Abstract
Symbolic melodic similarity aims to evaluate the degree of likeness of two or more sequences of notes. In this work, we propose the use of fuzzy c-means clustering as a tool for the measurement of the similarity between two melodies with a different number of notes. Moreover, we present an algorithm, FOCM, implemented in a computer program written in C\(\sharp \) able to read two melodies from files with MusicXML format and to perform the clustering to calculate the dissimilarity between any two melodies. In addition, for each iteration step in the convergence process of the algorithm, a family of intermediate states (transition melodies) are obtained that can be used as new thematic material. This last feature, could be especially useful in the near future, as a complement in computer-aided composition.
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References
Aloupis, G., Fevens, T., Langerman, S., Matsui, T., Mesa, A., Nuez, Y., Rappaport, D., Toussaint, G.: Algorithms for computing geometric measures of melodic similarity. Comput. Music J. 30(3), 67–76 (2006)
Apel, W.: Harvard Dictionary of Music, 2nd edn. The Belknap Press of Harvard University Press, Cambridge (1994)
Benson, D.: Music: A Mathematical Offering. Cambridge University Press, Cambridge (2006)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algoritms. Plenum Press, New York (1981)
Downie, J.S.: Evaluating a simple approach to musical information retreival: conceiving melodic N-grams as text. Ph.D. Thesis, University of Western Ontario, Ontario (1999)
Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. Cybern. 3, 32–57 (1973)
Haluska, J.: The Mathematical Theory of Tone Systems. Marcel Dekker Inc., Bratislava (2005)
Liern, V.: Fuzzy tuning systems: the mathematics of the musicians. Fuzzy Sets Syst. 150, 35–52 (2005)
Liern, V.: La música y sus materiales: una ayuda para las clases de matemáticas. Suma 14, 60–64 (1994)
Mongeau, M., Sankoff, D.: Comparison of musical sequences. Comput. Humanit. 24, 161–175 (1990)
Müllensiefen, D., Frieler, K.: Cognitive adequacy in the measurement of melodic similarity: algorithmic vs. human judgments. Comput. Musicology 13, 147–176 (2004)
Selfridge-Field, E.: Beyond MIDI: The Handbook of Musical Codes. MIT Press, Cambridge (1997)
Velardo, V., Vallati, M., Jan, S.: Symbolic melodic similarity: state of the art and future challenges. Comput. Music J. 40(2), 70–83 (2016)
Xenakis, I.: Formalized Music: Thought and Mathematics in Composition. Pendragon Press, Launceston (1992)
Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. Syst. Man Cybern. 18, 183–190 (1988)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
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Martínez, B., Liern, V. (2017). A Fuzzy-Clustering Based Approach for Measuring Similarity Between Melodies. In: Agustín-Aquino, O., Lluis-Puebla, E., Montiel, M. (eds) Mathematics and Computation in Music. MCM 2017. Lecture Notes in Computer Science(), vol 10527. Springer, Cham. https://doi.org/10.1007/978-3-319-71827-9_21
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DOI: https://doi.org/10.1007/978-3-319-71827-9_21
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