This case study presents a pedagogical approach to teaching the fundamentals of Fourier analysis through the intuitive and richly structured context of music. Conducted within the Engineering Mathematics ET course at the University of Rijeka, the project uses musical tones as a medium for exploring the decomposition of signals into their spectral components.

The educational objective was to move beyond procedural exercises and foster conceptual understanding of Fourier series and transforms by applying them to wave-based phenomena that students can both hear and visualise. By analysing recorded musical tones - ranging from pure notes to harmonically rich instrument sounds, students connected mathematical theory with perceptible acoustic structures. Signal processing was implemented hands-on using Python and open-source libraries such as NumPy and Librosa, allowing students to generate spectrograms, extract harmonic content, and work with frequency-domain representations.

Music, as an inherently mathematical and artistic form, served not merely as an illustrative example but as the core domain of inquiry. Its harmonic structure, periodicity, and expressiveness provided a multidimensional and authentic platform for active learning, bridging mathematical formalism with lived sensory experience.

Students responded positively to the integration of music, reporting increased motivation and a clearer grasp of key concepts. This interdisciplinary activity demonstrates how Fourier analysis can be taught not only as a mathematical tool, but as a conceptual bridge between scientific reasoning and artistic structure and a powerful educational strategy for cultivating deeper learning in STEM contexts.

Keywords: Fourier analysis, music and mathematics, signal processing, conceptual understanding, interdisciplinary STEM, engineering education, Python.