Novel numerical formulas for asymmetric scales (۱۷- and ۲۴-note systems) for psychological effects in music therapy

This research employs numerical rules and algebraic calculations within ۱۷- and ۲۴-note systems to identify the temperaments and zodiac signs associated with musical scales, linking them to specific psychological states and effects. It introduces new computational formulas for three types of asymmetric scales: those with two Shāhed notes, those derived from other modes, and those featuring a variable note. The Āvāzs of Iranian classical music serve as a case study to test the practical use of these formulas. Since these Āvāzs use quarter-tone intervals, the analysis is performed using both the ۱۷- and ۲۴-note numerical systems. The matching results in both systems confirm the strength of the proposed method. Importantly, analyzing the Iranian Radif with these ۱۷- and ۲۴-note systems shows that the common intervals among Dastgāhs and Āvāzs do not necessarily mean they come from a specific main mode. The results indicated that, contrary to the theory of some Iranian theorists, the Āvāzes of Abūatā, Bayāt-e Tork, Afshāri, and Dashti are each independent modes and are not derived from the Dastgāh of Shūr. Instead, their classification and the structure of the Radif is based on their shared connection to fundamental human temperaments. This finding highlights the view of Iranian scholars who focused on using music to support physical and mental health.

کلیدواژه ها:

Āvāzs of Musical Iranian Radif ، Four temperaments (Music) ، Music therapy ، ۱۷-note numerical system ، ۲۴-note numerical system