Novel numerical formulas for asymmetric scales (17- and 24-note systems) for psychological effects in music therapy

Document Type : Research Paper

Author

Bachelor of Music and Master of Personality Psychology, Islamic Azad University, Tehran Branch, Tehran, Iran.

Abstract

This research employs numerical rules and algebraic calculations within 17- and 24-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 17- and 24-note numerical systems. The matching results in both systems confirm the strength of the proposed method. Importantly, analyzing the Iranian Radif with these 17- and 24-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.

Keywords

Main Subjects

References

[1] M. Aslani, An innovative numerical system model to identify the effects and psychological states of musical rhythm and tempo through four temperaments. Mathematics and Computational Sciences, (2025) Articles in Press. https://doi.org/10.30511/mcs.2025.2044621.1252
[2] M. Aslani, Innovative 17-note number system and its computational method to identify the effects and psychological states of music scale. Transactions on Combinatorics (TOC), (2025). https://doi.org/10.22108/toc.2025.145560.2290
[3] M. Aslani, Innovative 24-Note Numerical System: Computational Method and Relationship Model Between Notes, Elements, and Planets, Mathematics and Computational Sciences, (2026) Articles in Press. https://doi.org/10.30511/mcs.2026.2075170.1514
[4] M. Aslani, Familiarity with Iranian Music Radif (Tar and Setar), Author publisher copyright, Tehran, 2012. [Persian]
[5] M. Aslani, (2018). The relationship between four temperaments with the preference mediation of Traditional Iranian music in people ranging 30–45 years Old: providing model, Islamic Azad university, Science and Research Brach, Master thesis. [Persian]
[6] Anonymous. Manuscript book of Ekhwān al-Safā or Mojmal al-Hekmah (Brothers of the same heart), 1912. [Persian]
[7] A. R. M. A. Al-Biruni, Al-Tafhim li-Awáil Sanáat al-Tanjim (Instruction in the Elements of the Art of Astrology), English translation, Reprint of the Edition London, 1934. [Persian]
[8] M. Barkeshley, Description of Iran’s Music Radif, The seven systems traditional of Iranian Music (Radif), Writing: M. Maroufi, Tehran : Fine arts of the country, First edition, 1963. [Persian]
[9] F. Fakhreddini, Analysis and Description of Iranian Musical (Radif), Seventh edition, Moein Publications, Tehran, 2021. [Persian]
[10] H. B. A. Ibn Sina, Shafā, javāme elme riyāziyat (Musicology societies from healing mathematics), First edition, Translation S. A. Anwar, Hamedān, Boali Sinā Scientific and Cultural Foundation Publication, 1972. [Persian]
[11] G. R. KordafShari, H. M. Kenari, S. S. Esmaili and M. Moghimi, Taghziyeh dar tebbe irane islami (Nutrition in Islamic Iranian medicine), Ninety Editions, Nesl Nikan Publishing, Tehran, 2019. [Persian]
[12] G. E. Kurtik, . On the origin of the 12 zodiac constellation system in ancient Mesopotamia, Journal for the History of Astronomy, 52 No. 1 (2021) 53-66.
[13] L. Miller, Music and Song in Persia (RLE Iran B) : The Art of Avaz, Routledge, 2012.
[14] S. H. Mashhun, History of Iranian Music, First edition, Farhang-e Nashr-e Now Publications, 2001. [Persian]
[15] M. Mohammadi, Modal Modernities: Formations of Iranian Classical Music and the Recording of a National Tradition, PhD thesis, Utrecht University, 2017.
[16] H. Moradian, Receive music 2, Theoretical Iranian music, First edition, Tehran, 2017. [Persian]
[17] J. S. Peters, Music Therapy: An Introduction, Second edition, Charles C. Thomas Pub Ltd, 2000.
[18] A. B. M. Reza, Al-Rasāla-tol al-Zahabiyyeh (A writing containing medical and health teachings), Translator M. R. Daryāei, Publisher Safīr Ardehal-Tehran-Iran, 2022. [Persian]
[19] A. Zadeh Mohamadi, New perspectives on Iranian music, First edition, Sorod Publications, Tehran, 2000. [Persian]
[20] P. Zarka, Astronomy and astrology, Proceedings of the International Astronomical Union, 5 No. S260 (2009) 420-425.
Algebraic Structures and Their Applications
Volume 13, Issue 2
May 2026
Pages 173-197

Files

Share

How to cite

Statistics