Math and Music
Have you ever wondered where the rules of music theory come from? Musical structure, i.e. songs, scales, chords, etc. are some of the most beautiful mathematical structures one can see. In fact on of the most interesting groups to look at in math is the dihedral groups. Dihedrals are the most symmetrical shapes in the world (triangle, square, pentagon, and so forth). Well there is actually an isomorphism between the set of all the major and minor triad chords and the D12 dihedral group, the group generated by the translations and inversions of the 12 sided dihedral. This is such an amazing outcome, these are both very complicated unrelated objects, but written as a mathematical structure, you cannot tell the difference between the two.
What other kinds of musical structures do you think could be represented using mathematical structures?
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