Somewhere in the warren of streets near the Yavuz Selim (or a bit closer to the Kariye Church) I came across a small court where a “centre for research into and the keeping alive of Turkish mystic music and folklore” was situated. The Türk tasavvuf musiki ve folklorunu arashtirma ve yashatma vakfi. The corridor you see leads past a number of tombs, I think the whole complex must have been a "tekke" (convent for dervishes).

The tiles look pretty modern, but the whole complex is much older, though restored.