208 Music and Mathematics: Processing Repetition Techniques with the Least Common Multiple (LCM) in Rajékan Music Composition Hery Budiawan, Rizky Fauzy Ananda Universitas Negeri Jakarta, Indonesia Submitted: 2022-12-17. Revised: 2023-02-13. Accepted: 2023-03-29 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 rela- tionship; 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 Re- search 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 repeti- tive 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 under- standing something. Repetition processing whose ideas come from the phenomenon of research- ers’ 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. Keywords: Practice-Led Research, Repetition, Least Common Multiple (LCM), Music Composition, Mathematics How to Cite: Budiawan, H., & Ananda, R. F. (2023). Music and Mathematics: Processing Repetition Techniques with the Least Common Multiple (LCM) in Rajékan Music Composition. Harmonia: Journal of Arts Research and Education, 23(1), 208-222 Harmonia: Journal of Arts Research and Education 23 (1) (2023), 208-222 Available online at http://journal.unnes.ac.id/nju/index.php/harmonia DOI: http://dx.doi.org/10.15294/harmonia.v23i1.41034 is a measure of how many vibrations per second a sound wave produces (Raghu, 2018)wood, membranes. Likewise, the du- ration of a note can be represented using time, which is a measure of how long the note lasts. There are many mathematical con- cepts, some of which include algebra, geometry, calculus, trigonometry, and INTRODUCTION Music and mathematics are two fields that are often thought to be closely related. This is because many aspects of music, such as rhythm and melody, can be represented using mathematical concepts. For example, the pitch of a musical note can be represented using frequency, which Corresponding author: E-mail: herybudiawan@unj.ac.id p-ISSN 2541-1683|e-ISSN 2541-2426 Hery Budiawan et al., Music and Mathematics: Processing Repetition Techniques with the 209 number theory (Maifi et al., 2021; Stou- temyer, 1983). Algebra is the branch of mathematics that deals with the study of equations and variables, while geometry is the branch that deals with the properties and relationships of points, lines, angles, and shapes. Calculus is a branch of mathe- matics that deals with the study of rates of change, such as rates of change of position or rates of change of acceleration (Noor Afniandari et al., 2021). Trigonometry is a branch of mathematics that deals with the study of triangles and the relationships between the sides and angles of triangles. Number theory is the branch of mathema- tics that deals with the study of numbers and their properties of numbers. The least common multiple (LCM) of two or more numbers is the smallest po- sitive integer, a multiple of all numbers (Djanković, 2021). For example, the LCM of 2 and 3 is 6, because 6 is the smallest po- sitive integer that is a multiple of 2 and 3. Likewise, the LCM of 4 and 6 is 12 because 12 is the smallest positive integer, a mul- tiple of 4 and 6 (Dias, 2005). Therefore, to find the LCM of two numbers, you can use the following steps: List the multiples of each of the num- bers, starting with the smallest multiple of each number. Find the smallest multiple that appears on both lists. This is the LCM of the two numbers. For example, to find the LCM of 4 and 6, you could list the mul- tiples of 4 and 6 as follows: Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ... Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72,... The smallest multiple that appears on both lists is 12, so the LCM of 4 and 6 is 12 (Essouabri et al., 2022). The least common multiple (LCM) is a concept from mathematics that is not typically used in music. In music, the most common use of the term “LCM’’ is in the context of “lowest common multiple,” which is a term used to describe a group of notes that are played at the same time, with the lowest note being the “lowest common multiple” of the group (Runisah & Ismu- nandar, 2020). Some many other concepts and techniques are more central to the stu- dy and practice of music. For example, mu- sical notation, melody, harmony, rhythm, and form are all important concepts in music theory. LCM makes Rajékan’s musi- cal work an idea of creation. Many com- posers depart from mathematics and phy- sics. Rajékan is a term for rajékan soy sauce, a linguistic term for repeating words in the Sundanese language. These interjec- tions are then used as ketchup rajékan or a repetitive word such as “trang-tréng-trong” from the word ‘trang’ which mimics the sound of a pot repeatedly clashing or coo- king in the kitchen, and “dar-dér-dor” from the word ‘dor’ which mimics the sound of repeated pistol fire (Yudibrata, 2003). The- se two examples include ketchup rajékan trilingga, a rewording that is a word repea- ted three times and undergoes a change in the sound of the vowel. Kecap Rajekan is a base word that is used repetitively or mentioned twice. It can be said twice as a full word for the first and second word (such as aki-aki, bapa-bapa, etc.); or only the first syllable for the first word and full word for the second word (such as babagi from bagi-bagi ). However, there is also an exception called kecap raje- kan semu, in which the repetition is part of the base word. For example, the words pa- patong, kukupu , and pipiti have repetition, but the first syllable has no base word. Ke- cap rajekan is classified into six categories: 1. kecap rajekan dwipurwa 2. kecap rajekan dwi madya 3. kecap rajekan dwi murni 4. kecap rajekan dwi reksa 5. kecap rajekan trilingga 6. kecap rajekan binarung rarangken (Fit- riyani, 2019). This work puts forward a concept of developing mathematical theory (LCM), which is the basis for the idea of music composition, where LCM is a technique for processing reps in Rajekan’s music com- position. There are a lot of musical works about repetition techniques, from simple to complex. This work as an offer techni- Harmonia: Journal of Arts Research and Education 23 (1) (2023): 208-222210 que to process repetition with the least common multiple (LCM). Repetition can generally be inter- preted as repetition. Repetition in linguis- tics can be interpreted as an iteration app- lied to an important sound, word, or part with the intention of affirmation. In educa- tional psychology, repetition is a method to understand a learning concept by rete- aching after remembering, saying, hearing, and doing than understanding (Wikaneng- sih, 2010). The word in music can be inter- preted as the iteration of motifs, rhythm patterns, chords, and parts. It is one of the simplest and most fundamental composi- tion techniques. In addition to minimalist music, reps also appear in sonatas-shaped works. The recapitulation section has im- portant points for recapturing, renoun- cing, reviewing, and repeating what has been introduced in the exposition section at the beginning of the (Hammerschmidt et al., 2021; London, 1994)absolute durations may seem longer as the tempo—the rate of an underlying pulse or beat—increases. Yet, the perception of tempo itself is not absolute. In a study on perceived tempo, participants were able to distinguish bet- ween different tempo-shifted versions of the same song (± 5 beats per minute (BPM. Psychologist Diana Deutsch discove- red the illusion of “The Speech-to-Song illu- sion” in which a recording of a repetitively played part of a speech can make the pas- sage sound musical (Rowland et al., 2019). The repetitive part gives rise to a regularity of tempo and rhythm that makes it sound musical. Reps also cause expectations for their listeners. A study of the repetitive works of Howard Skempton states the role of repe- tition from a psychological point of view can lead to a sense of expectation/expec- tation and thus the desire to make a repe- tition of disturbing patterns (Suhaya et al., 2020), which are then recreated to present a sensation of satisfaction in a particular moment (Cavett, 2022; Hananto & Suker- ta, 2020). From the above statement, it can be concluded that reps play an important role in music. Repetition is widely used as the basis for development in music. In music composition from Reich’s work, Reich’s previous repetitive pattern of “Come Out” into a tape is looped, and then Reich tries to play the same figure on the keyboard along with the tape loop, then tries to accelerate ahead of the tape loop which results in (Reich & Paul, 2004; Schwarz, 2009). The experiment was then continued with the work “Piano Phase” in which two acoustic piano instruments with humans playing them tried to pro- duce phasing without the aid of electronic devices (Schwarz, 2009). Several piano works that can be found to explore repetition in both solo piano and piano four hands can be exemp- lified by the piece ‘Piano Phase’ by S. Reich, composed in 1980. In this work, two pia- nists play simultaneously with the same rhythmic pattern but at different tempos. This concept of repetition becomes intri- guing to listen to as a form of developmen- tal repetition. The tempo increase lasts until the pattern shifts to one-sixth of the notes and then again holds the initial tempo; after some repetition, the tempo is raised again until the pattern shifts to one-eighth of the pattern play played by the first pianist, and so on until the second pianist again plays a pattern identical to the first pianist (Digney, 2022; Epstein, 1986)organizatio- nal support, and service under pressure. Figure 1. The final phase of pattern 1 is in the “ Piano Phase” (Reich, 1980). Repetition through the LCM techni- que becomes interesting to discuss and can be used as a separate composition techni- que with various kinds of processing. Mo- reover, the process of creating and analy- zing this work is a step in how the world of musical composition is not only related to taste, but music is very close to the exact Hery Budiawan et al., Music and Mathematics: Processing Repetition Techniques with the 211 sciences, so many possibilities for the use of LCM are able to provide a new style of music with the processing of new techni- ques as well. This LCM research novelty in a technique of processing reps in musical composition. By using this technique, com- posers can create musical works by ma- king only one musical sentence, then the theme of the work sentences is processed with this LCM to make the music work in- tact. Composers do not need to think about the melodic ideas of the next sentence of the song; just with the concept of LCM the musical work will be created and have its own sensation with the processing of reps through LCM. Moreover, the LCM techni- que in music lies in its ability to simplify the composition process by using the concept of LCM to process repetitions of a single musical sentence into a cohesive and uni- que musical work. It allows composers to focus on a single melodic idea and create a complete musical work without the need for additional melodic ideas. This can lead to a new approach to music composition and may result in new and innovative mu- sical works. METHOD The creation research methodology used is artistic research through a Practi- ce-Led Research approach which is also in- tegrated with mathematical theory and musicology, especially music composition. This approach is a scientific research met- hodology that reveals the creative process of art creation from the artistic experience. Artistic research can also be understood as conducting historical or historiographi- cal research to re-actualize older forms, technical objects, or modes of expression (Schwab, 2019). Practice-Led Research is a research approach that combines creative practice, creative methods, and creative re- sults into a research design and as part of the research results (Candy, 2006, 2011). In creative practice, of course, a crea- tive thinking process is needed. A thought can be said to be creative if it becomes an original and adaptive idea, solution, or in- sight (Runco & Chand, 1995). Figure 2 is a diagram of the process and basic compo- nents of creative thinking. Figure 2. The creative process (Runco & Chand, 1995). In this diagram, there are two levels where the first level (Problem discovery, Ideation, and Evaluation) has a relation- ship between simple but important abi- lities (skills) to understand creative thin- king, while the second level (Knowledge and Motivation) is a component that in- fluences but does not control factors but depends on the main factor (Budiawan & Martyastiadi, 2020; Runco & Chand, 1995). The stages of creation in Practice-led Rese- arch are dynamic, so they do not have bin- ding and structural steps, adjusting to the researcher’s unique way. The stages of cre- ation research that researchers go through are derived from literature reviews and some of the researcher’s artistic past expe- riences; Data Collection (Minimalist Mu- sic, Repetition, Sundanese), Creation Dee- pening, and Studio Works. RESULT AND DISCUSSION The work entitled “Rajékan” (with the letter é voiced the same as e in the word evaluation) is taken from the term ketchup rajékan, a linguistic term for repeating words in the Sundanese language. This work is an absolute piece of music based on the development of a repetition techni- que with an enlargement (augmentation) and reduction (diminish) of the value of notes to a series of melodies. In this work, the researcher enlar- Harmonia: Journal of Arts Research and Education 23 (1) (2023): 208-222212 ged the note value by 1 ½ times, 2 times, 3 times, and 4 times, and reduced the note value by ½ times and ¾ times presented in the form of a marimba ensemble. In its processing, researchers chose a Pitched Per- cussion type instrument because this type of instrument can be freer to sound notes that are rather tight and fast with clearer attack articulation compared to wind or friction instruments. Audio is presented with VST (Virtual Studio Technology) on the Sibelius notation writing an application which can be acces- sed via the following link: Rajékan Audio. In this practice-based Research, the com- poser had a special set of plots in creating Rajékan’s work. The following are the steps that composers perform: Movement I (Exposition) The initial part of the work includes the introduction of the main motif or the- me and its development in the same way as the exposition part in Fuga. Motifs are introduced one by one, starting from the theme, followed by its development with certain rules called the repetition cycle. To create a repetition cycle, researchers per- form several stages. In the initial stage, composers can create an original motif or theme that will be repeated and developed in terms of its pitch values. This serves as the ba- sis for applying the least common mul- tiple (LCM) as a technique for processing repetition. The researcher then observes the composer performing calculations by determining the potential rhythmic occu- pancy based on the duration of the notati- on and time signatures of the theme. If the duration of a theme occupies one complete measure, the rhythmic occupancy is con- sidered 100%. Similarly, if the duration of a theme occupies two complete measures, the rhythmic occupancy is valued at 200%. In cases where the theme does not occupy a complete measure, the ratio of filled beats to the time signature used can be used to calculate the rhythmic occupancy. The number of voice divisions and the types of value developments are deter- mined, ensuring that the number of voice divisions corresponds to the number of value developments. This step is essen- tial for determining the LCM of the value developments and recording the result. In the first movement, the resulting LCM is divided by the predetermined types of value developments, and each result is re- corded. This step is necessary to calculate the number of repetitions for each type of value development within one cycle. Multiplying the LCM result and the calculated results from the fifth step by the respective rhythmic occupancy percenta- ges allows for the determination of the du- ration (in beats/time signatures) for each type of value development and a cycle. A crucial point to consider is creating a repe- tition cycle mapping diagram. The number of voice rows corresponds to the number of value developments in the motif, the number of measure columns matches the duration of the cycle (in terms of measu- res), and the highest value augmentation is placed in the top row while the lowest value diminution is placed in the bottom row. In this research, the table was made to guide the work process of the compo- sers, but for the filling of the value of the rhythm change notes and others, the com- poser has the full right to enter the number of repetitions of motifs that refer to previo- us compositional work. Figure 3. Music Composition Proses. Figure 4. Mapping reps that have been filled in with the calculation results. After the diagram is finished, it is applied to the score by introducing the https://drive.google.com/file/d/1WBCCJnFhG76uBsSiAT6M8IsdVcK-gGyr/view?usp=sharing Hery Budiawan et al., Music and Mathematics: Processing Repetition Techniques with the 213 repetitioned theme first, followed by the development motif one by one, as is the case in Fuga’s works. The appearance of the motive must exactly correspond (or to multiples) with what is already calculated in the diagram; otherwise, the repetition cycle will not occur. After all the voices and motives of development have emer- ged and there has been a cycle, the work with this development rep technique can be continued to the second part. Movement II (Development) In this section, each instrument/ sound division plays a whole variety of predefined note value development types alternately and sequentially. In order not to have the same repetition in one cycle or parallel (there is a type of repetition of the development of the same motif that is reviewed vertically or horizontally), the author performs the following steps that make this work processed serialism. The table below is an example of what com- posers can do in repetition through LCM Instruments Order. Table 1. Presentation of Motive. In the second movement of deve- lopment, several important compositional tasks are carried out, with the primary task being the selection of desired instruments by the composer, which are placed in the index column for instrument allocation. Meanwhile, the index rows are filled with the presented order a voice/instrument di- vision, following a series of development presentations applying the following se- quence: ×0.5, ×0.75, ×1, ×1.5, ×2, ×3, ×4 (this series can be adjusted and does not have to be sequentially arranged from smallest to largest as used by the composer). Table 2. The initial filling of the motif presen- tation table with a predetermined row. After the series is placed in the bot- tom row, the researcher or composer proceeds to fill the table with subsequent rows, ensuring that each row follows the same sequence as the bottom row without introducing any gradual changes in the se- ries. Table 3. Advanced filling of tables with the same series but in different sequence sequenc- es. In the next step to apply LCM here, the composer places the smallest multip- le by multiplying the number as shown in the table below. What needs to be no- ted is that all rows and columns are filled, this stage is carried out by researchers to ensure and verify that the series remains consistent and that no development is the same reviewed horizontally (rows) or ver- tically (columns), so that each column and row has a different number before the mo- tif is executed in the musical work. Table 4. Sof completed sequences are filled in and verified. In order to apply LCM in musical Harmonia: Journal of Arts Research and Education 23 (1) (2023): 208-222214 works (composition), the next step in- volves composers verifying the division of sounds or instruments and entering them into the instrument index column, as shown in table 5. The sequence of note value development in the piece “Rajékan” is then presented. Once the sequence of development for each voice division or instrument is determined, the researcher applies it to a musical script (sheet music) with all the sounds distributed simulta- neously according to the order specified in the table. Each development is played once without repetition. A repetition cycle may occur in this second part, and its duration can be calculated by adding up the values of the entire note value development. In the case of this work, changes in tone va- lues of 0.5, 0.75, 1, 1.5, 2, 3, and 4 result in a cycle duration of 12.75 (11 full rhythms + 3 beats). If the cycle continues, the subse- quent cycle will end on the rhythmic seg- ment of the 25th order of the 2nd beat. To conclude this part of the work, researchers chose to use the initial tone of one theme throughout the entire sound section, ma- king a few simple adjustments. Table 5. Order of presentation of the develop- ment of the value of notes on the work “Ra- jékan”. Description and Analysis of the Work “Rajékan” Rajékan is taken from a linguistic term in Sundanese kecap rajékan, which me- ans reword. This work is given the title be- cause it is based on reps or commensurate terms in music for repetition. The repetiti- on technique in this work was developed by means of enlargement (augmentation) and reduction (diminus) of the value of no- tes. The work is presented in the form of a marimba ensemble with seven presenters. The main motif or theme found in rhythm 1 contains (similar) notes found in the barrel degung with da tones appro- aching Ab tones in the Western scale (Fi- gure 6). The symbol contained in the score is a sign that the motif is an original the- me or motif without any development of augmentation or diminution. This pattern continues to be played until one rhythm before part B, (time to 32). Figure 5. The main motif or theme in work “Rajékan” is found in Marimba II (b) in rhythm 1. The development of motifs and the magnification of note values can be seen and observed in rhythm 3, particularly fo- cusing on Marimba IV (a) in the composi- tion “Rajékan.” This is done by researchers with a view to analysing the technique of magnifying the value not as much as twi- ce the value of the main motive, which is visually indicated by a certain symbol . Through a detailed examination of the musical script (score) and musical inter- pretation, the researcher has the full right to select the creative work created by the composer and explore the artistic impact of this technique on the overall music com- position. Hery Budiawan et al., Music and Mathematics: Processing Repetition Techniques with the 215 Figure 6. The appearance of the main motif that has been augmented two times in Marim- ba IV (a) in conjunction with the original motif in Marimba II (b) starting from rhythm 3. A motif with the development of a one-and-a-half-time note value augmen- tation begins to appear in rhythm 6 on Marimba III (a) with a symbol (X1. 5) as its marker. By looking at table 5 in row III marimba with LCM usage used; x 1.5; x 2; x 3; x 4; x 0.5; x 0.75. The use of these mul- tiples means that the musical movements in Marimba III and others will never be the same, but unlike canon works, with LCM we make the works seem to be complex Fuga movements. Figure 7. The appearance of the augmentation development motive 1.5 times in rhythm 6 in Marimba III (a). A motif with the development of a three-time addition of note values begins to appear in rhythm 9 on Marimba III (b) with a symbol as its marker . In marim- ba III (b) this becomes a based line of mu- sical works which is a repetition technique with LCM through enlargement of note values by magnification multiplication; x 1; x 1.5; x 2; x 3; x 4; x 0.5; x 0.75. LCM provides space for movement in each note that is written, making the motif or theme of the position like a bass sound separate from the repetition processing through the LCM approach. Figure 8. The appearance of the motive for the development of augmentation 3 times in rhythm 9 in Marimba III (b). A motif featuring a four-time addi- tion of note values emerges in the twelfth rhythm on Marimba IV (b), marked by a distinctive symbol . This development runs parallel to other musical elements and never coincides with the same motif. However, the composer has the ability to control the duration of this motif’s presen- ce by manipulating a predetermined table. By employing calculations involving small and large multiplication units in relation to the departing notes from the initial motif, the composer can determine the length of time this motif will be heard. This motif, characterized by the addition of note va- lues in multiples of four, makes its appe- arance in the twelfth rhythm on Marimba IV (b) and is denoted by a symbol. Throug- hout its development, this motif remains independent from other musical motifs, running in parallel without ever intersec- ting. Nevertheless, the composer has the flexibility to dictate how long this motif will be heard by employing a precalcula- ted table. By calculating the multiplication units for both small and large note values in relation to the departing notes from the original motif, the composer can control the duration of this motif’s presence in the composition. Harmonia: Journal of Arts Research and Education 23 (1) (2023): 208-222216 Figure 9. The appearance of the motive for the development of augmentation 4 times in rhythm 13 in Marimba IV (b). In the composition, a motif undergo- es a development characterized by a dimi- nution of three-quarters of its original time value. This development commences in the fifteenth rhythm on Marimba I, and it is distinctly marked by a symbol . As this motif evolves, its temporal duration becomes increasingly condensed, creating a sense of compression and acceleration within the musical structure. Initially, the motif is introduced in its full time value, occupying a certain duration within the rhythmic framework. However, as the de- velopment unfolds, the composer imple- ments a diminution technique that reduces the motif’s time value by three-quarters. This means that the motif’s duration be- comes significantly shorter, creating a compressed and intensified musical effect. The 1/16 rhythm serves as the star- ting point for this development, with Ma- rimba I being the instrument that brings forth the motif. The motif’s presence is emphasized through the use of a symbol as its marker, indicating its significance wit- hin the composition. This symbol acts as a visual cue, alerting the performers and lis- teners to the evolving nature of the motif. As the development progresses, the motif with the diminished time value continues to reappear throughout the composition, contributing to its overall rhythmic comp- lexity. The repetition and variation of this motif, now condensed in duration, adds a sense of urgency and forward motion. It becomes a recurring element that engages the listeners’ attention, creating a dynamic and evolving musical experience. Figure 10. The appearance of the development motif is minuses 3/4 times in rhythm 15 in Marimba I. The composition introduces a motif that undergoes a development characteri- zed by a reduction of half its original time value. This development emerges in the rhythm of the 18 pads on Marimba II (a) and is distinctly marked by the symbol X 0.5. The motif, initially presented with its original time duration, undergoes a trans- formation as its temporal value is halved, resulting in a more compact and accelera- ted musical effect. Starting in the 18th rhythm, Marim- ba II (a) takes centre stage in introducing this motif development. The symbol X 0.5 acts as a marker, signalling the change in the motif’s time duration. It serves as a vi- sual cue for both performers and listeners, drawing attention to the altered rhythmic structure and the subsequent intensificati- on of the musical passage. As the motif de- velops, its time value is consistently redu- ced by half. This means that its duration becomes progressively shorter, creating a sense of compression and increased tempo within the composition. The motif reap- pears at various points, maintaining its halved time value, and contributes to the overall rhythmic complexity and energy of the piece. The recurrence and variation of this motif, now condensed in duration, im- parts a sense of urgency and forward mo- mentum. It becomes a prominent element that shapes the musical narrative, evoking a sense of tension and heightened dyna- mics. The deliberate use of the X 0.5 mar- ker ensures that performers and listeners can follow the motif’s development and appreciate the transformative effect it has on the composition. Hery Budiawan et al., Music and Mathematics: Processing Repetition Techniques with the 217 Figure 11. The appearance of the development motif is minuses 1/2 of the time in rhythm 18 in Marimba II (a). The polyrhythmic formed from the presentation of development motifs and original motifs played simultaneously is 1:11/2:2:3: 4:6:8 with motif patterns that cross several rhythmic segments to be able to start from the beginning of the motif with the exact same tone simultaneously. The pattern collides on rhythm 21 with the explanation of the graph below then the repetition pattern will collide back on rhythm 33 (although researchers eventual- ly in rhythm 33 continue with part B), thus forming an asymmetric polyrhythmic. In the case of this work, a repetition collisi- on will occur once every 12 times. This can be found using the LCM formula (Smallest Guild Multiple) of the value of the entire amount of development, both augmentati- on and diminution. In the second part (time 33-45), each presenter plays a variety of motif develop- ments sequentially and alternates with the order that has been created in Table 6. Af- ter the entire series of each end, the work closes with a slowdown in tempo (molto rall) 2 rhythms before the last rhythm and ending with the note G beginning with marimba IV (b) as the lowest note, then followed later by Marimba I, II, III, and IV (a) on time 46. Table 6. Mapping the repetition cycle in work “Rajékan”. Figure 12. Rhythm 43-46 “Rajekan” As the title implies, this work is inspi- red and based on repetition. The phenome- non of repetition in the researcher’s self- experience is interpreted into repetition in musical terms which is then developed by magnification (augmentation) and reduc- tion (diminish) of the value of notes. This work is an absolute piece of music who- se interpretation is focused on numerical computing (calculation). The main motif in this work uses the application of the de- gung barrel in the Sundanese degung kara- witan with the distance between the notes in cents of (in order) 424-70-212-424-70 (Fa- usta, 2019a) with the da tone (in Sundanese terms) approaching the Ab tone (in Wes- tern terms), then the Mi tone approaches the G tone, Na approaches the Eb tone, the It tone approaches the Db tone, and the La tone approaches the C tone. The emergence of development mo- tifs that are played simultaneously with original motifs and other developments produces chords incidentally and polyr- hythmically. These namely rhythmic pat- terns, contrast, and are independent at the same time (Kamien & Kamien, 2013). However, the polyrhythmic formed is an asymmetric polyrhythmic with the possi- bility of collision that can be calculated by the smallest common multiple (LCM) of the 2 largest developments (enlargement or reduction) of the note value. In this work “Rajékan” the greatest multiple of his com- munion is worth 12 with an original motif of 1 rhythm. Thus, collisions or cycles will occur in every 12 rhythmic segments. Discussion In the context of composition, reps are the easiest and most basic way to de- Harmonia: Journal of Arts Research and Education 23 (1) (2023): 208-222218 velop musical composition techniques. The repetition processing carried out by researchers produces a repetition proces- sing technique with the magnification and reduction of the sound value that forms the cycle (Ananda et al., 2022; Hargreaves, 1984, 2012). Minimalist music produces several works that use repetition who- se components do not change. Originally repetitive moments were the most striking feature of minimalist music. Many mini- malist composers work with highly repe- titive patterns, such as Philip Glass, who essentially concentrated on static repetiti- on and harmony for electrically amplified violins in his composition “Strung Out” (1967) (Ensemble & Culture, 1990). While Glass tends to vary repetition, Steve Reich uses this musical technique for his audio cassette compositions and his work “Piano Phase” (1967) in a way that continues un- changed (Hill et al., 2018; Schwarz, 2009). In Rajékan’s work its use and application is different from research or repetition pro- cessing techniques from other composers, LCM works in music composition work is perceived by researchers as a new way that can ease the making of musical works (Azaryahu et al., 2023), just as the mani- pulation of motifs in music composition can make the time of working on musical works more effective ways (A. L. Uitden- bogerd & Zobel, 1998; A. Uitdenbogerd & Zobel, 1999). In this research, the least common multiple of the time signatures in a piece of music is if one part of a song is in 3/4 time and another part is in 4/4 time, the LCM of these time signatures would be 12/4, which is equivalent to 3/1 (also known as “whole note” or “quadruple whole note” time). In particular, discovered that there are three methods for determining the le- ast common multiple (LCM) between two numbers: Creating a multiple and divide involves creating an ordered list of con- secutive multiples of one number while simultaneously checking each new entry for divisibility by the second number (Bol- lobás, 2022). Prime-factorization involves comparing the prime factorization of the two numbers and locating the minimal product of prime powers that contains both of their factorization (Heyman & Tóth, 2022). Set intersection involves cre- ating an ordered list of consecutive mul- tiples of each number and finding the first one that appears in both lists. This tells the musician the length of one cycle or measu- re of the repeating pattern in the music and helps to synchronize the different parts of the solo, duet, trio, and ensemble. From the results of the discussion above, techni- ques for enlarging and reducing note va- lues using LCM were carried out. In the mathematical sciences this technique aims to take two or more integers as input and returns the smallest positive integer divi- sible by all input integers without leaving a remainder (Bagdasar, 2014). In other respects, the use of reps in music generally aims to influence the emo- tions of the human beings who listen to it; in minimalist music, the listener is de- liberately invited to listen to a repetitive theme in order for the listener to go “tran- ce” (Rowland et al., 2019). Similarly, in In- donesian ethnic art performances, one of which is the “lumping horse” in the music kuda lumping deliberately repeated so that listeners, in this case the “kuda lumping” ac- tor, can “trance” so that the show is more interesting (Hendriko & Effendy, 2019a, 2019b). In this Research, LCM as a repe- tition technique was not used to influen- ce human emotions but as a technique for making compositions in the processing of musical themes which were used as tools to create musical works with only short the- mes. In the sub-discussion, several ways have been given to use this LCM technique as a concrete form of application of compo- sition techniques (Azaryahu et al., 2023). In contrast to minimalist musical works in repetition processing such as Steve Rich does repetition processing techniques, but he does it by way of playing tempo (Dau- er et al., 2021). Steve Reich’s piano pha- se offers listeners an easy-to-hear formal structure with unpredictable local events. For example, repeating patterns can create strong expectations broken by small devi- Hery Budiawan et al., Music and Mathematics: Processing Repetition Techniques with the 219 ations in time and pitch. In musical composition, Rajékan is very different from Steve Rich’s style of music processing (Schwarz, 2009). Du- ring the development of his composition “piano phase,” Steve Reich became capti- vated by the idea of creating an electronic device specifically designed to execute the phasing process. This device would serve as an instrument, capable of being played in live performances to replicate a distinct type of phasing activity. Unlike previous phasing techniques that focused on alte- ring the rhythmic relationship between two identical melodic patterns (Schwarz, 2009), Reich’s new approach involved ini- tiating with a chord and gradually shifting individual tones out of phase. This trans- formation would transition the initial ver- tical harmonic entity into a continuously evolving series of horizontal melodic pat- terns. Reich’s fascination with this concept drove him to explore new avenues of musi- cal expression and expand the possibilities of phasing composition. Rajékan repetition processing with LCM technique plays at note value and plays ensemble marimba with the same tempo; in minimalist music above ensemble plays with different tem- pos in each instrument. Weakness in tem- po processing there is a tendency to inac- curate the end of the musical work as well as when playing in the middle of the work. However, when using the LCM technique, players can minimize and even be accurate in playing the work in the middle and at the end of the work. The different musical works in the classical era also used the repetition techni- que; in that era, the repetition technique was used by means of a pitch modulati- on system or instrument change with the same motif. An example can be taken from Beethoven’s Fifth Symphony. Beethoven did a lot of reps by means of modulation and instrument displacement. Repetition with the use of LCM in its development and utilization can be found in-game music or game music, where the music acts as background music that cons- tantly undergoes repetition or looping and puts the function of music as a state of mind. A type of music with repetition con- sidered to work effectively “hypnotizing” to bring game players into the desired mindset towards gaming, Rajékan is one part of manipulation the listener through the LCM technique. Figure 13. Beethoven’s Fifth Symphony with analysis music computing (Hu et al., 2022). CONCLUSIONS Finally, the use of The Least Com- mon Multiple (LCM) in “Rajékan,” a work by Rizky Fauzy Ananda, has shown how closely mathematics and music are rela- ted. The study looks at how mathematical elements, especially those derived from physics, are fascinating and extremely im- portant in the realm of music composition, producing new knowledge that is useful for the composition process. By examining the effectiveness of employing LCM, this study sought to identify novel techniques in the field of music composition. A prac- tice-led research strategy was used in the technique, which combined musicology, mathematical theory, and creative study specifically in the context of music compo- sition. Repetition in music, independent of context, strongly overlaps with mathema- tics, according to the study, making LCM a useful tool for composing music. Composers concentrate on creating themes or motifs that are then imple- mented utilizing the LCM technique, as described in this article. Additionally, composers continually develop new met- hods and produce comprehensive musical works of art by incorporating insights from several fields. Through personal experien- ces, the researcher has found two repetiti- Harmonia: Journal of Arts Research and Education 23 (1) (2023): 208-222220 on processing methods that use the LCM mathematical style: (1) multiplication and reduction of sound values to form cycles, and (2) imitation. Repetition has been crucial to the development of music. The use of LCM in “Rajékan” exemplifies the intimate relationship between music and mathematics. This study highlights the potential and benefits of using LCM and advances the study of innovative compo- sitional strategies. By fusing mathematical concepts with creative research. 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