Research Article
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Hesaplamalı Müzik Teorisi

Year 2022, Issue: 22, 7 - 22, 01.09.2022

Abstract

Bu makale, hesaplamalı müzik teorisine bir giriş niteliğindedir. Müzik teorisi, müziğin yapısını melodi, armoni, ritim ve ölçü, tını, doku ve form boyutlarıyla inceler. Hesaplamalı müzik teorisi ise müziği incelemek için matematik dilini, algoritmaları ve bilgisayar hesaplama gücünü kullanır. Bu inceleme hem müzikal yapıların statik modellemesini hem de müzikal süreçlerin dinamik modellemesini içerir. Müzik teorisinde hesaplama gücünün kullanımının ses/sinyal düzeyinde değil de sembolik düzeyde, yani notalar ve daha yüksek soyutlamalar düzeyinde yapılması nispeten yenidir. MIDI, MusicXML, vb. sembolik seviyedeki müziksel bilginin yaygın formatları olmuştur. Makalede “hesaplanabilirliği” tanımladıktan sonra, müzik bilgisinin analitik işlenmesiyle ilgili müzik teorik kavramları ve müziğin bilimsel modellemesinin örneklerini irdeliyoruz. Matematiksel müzik teorisindeki armoni ve ölçü modellemelerini diğer modellerden farklılıklarıyla anlatıyoruz. Ayrıntılı olarak inceleyeceğimiz bir örnek araştırma, 1980’lerden itibaren geliştirilen matematiksel müzik teorisinin uygulama platformu da olan, Java tabanlı bir müzik besteleme ve analiz yazılımı olan Rubato üzerindedir. Armoni ve ölçü için matematiksel ve hesaplamalı modellerin Rubato üzerindeki uygulaması ve örnek müzikler üzerindeki sonuçları, hesaplamalı müzik teorisinin kapsamlı deneyleri mümkün kıldığı, müzik teorisine dair tezleri hızlıca test edebilme olanağı verdiğini ortaya koymaktadır.

References

  • Agon, C., Assayag, G., Laurson, M., Rueda, C. & Delerue, O. (1999). Computer Assisted Composition at Ircam: PatchWork & OpenMusic. Computer Music Journal, 23(3).
  • Agustín Aquino, O. A. (2011). Extensiones microtonales de contrapunto. (Tesis de Doctorado). Universidad Nacional Autónoma de México, México. Recuperado de <https://repositorio.unam.mx/contenidos/92950>.
  • Alpaydin, R. &Mazzola G. (2015). A Harmonic Analysis Network. Musicae Scientiae, 19(2), 191-213.
  • Alpaydin, R. (2022, March 20). “Harmonic Analysis with Rhythmical Metrical Weights”. (PhD thesis in preprint).https://www.researchgate.net/publication/347555700_Computational_Harmonic_Analysis_with_Rhythmical_Weights_PhD_thesis.
  • Andreatta, M., Ehresmann, A., Guitart, R. & Mazzola, G. (2013). Towards a categorical theory of creativity. Proceedings of the Conference MCM 2013, McGill University, Montreal. Lecture Notes in Computer Science / LNAI, Springer, 19-37.
  • Bibby, N. (2006). Tuning and Temperament: Closing the Spiral. In: Music and Mathematics, Oxford University Press. 13-28.
  • Boolos G.,Burges, J.P., &Jeffrey, R.C. (1974). Computability and Logic. (1st ed.). Cambridge University Press.
  • Bresson, J. & Carlos, A. (2010). Processing Sound and Music Description Data using OpenMusic. Proc. International Computer Music Conference, New York, USA.
  • Burkholder J.P., Grout D.J. & Paisca J.V. (2014). A History of Western Music. New York: WWNorton & Co.
  • Caplin, W.E. (1998). Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven. New York: Oxford University Press.
  • Di Guigno, G., & A. Gerzso. (1986). La station de travail musical 4X. IRCAM Technical Report. Paris: IRCAM.
  • Edwards, C.H. (1982). The Historical Development of the Calculus. Springer Study edition. (2nd ed.). Springer-Verlag.
  • Fiore, T. & Noll T. (2018). Voicing Transformations of Triads, SIAM J. Appl. Algebra Geometry, 2(2), 281–31.
  • Fleischer, A. (2002). A Model of Metric Coherence. In Proceedings of the 2nd international conference understanding and creating music. Caserta, Italy. https://webspace.science.uu.nl/~fleis102/Casertaletter.pdf.
  • Forte, A. (1977). The Structure of Atonal Music. Yale University Press.
  • Hiller, L. A. & Issacson, L. M.. (1957). Illiac Suite for String Quartet. New Music Edition. Theodore Presser Company, Bryn Mawr, Pa.
  • Hilton, P. (1984). Cryptanalysis in World War II —and Mathematics Education, The Mathematics Teacher, 77(7), 548-552. https://pubs.nctm.org/view/journals/mt/77/7/article-p548.xml
  • Hirschberg, A., Gilbert, J., Msallam, R., &Wijnands, A.P.J. Shock Waves in Trombones. Journal of the AcousticalSociety of America, 99(3), 1754-1758.
  • Krumhansl, C.L. (1990). Cognitive Foundations of Musical Pitch. Oxford University Press, New York.
  • Lerdahl, F.&Jackendoff, R. (1983). A Generative Theory of Tonal Music. Cambridge, MA: MIT Press.
  • Lewin, D. (1982). A Formal Theory of Generalized Tonal Functions. Journal of Music Theory, 16 (1), 23-60.
  • Lewin, D. (1993). Musical Form and Transformation: Four Analytic Essays. Yale University Press: New Haven, Connecticut.
  • Mazzola, G. (1985). Gruppen und Kategorien in der Musik. Heldermann, Berlin.
  • Mazzola, G. (2002). The Topos of Music. Basel-Boston-Berlin: Birkhauser Verlag.
  • Mazzola, G. (2011). Oniontology. In Musical Performance. Computational Music Science. Springer, Berlin, Heidelberg. 21-34.
  • Mazzola, G., Alpaydin, R. &Heinze, W. (2020). Software-based Experimental Music Theory: Rubato’s Metrorubette for Brahms’ Sonata Op. 1. In: The Future of Music - Towards a Computational Musical Theory of Everything. Springer. 49-61.
  • Milmeister, G. & Mazzola, G. (2007). Rubato Composer Software. https://www.rubato.org/rubatocomposer.html.
  • Milmeister, G. (2007). Overview of Music Theories. In: The Rubato Composer Music Software, Springer, 3-6.
  • Montiel, M. (2011). The Rubato Composer Software Concept for Learning Advanced Mathematics. In Emilio Lluis-Puebla & Octavio Agustín-Aquino (Eds), Memoirs of the Fourth International Seminar on Mathematical Music Theory. Electronic Publications of the Mexican Mathematical Society, 77-96.
  • Noll, T. (1997). Morphologische Grundlagen der abendländischen Harmonik. Brockmeyer, Bochum.
  • Noll, T. &Garbers, J. (2001). Harmonic path analysis. International Seminar on Mathematical and Computational Musik TheoryAt: SauenVolume: Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio (eds): Perspectives in Mathematical and Computational Music Theory.
  • Agustín Aquino, O. A.&Mazzola, G. (2019). Contrapuntal Aspects of the Mystic Chord and Scriabin's Piano Sonata No. 5. In Montiel M., Gomez-Martin F., Agustín-Aquino O. (Eds), Mathematics and Computation in Music. MCM 2019. Lecture Notes in Computer Science, vol 11502. Springer, Cham.
  • Parncutt. R. (2008). Interdisciplinarity in JIMS. Journal of Interdisciplinary Music Studies, (2) (1&2). http://musicstudies.org/wp-content/uploads/2017/01/interdisciplinarity_JIMS.pdf.
  • Roads, C., & Mathews, M. (1980). Interview with Max Mathews. Computer Music Journal. 4(4), 15–22. https://doi.org/10.2307/3679463.
  • Schedl, M., Gómez, E. & J. Urbano.Music. (2014). Music Information Retrieval:Recent Developments and Applications. In Foundations and Trends In Information Retrieval, 8(2-3), 127–261. http.//doi.org/10.1561/1500000042.
  • Sipser, M. (2007). Context-Free Grammars, In: Introduction to the Theory of Computation, (2nd ed.), Thomson Course Technology, 100-104.
  • Temperley, D. (1997). An Algorithm for Harmonic Analysis. Music Perception, 15(1), 31–68. https://doi.org/10.2307/40285738
  • Temperley, D. (2002). A Bayesian approach to key-finding. In C. Anagnostopoulou, M. Ferrand & A. Smaill (Eds.), ICMAI 2002, LNAI 2445. Berlin, Germany, Springer-Verlag. 195-206.
  • Thalmann, F. (2014). Gestural composition with arbitrary musical objects and dynamic transformation networks. Retrieved from the University of Minnesota Digital Conservancy. https://hdl.handle.net/11299/165105.
  • Tzanetakis, G.,A Kapur, WA Schloss& Wright, M. (2007). Computational ethnomusicology, Journal of interdisciplinary music studies, 1(2), 1-24.
  • Turing, A.M. (1939). Systems of Logic Based on Ordinals. Proceedings of the London Mathematical Society, 2-45 and 161-228.
  • Turing Machine Visualization. (2022, March 12). https://turingmachine.io/.
  • Turing Machine Physical Realization (2022, March 12). https://hyperglitch.com/articles/turing-machine.
  • Volk, A. (2009). Applying Inner Metric Analysis to 20th Century Compositions. In Communications in Computer and Information Science. Berlin Heidelberg: Springer. 204-210.
  • Weyl, H. (1983). Symmetry. Princeton University Press.

Computational Music Theory

Year 2022, Issue: 22, 7 - 22, 01.09.2022

Abstract

This article is an introduction to computational music theory. Music theory examines the structure of music at the neutral level through its dimensions: melody, harmony, rhythm and meter, timbre, texture and form. Computational music theory uses the language of mathematics, algorithms and computational power to examine music. This examination includes both static modelling of musical structures and dynamic modelling of musical processes. The use of computational power in music theory —not at the sound level, but at the symbolic level, i.e., at the level of notes and higher abstractions— is relatively new. MIDI, MusicXML and similar formats have become popular forms of musical information exchange for music at symbolic level. We define “computability” and examine music theoretical concepts relevant to analytical processing of musical information. We review recent mathematical and computational models for music. These models include the Rubato line of research, i.e., mathematical music theory which has been in continuous development on since 1980’s. The example we will examine in detail is both a mathematical and a computational model for analysis of harmony and meter and associated software implementations on Rubato, a Java-based music composition and analysis framework. Results show that detailed experiments on musical information is possible for testing various theses about music theory via computational modelling of musical information.

References

  • Agon, C., Assayag, G., Laurson, M., Rueda, C. & Delerue, O. (1999). Computer Assisted Composition at Ircam: PatchWork & OpenMusic. Computer Music Journal, 23(3).
  • Agustín Aquino, O. A. (2011). Extensiones microtonales de contrapunto. (Tesis de Doctorado). Universidad Nacional Autónoma de México, México. Recuperado de <https://repositorio.unam.mx/contenidos/92950>.
  • Alpaydin, R. &Mazzola G. (2015). A Harmonic Analysis Network. Musicae Scientiae, 19(2), 191-213.
  • Alpaydin, R. (2022, March 20). “Harmonic Analysis with Rhythmical Metrical Weights”. (PhD thesis in preprint).https://www.researchgate.net/publication/347555700_Computational_Harmonic_Analysis_with_Rhythmical_Weights_PhD_thesis.
  • Andreatta, M., Ehresmann, A., Guitart, R. & Mazzola, G. (2013). Towards a categorical theory of creativity. Proceedings of the Conference MCM 2013, McGill University, Montreal. Lecture Notes in Computer Science / LNAI, Springer, 19-37.
  • Bibby, N. (2006). Tuning and Temperament: Closing the Spiral. In: Music and Mathematics, Oxford University Press. 13-28.
  • Boolos G.,Burges, J.P., &Jeffrey, R.C. (1974). Computability and Logic. (1st ed.). Cambridge University Press.
  • Bresson, J. & Carlos, A. (2010). Processing Sound and Music Description Data using OpenMusic. Proc. International Computer Music Conference, New York, USA.
  • Burkholder J.P., Grout D.J. & Paisca J.V. (2014). A History of Western Music. New York: WWNorton & Co.
  • Caplin, W.E. (1998). Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven. New York: Oxford University Press.
  • Di Guigno, G., & A. Gerzso. (1986). La station de travail musical 4X. IRCAM Technical Report. Paris: IRCAM.
  • Edwards, C.H. (1982). The Historical Development of the Calculus. Springer Study edition. (2nd ed.). Springer-Verlag.
  • Fiore, T. & Noll T. (2018). Voicing Transformations of Triads, SIAM J. Appl. Algebra Geometry, 2(2), 281–31.
  • Fleischer, A. (2002). A Model of Metric Coherence. In Proceedings of the 2nd international conference understanding and creating music. Caserta, Italy. https://webspace.science.uu.nl/~fleis102/Casertaletter.pdf.
  • Forte, A. (1977). The Structure of Atonal Music. Yale University Press.
  • Hiller, L. A. & Issacson, L. M.. (1957). Illiac Suite for String Quartet. New Music Edition. Theodore Presser Company, Bryn Mawr, Pa.
  • Hilton, P. (1984). Cryptanalysis in World War II —and Mathematics Education, The Mathematics Teacher, 77(7), 548-552. https://pubs.nctm.org/view/journals/mt/77/7/article-p548.xml
  • Hirschberg, A., Gilbert, J., Msallam, R., &Wijnands, A.P.J. Shock Waves in Trombones. Journal of the AcousticalSociety of America, 99(3), 1754-1758.
  • Krumhansl, C.L. (1990). Cognitive Foundations of Musical Pitch. Oxford University Press, New York.
  • Lerdahl, F.&Jackendoff, R. (1983). A Generative Theory of Tonal Music. Cambridge, MA: MIT Press.
  • Lewin, D. (1982). A Formal Theory of Generalized Tonal Functions. Journal of Music Theory, 16 (1), 23-60.
  • Lewin, D. (1993). Musical Form and Transformation: Four Analytic Essays. Yale University Press: New Haven, Connecticut.
  • Mazzola, G. (1985). Gruppen und Kategorien in der Musik. Heldermann, Berlin.
  • Mazzola, G. (2002). The Topos of Music. Basel-Boston-Berlin: Birkhauser Verlag.
  • Mazzola, G. (2011). Oniontology. In Musical Performance. Computational Music Science. Springer, Berlin, Heidelberg. 21-34.
  • Mazzola, G., Alpaydin, R. &Heinze, W. (2020). Software-based Experimental Music Theory: Rubato’s Metrorubette for Brahms’ Sonata Op. 1. In: The Future of Music - Towards a Computational Musical Theory of Everything. Springer. 49-61.
  • Milmeister, G. & Mazzola, G. (2007). Rubato Composer Software. https://www.rubato.org/rubatocomposer.html.
  • Milmeister, G. (2007). Overview of Music Theories. In: The Rubato Composer Music Software, Springer, 3-6.
  • Montiel, M. (2011). The Rubato Composer Software Concept for Learning Advanced Mathematics. In Emilio Lluis-Puebla & Octavio Agustín-Aquino (Eds), Memoirs of the Fourth International Seminar on Mathematical Music Theory. Electronic Publications of the Mexican Mathematical Society, 77-96.
  • Noll, T. (1997). Morphologische Grundlagen der abendländischen Harmonik. Brockmeyer, Bochum.
  • Noll, T. &Garbers, J. (2001). Harmonic path analysis. International Seminar on Mathematical and Computational Musik TheoryAt: SauenVolume: Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio (eds): Perspectives in Mathematical and Computational Music Theory.
  • Agustín Aquino, O. A.&Mazzola, G. (2019). Contrapuntal Aspects of the Mystic Chord and Scriabin's Piano Sonata No. 5. In Montiel M., Gomez-Martin F., Agustín-Aquino O. (Eds), Mathematics and Computation in Music. MCM 2019. Lecture Notes in Computer Science, vol 11502. Springer, Cham.
  • Parncutt. R. (2008). Interdisciplinarity in JIMS. Journal of Interdisciplinary Music Studies, (2) (1&2). http://musicstudies.org/wp-content/uploads/2017/01/interdisciplinarity_JIMS.pdf.
  • Roads, C., & Mathews, M. (1980). Interview with Max Mathews. Computer Music Journal. 4(4), 15–22. https://doi.org/10.2307/3679463.
  • Schedl, M., Gómez, E. & J. Urbano.Music. (2014). Music Information Retrieval:Recent Developments and Applications. In Foundations and Trends In Information Retrieval, 8(2-3), 127–261. http.//doi.org/10.1561/1500000042.
  • Sipser, M. (2007). Context-Free Grammars, In: Introduction to the Theory of Computation, (2nd ed.), Thomson Course Technology, 100-104.
  • Temperley, D. (1997). An Algorithm for Harmonic Analysis. Music Perception, 15(1), 31–68. https://doi.org/10.2307/40285738
  • Temperley, D. (2002). A Bayesian approach to key-finding. In C. Anagnostopoulou, M. Ferrand & A. Smaill (Eds.), ICMAI 2002, LNAI 2445. Berlin, Germany, Springer-Verlag. 195-206.
  • Thalmann, F. (2014). Gestural composition with arbitrary musical objects and dynamic transformation networks. Retrieved from the University of Minnesota Digital Conservancy. https://hdl.handle.net/11299/165105.
  • Tzanetakis, G.,A Kapur, WA Schloss& Wright, M. (2007). Computational ethnomusicology, Journal of interdisciplinary music studies, 1(2), 1-24.
  • Turing, A.M. (1939). Systems of Logic Based on Ordinals. Proceedings of the London Mathematical Society, 2-45 and 161-228.
  • Turing Machine Visualization. (2022, March 12). https://turingmachine.io/.
  • Turing Machine Physical Realization (2022, March 12). https://hyperglitch.com/articles/turing-machine.
  • Volk, A. (2009). Applying Inner Metric Analysis to 20th Century Compositions. In Communications in Computer and Information Science. Berlin Heidelberg: Springer. 204-210.
  • Weyl, H. (1983). Symmetry. Princeton University Press.
There are 45 citations in total.

Details

Primary Language English
Subjects Music
Journal Section Research Article
Authors

Ruhan Alpaydın 0000-0002-2472-9563

Publication Date September 1, 2022
Submission Date January 15, 2022
Published in Issue Year 2022 Issue: 22

Cite

APA Alpaydın, R. (2022). Computational Music Theory. Porte Akademik Müzik Ve Dans Araştırmaları Dergisi(22), 7-22. https://doi.org/10.59446/porteakademik.1058088
AMA Alpaydın R. Computational Music Theory. Porte Akademik Müzik ve Dans Araştırmaları Dergisi. September 2022;(22):7-22. doi:10.59446/porteakademik.1058088
Chicago Alpaydın, Ruhan. “Computational Music Theory”. Porte Akademik Müzik Ve Dans Araştırmaları Dergisi, no. 22 (September 2022): 7-22. https://doi.org/10.59446/porteakademik.1058088.
EndNote Alpaydın R (September 1, 2022) Computational Music Theory. Porte Akademik Müzik ve Dans Araştırmaları Dergisi 22 7–22.
IEEE R. Alpaydın, “Computational Music Theory”, Porte Akademik Müzik ve Dans Araştırmaları Dergisi, no. 22, pp. 7–22, September 2022, doi: 10.59446/porteakademik.1058088.
ISNAD Alpaydın, Ruhan. “Computational Music Theory”. Porte Akademik Müzik ve Dans Araştırmaları Dergisi 22 (September 2022), 7-22. https://doi.org/10.59446/porteakademik.1058088.
JAMA Alpaydın R. Computational Music Theory. Porte Akademik Müzik ve Dans Araştırmaları Dergisi. 2022;:7–22.
MLA Alpaydın, Ruhan. “Computational Music Theory”. Porte Akademik Müzik Ve Dans Araştırmaları Dergisi, no. 22, 2022, pp. 7-22, doi:10.59446/porteakademik.1058088.
Vancouver Alpaydın R. Computational Music Theory. Porte Akademik Müzik ve Dans Araştırmaları Dergisi. 2022(22):7-22.