The Applications of Fourier Series Harmonics in Musical Tones

The Fourier Series is considered one of the most important computational tools in mathematics and has widespread usage, specifically in music. The present paper aims at presenting Fourier Series in the context with sound analysis and synthesis. Since Fourier Series decomposes complicated waves into simple sinusoids, that improves our approach to harmonics and thereby the synthesis of sounds. The present discussion how this mathematical method offers to musicians and sound engineers new approaches as to how to generate and evaluate musical tones and sounds. Analyzing various examples, this paper will help to explain the relationship between mathematics and music, with a focus on the role of Fourier analysis in modern music production and its role in creating and designing the new exceptional sound.