TWMS (TURKİC WORLD MATHEMATİCAL SOCİETY) JOURNAL OF APPLİED AND ENGİNEERİNG MATHEMATİCS, vol.4, pp.175-198, 2014 (International Refereed University Journal)
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 Us¸s¸ak, 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.