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.
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References
M. Andreatta, D.T. Vuza: Tata Mountains Math. Publications 22 (to appear, 2001)
U. D’Ambrosio: ISGEm Newsletter, 4, 1 (1988) pp. 5–8 (http://web.nmsu.edu/~pscott/isgem41.htm)
D. Andler (ed.): Introduction aux sciences cognitives, coll. Cerisy, Paris, Folio, 1992
D. Andler: ‘Logique, raisonnement et psychologie’, J. Dubucs, F. Lepage (eds.), Méthodes logiques pour les sciences cognitives (Hermès, Paris 1995) pp. 25–75
R. D’Andrade: The Development of Cognitive Anthropology (Cambridge University Press, 1995)
S. Arom: Polyphonies et polyrythmies d’Afrique Centrale. Structure et méthodologie (Selaf, Paris 1985) (English translation: African polyphony and polyrhythm, Cambridge, 1991)
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. 209–215
S. Arom, J. Khalfa: Revue de musicologie, 84, 1 (1998) pp. 5–17
M. R. Ascher: ‘Ethnomathematics’, History of Science, xxiv (1986) pp. 125–144
M. Ascher: ‘Graphs in cultures: a study in ethnomathematics’, Historia Mathematical xv (1988) pp. 201–227
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)
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)
J.-P. Cabane: Ululan, les sables de la mémoire (Grains de sable, Nouméa, 1997)
M. Chemillier: ‘La musique de la harpe’, E. de Dampierre (ed.), Une esthétique perdue (Presses de l’Ecole Normale Supérieure, Paris, 1995) pp. 99–208
M. Chemillier: ‘Mathématiques et musiques de tradition orale’, H. Genevois, Y. Orlarey (éds.), Musique & Mathématiques (Aléas-Grame, Lyon, 1997) pp. 133–143
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)
M. Cole, J. Gay, J.A. Glick, D.W. Sharp: Cultural Context of Learning and Thinking (Basic Books, NY, 1971)
T. Crump: Anthropology of numbers (1990) (French translation by P. Lusson, Anthropologie des nombres (Seuil, Paris, 1995))
É. de Dampierre: Penser au singulier (Société d’ethnologie, Nanterre, 1984)
E. de Dampierre (ed.): Une esthétique perdue (Presses de l’Ecole Normale Supérieure, Paris, 1995)
P.J. Davis, R. Hersh: The mathematical experience (Birkhäuser, Boston, 1982) (French translation by L. Chambadal, L’univers mathématique (Gauthier-Villars, Paris, 1985))
B. Deacon: J. of the Royal Anthro. Institute, 64 (1934) pp. 129–175
E.E. Evans-Pritchard: Bull, of the Faculty of Arts, University of Egypt, Cairo, ii, 1 (1934) pp. 1–36
P. Gerdes: Une tradition géométrique en Afrique. Les dessins sur le sable (L’Harmattan, Paris, 1995)
R. Graham, B. Rotschild, J. Spencer: Ramsey Theory (Wiley, 1980)
J.L. Grootaers: Witchcraft substance and “Zande logic”, unpublished
J. Habermas: Théorie de l’agir communicationnel, tome 1: Rationalité de l’agir et rationalisation de la société (Fayard, Paris, 1987) (original edition 1981)
M. Hollis, S. Lukes (eds.): Rationality and relativism (Basil Blackwell, Oxford, 1982)
R. Horton (ed.): La pensée métisse (IUED, Genève, 1990)
G. Ifrah: Histoire universelle des chiffres (Seghers, Paris, 1981) (English translation From One to Zero: A Universal History of Numbers (Viking, New York, 1985)
P.N. Johnson-Laird, R.M.J. Byrne: Deduction, Essays in Cognitive Psychology (LEA, 1991)
I. Lakatos: Proofs and Refutations (Cambridge University Press, 1976) (French translation by N. Balacheff, J.-M. Laborde, Preuves et réfutations (Hermann, Paris, 1984))
L. Lévy-Brühl: Les fonctions mentales dans les sociétés inférieures (Paris, 1910) (English translation How Natives Think (George Allen and Unwin, London, 1926))
L. Lévy-Brühl: La mentalité primitive (Paris, 1922)
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))
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))
G. Pölya: Z. f. Kristal., ix (1924) pp. 278–282
J. Retschitzki: Stratégies des joueurs d’awélé (L’Harmattan, Paris, 1990)
A. Rosenfeld, R. Siromoney: Languages of design 1 (1993) pp. 229–245
A. Speiser: Die Theorie der Gruppen von endlicher Ordnung, 2e ed. (Springer, Berlin, 1927)
D. Sperber: La contagion des idées (Odile Jacob, 1996)
A. Szabo: Les débuts des mathématiques grecques (Vrin, Paris, 1977) (original edition Budapest, 1969)
E.B. Tylor: Primitive Culture, 2 vol. (London, 1871)
Vanuatu, Océanie. Arts des îles de cendre et de corail, catalogue de l’exposition, (Musée des Arts d’Afrique et d’Océanie, Paris, 1997)
H. Weyl: Symétrie et mathématique moderne (Flammarion, Paris, 1964)
B.R. Wilson (ed.): Rationality (Basil Blackwell, Oxford, 1970)
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))
Audio CDs and CD-ROMs
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, 1996
La parole du fleuve. Harpes d’Afrique Centrale, Cité de la musique, CM001, Paris, 1999
Pygmées Aka. Peuple et musique, CD-ROM realized by S. Arom, S. Bahuchet, A. Epelboin, S. Fürniss, H. Guillaume, J. Thomas, Montparnasse Multimédia, Paris, 1998
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Chemillier, M. (2002). Ethnomusicology, Ethnomathematics. The Logic Underlying Orally Transmitted Artistic Practices. In: Assayag, G., Feichtinger, H.G., Rodrigues, J.F. (eds) Mathematics and Music . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04927-3_10
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DOI: https://doi.org/10.1007/978-3-662-04927-3_10
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