Group Theory in Indonesian Music Themes Ditianti Julrizkiah Khoirunissa, Irawati
Institut Teknologi Bandung
Abstract
This project discusses group theory in Indonesian music themes. Group theory is one of the foundations of algebra. Because of its abstract nature, algebra is seen more as a subject in art than as a subject in science. Algebra is considered too abstract, so it seems that abstract algebra can not be seen in everyday life. Seeing group theory in everyday life, especially in the field of music in Indonesia is not plenteous, so this project aims to look at group theory in Indonesian music themes and from a teaching point of view, this project aims to show that studying group theory can be more enjoyable without compromising basic essence of group theory. The group theory used in this study is the basic properties of group theory, namely the nature of closure, associativity, the presence of an identity element, and for each element in the group there is an inverse. This includes Lagrange^s theorem which states that the order of subgroup H of a finite group G divides the order of group G, and the theorem regarding left cosets, namely: Suppose G is a group, H is a subgroup of G, and g∈-G, then: (i) g∈-gH, (ii) For the left coset of H in G, both are equal or disjoint, and (iii) The number of members in gH is |H|. The Indonesian music themes used include: romance, separation, self-view, religious, escapism, nationality, politics, economics, morals, and tradition. The ordering of these themes is based on Five Principles of The Indonesian State, namely Pancasila. So the order becomes: religious, moral, tradition, romance, separation, self-view, escapism, nationality, politics, and economics. The musical themes that have been sorted are corresponded with integers 0 - 9, so it will be obtained that the Indonesian music themes form a group of integers from modulo 10, and under the addition operation, the musical theme group is also isomorphic to Z_10. Then, using the addition operation that applies to the group, it is found that the themes of Indonesian music fulfill all the axioms of the group and are also related to group theory, including Lagrange^s Theorem and left cosets^s theorem.
Keywords: Group Theory, Indonesian Music Themes, Lagrange^s Theorem, Theorem Regarding Left Cosets, Algebra.
