Música fractal: um painel de técnicas de geometria fractal aplicadas em música

Marcelo Queiroz, Fabio Kon

Resumo


Este artigo apresenta um painel de trabalhos de autores diversos que utilizam conceitos e técnicas relacionados à geometria fractal aplicados à música. São tratadas técnicas de análise de obras musicais voltadas à detecção de padrões fractais em repertório musical pré-existente, bem como técnicas que utilizam construções fractais na síntese de elementos musicais, tais como notas, acordes, melodias e ritmos, ou sinais sonoros. As principais contribuições são apresentadas resumidamente, bem como algumas ferramentas de software relacionadas ao tema. Ao final do texto são expostas perspectivas futuras de pesquisa envolvendo música e fractais. 


Palavras-chave


Geometria fractal; Modelos matemáticos; Análise musical; Composição fractal.

Texto completo:

PDF

Referências


BEAUVOIS, M. W. Quantifying Aesthetic Preference and Perceived Complexity for Fractal Melodies. Music Perception, n. 24, v. 3, p. 247-264, 2007.

BERAN, J. Statistics in Musicology. Chapman & Hall/CRC Press, 2004.

BIDLACK, R. Chaotic Systems as Simple (But Complex) Compositional Algorithms. Computer Music Journal, v. 16, n. 3, p. 33-47, 1992.

BIGERELLE, M; IOST, A. Fractal Dimension and Classification of Music. Chaos, Solitons and Fractals, v. 11, n. 14, p. 2179-2192, 2000.

BOLOGNESE, T. Automatic Composition: Experiments with Self-Similar Music. Computer Music Journal, v. 7, n. 1, p. 25-36, 1983.

BORTHWICK, A. Review of “Fractals in Music” by Charles Madden. Music & Letters,n. 81, v. 4, p. 661-662, 2000.

CHAPEL, R. H. Realtime Algorithmic Music Systems from Fractals and Chaotic Functions: Toward an Active Musical Instrument. PhD Thesis, Universitat Pompeu Fabra, 2003.

CHIROLLET, J.-C. L'approche de l'Art d'un Point de Vue Fractaliste. Tangence, v. 69, p. 103-132, 2002.

DARBON, N. Les Musiques du Chaos. Collection Sémiotique et philosophie de la musique. Harmattan, 2006.

DODGE C. Profile: A Musical Fractal. Computer Music Journal, v. 12, n. 3, p. 10-14, 1988.

DODGE, C.; Bahn, C. R. Musical Fractals. Byte, v. 11, n. 6, p. 185-196, 1986. GARDNER, M. White and Brown Music, Fractal Curves and 1/f Fluctuations.Scientific American, v. 238, n. 4, p.16-31, 1978.

GOGINS, M. Iterated Functions Systems Music. Computer Music Journal, v. 15, n. 1, p. 40-48, 1991.

GÜNDÜZ, G.; GÜNDÜZ, U. The Mathematical Analysis of the Structure of Some Songs. Physica A, n. 357, p. 565-592, 2005.

HILLER Jr., L.; ISAACSON, L. Musical Composition with a High Speed Digital Computer. Audio Engineering Society Convention 9. Audio Engineering Society, 1957.

HSÜ, K. J.; HSÜ, A. Fractal Geometry of Music. Proceedings of the National Academy of Sciences, n. 87, p. 938-941, 1990.

HSÜ, K. J.; HSÜ, A. Self-similarity of the 1/f noise Called Music. Proceedings of the National Academy of Sciences, n. 88, p. 3507-3509, 1991.

JOHNSON, R. S. Composing with Fractals. In: FAUVEL, J.; FLOOD, R.; WILSON, R. (Ed.). Music and Mathematics: From Pythagoras to Fractals. Oxford: Oxford University Press, 2003.

JONES, K. Generative models in computer-assisted musical composition. Contemporary Music Review, v. 3, n. 1, p. 177-196, 1989.

KON, F. O Som do Futuro: Música, Computadores e Fractais. Jornal da Tarde, São Paulo, QUEIROZ; KON 26 set. 1992.

KON, F. Música, Computadores e Fractais II. Relatório Técnico FAPESP, IA-UNESP, 1992b.

LEACH, J.; FITCH, J. Nature, Music, and Algorithmic Composition. Computer Music Journal, v. 19, n. 2, p. 23-33, 1995.

LERDAHL, F.; JACKENDOFF, R. A Generative Theory of Tonal Music. MIT Press, 1983. MADDEN, C. Fractals in Music: Introductory Mathematics for Musical Analysis. High Art Press, 1999.

MANARIS, B.; V AUGHAN, D.; W AGNER, C.; ROMERO, J.; D A VIS, R. B. Evolutionary Music and the Zipf-Mandelbrot Law: Developing Fitness Functions for Pleasant Music. Lecture Notes in Computer Science, n. 2611, p. 522-534, 2003.

MANDELBROT, B. B. How Long is the Coast of Britain: Statistical Self-Similarity and Fractional Dimension. Science, n. 156, v. 3775, p. 636-638, 1967.

MANDELBROT, B. B. The Fractal Geometry of Nature. W. H. Freeman, 1983. MANDELBROT, B. B.; van NESS, J. W. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, v. 10, n. 4, p. 422-437, 1968.

MANOUSAKIS, S. Non-Standard Sound Synthesis with L-Systems. Leonardo Music Journal, v. 19, p. 85-94, 2009.

MANZOLLI, J. Non-linear Dynamics and Fractals as a Model for Sound Synthesis and Real Time Composition. Tese de Doutorado, University of Nottingham, UK, 1993.

MANZOLLI, J. Musical Applications Derived from the FracWave Sound Synthesis Method. Proceedings of the 94th Audio Engineering Society Convention, Berlin, 1993b.

MANZOLLI, J. et al. A Non-Linear Sound Synthesis Method. Proceedings of the 7th Brazilian Symposium on Computer Music, 2000.

MASON, S.; SAFFLE, M. L-Systems, Melodies and Musical Structure. Leonardo Music Journal, v. 4, p. 31-38, 1994.

MIRANDA, E. R. Composing Music with Computers. Focal Press, 2001.

MOORE, F. R. Elements of Computer Music. Prentice Hall, 1990.

PETERS, M. From Strange to Impossible: Interactive Attractor Music. Contemporary Music Review, v. 29, n. 4, 2010.

POLOTTI, P; EVANGELISTA, G. Fractal Additive Synthesis via Harmonic-Band Wavelets. Computer Music Journal, v. 25, n. 3, p. 22-37, 2001.

QUAGLIA, B. Review of “Fractals in Music” by Charles Madden. Computer Music Journal, v. 24, n. 3, p. 84-86, 2000.

RICHTER, F. Musica Fractal: As Novas Tecnologias da Música Contemporânea. Proceedings of the 5th Brazilian Symposium on Computer Music, 1998.

SCHROEDER, M. Is There Such a Thing as Fractal Music? Nature, v. 325, p. 765-766, 1986.

SOUZA, R. C.; FARIA, R. R. A. Oito Reflexões sobre a Criatividade na Composição Auxiliada por Computadores. 13th Brazilian Symposium on Computer Music, SBCM'2011, Vitória, 2011.

SU, Z.-Y.; WU, T. Multifractal Analyses of Music Sequences. Physica D: Nonlinear Phenomena, v. 221, n. 2, p. 188-194, 2006.

SU, Z.-Y.; WU, T. Music Walk, Fractal Geometry in Music. Physica A: Statistical Mechanics and its Applications, v. 380, n. 1, p. 418-248, 2007.

VOSS, R. F.; CLARKE, J. 1/f Noise in Music and Speech. Nature, v. 258, n. 5533, p. 317-318, 1975.

VOSS, R. F.; CLARKE, J. 1/f Noise in Music: Music From 1/f Noise. Journal of the Acoustical Society of America, v. 63, n. 1, p. 258-263, 1978.


Apontamentos

  • Não há apontamentos.


Bookmark and Share


Direitos autorais 2013 Marcelo Queiroz, Fabio Kon

Licença Creative Commons
Esta obra está licenciada sob uma licença Creative Commons Atribuição 4.0 Internacional.

 
OPUS - Revista Eletrônica da Associação Nacional de Pesquisa e Pós-graduação em Música (ANPPOM)
ISSN 0103-7412 (versão impressa, 1989-2008), ISSN 1517-7017 (versão online, 2009- )