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  • Title

    Consonant chord model of musical compositions for harmonizing melodies by a genetic algorithm

  • Authors

    Komarov Oleksandr
    Galchonkov Oleg M.
    Nevrev Alexander I.
    Babilunga О. Yu.

  • Subject


  • Year 2018
    Issue 3(56)
    UDC 004.4:519.6
    DOI 10.15276/opu.3.56.2018.07
    Pages 63 - 79
  • Abstract

    In spite of the well-developed theory for the musical compositions creation, there is a lack of implementation of computer program methods that facilitate the work of composers. The purpose of this work is to develop a model of musical compositions that allows using genetic algorithms for automatization the addition of chords to a well–known melody with maximum satisfaction the rules of musical theory. A new model has been developed for representing musical compositions, which makes it possible to increase the speed of harmonization of specified melodies by a genetic algorithm. The result is obtained due to the construction of the model at the higher level of structural generality, compared with the well–known tonal model. The analysis of the tonal model shows the redundancy of the definition area of the quality function for a musical composition using this model. This leads to insufficiently high speed of melody harmonization. Limitation the definition area of the quality function by taking into account the rules of harmony for musical composition allowed to exclude clearly inappropriate chords, which led to acceleration of harmonization with the use of the developed consonant chord model. The obtained relations allow the transition from the chord model to the tonal model and from it to the usual musical notation. Computer modeling of harmonization for the known melody showed higher level of harmonization by automatic methods in comparison with the work of the composer, as well as significant acceleration of the harmonization process using the consonant chord model, compared with the tonal model. This allows us to recommend the use of the developed model in the program of automatic harmonization of melodies. The contribution of the study to the theory of genetic algorithms is in creation of the new approach to the formation of chromosomes and a multi-factorial quality function, which made it possible to effectively apply genetic algorithms to the task of harmonizing music. The practical significance of the research results consists in automation of the composer work who can concentrate entirely on the creation of a melody. The task of harmonizing the melody with chords can be assigned to a computer. In addition, the obtained high speed of harmonization allows improving the quality of the generated melodies and their compliance with the dynamic situations in computer games.

  • Keywords genetic algorithm, fitness function, chromosome, musical composition, chord, harmony rules
  • Viewed: 765 Dowloaded: 16
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  • References

    1. Iannis Xenakis. (1992) Formalized Music. Thought and Mathematics in Composition. . NY: Pendragon Press. Stuyvesant.
    2. Dubovsky, I.I., Evseev, S.V., Kobinin, I.V., & Sokolov, V.V. (1965). Harmony Textbook. Moscow: Ed. Music.
    3. Tyulin, Y.N., & Privano, N.G. (1965). Theoretical Foundations of Harmony. Moscow: Ed. Music.
    4. Meinard Müller. Fundamentals of Music Processing. Audio, Analysis, Algorithms, Applications. (eBook) Springer. DOI 10.1007/978-3-319-21945-5.
    5. Montiela, M., & Robert Peck R. (2016). Mathematics and Music: Reports on the American Mathematical Society Special Sessions at the 2016 Spring Southeastern Sectional Meeting and the Forthcoming 2017 Joint Mathematics Meetings. Journal of Mathematics and Music, 10, 3, 245–249. Retrieved from: http://dx.doi.org/10.1080/17459737.2016.1261951.
    6. Patrício da Silva. (2003). David Cope and Experiments in Musical Intelligence. Retrieved from: https://pdfs.semanticscholar.org/82fe/48dcb32bacdb03ce4a95b0bbb3600e56386e.pdf?_ga=2.37590560.1818681109.1552491152-898199006.1552491152.
    7. Collins, T., Laney, R., Willis, A., & Garthwaite, P.H. (2016). Developing and Evaluating Computational Models of Musical Style. Artificial Intelligence for Engineering Design, Analysis and Manufacturing. 30 (1), 16–43. DOI:10.1017/S0890060414000687.
    8. Conklin, D. (2016) Chord sequence generation with semiotic patterns. Journal of Mathematics and Music, 10. Retrieved from http://dx.doi.org/10.1080/17459737.2016.1188172.
    9. Bozapalidou, M. (2013). Automata and music contour functions. Journal of Mathematics and Music, 7, 3, 195–211. Retrieved from http://dx.doi.org/10.1080/17459737.2013.822576.
    10. Barat`e, A., Haus, G., & Ludovico, L.A. (2014). Real-time Music Composition through P-timed Petri Nets. Proc. International Computer Music Conference, 14–20 September 2014, Athens, Greece, 408–415.
    11. Lattner, S., Grachten, M., & Widmer, G. (2018). Imposing Higher-Level Structure in Polyphonic Music Generation using Convolutional Restricted Boltzmann Machines and Constraints. Journal of Creative Music Systems, 2, 1, March 2018. Retrieved from https://arxiv.org/pdf/1612.04742, DOI: 10.5920/jcms.2018.01.
    12. Deng, J., & Kwok, Y.-K. (2017). Large vocabulary automatic chord estimation using bidirectional long short-term memory recurrent neural network with even chance training. Journal of New Music Research. DOI: 10.1080/09298215.2017.1367820.
    13. Kaliakatsos-Papakostas, M., Queiroz, M., Tsougras, C., & Cambouropoulos, E. (2017). Conceptual Blending of Harmonic Spaces for Creative Melodic Harmonisation. Journal of New Music Research. DOI: 10.1080/09298215.2017.1355393.
    14. Phon-Amnuaisuk, S., Tuson, A., & Wiggins, G. (1999). Evolving Musical Harmonisation. Proc. International Conference: Artificial Neural Nets and Genetic Algorithms. Portorož, (pp. 229–234). Slo-venia, Retrieved from https://pdfs.semanticscholar.org/f560/abdb8b5fd0c23bc5812c5b9b071 d907dd928.pdf.
    15. Semenkin, E.S., Zhukova, M.N., Zhukov, V.G., Panfilov, I.A., & Tynchenko, V.V. (2007). Evolutionary Methods for Modeling and Optimizing Complex Systems. Lecture notes. Krasnoyarsk.
    16. Panchenko, T.V. (2007). Genetic methods. University of Astrakhan.
    17. Ferreira, C. (2001). Gene expression programming: a new adaptive algorithm for solving problems. Complex Systems, vol. 13, 87–129.
    18. Burton, A. R., & Vladimirova, T. (1997). Applications of genetic techniques to musical composition. Retrieved from https://www.researchgate.net/publication/243766382_Applications_of_Genetic_ Tech-niques_to_Musical_Composition.
    19. Matic, D. (2010) A Genetic Algorithm for Composing Music. Yugoslav Journal of Operations Research, 20, 1, 157–177. DOI: 10.2298/YJOR1001157M.
    20. Tomasz M. Oliwa. (2007). Genetic Algorithms and the abc Music Notation Language for Rock Music Composition. Miranda, E. R., and Biles, J. A., (Editors). Evolutionary Computer Music, Springer. 1603–1609.
    21. Bresson, J., Bouche, D., Carpentier, T., Schwarz, D., & Garcia, J. (2017). Next-generation Computer-aided Composition Environment: A New Implementation of OpenMusic. International Computer Music Conference Proceedings, 253–258.
    22. Carlos Guedes. (2017). Real-Time Composition, why it still matters: A look at recent developments and potentially new and interesting applications. International Computer Music Conference Proceedings, 162–167.
    23. Biles, J. A. (1994). GenJam: A genetic algorithm for generating jazz solos. In ICMC Proceedings 1994. The Computer Music Association. P. 131–137.
    24. Spector, L. & Alpern, A. (1994). Criticism, culture, and the automatic generation of artworks. In Proceedings of the 12th National Conference on Artificial Intelligence. P. 3–8.
    25. Burton, A. R., & Vladimirova, T. (1997). A genetic algorithm for utilising neural network fitness evaluation for musical composition. In Proceedings of the 1997 International Conference on Artificial Neural Networks and Genetic Algorithms, 220–224.
    26. Johanson, B., & Poli, R. (1998). Gp-music: An interactive genetic programming system for music generation with automated fitness raters. In Proceedings of the 3rd International Conference on Genetic Programming, GP’98. MIT Press.
    27. Ponce de León, P.J., Iñesta, J.M., Calvo-Zaragoza, J., & Rizo, D. (2016). Data-based melody generation through multi-objective evolutionary computation. Journal of Mathematics and Music. Retrieved from http://dx.doi.org/10.1080/17459737.2016.1188171.
    28. Whorley R.P., Conklin D.(2016) Music Generation from Statistical Models of Harmony / Journal of New Music Research. DOI: 10.1080/09298215.2016.1173708.
    29. McIntyre, R. A. (1994). Bach in a box: The evolution of four-part baroque harmony using a genetic algorithm. In First IEEE Conference on Evolutionary Computation, 852–857.
    30. Horner, A. & Ayers, L. (1995). Harmonisation of musical progression with genetic algorithms. In ICMC Proceedings 1995, (pp.483–484). The Computer Music Association.
    31. Honing, H. (1993). Issues on the representation of time and structure in music. Contemporary Music Review, 9, 1 & 2, 221–238.
    32. Wiggins, G., Miranda, E., Smaill, A., & Harris, M. (1993). A Framework for the Evaluation of Music Representation Systems. Computer Music Journal, 17(3), October, 31–42, DOI: 10.2307/3680941.
    33. Janikow, C. Z. (1993). A knowledge-intensive genetic algorithm for supervised learning. Machine Learning, 13, 189–228, DOI: 10.1007/BF00993043.
    34. Togelius, J., Yannakakis, N. G., Stanley, K. O., & Browne, C. (2011). Search-Based Procedural Content Generation: A Taxonomy and Survey. IEEE Transactions on Computational Intelligence and AI in Games, 3, 3, 172–186. DOI: 10.1109/TCIAIG.2011.2148116.
    35. Gen, M., & Cheng, R. (2007). Genetic Algorithms and Engineering Optimization. John Wiley & Sons, Inc. DOI:10.1002/9780470172261.
    36. Scirea, M., & Brown, J.A. (2015). Evolving Four Part Harmony Using a Multiple Worlds Mode. Conference: 7th International Conference on Evolutionary Computation Theory and Applications. (pp. 220–227). Lisbon, Portugal. DOI: 10.5220/0005595202200227.
    37. Sposobin, I.V. (1996). Elementary theory of music. Moscow: Kifara.
    38. MIDI. wikipedia.org. Retrieved from https://ru.wikipedia.org/wiki/MIDI.
    39. Amelie Anglade, Rafael Ramirez, & Simon Dixon. (2009). Genre Classification Using Harmony Rules Induced from Automatic Chord Transcriptions. 10th International Society for Music Information Retrieval Conference (ISMIR 2009). (pp. 669–674).
    40. Phon-Amnuaisuk, S., & Wiggins, G. (1999). The Four-Part Harmonisation Problem: A comparison between Genetic Algorithms and a Rule-Based System. In Proceedings of the AISB’99 Symposium on Musical Creativity, (pp. 28–34), AISB.
    41. Benward, B., & Saker, M. (2015). Music in Theory and Practive. Eighth Edition, Volume I. McGraw-Hill.
    42. Kholopov, Yu.N. (2005). Harmony. A practical course. Moscow, publishing house Composer.

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