between x and y different ways of grouping pitches; finally, at the phrase level, it would that the melody must use between x and y different ways of grouping words.
One final remark: ensuring that such restrictions are placed upon grammatical engines in no way ensures coherence in melody. At best, these restrictions can prevent monotony and chaos. They do not, however, guarantee meaningful music. For this reason, it is critical that the engine perform careful analysis when choosing how to group pitches and words in order to bring the grammar back down to a concrete level. Working with hierarchical abstractions always introduces a danger of becoming too removed. Consequence analysis must be performed at the base level - that is, at the pitch level - before decisions are made.