Developing Algorithm of Music Concepts and Operations Using The Modular Arithmetic

Abstract

The rapid development of digital music technology is closely intertwined with advancements in both music theory and mathematical formalism. This study aims to bridge the gap between these fields by exploring how mathematical concepts can enhance the understanding and analysis of music theory. Specifically, the research focuses on the application of modular arithmetic to analyze the circular structure of the chromatic scale, a key concept in music. Modular arithmetic enables the identification of patterns in pitch relationships and the manipulation of musical elements like transposition and interval calculations. In addition to modular arithmetic, the study also highlights the role of regular expressions in music theory. Regular expressions provide powerful tools for pattern matching, which can be applied to recognize and categorize musical components, such as enharmonic equivalents (notes that sound the same but are named differently). These tools allow for the development of algorithms capable of generating chords from given notes or identifying chords from existing sets of notes. By integrating modular arithmetic and regular expressions, the study proposes a framework for developing mathematical models and algorithms to facilitate digital music analysis. This approach not only enhances the theoretical understanding of music but also holds practical applications in digital music production and education.