An innovative ۱۷-note numerical system and its computational method for identifying the psychological effects and states of musical pitch

For centuries, Iranian philosophers and scientists believed that music was related to sciences such as mathematics, the four human temperaments, and astronomy; unfortunately, none of them provided explicit laws or mathematical formulas to prove their claims. Addressing this gap, this paper introduces a ۱۷-note numerical system along with a computational method designed to identify the psychological effects and emotional states associated with musical pitches. New concepts, in particular, the “intrinsic pitch” and the “acquired pitch,” are explored with their distinctions and applications in musical and numerical frameworks. Furthermore, this study uses computational techniques and principles of numerical analysis to investigate the early modes of the ۷-note system in Iranian classical music. Although the ۱۷-note system shares interval similarities with the ۱۸-note system of the ancient Abjad, it has fundamental differences in numerical valuation, computational methodology, structural efficiency, and systematic approach to application. These findings can be applied in music therapy and music theoretical studies as an innovative, number-based method that provides deeper insight into the psychological properties of musical steps. The results show a significant correlation between the psychological states evoked by musical steps and their inherent temperamental characteristics, and by identifying the zodiac constellations associated with each step, the psychological effects of melodies can be further discerned. For example, the analysis of the main mode in the Chargah system shows that the feeling of excitement is aligned with the warm and dry psychological quality. Furthermore, the computational approach showed the Chargah to be astrologically aligned with the Leo zodiac sign, showing that its melodies naturally evoke the qualities of courage, excitement, and radiant joy.

کلیدواژه ها:

note-۱۷ ، music ، temperament ، zodiac ، octave ، Scale