With the sciences what you study, say chemistry or maths, necessarily is chemistry or maths.
It's not so simple. In physics, for instance, you study the natural world and construct models of it which are then tested and if necessary, refined or discarded. So there's a continual interplay between the study of physics (that is, the study of the models we invent) and the study of the natural world. (And even
this is too simple, because somewhere in this we need to consider the role of the imagination in the invention of the models.)
With the humanities though there's slightly more room for a personal experiential dimension in addition to the subject's study- you can take an interest in history in terms of the magic of past cultures, perhaps more independent a thing than any magic of maths.
This isn't unique to the humanities. One can equally study the development of scientific or mathematical thought through history. How one regards the Kuhnian view of the progress of science in relation to the Popperian view (for instance) opens up quite a substantial personal experiential dimension.
With the arts there begins to be a distinct bifurcation between what's studied and what's experienced: you can experience all the aesthetic content of paintings and literature in separation from their intellectual understanding, their technical matters or social context etc.
There's an aesthetic component to the experience of science, too. You don't need to understand the technical aspects of relativity to experience awe while contemplating the physical model of the expanding universe. Indeed, aesthetics can play a part in the invention of models. I'm not an expert in particle physics, but I understand that the most successful models are often those that might be thought the most beautiful. Maybe someone here knows more about that.
And with music the separation is complete. Whereas with architecture, scuplture, painting or literature the object of experience is the still same as the object of study
Whether we agree with this or not will depend on our philosophy of art as observers - and/or even the philosophy which underlies its creation. If you adopt a philosophy of art something like Susanne Langer's, then works of art present us with symbols of feeling. We study the art object, and experience the feeling. On that basis, the object of experience is not the same as the object of study. One can see there's at least some truth in this by considering, say, Duchamp's
Fountain. We see it as a urinal, presented on its side. Then we read the title, and see it differently. The object of
study is the urinal; what we
experience is a perception-shift.
I think it helps more clearly to distinguish between these two activities by thinking in terms of 'contemplation' (of an object) and 'enjoyment' (of an experience). We
contemplate the painting, and
enjoy the feeling it evokes.
in the case of music they don't intersect at all. Music is that thing you listen to, the sound in the air, and what is studied is merely books of scores and analysis: the experience is completely transcendent, left brain and right brain in parallel.
Is music so very different to literature in that respect?
The Pickwick Papers is just so many words on a page, rather like a musical score. Only when it's read, and the imagination engages with the words, does Mr Pickwick come to life - rather as the Moonlight sonata comes to life when the pianist plays the music. It's equally possible to study
The Pickwick Papers as a merely intellectual activity, robbing it of imaginative life - just as I presume can be done with a musical score.
Not sure why you brought in the unification of left and right brain activity; that certainly isn't unique to music, and I would say is a potential characteristic of all artistic activity. Scientific, too - potentially. Separate issue, I think.