You've pretty much got it, Kim--Contemporary early music groups generally play the Spanish music as if it were Arabic music, on the assumption that the instrumentation and the musical stylings would have to be pretty similar to the existing folk music of North Africa---Unfortunately, this is somewhat of a guess, because the surviving notation is pretty ambiguous stuff--there are no measures, no indications of sharp or flat, and no one really is sure what the pitch values for the notes(particularly the thirds) are suposed to be--also, the notation tends to leave out the drum parts, and those are often either extrapolated from the text, or borrowed from contemporary middle eastern music--

On the other end, the Turks certainly had an impact--The Turks at one point bombarded the walls of Vienna, and had much of eastern europe within their suzerain(sorry, I love that word, and almost never get a chance to use it) and it was the custom of the Sultan to send an ensemble of court musicians as a gift to the regents in newly acquired realms. Of course, the Janissaries (the Sultan's elite guard) travelled with military bands(complete with kettledrums) whose Mehter music was often assimilated in the local dance music, and who had a great influence on the classical composers--

The Turkish court music was(and is) a classical music--which is to say that the musicians are formally trained, and the music is composed by composers who are schooled in a system of theoretical principles-- Western instrumental music was developing at the time when Turkish classical music was at a peak, and it probably had a strong impact--to my ears, the development of melodic ideas in Baroque and Roccoco music seems very Turkish, though the music doesn't sound particularly Turkish because western music uses fixed pitch values, and Turkish music stretches, bends and twists the pitch around--