The "Music of the Spheres" is a philosophical concept that the movement of the planets of the solar system relate to each other in mathematical terms not unlike the relationships of some musical tones. Although the people talking about it didn't necessarily think that the musica universalis would be actual notes, they saw what they thought was a harmonic relationship between them as they moved across the sky.
As late as the 1600s, musica universalis was not just an idea limited to astrologers and mystics. Johannes Kepler, who devised his laws of planetary motion based on Copernicus' claim that the Earth revolved around the sun rather than vice-versa, wrote a book in 1619 called Harmonices Mundi, which outlined different harmonic congruences between geometrical forms and physical phenomena. His third law of planetary motion arose from this work.
In 2010, musician Daniel Starr-Tambor assigned different notes to the different planets along what's called the "natural harmonic series," or notes that fall at natural vibrational intervals from each other -- in other words, a complicated musical-scientific relationship that I would have to know a lot more about to fully understand. What it amounts to is that the notes stairstep upwards in a natural relationship to each other. He then pictured the solar system at a certain point and started playing his notes in the sequence of the planetary orbits, with two seconds standing in for one Earth year. That means that every two seconds, the note representing the Earth would be played. Just under every half-second, the note representing Mercury is played, because Mercury orbits the sun in 88 Earth days -- a shade over 40% of an Earth year. Pluto orbits the sun in 248 Earth years, which means its note is played every 124 seconds, or just over two minutes. A YouTube video of the composition with some notes from Starr-Tambor that describe how he wrote the piece, which he calls "Mandala," is here. Mercury's note provides the rhythm, and the others sometimes sound separately, sometimes in chords as they play through the history of the solar system.
When Starr-Tambor created the tune, he realized that it was a palindrome, meaning it would be the same backwards and forwards. But no one could ever listen to the whole piece, because even at the two-seconds-per-year pace it would take 532.25 "septendecillion" years to finish, or 53,225 followed by 56 zeroes. By contrast, the entire history of the universe to this point is only somewhere around 15 to 17 billion years, or a 15 or 17 followed by nine zeroes. It contains 62 "vigintillion" notes, which is 6.2 followed by 64 zeroes. So in other words, at the end of those 532.25 septendecillion years, "Mandala" would come back to where it had started and any notes played thereafter would repeat the song the way it had begun. Should the theory be true that the physical universe will one day stop expanding and begin to collapse into a singularity like that which spawned the Big Bang, Mr. Starr-Tambor's piece might be a fitting finale to play.
In non-physical matters, "Mandala" bears no resemblance to the hymn "This Is My Father's World," which contains the note of praise to God, "All nature sings and round me rings/The music of the spheres." But on the other hand, the poem which makes up the lyrics was written by Presbyterian minister Maltbie D. Babcock some 15 years before Franklin Shepherd set it to music, so who knows what he had in mind on how to sing it.
(H/T Brain Pickings)