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While one can think very philosophically about music without ever mentioning the concept of "note", or talk about how music makes one feel without knowing what a diatonic scale is, there is a well established, intellectual body of knowledge that allows one to better understand a large percentage of Western music before 1920. Some of it is facts to memorize, like the intervals of a scale, but we also learn the logical implications of those memorized facts, like that the fifth degree of a major scale has a leading tone to the first degree. One can choose to deliberately not write or listen to music for which these categories matter, but every musicologist and composer should have some competency in these technical details, at the very least so they know what rules they're breaking.
Does any analogue exist in visual arts? I see a connection between drawing and playing an instrument, in that both require a technique that is very physical as well as interpretive imagination, but is there any theory in the visual arts (particularly drawing/painting) that is at all like what is considered "music theory"?