Johann Joseph Fux - Sinfonia a 3 in C major 'Turcaria', K.331. {w/ score.} 

To my knowledge Turkish music became known to the West through the failed meeting of the Ottoman ambassador Suleiman Aga with the Sun King Louis XIV, where he disrepected the King, and so Jean Baptiste Lully composed his Comédie-ballet "Le bourgeois gentilhomme", a Turkish March (the first?) to mock the Ambassador and his culture.

@@TheOneAndOnlyZeno That's really interesting. I suppose it just stuck around in the culture for a while before being left behind, then. As things do.

@@TheOneAndOnlyZeno All so called Turkish music is deliberately primitive. And it still is. On Turkish television one can see performances with lots of musicians who play all together the same pentatonic melody over and over again. A very funny satire on muslims is Glucks' La Rencontre Imprevue ou Les Pelerins de la Mecque.

@@klop4228 it stuck way longer than many might assume. Basically European musicians tried imitating the sound of ottoman military bands by using their drums cimbals etc. For a long time the percussion section of an orchestra was even called the "turkish section". This style of music is called "Janitscharenmusik" in german and probably janissary music in english. I think Britannica has a good article about this.

@@TheOneAndOnlyZeno but there was also the side of fascination. After the siege of vienna, when the europeans kind of started to lose their fear of the ottomans they started to look into their culture. For example August der Starke was one of the greatest rivals of the turks, but had a turkish style wedding for his son, which lasted several days.