bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Isola, Stefano:
Su alcuni rapporti tra matematica e scale musicali
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana Serie 1 1 (2016), fasc. n.1, p. 31-50, (Italian)
pdf (741 Kb), djvu (734 Kb). | MR 3559737

Sunto

In questo lavoro si discutono alcuni aspetti del modo in cui la matematica moderna interviene nella questione aperta dagli antichi sulla divisione dell'ottava.
Referenze Bibliografiche
[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 1216.00007
[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 1119.00008
[6] C. BONANNO, S. ISOLA, Orderings of the rationals and dynamical systems, Colloquium Mathematicum 116 (2009), 165-189 | fulltext EuDML | Zbl 1218.37008
[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 1051.00007
[17] G. H. HARDY, E. M. WRIGHT, An introduction to the theory of numbers, Oxford University Press, 1979. | Zbl 0423.10001
[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 1001.68093
[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 1014.11015
[25] C. SERIES, The geometry of Markoff numbers, The Mathematical Intelligencer 7 (1985), 20-29. | Zbl 0566.10024
[26] N. B. SLATER, Gaps and steps for the sequence $n\theta \mod 1$, Proc. Camb. Phil. Soc. 63 (1967), 1115-1123. | Zbl 0178.04703
[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.

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