Research article

The Technique of Musical Icosahedra

Research article

The Technique of Musical Icosahedra

This article is written in Russian. You can read it here.

References

  1. Akopyan, L. O. “The laws of Xenakis’ music not formulated by the composer himself,” Muzykal’naya akademiya [Music Academy], no. 1 (773), 2021, pp. 40–59, doi:10.34690/127. (In Russ.)
  2. Gen-Ir, U. Istoriya muzyki Vostochnoj Azii (Kitay, Koreya, Yaponiya). Uchebnoe posobie [History of Music of East Asia (China, Korea, Japan). Study Guide], St. Petersburg : Planeta muzyki, 2011. (In Russ.)
  3. Golubev, A. “Music as artistic mathematics,” Mu­zykal’­naya akademiya [Music Academy], no. 2 (659), 1997, pp. 133–137. (In Russ.)
  4. Okuneva, E. G. “Serial technique in Western Europe: history and aesthetics, theory and practice,” Doc­toral (Art History) Dissertation, Petrozavodsk : Petrozavodsk State Glazunov Conservatoire, 2021, http://mosconsv.ru/upload/images/Docu­ments/DiserDoctor/okuneva_diss.pdf (accessed 21 July 2024). (In Russ.)
  5. Pereverzeva, M. V. Teoriya sovremennoy kompozitsii: algoritmicheskaya muzyka. Uchebnoe posobie [Theory of Contemporary Composition: Algorithmic Music. Study Guide], Moscow : Rossijskij gosudarstvennyj social’nyj universitet, 2021. (In Russ.)
  6. Kharms, D. I. Starukha: Rasskazy, stseny, povest’ [The Old Woman: Stories, Scenes, A Tale], ed. by V. Glotser, Moscow : Yunona, 1991. (In Russ.)
  7. Kholopov, Yu. N., Kirillina, L. V., Kyuregyan, T. S.,
    Ly­zhov, G. I., Pospelova, R. L., Tsenova, V. S. Mu­zykal’no-­teoreticheskie sistemy [Musical-Theo­retical Systems], Moscow : Kompozitor, 2006. (In Russ.)
  8. Tsaregradskaya, T. V. “Set theory in the USA: Mil­ton Babbit and Allen Forte,” Iskusstvo muzyki: teoriya i istoriya [The Art of Music: Theory and History], vol. 6, 2012, pp. 157–177. (In Russ.)
  9. Babbitt, M. “Twelve-tone invariants as compo­si­tional determinants,” Musical Quarterly, vol. 46, no. 2, 1960, pp. 246–259, https:// jstor.org/stable/740374 (accessed 12 July 2024).
  10. Catanzaro, M. J. “Generalized Tonnetze,” Journal of Mathematics and Music, vol. 5, 2011, pp. 117–139, doi:10.1080/17459737.2011.614448.
  11. Cohn, R. “Introduction to neo-Riemannian theory: a survey and a historical perspective,” Journal of Music Theory, vol. 42, no. 2, 1998, pp. 167–180, doi:10.2307/843871.
  12. Euler, L. Tentamen Novae Theoriae Musicae Ex Cer­tissismis Larmoniae Principiis Dilucide Expo­sitae, Petropoli : Ex typographia Academiae Scien­tia­rum, 1739, https://archive.org/details/bub_gb_aekm­N1V98GcC (accessed 21 July 2024).
  13. Frederick, L. “Diatonic voice-leading transforma­tions,” Music Theory Spectrum, vol. 46, no. 1, 2023, pp. 37–69, doi:10.1093/mts/mtad017.
  14. Hopkins, B. “Hamiltonian paths on Platonic graphs,” International Journal of Mathematics and Mathe­matical Sciences, vol. 30, 2004, pp. 1613–1616, doi:10.1155/s0161171204307118.
  15. Imai, Y. “General theory of music by icosahedron 2: analysis of musical pieces by the exceptional mu­sical icosahedra,” ArXiv, 2021, https://arxiv.org/pdf/­2108.10294 (accessed 21 July 2024), doi:10.48550/­arXiv.2108.10294.
  16. Imai, Y. “General theory of music by icosahedron 3: musical invariant and Melakarta raga,” ArXiv, 2021, https://arxiv.org/pdf/2109.12475 (accessed 21 July 2024), doi:10.48550/arXiv.2109.12475.
  17. Imai, Y., Dellby, S. C., Tanaka, N. “General theory of music by icosahedron 1: a bridge between ‘arti­ficial’ scales and ‘natural’ scales,” ArXiv, 2021, https://arxiv.org/pdf/2103.10272 (accessed 21 July 2024), doi:10.48550/arXiv.2103.10272.
  18. Jevtić, F. D., Živaljević, R. T. “Generalized Tonnetz and discrete Abel-Jacobi map,” Topological Methods in Nonlinear Analysis, vol. 57, no. 2, 2021, pp. 547–567, doi:10.12775/tmna.2020.049.
  19. Kepler, J. Harmonices mundi libri V, Lincii Austriae : sumptibus Godofredi Tampachii…, pr. by Ioannes Plancus, 1619, https://archive.org/details/ioannis­kepplerih00kepl (accessed 19 July 2024).
  20. Kepler, J. Prodromus Dissertationum Cosmo­graphi­ca­rum, Continens Mysterium Cosmographicum, De Ad­mirabili Proportione Orbium Coelestium <...>, Tu­bingae : pr. by Georgius Gruppenbachius, 1596, https://archive.org/details/1596-kepler-prod­romus-­dis­sertationum-cosmographicarum-conti­nens-myste­rium-cosmographicum (accessed 21 July 2024).
  21. Rietsch, K. “Generalizations of Euler’s Tonnetz on triangulated surfaces,” Journal of Mathema­tics and Music, vol. 18, no. 3, 2024, pp. 328–346, doi:­10.1080/­17459737.2024.2362132.
  22. Shapiro, S. Thinking About Mathematics. The Philo­sophy of Mathematics, Oxford, New York : Oxford University Press, 2000.
  23. Tymoczko, D. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice, New York : Oxford University Press, 2011.
  24. Tymoczko, D. “The Generalized Tonnetz,” Jour­nal of Music Theory, vol. 56, no. 1, 2012, pp. 1–52, doi:10.1215/­00222909-1546958.
  25. Tymoczko, D. Tonality: an Owner’s Manual, New York : Oxford University Press, 2023, doi:10.1093/oso/9780197577103.001.0001.
  26. Weisstein, E. W. “Icosian game.” Wolfram Math­World, https://mathworld.wolfram.com/Icosian­Game.html (accessed 21 July 2024).
  27. Yust, J. “Generalized Tonnetze and Zeitnetze, and the topology of music сoncepts.” Journal of Mathematics and Music, vol. 14, no. 2, 2020, pp. 170–203, doi:10.1080/17459737.2020.1725667.
  28. Ziegler, G. M. Lectures on Polytopes, Berlin, Heidel­berg, New York, London, Paris, Tokyo, Hong Kong : Springer-Verlag, 1995. doi:10.1007/978-1-4613-8431-1. (Graduate Texts in Mathematics, vol. 152).