Well, it's deep insofar as it's wonderful we have the ability to reason out these complex emotions and experiences. But it's not deep insofar as our being able to reason out these complex emotions and experiences is anything mystical. There's nothing mystical about what's going on, but I'll agree it's wonderful.
I just say this because people tend to overstate and get very emotional when there's a discussion about human experience (including things like perceiving beauty). Yes, it's great we can experience all these wonderful things, but let's not start getting grandiose. Know what I mean?
Well sort of, but part of experiencing beauty is to be influenced by it on a level that is not merely sensual or merely cerebral though perhaps, as Schiller believed, somewhere in between the two. The aesthetic sense acts as a bridge.
For me the experience of seeing, hearing etc. something beautiful is an experience of clarity and focus. It is similar to the feeling
that accompanies being convinced, of say, a line of reasoning or a logical proof. This is similar again to Schiller's idea as outlined in Letters On the Aesethetic Education of Man. In inevitably drop Schiller's name whenever the conversation turns to "What is Beauty?" Would you call Schiller mystical?