Harmony vs Symmetry: Kepler’s view and the role of Spielraum

In a famous passage in De revolutionibus, Copernicus remarked that ‘in this arrangement [ordinatione] ... we discover a marvellous symmetry of the universe [mundi symmetriam], and an established harmonious linkage [harmoniae nexum] between the motion of the orbs and their size, such as can be found in no other way’. Copernicus has brought together two previously distinct aesthetic values: symmetry as proportionality in what is efficient or pleasing to the eye; and harmony as proportionality in what is pleasing to the ear. This is a critical passage where two aesthetic criteria are put to use to capture two different aspects of the universe: its design and its motion. Symmetry captures the design, that is, the relation of the parts (the planetary orbs) to the whole (the Universe), whereas motion (understood as the planetary periods) is linked to size (understood as the planetary distances from the Sun). What was Kepler’s view of these two distinct aesthetic criteria? I conclude that Kepler did not invoke the criterion of symmetry in any of his writings and appealed only to harmony, but he had a sophisticated view of this concept which required—so my argument goes—a certain degree of freedom which I call Spielraum. This view is in stark opposition to that of Galileo’s.