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Elena A. Ermak – a 5-year student of Belarusian State Academy of Music, Republic of Belarus.
Belarusian State Academy of Music, Minsk, Republic of Belarus, lenaermak355@gmail.com
Abstract
The article is devoted to the study of fractals structures in musical chamber-instrumental works by Western European composers of the XX-XXI centuries – D. Ligeti, A. Key, M. Nichan. The author gives a review of research positions on the fractals embodiment in various art forms and suggests fractals classification in relation to music. In musical works, self-similarity is considered as the main structure-forming principle of fractal embodiment. In the process of its implementation, the role of repetition in music (exact or varied) is accentuated, which is manifested in sound and pitch organization, compositional techniques, principles of development and form shaping.
Keywords
science and art, fractals, iterativity, self-similarity in music, serial technique, principles of form shaping
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2. Mandel’brot B. Fraktaly i vozrozhdenie teorii iteracij // Pajtgen H.-O., Rihter P. H. Krasota fraktalov. Obrazy kompleksnyh dinamicheskih system [Fractals and the revival of iteration theory // Fractal beauty. Images of complex dynamical system]. Moscow, 1993. 217 p.
3. Voloshinov A. V. Matematika i iskusstvo [Maths and Art]. Izd. 2-e. Moscow, 2000. 399 p.
4. Duhno A. B. Fraktal kak jazyk iskusstva. Vzaimovlijanie nauchnogo i hudozhestvennogo opyta // Hudozhestvennaja kul’tura [Fractal as a language of art. Interaction of scientific and artistic experience // Art culture]. 2018. № 3 (25). P. 39 -61.
5. Bonch-Osmolovskaja T. B. Fraktaly v literature [Fractals in literature]. [Jelektronnyj resurs]. URL: www.ashtray.ru/main/texts/experlit/fractallit2.htm (date of request: 15.01.2025).
6. Garbuz O. V. Vstrechi po obe storony zerkala ili matreshka i postmodern // Analitika kul’turologii [Meetings on both sides of the mirror or Matryoshka dolls and postmodernity // Cultural analytics]. 2007. № 9. P. 175−184.
7. Bekman I. N. Fraktaly: kurs lekcij [Fractals: a course of lectures]. [Jelektronnyj resurs]. URL: beckuniver.ucoz.ru/index/fractaly_predislovie/0−76 (date of request: 17.02.2025).
8. Dmitrjukova Ju. G. Fraktaly v sovremennoj kompozicii: konspekt doklada [Fractals in contemporary composition: report outline] [Jelektronnyj resurs]. URL: www.mmv.ru/p/link/fractal_report.html (date of request: 30.09.2023).
9. Gundorina A. A. Graficheskaja notacija v rakurse fraktal’nosti // Muzykal’noe obrazovanie v kontekste kul’tury: voprosy teorii, istorii i metodologii: sbornik statej [Graphical notation in the perspective of fractality // Music Education in the Context of Culture: Issues of Theory, History and Methodology]. Moscow, 2017. P. 61−76.
10. Lavrova S. V. Transformacija strukturnogo myshlenija muzykal’nogo postserializma v kontekste otkrytij sovremennoj nauki // Vestnik Akademii russkogo baleta A. I. Vaganovoj [Transformation of structural thinking of musical post-serialism in the context of discoveries of modern science // Vestnik of the A. I. Vaganova Academy of Russian Ballet]. 2014. № 3 (32). P. 184−191.
11. Teorija sovremennoj kompozicii: uch. posobie [Theory of modern composition]. Otv. red. V. S. Cenova. Moscow, 2007. 616 p.
12. Ruch’evskaja E. A. Klassicheskaja muzykal’naja forma [Classical music form]. Saint Petersburg, 1998. 268 p.
13. Kurbatskaja S. A. Serijnaja muzyka: voprosy istorii, teorii, jestetiki [Serial music: questions of history, theory, aesthetics]. Moscow, 1996. 128 p.
14. Vebern A. Lekcii o muzyke. Pis’ma [Lectures on music. Letters]. Moscow, 1975. 143 p.
15. Key J. A. Fractal music № 1 Iterations. [Jelektronnyj resurs]. URL: www.jordanalexanderkey.com/_files/ugd/b9cb66_07f2d252cb504edb9ba68c49d242080a.pdf (date of request: 14.01.2025).
16. Kjuregjan T. S. Forma v muzyke XVII — XX vekov [Form in music of the XVII-XX centuries]. Moscow, 1998. 344 p.
17. Satory S. An Interview with György Ligeti in Hamburg. [Jelektronnyj resurs]. URL: www.erudit.org/fr/revues/cumr/1990-v10-n1-cumr0505/101 4897ar.pdf (date of request: 26.01.2025).
18. Steinitz R. György Ligeti: Music of the Imagination. Faber & Faber, 2013. 429 p.
19. Frantova T. V. Kanon v muzyke otechestvennyh kompozitorov vtoroj poloviny XX veka [Canon in the music of Russian composers of the second half of the XX century]. Rostov-on-don, 2008. 92 p.
20. Zaderackij V. V. Muzykal’naja forma [Musical form]. Moscow, 2008. Issue 2. 528 p.
21. Wen Ya. Analysis of Ligeti’s piano etude "Columna Infinita" [Jelektronnyj resurs]. URL: www.parlando.hu/2022/2022−3/Wen-Ligeti.pdf (date of request: 09.02.2025).
Received: 15.04.2025
Accepted: 17.05.2025
Issue №2 (7) June 2025
Pages
78-94
Pages
78-94
