it’s possible to put aesthetics into several levels:
this is the scientific way the notes are arranged in microtonal music classified mathematically by pythagoras and later expanded, experimented with, and explained by alfarabi in his book musiqi-ye kabir (great book of music).
after pythagoras greeks adopted another system which still exists today but farabi believed the original pythagorian music was the only sensory and scientific way to explain order and chaos in any known scientific system including math, astronomy, and obviously logic which was the principal tool for philosophy.
it’s possible aristotle and pythagoras in ancient greece had reached the same conclusion previously since in the world of philosophy aristotle is regarded as the first teacher of philosophy and farabi the second teacher although they did not exactly show how it worked because they also put a lot of emphasis on the individual elements as being non-sensory by themselves like the way for instance alphabet works in poetry, the difference being that music is in fact sound while poetry in essence is language.
sound could be physically measured while language lacking that quality.
ironically language was used for philosophy and music for language. to go beneath the skin on music for farabi was an important issue since it broke the language barrier challenging the scientists to distinguish between math and logic when they believed math was inseperable from logic.
also it was a difficult task to convince philosophers of their time that music was something beyond language, sound or feeling, rather a scientific tool to do things numbers by themselves can’t provide. a seperate platform to test numbers on what they can do in nature or even outside nature. farabi didn’t succeed to prove his theories because the science of that time was way too primitive to do experimentations but managed to put them down in detail explaining what pytrhagoras and those before him had done and what he thought was a more complete version of that system for future observers and scientists.
after farabi there were a few other theorists with books which mostly have refined, updated, or argued for or against some details but they couldn’t deny the major work farabi had done. they also lacked the advanced tools.
but right now math has advanced forward into things like number theory, graphs,and all sorts of discrete formulations.
now we can understand how math and logic can be two different things.
aesthetics too could be something that might be either based on logic or math or a seperate scientific or non scientific system of thought. the importance is that it’s based on something otherwise how could a future observer from another advanced time truly digitize it in a non-sensory form?