Abstract
Modeling the musical notes as fuzzy sets provides a flexible framework which better explains musicians’ daily practices. Taking into account one of the characteristics of the sound: the pitch (the frequency of a sound as perceived by human ear), a similarity relation between two notes can be defined. We call this relation compatibility. In the present work, we propose a method to asses the compatibility between musicians based on the compatibility of their interpretations of a given composition. In order to aggregate the compatibilities between the notes offered and then obtain the compatibility between musicians, we make use of an OWA operator. We illustrate our approach with a numerical experiment.
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References
Apel, W.: Harvard Dictionary of Music, 2nd edn., Revised and Enlarged. The Belknap Press of Harvard University Press, Cambridge (1994)
Borup, H.: A History of String Intonation, http://www.hasseborup.com/ahistoryofintonationfinal1.pdf
Del Corral, A., León, T., Liern, V.: Compatibility of the Different Tuning Systems in an Orchestra. In: Chew, E., Childs, A., Chuan, C.-H. (eds.) Communications in Computer and Information Science, vol. 38, pp. 93–103. Springer, Heidelberg (2009)
Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)
Goldáraz Gaínza, J.J.: Afinación y temperamento en la música occidental. Alianza Editorial, Madrid (1992)
Halušca, J.: Equal Temperament and Pythagorean Tuning: a geometrical interpretation in the plane. Fuzzy Sets and Systems 114, 261–269 (2000)
Halušca, J.: The Mathematical Theory of Tone Systems. Marcel Dekker, Inc., Bratislava (2005)
Leon, T., Liern, V.: Mathematics and Soft Computing in Music (2009), http://www.softcomputing.es/upload/web/parrafos/00694/docs/lastWebProgram.pdf
Leon, T., Zuccarello, P., Ayala, G., de Ves, E., Domingo, J.: Applying logistic regression to relevance feedback in image retrieval systems. Pattern Recognition 40, 2621–2632 (2007)
Liern, V.: Fuzzy tuning systems: the mathematics of the musicians. Fuzzy Sets and Systems 150, 35–52 (2005)
Piles Estellés, J.: Intervalos y gamas. Ediciones Piles, Valencia (1982)
R Development Core Team. R: A language and environment for statistical computing. In: R Foundation for Statistical Computing, Vienna, Austria (2009), http://www.R-project.org , ISBN 3-900051-07-0
Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. Systems Man Cybernet. 18, 183–190 (1988)
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Leon, T., Liern, V. (2010). Obtaining the Compatibility between Musicians Using Soft Computing. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2010. Communications in Computer and Information Science, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14058-7_8
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DOI: https://doi.org/10.1007/978-3-642-14058-7_8
Publisher Name: Springer, Berlin, Heidelberg
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