The Turkish influence on western music came through the Turkish military band music (Mehter), which was at the time was the only military band in Europe. It was once popular among western composers like Mozart to write Turkish-style (alla Turca) works, Turkish music being known at that time as Turkish band music. That’s why the Turkish-influenced music works by Mozart, Beethoven or Strauss are in march ritm as they are called march.
The other effects of Turkish music on western classical music are also visible in military/band formats as well: usage of drums, chimbals, inclusion of brass instruments, monumental characteristic of symphony music, usage of Turkish ritms (palse)…
What is interesting is that the this band music has no effect on Turkish Art Music (Turkish Classical Music). It has remained a separate performance.

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