Novel Numerical Formulas for Asymmetric Steps (۱۷- and ۲۴-Note Systems) to Induce Psychological Effects in Music Therapy

Utilizing numerical rules and algebraic calculations within the frameworks of ۱۷-note and ۲۴-note systems, this study identifies the temperaments and zodiac signs associated with musical scales and links them to specific psychological states and effects. The research introduces novel computational formulas for three types of asymmetrical scales: scales featuring two "witness" (pivotal) notes, scales derived from other modes (*mayehs*), and scales containing variable notes. The *Avaz* forms of classical Iranian music serve as case studies to test the practical application of these formulas. Given that these *Avaz* forms employ quarter-tone intervals, their analysis was conducted using both the ۱۷-note and ۲۴-note numerical systems. Consistent results across both systems confirm the efficacy and robustness of the proposed method. Significantly, the analysis of the Iranian *Radif* using these ۱۷-note and ۲۴-note systems reveals that shared intervals between *Dastgahs* and *Avaz* forms do not necessarily imply a common root in a single primary mode. The findings indicate that—contrary to the theories of certain Iranian experts—the *Avaz* forms of Abu-Ata, Bayat-e Tork, Afshari, and Dashti are independent modes rather than derivatives of *Dastgah-e Shur*; instead, their classification and the structure of the *Radif* are grounded in their shared connection to fundamental human temperaments. This finding highlights the perspective of Iranian thinkers who have emphasized the role of music in enhancing physical and mental well-being.

کلیدواژه ها:

note-۲۴ ، music ، temperament ، zodiac ، octave ، Scale ، Psychological