Geodesic
Su alcuni rapporti tra matematica e scale musicali
Matematica, cultura e società, Série 1, Tome 1 (2016) no. 1, pp. 31-50.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In questo lavoro si discutono alcuni aspetti del modo in cui la matematica moderna interviene nella questione aperta dagli antichi sulla divisione dell'ottava.
In this paper we discuss some aspects of the way in which modern mathematics intervenes in the question open in the antiquity about the division of the octave. 
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Isola, Stefano. Su alcuni rapporti tra matematica e scale musicali. Matematica, cultura e società, Série 1, Tome 1 (2016) no. 1, pp. 31-50. http://geodesic.mathdoc.fr/item/RUMI_2016_1_1_1_a3/

[1] C. AGON, M. ANDREATTA, G. ASSAYAG, E. AMIOT, J. BRESSON, J. MANDEREAU (EDS.), Mathematichs and Computation in Music, Lecture Notes in Artificial Intelligence 6726, Springer, 2011 | Zbl

[2] T. M. Apostol, Modular functions and Dirichlet series in number theory, Graduate Text in Mathematics, Springer-Verlag, 1976.

[3] C. A. Barbera, Arithmetic and geometric division of the tetrachord, Journal of Music Theory 21 (1977), 294-323.

[4] J. M. Barbour, Tuning and Temperaments. A Historical Survey, East Lansing, Mich. 1951, reprint: New York, 1972.

[5] D. J. Benson, Music. A Mathematical Offering, Cambridge University Press, 2007 | Zbl

[6] C. Bonanno, S. Isola, Orderings of the rationals and dynamical systems, Colloquium Mathematicum 116 (2009), 165-189 | fulltext EuDML | Zbl

[7] A. Brocot, Calcul des rouages par approximation, nouvelle méthode, Revue Chronométrique 6 (1860), 186-194.

[8] W. Burkert, Lore and science in ancient Pythagoreanism, Harvard University Press, 1972.

[9] N. Carey, Distribution modulo 1 and musical scales, PhD-Thesis, 1998.

[10] N. Carey, D. Clampitt, Aspects of well-formed scales, Music Theory Spectrum 11 (1989), 187-206.

[11] E. B. Christoffel, Observatio arithmetica, Annali di Matematica Pura ed Applicata 6 (1875), 148-152.

[12] H. F. Cohen, Quantifying Music: The Science of Music at the First Stage of Scientific Revolution, 1580-1650, Dordrecht, 1984.

[13] M. Domínguez, D. Clampitt, T. Noll, WF Scales, ME Sets, and Christoffel Words, in T. Klouche and T. Noll (Eds.): MCM 2007, CCIS 37, pp. 477-488, Springer-Verlag 2009.

[14] Euclide, Sectio Canonis, (III sec. a.C.), (in Euclide, Tutte le opere, a cura di F. Acerbi, Bompiani (2007)).

[15] J. Farey, On a curious property of vulgar fractions, London, Edinburgh and Dublin Phil. Mag. 47 (1816), 385.

[16] J. FAUVEL, R. FLOOD, R. WILSON Eds., Music and Mathematics. From Pythagoras to Fractals, Oxford University Press 2003. | Zbl

[17] G. H. Hardy, E. M. Wright, An introduction to the theory of numbers, Oxford University Press, 1979. | Zbl

[18] Y. Hellegouarch, Gammes naturelles, Prima parte in Gazette SMF 81 (1999) 25-39; Seconda parte in Gazette SMF 82 (1999), 13-25.

[19] A. Honingh, Group theoretic description of just intonation, Proceedings UCM, Caserta, 2003.

[20] S. Isacoff, Temperamento, (trad. it. EDT, Torino, 2005).

[21] F. Jedrzejewski, Mathematical Theory of Music, Collection "Musique/Sciences", Ircam/Delatour France, 2006.

[22] M. Lotharie, Algebraic Combinatorics on Words, Cambridge University Press, 2002. | Zbl

[23] T. Noll, Facts and Counterfacts: Mathematical Contributions to Music-theoretical Knowledge, in Bab, S., et al. (eds.) Models and Human Reasoning - Bernd Mahr zum 60. Geburtstag. WT Verlag, Berlin (2006).

[24] N. Pytheas Fogg, Substitutions in Dynamics, Arithmetics and Combinatorics, LNM 1794, Springer 2002. | Zbl

[25] C. Series, The geometry of Markoff numbers, The Mathematical Intelligencer 7 (1985), 20-29. | Zbl

[26] N. B. Slater, Gaps and steps for the sequence $n\theta \mod 1$, Proc. Camb. Phil. Soc. 63 (1967), 1115-1123. | Zbl

[27] M. Stern, Über eine zahlentheoretische Funktion, Journal für die reine und angewandte Mathematik 55 (1858), 193-220. | fulltext EuDML

[28] D. Vicinanza, Paths on Stern-Brocot tree and winding numbers of modes, Proceedings of the ICMC, Barcellona, 2005.