Perfection and More: Platonic Solids are the only five perfect solids that can be constructed. By comparing the ratios of angular degrees each solid has, these ratios translate to ratios of perfect musical intervals. The equation of these perfect musical intervals to geometrical figures is given immediately below; however, one comparison does not form a perfect interval according to this way of looking at the traditional definition: that of the major third which by degrees translates into the number of degrees in an icosahedron as compared to to cube. That ratio stands as 5 to 3. I think it should also be called perfect for that reason. 
An interval, by the traditional way of thinking, can only be described as a perfect interval when the space between the first note in a major scale is one of the following: unison, a fourth, a fifth, or an octave. I, however, would argue that this perfection should include the “major third”. Since the five to three ratio by degrees is characteristic of the number of degrees in a dodecahedron (6480) compared to the icosahedron (3600) and both of these are perfect solids; therefore, the five to three ratio of the major third musical interval should also be considered perfect.
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