A pregroup grammar for chord sequences
Richard Terrat · Journal of New Music Research · 2005
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 Pachet, F. 1998. “Sur la structure algébrique des séquences d'accord de Jazz”. In Journées d'Informatique Musicale Agelonde 1998 [Google Scholar]) developed a method for analysing jazz chord sequences. Then, Marc Chemiller (2004a Chemillier, M. 2004a. “ Grammaires, automates et musique”. In Informatique musicale Edited by: Briot, J. -P. and Pachet, F. 195–230. IC2 Hermes [Google Scholar] b Chemillier, M. 2004b. Toward a formal study of jazz chord sequences generated by Steedman's grammar. Soft Computing, 8 vol.(#9): 617–622. [Web of Science ®] , [Google Scholar]) 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 Steedman, M. 2003. “Formal grammars for computational music analysis: The blues and the abstract truth”. Atlanta INFORMS, October 2003 [Google Scholar]) 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 Lambek, J. 2001. Type grammars as pregroups. Grammars, 4: 21–39. [Google Scholar] 2004 Lambek, J. 2004. A computational algebraic approach to English grammar. Syntax, 7(2): 128–147. [Crossref] , [Google Scholar]; Degeilh, S. & Preller, 2005 Degeilh, S. and Preller, A. 2005. Efficiency of pregroups and the French noun phrase. Journal of Logic, Language and Information, 14(4): 423–444. [Crossref] , [Google Scholar]). 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.