A Quantitative Model of Tension and Resolution in Turkish Makam Music Using an Entropy‑Based Approach

This study proposes an entropy‑based analysis model that can quantitatively explain the relationship between tension and resolution in Turkish makam music. The model combines psychoacoustics‑based consonance–dissonance approaches with Erlich’s ‘Harmonic Entropy’ model and the melodic nucleus theory for makam music. Thus, the characteristic melodic hierarchies and temporary centralizations in makam music can be represented using an information theory‑based measurement system. The method consists of four stages: (1) analysis of positional and orientational melodic figures, (2) creation of a relative hierarchy tree derived from the figures, (3) entropy calculation based on Erlich’s model for each pair of pitches, and (4) plotting of event‑ and time‑based entropy graphs. The method is illustrated by its application to a melody belonging to the Hüseyni makam. The analysis results show that the tension–resolution patterns observed in melodic nuclei are consistent with the psychoacoustic disorder–order relationship. Tension increases as pitches move away from the center; resolution occurs when they return to the center. By converting the tension–resolution behavior intuitively felt in makam music into a measurable form, this study proposes a new method for cognitive musicology, algorithmic composition, and computer‑based makam analysis.