Dancer's Bangles  

To obtain DNC's Bangles go to talk to Olgald in Upper Jeuno (G-7) to activate the quest. He will tell you of a tailor in Bastok Markets named Matthias (J-9).
Matthias will require the following items to make your order:
Square of Karakul Cloth
Square of Rainbow Cloth
Square of Rainbow Velvet

You must wait 1 game day and change zones
All of these items can be purchased at AH. At time of post on Sylph server each item costs as follows:
Karakul Cloth - 9500gil
Rainbow Cloth - 15,500gil
Rainbow Velvet -19,300gil