A frequency-based comparative analysis of Arabic maqâmât and the Western equal-tempered system: Interval structure and psychoacoustic implications

Arabic maqâm practice is grounded in intervallic structures that do not always correspond to the twelve- tone equal-tempered (12-TET) system used in much Western music. This study examines the acoustic and comparative significance of that difference through a frequency-based interval analysis of six Arabic maqâmât - Râst, Bayâtî, Sîkâh, Hijâz, ʿAjam, and Nahawand - performed on the qânûn, alongside Western C-major and C-minor reference scales. The research follows a controlled single-performer case-study design supported by quantitative comparison and psychoacoustically informed interpretation. Primary data were collected through studio recordings using a fixed microphone position, stable environmental conditions, and three repeated performances of each tone by an expert qânûn performer. Fundamental frequencies were extracted in Praat, averaged across repetitions, and converted into cents in order to compare adjacent intervals and cumulative scale-degree positions with 12-TET reference values. Descriptive statistics were added to summarize the magnitude of interval deviations across maqâmât, including mean absolute deviation, standard deviation, variance, confidence intervals, root-mean-square error, and exploratory group comparison. The results show that Râst, Bayâtî, Sîkâh, and Hijâz contain substantial deviations from equal-tempered reference points, especially in neutral or microtonal scale degrees, whereas ʿAjam and Nahawand align more closely with Western major and minor interval patterns. These deviations are interpreted in relation to psychoacoustic literature on pitch discrimination, critical-band interaction, consonance, and culturally learned listening. The study concludes that cent-based measurement provides a rigorous framework for documenting maqâm intonation and for explaining why microtonal intervals may be perceptually salient without claiming direct listener-test evidence. It recommends expanding the dataset to include multiple performers, regional schools, cross-cultural listening experiments, and direct spectral-roughness testing so that acoustic measurement, cultural listening, and perception can be linked more securely in future maqâm research.