maghister, wharfy, I think I understand the concept of a musical gesture. The musical impulse must begin in a human who then has to embody that internal gesture into music, poetry, dance, etc. I think, however, that you are talking about music with a spiritual component. By "spiritual" we may mean different things, but I'll leave it for now.
In my poem on Coltrane, I said music comes from the streets, because if you study music it might seem it came from the courts. We must remember that up until Beethoven musicians wrote solely for royalty, and even Beethoven tried to curry the favor of royalty. Therefore, all music had to have pleased the lord for whom it was written. This is still true to some extent in that most musicians write to please the masses. And that has little to do with spirituality in music.
I think we should separate music with a spiritual impulse from "chamber" music. To me, some jazz resembles chamber music in that it does not have that spiritual component informing its musical gestures.
When Parker played bebop it came from his soul. That is not necessarily true of those who followed him. Coltrane infused his music with his own original musical gestures. (Hope I'm using that word correctly.) John Klemmer who was influenced by Trane was just copying the man, but had no soul.. That's why we call him commercial.
Since you brought up poetry, I know all about embodying words with the gesture. My poetry becomes more spiritual the more "lost" I become. In other words, I can't think through it. I just do it. And my best poems have been written that way.
In some jazz, although they have improvisation, the improvisation seems "of a piece" with the composition not rising above the written music. When a spiritual musician goes off on a riff, it rises very high into the stratospheres.
I disagree with mahgister about his assumption that music was written by men on their hunts. As difficult as it's going to be we need to get beyond the patriarchal lens. Yes, we think of men making art because they have for all the history we know of. I think the first music was integrated with art (body painting and adorrment) and was practiced by men and women. They were first acknowledging their own existence and second expressing awe that their existence was part of the existence of the universe. I'll stop here because it becomes complicated and I don't want to start citing books on the subject.