Su alcuni rapporti tra matematica e scale musicali
Isola, Stefano
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana, Tome 1 (2016), p. 31-50 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Publié le : 2016-04-01
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     author = {Stefano Isola},
     title = {Su alcuni rapporti tra matematica e scale musicali},
     journal = {Matematica, Cultura e Societ\`a. Rivista dell'Unione Matematica Italiana},
     volume = {1},
     year = {2016},
     pages = {31-50},
     mrnumber = {3559737},
     language = {it},
     url = {http://dml.mathdoc.fr/item/RUMI_2016_1_1_1_31_0}
}

Isola, Stefano. Su alcuni rapporti tra matematica e scale musicali. Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana, Tome 1 (2016) pp. 31-50. http://gdmltest.u-ga.fr/item/RUMI_2016_1_1_1_31_0/

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

[3] Barbera, C. A., Arithmetic and geometric division of the tetrachord, Journal of Music Theory21 (1977), 294-323.

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

[5] Benson, D. J., Music. A Mathematical Offering, Cambridge University Press, 2007 | Zbl 1119.00008

[6] Bonanno, C., Isola, S., Orderings of the rationals and dynamical systems, Colloquium Mathematicum116 (2009), 165-189 | Zbl 1218.37008

[7] Brocot, A., Calcul des rouages par approximation, nouvelle méthode, Revue Chronométrique6 (1860), 186-194.

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

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

[10] Carey, N., Clampitt, D., Aspects of well-formed scales, Music Theory Spectrum11 (1989), 187-206.

[11] Christoffel, E. B., Observatio arithmetica, Annali di Matematica Pura ed Applicata6 (1875), 148-152.

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

[13] Domínguez, M., Clampitt, D., Noll, T., 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] Farey, J., 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] Hardy, G. H., Wright, E. M., An introduction to the theory of numbers, Oxford University Press, 1979. | Zbl 0423.10001

[18] Hellegouarch, Y., Gammes naturelles, Prima parte in Gazette SMF81 (1999) 25-39; Seconda parte in Gazette SMF 82 (1999), 13-25.

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

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

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

[22] Lotharie, M., Algebraic Combinatorics on Words, Cambridge University Press, 2002. | Zbl 1001.68093

[23] Noll, T., 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] Pytheas Fogg, N., Substitutions in Dynamics, Arithmetics and Combinatorics, LNM1794, Springer2002. | Zbl 1014.11015

[25] Series, C., The geometry of Markoff numbers, The Mathematical Intelligencer7 (1985), 20-29. | Zbl 0566.10024

[26] Slater, N. B., Gaps and steps for the sequence n⁢θmod1, Proc. Camb. Phil. Soc.63 (1967), 1115-1123. | Zbl 0178.04703

[27] Stern, M., Über eine zahlentheoretische Funktion, Journal für die reine und angewandte Mathematik55 (1858), 193-220.

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