Grammar Induction Algorithms for Rhythm: Exploring Melodic Structure and Text-Setting
Formal musical grammars offer the opportunity to study musical structure, as well as its underlying cognitive substrates, within a rigorous scientific framework. Grammar induction is the algorithmic extraction of a formal grammar from a corpus of musical examples. Computer-encoded music corpora have been increasingly available in recent years, spurring a growth in formal computational studies of music theory and cognition. Grammar induction promises to be a powerful and timely tool in this increasingly prominent research paradigm.
I will outline two grammar induction techniques that I developed, illustrating them with representative examples from the domain of musical and linguistic rhythm. The first technique builds a finite-state probabilistic musical grammar using an adaptation of a Hidden Markov Model (HMM) algorithm. The second technique extends the first by introducing structural hierarchy: using a vector-quantizer to identify recurring musical segments, one can progressively build a hierarchical HMM that models different levels of structure.
The examples used to illustrate the technique will include: (i) the rhythmic grammar of Renaissance vocal polyphony; and (ii) the rhythmic dimension of text-setting in a variety of musical styles. In all cases, the algorithmically-induced grammar reveals detailed and precise stylistic rules that govern the rhythmic profile of a melody as well as the correspondence between musical rhythm on the one hand and the prosody and meter of the sung text on the other.