See this Wikipedia page for Harmonices Mundi, a book by Kepler (yes, he was the one to discover the three Kepler's laws). The author writes:
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).
Can anyone explain why this is the case physically (possibly with mathematical formulae)? Or is it just a coincidence?