jaem TWMS Journal of Applied and Engineering Mathematics 2146-1147 2587-1013 Işık University Press "YARMAN-36 MAKAM TONE-SYSTEM" FOR TURKISH ART MUSIC Yarman Ozan Musicology Department, İstanbul University State Conservatory, 81300 Kadıköy, İstanbul, Turkey Karaosmanoglu M. Kemal Art and Design Faculty, Yıldız Teknik University, Esenler 34220, İstanbul, Turkey. 12 01 2014 4 2 175 198 Copyright © 2010, TWMS Journal of Applied and Engineering Mathematics 2010 TWMS Journal of Applied and Engineering Mathematics

This study offers a mathematically rigorous, yet straightforward, fixed-pitch tuning strategy to the problem of adequate sounding and notating of essential Turkish makam genera, in contradistinction to the praxis-mismatched music theory cast in effect known as Arel-Ezgi-Uzdilek AEU . It comprises 36 tones locatable just by ear, via counting exact 0, 1 and 2 beats per second when listening to given octave, fifth and third intervals, starting from an algebraically attained reference frequency for A at 438.41 Hertz, very near the international standard A=440 Hz. The so-named Yarman-36 makam tone-system proposed in this paper accounts for hitherto omitted pitches in Uşşak, Saba, Hüzzam, etc... at popular transpositions, each corresponding to a habitually used Ahenk concert pitch level specified by a chosen Ney reed , by virtue of being based on a twelve-by-twelve triplex structure of exclusively tailored Modified Meantone Baroque Temperaments. It thus also features pleasant shades of key-colors supporting polyphonic endeavours in line with Western common-practice music

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