A pregroup grammar for chord sequences

Abstract

In 1984, Mark Steedman proposed a generative grammar based on six context sensitive rewriting rules able to produce a large variety of blues chord sequences. Later, François Pachet (1998) developed a method for analysing jazz chord sequences. Then, Marc Chemiller (2004a b) uses Steedman's grammar to compose by computers jazz music based upon chord sequences generated by this grammar. About twenty years after his first work, Steedman (2003) came back to chord sequences analysis, but now with the aim of recognition based upon categorial grammars. Meanwhile, pregroup grammars have been conceived as an algebraic tool to recognize well-formed sentences in natural languages (Lambek, 2001 2004; Degeilh, S. & Preller, 2005).

Here we wish to use pregroup grammars to recognize well-formed sequences of chords, especially in Jazz music. Our recognition process reduces the chord sequence to a simpler one. If this later sequence is similar to a well-known pattern like blues, rag, ‘anatole’, etc., we can classify the original sequence as conforming to this pattern.