In this paper, we introduce a new deep-learning-based system that can compose structured Turkish makam music (TMM) in the symbolic domain. Presented artificial TMM composer (ATMMC) takes eight initial notes from a human user and completes the rest of the piece. The backbone of the composer system consists of multilayered long short-term memory (LSTM) networks. ATMMC can create pieces in Hicaz and Nihavent makams in Şarkı form, which can be viewed and played with Mus2, a notation software for microtonal music. Statistical analysis shows that pieces composed by ATMMC are approximately 84% similar to training data. ATMMC is an open-source project and can assist Turkish makam music enthusiasts with creating new pieces for professional, educational, or entertainment purposes.