That different people with different types of perceptive sensibilities experience different music differently, does not mean that the characteristics of the music concerned, can only be found in the listener.
The similar aspect of Bach and sonic art (say, of Boulez) is that both forms use patterns. Compared on the point of pattern making, Bach is very regular and rather straight-forward in terms of timbre, and Boulez extremely rich in variety in both patterns and timbres. Listened to Bach in terms as with Boulez, Bach is rather boring. But in music like Bach's, the pitches are tones in a musical network of relationships which together form an 'inner space' where energies flow from one note to the next and from one location to the next in a linear narrative, creating an imaginary space as if something flows like a river in a bedding, forming a structure from A to B to C etc., complete with directions, articulation points, balanced stretches and the like, creating a coherent structure in the mind during the performance. This creates a certain emotional effect in the listener, unfolding the many layers of meaning embedded in the structure. With Boulez, the pitches do not form such relations and do not create this inner space, and the patterns as such (and the gestures they make), is all there is. This is the difference between music and sonic art, and expecting mere patterns from Bach and a musical flow in a bedding within an inner space from Boulez, would be unfair to both art forms.
Order and chaos: I just wanted to describe how music reflects the dynamics of the human psyche. And music which creates the balance in such way that both aspects are working together in a harmonious way, has the effect of harmonizing such dynamics in the listener, or at least: getting the listener in touch with the 'Self' on the level where these dynamics are operating'. This is the 'therapeutic' effect of much classical music and the reason that so many people want to hear such music again and again, and again. They derive not only pleasure from it, but feel the restoring effect of the listening experience. This is not some sort of nice romantic wishful thinking, but is evidenced by many music lovers, and has been described by people capable of putting such interior experiences in words. I can't remember the author, but somewhere in a novel, the protagonist - a young woman in some difficult situation - unexpectedly hears some classical music coming from an open window, and she suddenly has the strange experience as if the music is 'speaking' to her, as an individual voice with something stringent to tell her, and telling her something about herself, touching her on a level deeper than words. That is why it is so hard to describe the experience and you have to be a novelist, a poet or a philosopher to find the right terms.
Music is 'non-conceptual' in the sense that it is abstract and can be put under different words and still function in the same way. The essence of emotion is non-verbal and non-conceptual in a similar way, this is the way music relates to emotion at all: it is a psychic art, bypasing the intellect, and capable of resonating with emotional processes in the listener. Sonic art does not do that, and does not want to do that, it wants the listener to become aware of the 'object in itself' which is the work. That can also have an emotional effect but the quality of that effect is different from music, sonic art is not addressing the deeper psychic layers of the listener in the same way. It can affect the listener as any thing in the outside world can affect him - like the repulsion one may feel by looking at the dirty, unmade bed of Tracey Emin, the British artist who put a dirty bed in a gallery as a work of art. It does not express anything as a painting of a dirty bed would, but merely presents the thing itself. (The 19C painter Delacroix painted a canvas with an unmade bed as subject, and suddenly such subject becomes art, expressing something about the mystery of reality, as filtered through an emotional and aesthetic sensibility.)
The anecdote of the African tribesman is a well-known one, I heard it told as an Arab visiting a concert in W-Europe. But the accessibility of Western classical music does not automatically mean that everybody has the perceptive framework for it. There is a difference between accessibility and perception, if music is not understood it can still be and remain accessible, as a potentiality. The problem is not located in the music, but on the side of the listener. This non-European was obviously not familiar with the music, and if he were musically sensistive he could, in the course of time, become perceptive, I'm sure. Since music - all musics - are human, it is possible to understand any music from any tradition. It works also the other way around: I remember a class at Cambridge were Arab music was treated and many recordings of the same 'maqam' were played with all the variations the performers are allowed. After a while it became clear that not every singer was on the same artistic level, you could distinguish the more primitive rendering from the more sophisticated one, even without completely knowing the fine analytic properties of the maqam concerned - the aesthetic effect was different: poorer or richer, less or more musically expressive. So it is will all music, and of course, people differ immensily in their perception, also within traditions - lots of Westerners don't hear the music but only the sound it makes - but that does not mean that all perception of music is entirely subjective and that for that reason, there are no artistic standards. The properties of classical music are part of the music, however differently interpreted. Cultural relativism may open perception to other cultures, but may also 'remove' the properties of works of art and treating all art as merely existing in the perception. (In the end, this is a philosophical problem, going back to Kant.)