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Tablatures for Stringed Instruments and Generating Functions

  • Davide Baccherini
  • Donatella Merlini
  • Renzo Sprugnoli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4475)

Abstract

We study some combinatorial properties related to the problem of tablature for stringed instruments. First, we describe the problem in a formal way and prove that it is equivalent to a finite state automaton. We define the concepts of distance between two chords and tablature complexity in order to study the problem of tablature in terms of music performance. By using the Schützenberger methodology we are then able to find the generating function counting the number of tablatures having a certain complexity and we can study the average complexity for the tablatures of a music score.

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References

  1. 1.
  2. 2.
    Dylan, B.: Knockin’ on heaven’s door, http://www.bobdylan.com/songs/knockin.html
  3. 3.
  4. 4.
    Midi committee of the association of musical electronic industry, http://www.amei.or.jp
  5. 5.
    Midi manufacturers association, http://www.midi.org
  6. 6.
    Baccherini, D.: Behavioural equivalences and generating functions. preprint (2006)Google Scholar
  7. 7.
    Baccherini, D., Merlini, D.: Combinatorial analysis of tetris-like games. preprint (2005)Google Scholar
  8. 8.
    Flajolet, Ph., Sedgewick, R.: The average case analysis of algorithms: complex asymptotics and generating functions. Technical Report 2026, INRIA (1993)Google Scholar
  9. 9.
    Flajolet, Ph., Sedgewick, R.: The average case analysis of algorithms: counting and generating functions. Technical Report 1888, INRIA (1993)Google Scholar
  10. 10.
    Goldman, J.R.: Formal languages and enumeration. Journal of Combinatorial Theory, Series A. 24, 318–338 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Merlini, D., Sprugnoli, R., Verri, M.C.: Strip tiling and regular grammar. Theoretical Computer Science 242(1-2), 109–124 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Miura, M., Hirota, I., Hama, N., Yanigida, M.: Constructiong a System for Finger-Position Determination and Tablature Generation for Playing Melodies on Guitars. System and Computer in Japan 35(6), 755–763 (2004)Google Scholar
  13. 13.
    Moore, R.F.: Elements of computer music, vol. XIV, p. 560. Prentice-Hall, Englewood Cliffs (1990)Google Scholar
  14. 14.
    Sayegh, S.: Fingering for String Instruments with the Optimum Path Paradigm. Computer Music Journal 13(6), 76–84 (1989)CrossRefGoogle Scholar
  15. 15.
    Schützenberger, M.P.: Context-free language and pushdown automata. Information and Control 6, 246–264 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Sedgewick, R., Flajolet, P.: An introduction to the analysis of algorithms. Addison-Wesley, London (1996)zbMATHGoogle Scholar
  17. 17.
    Sudkamp, T.A.: Languages and machines. Addison-Wesley, London (1997)Google Scholar
  18. 18.
    Tuohy, D.R., Potter, W.D.: A genetic algorithm for the automatic generation of playable guitar tablature. In: Proceedings of the International Computer Music Conference (2004)Google Scholar
  19. 19.
    Wilf, H.S.: Generatingfunctionology. Academic Press, San Diego (1990)zbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Davide Baccherini
    • 1
  • Donatella Merlini
    • 1
  • Renzo Sprugnoli
    • 1
  1. 1.Dipartimento di Sistemi e Informatica, viale Morgagni 65, 50134, FirenzeItalia

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