Ave Maria, Fraetals & Mathematics

摘要

Music critics have compared some classical music, like that from Bach, to the precision of mathematics. Mathematicians disagree on a precise definition, but a fractal is typically described as exhibiting self-similarity, which means identical (or nearly identical) patterns appear, whether the shape is viewed from up close or far away. That is, the part looks like the whole, and the whole looks like a part. However, identifying fractals in music requires a different approach than seeing them in an image. The purpose of this short note is to suggest that Ave Maria of Bach/Gounod could be related to mathematics, at least in part (or just viewed), as a sound example of Mandelbrot's fractal geometry, due to its simple self-similarity on melody.