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Has anyone ever considered the connection between the five perfect solids and the three most important music intervals of 2, 1.5, 1.25 and their two counterparts, 1.33333 and 1.6? The tetrahedron could be assigned to the octave 2, but what would be the best fit for the others, given there is a sort of duality between them, e.g. 1.5 x 1.33333 = 2?

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  • $\begingroup$ Kepler famously tried to explain his three laws of planetary motion from such connections in his Harmonices Mundi. $\endgroup$
    – David H
    Apr 13 '15 at 19:53
  • $\begingroup$ Tetrahedron is dual to itself, so $2$ doesn't work for it if the "duality" corresponds to the product being $2$. $\endgroup$
    – Conifold
    Apr 13 '15 at 23:08
  • $\begingroup$ Yes, a fair point but the reason I am exploring this subject is that I have found a duality between venus and mars.Mars to the power 1.875 devided by the 1.875 root of venus is Phi power 2! .723327942 for venus and 1.523732885 for mars.Nasa jpl .72332102 1.00000957 and mars 1.52371243 1.000013425.Also the ajusted mars power 7, times the adjusted venus power 32, equals1.These values are the result of the 13th root of phi 7 to the power 1.25( reciprical) and the 13th root of power 8 to the power 1.422222222. $\endgroup$ Apr 17 '15 at 1:40
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The notion that the proportions of geometrical shapes, musical harmony, and other natural relationships are all interconnected and reflect some all-embracing harmony of the spheres goes back to classical antiquity. It is expressed most clearly (in particular with regard to musical intervals) in the pseudo-Platonic Epinomis.

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