Ethnomusicology, Ethnomathematics. The Logic Underlying Orally Transmitted Artistic Practices

  • Marc Chemillier
Chapter

Abstract

Ethnomathematics is a new domain that has arisen during the last two decades, at the crossroad between history of mathematics and mathematics education. This domain consists in the study of mathematical ideas shared by orally transmitted cultures. Such ideas are related to number, logic and spatial configurations [9,11]. My purpose is to show how ethnomusicology could turn musical materials in this direction. Music will be considered here as a mean of organizing time through patterns of sound events. Thus we shall focus on musical forms and structures, rather than on other aspects of music (such as social aspects for instance). We will ask whether particular forms of traditional music share specific properties, namely combinatorial properties, that could be of some interest from an ethnomathematical point of view.

Keywords

Europe Transportation Ghost Egypt Tempo 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Andreatta, D.T. Vuza: Tata Mountains Math. Publications 22 (to appear, 2001)Google Scholar
  2. 2.
    U. D’Ambrosio: ISGEm Newsletter, 4, 1 (1988) pp. 5–8 (http://web.nmsu.edu/~pscott/isgem41.htm)Google Scholar
  3. 3.
    D. Andler (ed.): Introduction aux sciences cognitives, coll. Cerisy, Paris, Folio, 1992Google Scholar
  4. 4.
    D. Andler: ‘Logique, raisonnement et psychologie’, J. Dubucs, F. Lepage (eds.), Méthodes logiques pour les sciences cognitives (Hermès, Paris 1995) pp. 25–75Google Scholar
  5. 5.
    R. D’Andrade: The Development of Cognitive Anthropology (Cambridge University Press, 1995)CrossRefGoogle Scholar
  6. 6.
    S. Arom: Polyphonies et polyrythmies d’Afrique Centrale. Structure et méthodologie (Selaf, Paris 1985) (English translation: African polyphony and polyrhythm, Cambridge, 1991)Google Scholar
  7. 7.
    S. Arom: Symétrie et ruptures de symétrie dans la musique de tradition orale: le cas de l’Afrique Centrale’, Quadrivium. Musiques et sciences (Institut de pédagogie musicale et chorégraphique, Paris, 1992) pp. 209–215Google Scholar
  8. 8.
    S. Arom, J. Khalfa: Revue de musicologie, 84, 1 (1998) pp. 5–17CrossRefGoogle Scholar
  9. 9.
    M. R. Ascher: ‘Ethnomathematics’, History of Science, xxiv (1986) pp. 125–144MathSciNetGoogle Scholar
  10. 10.
    M. Ascher: ‘Graphs in cultures: a study in ethnomathematics’, Historia Mathematical xv (1988) pp. 201–227MathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Ascher: Ethnomathematics. A multicultural view of mathematical ideas (Chapman & Hall, New-York, 1991) (French translation by K. Chemla, S. Pa-haut, Mathématiques d’ailleurs, Seuil, Paris, 1998)MATHGoogle Scholar
  12. 12.
    K.P. Brenner: Die kombinatorisch strukturierten Harfen- und Xylophonpattern der Nzakana (Zentralafrikanische Republik) als klingende Geometrie — eine Alternative zu Marc Chemilliers Kanonhypothese (Holos-Verlag, Bonn, to appear)Google Scholar
  13. 13.
    J.-P. Cabane: Ululan, les sables de la mémoire (Grains de sable, Nouméa, 1997)Google Scholar
  14. 14.
    M. Chemillier: ‘La musique de la harpe’, E. de Dampierre (ed.), Une esthétique perdue (Presses de l’Ecole Normale Supérieure, Paris, 1995) pp. 99–208Google Scholar
  15. 15.
    M. Chemillier: ‘Mathématiques et musiques de tradition orale’, H. Genevois, Y. Orlarey (éds.), Musique & Mathématiques (Aléas-Grame, Lyon, 1997) pp. 133–143Google Scholar
  16. 16.
    M. Chemillier: La logique de la longue ligne Vanuatu, conférence au Musée des Arts d’Afrique et d’Océanie, 30 octobre 1997 (http://www.info.unicaen.fr/~marc/publi/vanuatu/ephemere.html)Google Scholar
  17. 17.
    M. Cole, J. Gay, J.A. Glick, D.W. Sharp: Cultural Context of Learning and Thinking (Basic Books, NY, 1971)Google Scholar
  18. 18.
    T. Crump: Anthropology of numbers (1990) (French translation by P. Lusson, Anthropologie des nombres (Seuil, Paris, 1995))CrossRefGoogle Scholar
  19. 19.
    É. de Dampierre: Penser au singulier (Société d’ethnologie, Nanterre, 1984)Google Scholar
  20. 20.
    E. de Dampierre (ed.): Une esthétique perdue (Presses de l’Ecole Normale Supérieure, Paris, 1995)Google Scholar
  21. 21.
    P.J. Davis, R. Hersh: The mathematical experience (Birkhäuser, Boston, 1982) (French translation by L. Chambadal, L’univers mathématique (Gauthier-Villars, Paris, 1985))MATHGoogle Scholar
  22. 22.
    B. Deacon: J. of the Royal Anthro. Institute, 64 (1934) pp. 129–175Google Scholar
  23. 23.
    E.E. Evans-Pritchard: Bull, of the Faculty of Arts, University of Egypt, Cairo, ii, 1 (1934) pp. 1–36Google Scholar
  24. 24.
    P. Gerdes: Une tradition géométrique en Afrique. Les dessins sur le sable (L’Harmattan, Paris, 1995)Google Scholar
  25. 25.
    R. Graham, B. Rotschild, J. Spencer: Ramsey Theory (Wiley, 1980)MATHGoogle Scholar
  26. 26.
    J.L. Grootaers: Witchcraft substance and “Zande logic”, unpublishedGoogle Scholar
  27. 27.
    J. Habermas: Théorie de l’agir communicationnel, tome 1: Rationalité de l’agir et rationalisation de la société (Fayard, Paris, 1987) (original edition 1981)Google Scholar
  28. 28.
    M. Hollis, S. Lukes (eds.): Rationality and relativism (Basil Blackwell, Oxford, 1982)Google Scholar
  29. 29.
    R. Horton (ed.): La pensée métisse (IUED, Genève, 1990)Google Scholar
  30. 30.
    G. Ifrah: Histoire universelle des chiffres (Seghers, Paris, 1981) (English translation From One to Zero: A Universal History of Numbers (Viking, New York, 1985)Google Scholar
  31. 31.
    P.N. Johnson-Laird, R.M.J. Byrne: Deduction, Essays in Cognitive Psychology (LEA, 1991)Google Scholar
  32. 32.
    I. Lakatos: Proofs and Refutations (Cambridge University Press, 1976) (French translation by N. Balacheff, J.-M. Laborde, Preuves et réfutations (Hermann, Paris, 1984))MATHCrossRefGoogle Scholar
  33. 33.
    L. Lévy-Brühl: Les fonctions mentales dans les sociétés inférieures (Paris, 1910) (English translation How Natives Think (George Allen and Unwin, London, 1926))Google Scholar
  34. 34.
    L. Lévy-Brühl: La mentalité primitive (Paris, 1922)Google Scholar
  35. 35.
    J.-J. Nattiez: Fondements d’une sémiologie de la musique (Paris, coll. 10/18, 1975) (English translation Music and Discourse: Towards a Semiology of Music (Princeton University Press, 1990))Google Scholar
  36. 36.
    J. Piaget, B. Inhelder: La naissance de la pensée logique de Venfance à Vadolescence (1958) (English translation The Growth of Logical Thinking from Childhood to Adolescence (Routhledge and Kegan Paul, London, 1958))Google Scholar
  37. 37.
    G. Pölya: Z. f. Kristal., ix (1924) pp. 278–282Google Scholar
  38. 38.
    J. Retschitzki: Stratégies des joueurs d’awélé (L’Harmattan, Paris, 1990)Google Scholar
  39. 39.
    A. Rosenfeld, R. Siromoney: Languages of design 1 (1993) pp. 229–245Google Scholar
  40. 40.
    A. Speiser: Die Theorie der Gruppen von endlicher Ordnung, 2e ed. (Springer, Berlin, 1927)MATHCrossRefGoogle Scholar
  41. 41.
    D. Sperber: La contagion des idées (Odile Jacob, 1996)Google Scholar
  42. 42.
    A. Szabo: Les débuts des mathématiques grecques (Vrin, Paris, 1977) (original edition Budapest, 1969)Google Scholar
  43. 43.
    E.B. Tylor: Primitive Culture, 2 vol. (London, 1871)Google Scholar
  44. 44.
    Vanuatu, Océanie. Arts des îles de cendre et de corail, catalogue de l’exposition, (Musée des Arts d’Afrique et d’Océanie, Paris, 1997)Google Scholar
  45. 45.
    H. Weyl: Symétrie et mathématique moderne (Flammarion, Paris, 1964)Google Scholar
  46. 46.
    B.R. Wilson (ed.): Rationality (Basil Blackwell, Oxford, 1970)Google Scholar
  47. 47.
    C. Zaslavsky: Africa counts. Number and Pattern in African Culture (Prindle, Weber & Schmidt, Boston, 1973) (French translation by V. Henderson (Ed. du Choix, Paris, 1995))Google Scholar

Audio CDs and CD-ROMs

  1. 48.
    Central African Républic. Music of the former Bandia courts, recordings, texts and photographs by M. Chemillier & E. de Dampierre, CNRS/Musée de l’Homme, Le Chant du Monde, CNR 2741009, Paris, 1996Google Scholar
  2. 49.
    La parole du fleuve. Harpes d’Afrique Centrale, Cité de la musique, CM001, Paris, 1999Google Scholar
  3. 50.
    Pygmées Aka. Peuple et musique, CD-ROM realized by S. Arom, S. Bahuchet, A. Epelboin, S. Fürniss, H. Guillaume, J. Thomas, Montparnasse Multimédia, Paris, 1998Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Marc Chemillier

There are no affiliations available

Personalised recommendations