The thesis describes a new database of uzun havas, a non-metered structured improvisation form in Turkish folk music, and a system, which uses Variable-Length Markov Models (VLMMs) to predict the melody in the uzun hava form. The database consists of 77 songs, encompassing 10849 notes, and it is used to train multiple viewpoints, where each event in a musical sequence are represented by parallel descriptors such as Durations and Notes. The thesis also introduces pitch-related viewpoints that are specifically aimed to model the unique melodic properties of makam music. The predictability of the system is quantitatively evaluated by an entropy based scheme. In the experiments, the results from the pitch-related viewpoints mapping 12-tone-scale of Western classical theory and 17 tone-scale of Turkish folk music are compared. It is shown that VLMMs are highly predictive in the note progressions of the transcriptions of uzun havas. This suggests that VLMMs may be applied to makam-based and non-metered musical forms, in addition to Western musical styles. To the best of knowledge, the work presents the first symbolic, machine-readable database and the first application of computational modeling in Turkish folk music.