A Comprehensive Review of Fourier Series Applications in Music Theory and Practice

Scholars have been fascinated by the intersection of math and music for centuries, with evolving into a powerful method that can unravel the complex connection between sound and numbers. This paper looks at the deep relationship between Fourier series and music theory including how mathematical ideas like harmonic analysis and frequency synthesis - drive musical composition, performance, audio synthesis among oth-ers. The objective being to demystify the basic components of music through historical insights, case studies, and mathematical analyses. We also explore its historical background in relation to music theory development starting from ancient Chinese dynasties up to modern day use such as compression algorithms for audio.