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On my algerian mandole, I really do need the 1/4 tone frets to play some of the mini scales that (when combined) produce a maqam.

It really gives a distinctive (uncomparable to western scales) colour to the sound. Although some of these mini scales perfectly fit the western Major or Minor tri/tetra chords... others (which are my prefered) just do not fit at all.

On my instrument there are only two 1/4 tone frets, and I think it the case for all algerian mandole. So it is not as versatile as an Aoud you are refering to, but it is sufficient to give access to a bunch of those micro tonal mini scales.

I don't remember the names of those. I have to search through my notes/links. I will update this answer accordingly with relevant names and information.