> Any musicologists lurking about that can explain to me how all this lovely rhythmic polytonal stuff got purged out of western music?
I'm sure Michael Smith would have a lot to say about this, but I'll make a few comments.
Although there are folk traditions that remain strong influences in fine art musics throughout this time, the purge started in the Carolingian period, with Hucbald (b. ~850) trying to "rationalize" northern church practice with ancient Greek music theory and that of Boethius. I don't want to make Hucbald out to be some kind of villain (he wasn't), but notated music started to drain local color at that time. So western music was "heading in away from Middle Eastern practice" by then.
Before this time, there's very little hard evidence that music of the Middle East played a part in northern styles. Some of the charm you mention probably had nothing to do with the Middle East, and was local to what is now France, Germany, etc.. Certainly polyphony isn't a characteristic property of Middle Eastern musical practice.
I'm ignorant of what influence the Crusades might have had on musical styles, and in addition, you have the problem of the lack of documentation for most popular music throughout this period. But the Crusades could have promoted reaction as easily as interest. You have the later examples of the Greeks, who after independence in ~1820, were busily consulting Ptolemy and purging their music of "narrow" thirds.
After the fall of the Byzantine empire (~1450), many Greeks ended up in Cyprus and Venice. There's not a lot of study of this influence, but I can't believe it didn't effect Venetian musical styles of the time.
Of course during the Italian Renaissance, there was a lot of interest in the classical world on the part of the ruling class. Theater was an important distraction, but most weren't to keen on ancient Greek tragedy. They just didn't want to see people of there own class being killed by their wives (Agamemnon) or poking their eyes out (Orestes). So the pastoral of Ovid's _Metamorphoses_ became the basis for theater. Because of their agricultural settings, peasants became a popular "type," and folk music was often inducted into art music. The villanella and canzonetta crazes of the late 1500s are about the re-incorporation of pop music (of which we have little documentation) into elite practice.
HTH, Charles