Abstract
Finding high-level structure in scores is one of the main challenges in music information retrieval. Searching for a formalization enabling variety through fixed musical concepts, we use parametric grammars, an extension of context-free grammars with predicates that take parameters. Parameters are here small patterns of music that will be used with different roles in the piece. We investigate their potential use in defining and discovering the structure of a musical piece, taking example on Bach inventions. A measure of conformance of a score with a given parametric grammar based on the classical notion of edit distance is investigated. Initial analysis of computational properties of the proposed formalism is carried out.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chemillier, M.: Grammaires, automates et musique. In: Briot, J.-P., Pachet, F. (eds.) Informatique Musicale, pp. 195–230. Hermès, Paris (2004)
Conklin, D.: Distinctive patterns in the first movement of Brahms’ string quartet in C minor. J. Math. Music 4(2), 85–92 (2010)
Cope, D.: Virtual Music: Computer Synthesis of Musical Style. MIT Press, Cambridge (2004)
Deutsch, D., Feroe, J.: The internal representation of pitch sequences in tonal music. Psychol. Rev. 88(6), 503–522 (1981)
Hamanaka, M., Hirata, K., Tojo, S.: Implementing “a generating theory of tonal music”. J. New Music Res. 35(4), 249–277 (2006)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Addison Wesley, Boston (2001)
Knuth, D.E.: Semantics of context-free languages. Math. Syst. Theory 2(2), 127–145 (1968)
Lartillot, O.: Taxonomic categorisation of motivic patterns. Music. Sci. 13(1 suppl), 25–46 (2009)
Lerdahl, F., Jackendoff, R.S.: A Generative Theory of Tonal Music. MIT Press, Cambridge (1983)
Marsden, A.: Schenkerian analysis by computer. J. New Music Res. 39(3), 269–289 (2010)
Meredith, D.: A geometric language for representing structure in polyphonic music. In: International Society for Music Information Retrieval Conference (ISMIR 2012) (2012)
Mesnage, M., Riotte, A.: Formalisme et modèles musicaux (2006)
Neumeyer, D.: The two versions of J.S. Bach’s A-minor invention, BWV 784. Indiana Theory Rev. 4(2), 69–99 (1981)
Schaefer, T.J.: The complexity of satisfiability problems. In: ACM Symposium on Theory of Computing (STOC), pp. 216–226 (1978)
Schenker, H.: Der freie Satz. Universal Edition, Wien (1935)
Shafer, J.: The two-part and three-part inventions of Bach: a mathematical analysis. Honors project, East Texas Baptist University, March 2010
Sidorov, K., Jones, A., Marshall, D.: Music analysis as a smallest grammar problem. In: ISMIR 2014 (2014)
Steedman, M.J.: A generative grammar for jazz chord sequences. Music Percept. 2(1), 52–77 (1984)
Sundberg, J., Lindblom, B.: Generative theories in language and music descriptions. Cognition 4, 99–122 (1976)
Winograd, T.: Linguistics and the computer analysis of tonal harmony. J. Music Theory 12, 2–49 (1948)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Giraud, M., Staworko, S. (2015). Modeling Musical Structure with Parametric Grammars. In: Collins, T., Meredith, D., Volk, A. (eds) Mathematics and Computation in Music. MCM 2015. Lecture Notes in Computer Science(), vol 9110. Springer, Cham. https://doi.org/10.1007/978-3-319-20603-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-20603-5_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20602-8
Online ISBN: 978-3-319-20603-5
eBook Packages: Computer ScienceComputer Science (R0)