Bağlama, also commonly called “saz” in western Europe has the advantage of having moving frets, which means that fret position can be easily modified until you get the suitable music scale. Moreover, it has extra frets that enables to play notes between the common semitones that you have on a guitar or a piano. Thus, we’re entering the very exciting world of “quarter-tones” and “commas” (you can read this to learn more about this topic).
But those “quarter-tones” can be very different from one culture to another, or even from one performer to another. I always have the feeling that quarter-tones are very (!) high in Turkish music (more technically, I would say they’re about 50-60 cents above the lower degree, a semitone equals say 100 cents) whereas they sound usually lower in Breton music (I would say 30-35 cents. I have made some pitch measurements on Breton singer old recordings, and it tends to agree these values).
Therefore, moving frets are very convenient for adapting the instrument to the suitable scale, since you can move some of the frets upwards.
I am pretty happy of the result, you can hear it on this live recording we made in Beirut last year : An Daou Gamerad Fidel