Music and Mathematics: Processing Repetition Techniques with the Least Common Multiple (LCM) in Rajékan Music Composition
(1) Universitas Negeri Jakarta, Indonesia
(2) Universitas Negeri Jakarta, Indonesia
Abstract
This article aims to find a new way to process repetition in musical composition with the least common multiple (LCM) mathematical approach. Music and mathematics have a very close relationship; in music, the element of mathematics with the derivation of physical science is the most relevant and always interesting study of musical composition. This study aims to analyse the music composition of Rizky Fauzy Ananda’s work, Rajékan, by looking at mathematical theory with the approach of The least common multiple (LCM). The method used with practice-led Research as an approach to music composition. The creation research methodology used is Artistic Research through a Practice-Led Research approach which is also integrated with mathematical theory and musicology, especially music composition. The results of this creative Research prove that repetition in music and in the context of life is important and mathematics always present in human life. Repetition has largely underpinned development in music. In the context of life, reps are things that always exist in everyday life, such as worship activities and lifestyles. Such repetitive phenomena can also provide certain learning or meaning for the individual. In the context of education, reps are the easiest and most basic way of learning to learn and recall about understanding something. Repetition processing whose ideas come from the phenomenon of researchers’ self-experience, produces two repetition processing techniques with the LCM mathematical style (1) magnification and reduction of sound values that make up the cycle, (2) imitation.
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Ananda, R. F., Limbong, H. E., & Budiawan, H. (2022). Saru Pakareman: Refleksi Pengalaman Diri sebagai Practice-led Research. Resital: Jurnal Seni Pertunjukan, 23(2), 75–87. https://doi.org/10.24821/resital.v23i2.7328
Azaryahu, L., Broza, O., Cohen, S., Hershkovitz, S., & Adi-Japha, E. (2023). Development of creative thinking patterns via math and music. Thinking Skills and Creativity, 47(1), 101196. https://doi.org/10.1016/j.tsc.2022.101196
Bagdasar, O. (2014). On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and Mechanics, 6(2), 91–100. https://doi.org/10.5937/spsunp1402091b
Bollobás, B. (2022). Minimum Least Common Multiple. In B. Bollobás (Ed.), The Art of Mathematics – Take Two: Tea Time in Cambridge (pp. 191–192). Cambridge University Press. https://doi.org/10.1017/9781108973885.066
Budiawan, H., & Martyastiadi, Y. S. (2020). The explanation of life experience reflection as ideas of artistic research (IJACS). 7(2), 145–152. https://doi.org/https://doi.org/10.24821/ijcas.v7i2.4658
Candy, L. (2006). Practice Based Research: A Guide. In document. https://www.creativityandcognition.com/wp-content/uploads/2011/04/PBR-Guide-1.1-2006.pdf
Candy, L. (2011). Research and creative practice. Interacting: Art, Research and the Creative Practitioner, 33–59. http://www.creativityandcognition.com/resources/PBR Guide-1.1-2006.pdf
Cavett, E. (2022). Desire, gratification and the moment: a music analytical and psychological enquiry into the role of repetition in the music of Howard Skempton, with a response by the composer. Interdisciplinary Science Reviews, 47(2), 147–166. https://doi.org/10.1080/03080188.2022.2035100
Dauer, T., Nguyen, D. T., Gang, N., Dmochowski, J. P., Berger, J., & Kaneshiro, B. (2021). Inter-subject Correlation While Listening to Minimalist Music: A Study of Electrophysiological and Behavioral Responses to Steve Reich’s Piano Phase. Frontiers in Neuroscience, 15(4). https://doi.org/10.3389/fnins.2021.702067
Dias, A. (2005). Using lattice models to determine Greatest Common Factor and Least Common Multiple. International Journal for Mathematics Teaching and Learning.
Digney, F. (2022). Steve Reich’s “Piano Phase” and David Cossin’s ’Video Phase’ : An exploration of David Cossin’s Video Phase with reference to Steve Reich’s original work Piano Phase. In Cowan University. https://doi.org/10.1057/978-1-349-96053-8_427
Djanković, G. (2021). The least common multiple of random sets in polynomial rings over finite fields. The Ramanujan Journal, 55(1), 13–23. https://doi.org/10.1007/s11139-020-00357-9
Ensemble, P. G., & Culture, M. (1990). Philip Glass on Composing for Film and Other Forms : The Case of Koyaardsqatsi An Interview by Charles Merrell Berg.
Epstein, P. (1986). Pattern structure and process in Steve Reich’s piano phase. Musical Quarterly, 72(4), 494–502. https://doi.org/10.1093/mq/lxxii.4.494
Essouabri, D., Salinas Zavala, C., & Tóth, L. (2022). Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function. Journal of Number Theory, 236, 404–442. https://doi.org/10.1016/j.jnt.2021.07.027
Fitriyani, R. (2019). Passive Acquisition of Preschool Children in Sundanese Language. In Syntax Literate; Jurnal Ilmiah Indonesia (Vol. 4, Issue 3, pp. 147–166). http://jurnal.syntaxliterate.co.id/index.php/syntax-literate/article/view/575/892
Hammerschmidt, D., Wöllner, C., London, J., & Burger, B. (2021). Disco Time: The Relationship Between Perceived Duration and Tempo in Music. Music and Science, Vol. 4(No. 1), 1–11. https://doi.org/10.1177/2059204320986384
Hananto, P. D., & Sukerta, P. M. (2020). Mixed choir and instruments in the composition of the worship music of the stations of the cross. Harmonia: Journal of Arts Research and Education, 20(2), 231–241. https://doi.org/10.15294/harmonia.v20i2.24843
Hargreaves, D. J. (1984). The Effects of Repetition on Liking for Music. Journal of Research in Music Education, 32(1), 35–47. https://doi.org/10.2307/3345279
Hargreaves, D. J. (2012). Musical imagination: Perception and production, beauty and creativity. Psychology of Music, Vol. 40(No. 5), 539–557. https://doi.org/10.1177/0305735612444893
Hendriko, T., & Effendy, E. (2019a). Kuda kepang: A case report of javanese cultural-related trance in medan. Open Access Macedonian Journal of Medical Sciences, Vol. 7(No. 16), 2705–2707. https://doi.org/10.3889/oamjms.2019.823
Hendriko, T., & Effendy, E. (2019b). Kuda Kepang: A Case Report of Javanese Cultural-Related Trance in Medan. Open Access Macedonian Journal of Medical Sciences, 7(16), 2705–2707. https://doi.org/10.3889/oamjms.2019.823
Heyman, R., & Tóth, L. (2022). Hyperbolic summation for functions of the GCD and LCM of several integers. Ramanujan Journal, 59(4). https://doi.org/10.1007/s11139-022-00681-2
Hill, M., Hill, B., & Walsh, R. (2018). Conflict in collaborative musical composition: A case study. Psychology of Music, Vol. 46(No. 2), 192–207. https://doi.org/10.1177/0305735617704712
Hu, Z., Ma, X., Liu, Y., Chen, G., & Liu, Y. (2022). The Beauty of Repetition in Machine Composition Scenarios. In Proceedings of the 30th ACM International Conference on Multimedia (MM ’22), October 10â•fi14, 2022, Lisboa, Portugal (Vol. 1, Issue 1). Association for Computing Machinery. https://doi.org/10.1145/3503161.3548130
London, J. (1994). The Fine Art of Repetition: Essays in the Philosophy of Music. In Music Theory Spectrum (Vol. 16, Issue 2, pp. 267–275). https://doi.org/10.2307/746038
Maifi, Y. K., Anwar, & Ahmad, A. (2021). Students’ understanding of mathematical concepts and their self-confidence through a discovery learning model. Journal of Physics: Conference Series, 1882(1), 0–8. https://doi.org/10.1088/1742-6596/1882/1/012081
Noor Afniandari, L., Imam Supardi, K., Asikin, M., & Islam Sultan Agung Semarang, U. (2021). Understanding Mathematical Concepts in the Missouri Mathematics Project Learning Model in terms of Student’s Independent Attitude. Journal of Primary Education, 10(2), 163–178. https://journal.unnes.ac.id/sju/index.php/jpe
Raghu, M. (2018). A Study to Explore the Effects of Sound Vibrations on Consciousness. International Journal of Social Work and Human Services Practice, 6(3), 75–88. https://doi.org/10.13189/ijrh.2018.060302
Reich, S., & Paul, H. (2004). Writings on Music 1965–2000: 1965-2000. In S. Reich & P. Hillier (Eds.), Writings on Music 1965–2000: 1965-2000. Oxford University Press. https://doi.org/https://doi.org/10.1093/acprof:oso/9780195151152.001.0001
Rowland, J., Kasdan, A., & Poeppel, D. (2019). There is music in repetition: Looped segments of speech and nonspeech induce the perception of music in a time-dependent manner. Psychonomic Bulletin & Review, 26(2), 583–590. https://doi.org/10.3758/s13423-018-1527-5
Runco, M. A., & Chand, I. (1995). Cognition and creativity. Educational Psychology Review, 7(3), 243–267. https://doi.org/10.1007/BF02213373
Runisah, F. G., & Ismunandar, D. (2020). The relationship between self regulated learning and mathematical creative thinking ability. Journal of Physics: Conference Series, 1657(1), 0–6. https://doi.org/10.1088/1742-6596/1657/1/012004
Schwab, M. (2019). Futures of the Contemporary. In Futures of the Contemporary (p. 183). https://doi.org/10.11116/9789461662866
Schwarz, K. R. (2009). Steve Reich: Music as a Gradual Process Part II. 20(1), 225–286.
Stoutemyer, D. R. (1983). Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus. The Two-Year College Mathematics Journal, 14(3), 233. https://doi.org/10.2307/3027093
Suhaya, S., Rachman, A., Sinaga, S. S., & Alfayad, D. M. (2020). Percussion pattern of terebang gede in panggung jati studio, panggung jati village, serang. Harmonia: Journal of Arts Research and Education, 20(2), 223–230. https://doi.org/10.15294/harmonia.v20i2.18067
Uitdenbogerd, A. L., & Zobel, J. (1998). Manipulation of music for melody matching. Proceedings of the 6th ACM International Conference on Multimedia, Multimedia 1998, August, 235–240. https://doi.org/10.1145/290747.290776
Uitdenbogerd, A., & Zobel, J. (1999). Melodic Matching Techniques for Large Music Databases. Multimedia 1999 - Proceedings of the 7th ACM International Conference on Multimedia (Part 1), 7(1), 57–66. https://doi.org/10.1145/319463.319470
Wikanengsih. (2010). Menerapkan Neurolinguistic Programming (NLP) dalam Pembelajaran. Semantik: Jurnal Ilmiah Program Studi Pendidikan Bahasa Dan Sastra Indonesia, 1(1), 31–45. https://e-journal.stkipsiliwangi.ac.id/index.php/semantik/article/view/277
Yudibrata, Y. S. A. P. K. (2003). Tatabasa Sunda Kiwari. UPI, 174. http://file.upi.edu/direktori/fpbs/jur._pend._bahasa_daerah/196302101987031-yayat_sudaryat/tatabasa_sunda_kiwari/tatabasa_sunda_kiwari.pdf
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