Mathematical Modelling of the Euphonium

This 76-page PDF report is based on my Master's project completed in 2019. I have rewritten it as a companion to my romance novel The Island Festival. To all you consummate nerds out there, you can let me know if there are any mistakes herein, but I must say I have no intention of returning to this project in any technical capacity! Enjoy or not, at your leisure!

Abstract: This report gives an overview of the mathematics of the euphonium. Sound waves are pressure oscillations in a fluid such as air. In a wind instrument, the resultant vibrations of the air particles are parallel to the direction of travel. Their motion is highly dependent upon the geometry of the confined space through which they travel. I examine the pressure oscillations in a simple cylindrical pipe, and extend the model, chapter by chapter, to more closely resemble the euphonium. In particular, I  extract the frequency spectrum of the euphonium from analysis of the pressure, and explore the sounds that it naturally produces.

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