"There can be no general definition of sensible things which are always changing," writes Aristotle in Metaphysics (987b). That single phrase is connected with mathematics, the universal, moral questions, and art.
The Pythagoreans, Aristotle writes, were the first to develop the science of mathematics, "and through studying it they came to believe that its principles are the principles of everything. And since numbers are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analogues of what is and comes into being". (985b) In other words, maths was the way to reach the underlying principles of the world (e.g. justice, soul, opportunity, the physical universe).
Socrates was not interested in the physical universe but moral questions. Plato developed his thoughts and concluded that as sensible things are always in flux, definition must pertain to something else: not to the sensible, but to Ideas. The sensible is related to Ideas not just in name but also in participation of. What a phrase: to share in but yet not be the original sounds religious.
Aristotle then points out that Plato's idea is very similar to a Pythagorean idea, except he changed a word: "whereas the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation". (987b)
"Imitation of numbers" was defined by Aristotle: we have seen that numbers are "first among these principles" of everything. There are harmonious numerical "proportions" in musical instruments and the universe: "the properties and ratios of the musical scales are based on numbers, and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe, they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion or number".
My reading here was prompted by Gadamer in The Relevance of the Beautiful. He notes Pythagoras' trinity of soul, music, and universe, observing that music plays a role in Plato's Republic. "The modes of music are never disturbed without unsettling of the most fundamental political and social conventions," Plato wrote, describing how music "infiltrates" character, drive, employment, moral standards... We hearken back to Pythagoras' emphasis on order and harmony.
Gadamer writes that modern art does not represent order or harmony because things can no longer be experienced, having been made unreal and disposable. His suggestion is for art to succeed "in elevating what it is or represents to a new configuration, a new world of its own in miniature, a new order of unity in tension" such as through "specific cultural content, familiar features of the world". I find it interesting that in Aristotle, Plato is said to have "held that all sensible things are named after [Ideas] sensible and in virtue of their relation to them" - which implies that it is a vice on the part of the sensible to defer from participation with order.