The deduction, calculation or assignment of musical parameters to the celestial bodies is known as the 'tradition of music of the spheres,' and, in the West, it goes back to the Pythagorean school of the sixth century BC. In this article, several proposals in this regard will be reviewed, cataloged and discussed, starting from the first century with the proposals of several authors of the Roman world, until the end of the 1980s, with the proposal of Swiss mathematician Hans Cousto. Here, I will limit myself to the proposals that assign the height parameter to the celestial bodies, and save for future publications the topic of the rhythm of celestial bodies, also addressed by the tradition of the music of the spheres, but which will not be covered here. I have grouped the reviewed proposals in four groups, based on their theoretical and procedural base perspective: either interpreting the translational speeds of the celestial bodies as musical heights, interpreting the orbital distances between them as musical intervals, or combinations between both parameters (as in the case of Johannes Kepler's proposal in his book The Harmony of the World, of 1619), or a more radical Pythagorean-Platonic perspective that ignores the observational and assigns these equivalences between music and celestial bodies from proportional mathematics and pure music theory.