'Harmony of the Spheres' or 'Harmony of the World' - is it debunked? I sincerely apologise for this vague question but I'm writing an essay for my music class on musical harmony and it's historical origins. I came across the Pythagorean notion of Harmony of the Spheres and how Johannes Kepler, inspired by this idea, tried to associate planetary motion with musical ratios. 
The problem is that I am not that well versed with physics and neither am I able to find any reliable source on the internet that speaks any further on this topic than Kepler's intent to prove his hypothesis. Do the angular velocities of the planets actually follow musical ratios, did Kepler get it right? if so, is it a happy coincidence? 
My intent is to not assert any speculation in my essay and hence I want to give a definite answer to whether or not the pythagorean school of thought was right or wrong about this notion as a conclusive statement. 
I'm really sorry if this post appears off topic but the internet is filled with mysticism in regards to this topic and hence there's a lot of informational bias regarding it - which led me to ask this question in one of the few reliable sources on the internet. 
 A: I have found this recent exploration

This paper, published by courtesy of the Royal Astronomical Society, is a revised version of “Heavenly harmony and earthly harmonics”, delivered as the 1971 Harold Jeffreys lecture of the Royal Astronomical Society, on 10 December 1971 at the meeting which marked the fourth centenary of the birth of Johannes Kepler in December 1571.
Two separate topics are discussed. The first is the numerical relationship between the orbital distances of the planets, the “heavenly harmony” which Kepler found so fascinating. The second topic is the study of the Earth's gravitational field and shape by analysis of satellite orbits, and in particular the determination of high-order harmonics in the geopotential by analysis of harmonious, or resonant, orbits which have orbital periods such that the satellite follows the same set of ground tracks over the Earth day after day.

It is behind a pay wall, unless your institute is affiliated. here is a copy of the first presentation, unfortunately an image:
It conludes:

So this supports the claim in the wikipedia article :

While medieval philosophers spoke metaphorically of the "music of the spheres", Kepler discovered physical harmonies in planetary motion. He found that the difference between the maximum and minimum angular speeds of a planet in its orbit approximates a harmonic proportion. For instance, the maximum angular speed of the Earth as measured from the Sun varies by a semitone (a ratio of 16:15), from mi to fa, between aphelion and perihelion. Venus only varies by a tiny 25:24 interval (called a diesis in musical terms).[5] Kepler explains the reason for the Earth's small harmonic range

.....

Kepler discovers that all but one of the ratios of the maximum and minimum speeds of planets on neighboring orbits approximate musical harmonies within a margin of error of less than a diesis (a 25:24 interval). The orbits of Mars and Jupiter produce the one exception to this rule, creating the inharmonic ratio of 18:19.[5] The cause of this dissonance might be explained by the fact that the asteroid belt separates those two planetary orbits, as discovered in 1801, 150 years after Kepler's death.

The numbers are still there, and in this sense it is not debunked. It is an observer's choice, an interpretation,  to treat it as numerology on a coincidence  or  a result of mathematical evolution of gravitational systems, as referred in the second link.
BTW,  as mentioned in the first link's abstract above, harmonius and resonant are the same. And in that sense the harmony of the spheres also applies to the atoms, that the same mathematics, differential wave equations, that applies to sound can model gravitational orbits  and even quantum mechanical orbitals.
