Did you know that the same math behind musical vibrato also explains planetary orbits and quantum mechanics? In this video, we explore the surprising connection between Fourier Transforms, Bessel Functions, and Kepler’s Equation, revealing how vibrato creates multiple notes and why this same phenomenon appears in astronomy and quantum physics.
00:00 intro
01:27 creating vibrato
03:12 listening to vibrato
04:38 fourier transform
07:16 contextualizing the fourier transform
07:54 analyzing vibrato
09:44 kepler's equation (astronomy)
11:52 relating astronomy to music
15:05 drum vibrations (quantum)
17:10 science is interconnected
References and Resources:
Frequency Modulation (Desmos) - https://www.desmos.com/calculator/iqiaknblfr
Fourier Transform (Desmos) - https://www.desmos.com/calculator/vac1cze4up
3Blue1Brown's video on Euler's Identity - https://youtu.be/v0YEaeIClKY?si=pOLGt4ynzghlrRm8&t=117
What are Bessel Functions - https://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html
I highly recommend Peter Colwell's Book Solving the Kepler Equation Over Three Centuries.
Why Drum Vibrations need Bessel functions - https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane
Music:
Mendelssohn Violin Concerto, Mov.3