How might a composer respond to this kind of stimulus? It seems a lot of the post-modern spirit in music has to do with this broad spectrum of influence: everything from 12th century organum to The Grateful Dead seems to be an influence on the latest couple of generations of composers. Sometimes I think that this can be exaggerated, either by critics and commentators or by the composers themselves. Perhaps this is just romantic of me, but I think, out of the myriad of possible influences (i.e. everything), we choose the ones that we like or that we think matter. Sometimes it is music that we feel closest to, but not always. Jigs and reels on the violin were what I grew up hearing my mother play, but I can't say that they have ever had the slightest influence on my music. Sometimes we go far afield to find something intriguing. Javanese gamelan has interested composers like Debussy, Ravel, Britten and myself.
But my own feeling is that we choose our influences because we have certain inherent tendencies, which is to say that we are individuals. As Borges observed, we even 'create' our own predecessors. This to me seems just as valid as the opposite theory put forth in Allan Bloom's Anxiety of Influence where creators stumble upon their own ideas by misreading their predecessors'. Personally, there always seems to be some music that attracts me and other music that repels me. I abhor massive pieces, full of seemingly pointless activity and redundancies. I love music that is sparing of material and I find the expression more effective as a result. So I prefer Debussy to Wagner and technical ingenuity or lack of it may be interesting, but it doesn't make the music better or worse.
So I suspect, at the end of the day, no matter how many different kinds of music you listen to, if you are a composer of any substance, you will pick and choose which ones will influence your work. I am reminded of the story of the composition of Elliot Carter's first string quartet. He was awarded a grant in aid of its composition so he temporarily moved from New York to the Sonora Desert outside Tucson where he spent a year composing the piece in complete isolation. It resembles, more than anything else, some of the mensurally complex music from the 13th and 14th centuries.