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Abstract
Harmonization with four voices is a musical problem which is subject to hard constraints, which absolutely need to be fulfilled, as well as to soft constraints, which preferably hold, but are not mandatory. In this paper, we model this problem as a valued constraint satisfaction problem (VCSP): costs are assigned to possible solutions based on the constraints they violate. We design an algorithm that finds a minimal-cost solution, thus solving the harmonization problem, and we present initial results obtained by this algorithm.
Keywords
soft constraints, valued constraint satisfaction problems, functional harmony

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Chicago
Verbiest, Nele, Chris Cornelis, and Yvan Saeys. 2009. “Valued Constraint Satisfaction Problems Applied to Functional Harmony.” In Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, ed. JP Carvalho, D Dubois, U Kaymak, and JMC Sousa, 925–930. Linz, Austria: European Society for Fuzzy Logic and Technology (EUSFLAT).
APA
Verbiest, N., Cornelis, C., & Saeys, Y. (2009). Valued constraint satisfaction problems applied to functional harmony. In JP Carvalho, D. Dubois, U. Kaymak, & J. Sousa (Eds.), Proceedings of the joint 2009 International Fuzzy Systems Association world congress and 2009 European Society for Fuzzy Logic and Technology conference (pp. 925–930). Presented at the Joint 2009 International Fuzzy Systems Association world congress and European Society for Fuzzy Logic and Technology conference (IFSA/EUSFLAT 2009), Linz, Austria: European Society for Fuzzy Logic and Technology (EUSFLAT).
Vancouver
1.
Verbiest N, Cornelis C, Saeys Y. Valued constraint satisfaction problems applied to functional harmony. In: Carvalho J, Dubois D, Kaymak U, Sousa J, editors. Proceedings of the joint 2009 International Fuzzy Systems Association world congress and 2009 European Society for Fuzzy Logic and Technology conference. Linz, Austria: European Society for Fuzzy Logic and Technology (EUSFLAT); 2009. p. 925–30.
MLA
Verbiest, Nele, Chris Cornelis, and Yvan Saeys. “Valued Constraint Satisfaction Problems Applied to Functional Harmony.” Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference. Ed. JP Carvalho et al. Linz, Austria: European Society for Fuzzy Logic and Technology (EUSFLAT), 2009. 925–930. Print.
@inproceedings{1225005,
  abstract     = {Harmonization with four voices is a musical problem which is subject to hard constraints, which absolutely need to be fulfilled, as well as to soft constraints, which preferably hold, but are not mandatory. In this paper, we model this problem as a valued constraint satisfaction problem (VCSP): costs are assigned to possible solutions based on the constraints they violate. We design an algorithm that finds a minimal-cost solution, thus solving the harmonization problem, and we present initial results obtained by this algorithm.},
  author       = {Verbiest, Nele and Cornelis, Chris and Saeys, Yvan},
  booktitle    = {Proceedings of the joint 2009 International Fuzzy Systems Association world congress and 2009 European Society for Fuzzy Logic and Technology conference},
  editor       = {Carvalho, JP and Dubois, D and Kaymak, U and Sousa, JMC },
  isbn         = {9789899507968},
  keyword      = {soft constraints,valued constraint satisfaction problems,functional harmony},
  language     = {eng},
  location     = {Lisbon, Portugal},
  pages        = {925--930},
  publisher    = {European Society for Fuzzy Logic and Technology (EUSFLAT)},
  title        = {Valued constraint satisfaction problems applied to functional harmony},
  year         = {2009},
}

Web of Science
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