Legend tells us the musicians on the Titanic continued to play until the ship went down, even forgoing their opportunity to escape on life-boats. As I now round nearly fifty years of life, I realize their act communicates something essential about the nature of music: At moments when it seems the rest of the world may be, in some sense, going to hell, the harmony we discover within and between ourselves communicates something just as essential, and conveys as much truth about what really is, as does the surrounding chaos. Realizing this about music tells me, also, something important about life.
Sometimes, it is time to retreat into music; in doing so, we are only again--in a different way--retreating back into life.

(Following the above post, a friend asked me if I could explain the source of music's psychological appeal. I answered as follows:)

I don't know if I can focus on the specifics you are asking about. I'm thinking of it more in terms of music expressing part of the field of existence--and that it has every bit as much capacity and authority to convey information about what is real as does any other purportedly real-world happening, including chaos. It is not the case that the sense of life, connection, etc., conveyed in experience of music is merely an illusory escape, because it is just as much an instance of life as whatever else may compete for the name, "reality," at that moment. Music represents, usually, the bringing together of some of our higher human instincts and abilities along with a measure of society. Many other things (war and barbarism, for example) seem intent to convince us that they reveal something more fundamentally real and necessary than mere music. It is that which I am challenging in my statement. Musicians on the Titanic could point to their music and claim (every bit as much as the waves, the screams, and mayhem around them could): "This is what is real. This is what holds meaning." There is nothing absurd in that.
With regard to what kind of music is capable of doing this, I deliberately refrain from mentioning specifics. That would take away the openness of the proposition I am trying to make here.

With regard to your question about what is at the "root": I suspect it is due to the fact we possess natural affinity to rhythm, cycle, and syncopation, because our own physiology operates according to such patterns--and, we are embedded in larger natural systems (as well as being the host for smaller systems) that operate according to these same music-like laws. Music does not introduce rhythm, harmony, and resonance to us. It merely brings them to our conscious attention, and allows us to participate in them in ways that affirm both our connection to broader natural cycles as well as our distinction from them. I think this is a highly orienting activity, from the standpoint of our identity as living things, humans, and individual persons--and potentially very comforting. 
Maybe that begins to address your question.