I’m talking about music that is similar to this. There’s a melody and a tone, and the transition between notes isn’t random or jarring, so it’s not anathema to Western ears. Nor is it, for lack of a better choice of words, random noise that could be categorized as music, such as atonal opera. But there is no call-and-response which, by my estimation, is pretty foundational to Western music.
So what would you call it?
Ambient?
Syncopation?
Or rather I should say non-syncopation. Syncopation is rhythmic style that is not common in Western music (but common in African influenced styles), that I think may be what the OP is talking about (I am way out of my depth here though 
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Drone music. The classic Western example of this style are the bagpipes.
As QQ said, ambient. Or trance music, perhaps?
I’m not sure that call-and-response is all that foundational though?
It’s a very common pattern, but only one of many. Most often seen in more improvisational contexts like jazz and blues where two or more soloists are playing off each other?
In the classical tradition I would say an equally common pattern is development of a theme. Where an initial seed becomes increasingly elaborated as the piece progresses. There’s no hard and fast distinction between the two, though…
I want to thank you for introducing me to “atonal opera.” Now I can give my Yoko Ono records a rest.