Skip to main content
SpringerLink
Log in

Using Mathematical Tools to Reduce the Combinatorial Explosion During the Automatic Segmentation of the Symbolic Musical Text

  • Conference paper
  • First Online:
Advanced Computational Methods for Knowledge Engineering

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 453))

Abstract

This document is going to focus on the modalities of management of the combinatorial explosion problem deriving from computer-aided music analysis: a major problem, most of all, for those who perform automatic analysis of the musical text considered at a symbolic level, due to the high number of recognizable “musical objects”. While briefly introducing the results of the application of different processing techniques, this article shall discuss the necessity to define a series of procedures meant to reduce the number of final “musical objects” to use in order to identify a melody (or a musical theme), by selecting the ones that do not carry redundant information. Consequently, the results of their application shall be presented in statistic tables, in order to provide information on how to reduce the musical objects to a small number, so as to ensure major precision in the musical analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Searle, J.: Minds Brains and Science. Harvard University Press, Cambridge (1984)

    Google Scholar 

  2. Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach. Prentice-Hall International, London (1995)

    MATH  Google Scholar 

  3. Cordeschi, R.: Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework. Cambridge Scholars Publishing (2011)

    Google Scholar 

  4. Shannon, C., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press, Urbana, Illinois (1949)

    MATH  Google Scholar 

  5. Bent, I.: L’analyse musicale—histoires et méthodes, éditione Main d’Oeuvre, collection musique et mémoire (1997)

    Google Scholar 

  6. Della Ventura, M.: Rhythm analysis of the “sonorous continuum” and conjoint evaluation of the musical entropy. In: Proceedings of Latest Advances in Acoustics and Music, Iasi, pp. 16–21 (2012)

    Google Scholar 

  7. Fraisse, P.: Psychologie du rythme. Puf, Paris (1974)

    Google Scholar 

  8. Lerdhal, F., Jackendoff, R.: A Generative Theory of Tonal Music. The MIT Press (1983)

    Google Scholar 

  9. Cambouropoulos, E.: Voice and Stream: Perceptual and Computational Modeling of Voice Separation. Music Perception (2008)

    Google Scholar 

  10. Cambouropoulos, E.: Conceptualizing Music: Cognitive Structure, Theory, and Analysis. Music Perception (2003)

    Google Scholar 

  11. Cambouropoulos, E.: Voice separation: theoretical, perceptual and computational perspectives. In: Proceedings of the 9th International Conference on Music Perception and Cognition (ICMPC), Bologna, Italy (2006)

    Google Scholar 

  12. Velarde, G., Weyde, T., Meredith, D.: An approach to melodic segmentation and classification based on filtering with the Haar-wavelet. J. New Music Res. 42(4), 325–345 (2013)

    Article  Google Scholar 

  13. Lartillot, O.: An efficient algorithm for motivic pattern extraction based on a cognitive modeling. Open Workshop of Musicnetwork, Vienna (2005)

    Google Scholar 

  14. Bigo, L., Ghisi, D., Spicher, A., Andreatta, M.: Representation of musical structures and processes in simplicial chord spaces. Comput. Music J. 39(3), 9–24 (2015)

    Article  Google Scholar 

  15. Lonati, F.: Metodi, algoritmi e loro implementazione per la segmentazione automatica di partiture musicali, tesi di Laurea in Scienze dell’informazione. Università degli studi, Milano (1990)

    Google Scholar 

  16. Della Ventura, M.: The Fingerprint of the Composer. GDE, Rome (2010)

    Google Scholar 

  17. Harald Baayen, R., Hendrix, p, Ramscar, M.: Sidestepping the combinatorial explosion. Lang. Speech 56(Pt 3), 329–347 (2013)

    Article  Google Scholar 

  18. Cambouropoulos, E.: Musical parallelism and melodic segmentation. Music Percept. 23(3), 211–233 (2006)

    Article  Google Scholar 

  19. Grindal, M.: Handling combinatorial explosion in software testing. Ph.D. thesis at University of Skövde (2007)

    Google Scholar 

  20. Kolata, G., Hoffman, P.: The New York Times Book of Mathematics: More Than 100 Years of Writing by the Numbers. Sterling, New York (2013)

    Google Scholar 

  21. Bose, P., Hermetz, K.E., Conneely, K.N., Rudd, M.K.: Tandem repeats and G-rich sequences are enriched at human CNV breakpoints (2014). doi:10.1371/journal.pone.0101607

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Technology, Music Academy “Studio Musica”, Treviso, Italy

    Michele Della Ventura

Authors
  1. Michele Della Ventura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michele Della Ventura .

Editor information

Editors and Affiliations

  1. International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria

    Thanh Binh Nguyen

  2. Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, Hungary

    Tien van Do

  3. Laboratory of Theoretical and Applied Computer Science (LITA), UFR MIM, University of Lorraine, Ile du Saulcy, Metz, France

    Hoai An Le Thi

  4. Institute of Informatics, Wrocław University of Technology, Wrocław, Poland

    Ngoc Thanh Nguyen

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Della Ventura, M. (2016). Using Mathematical Tools to Reduce the Combinatorial Explosion During the Automatic Segmentation of the Symbolic Musical Text. In: Nguyen, T.B., van Do, T., An Le Thi, H., Nguyen, N.T. (eds) Advanced Computational Methods for Knowledge Engineering. Advances in Intelligent Systems and Computing, vol 453. Springer, Cham. https://doi.org/10.1007/978-3-319-38884-7_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-38884-7_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-38883-0

  • Online ISBN: 978-3-319-38884-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation