Search for an optimal tonal-system for an authentic Turkish soundscape

Abstract

This study is the continuation of an older musicological work I had co-authored with Bozkurt et al. [2009, JNMR:38/1 pp.45-70], where I now analyze the match between several more alternative theoretical models and the histogram peaks of collated pitch measurements from audio recordings in 9 makam categories by prominent Turkish musicians. Previously, these histogram peaks were pitted against 53-tone Equal Temperament (53-tET), Yekta-Arel-Ezgi-Uzdilek (the 24-tone Pythagorean tuning in force), Yarman-24a (its notable substitute), Karadeniz-41 (a subset of 106-tET) and Yavuzoğlu-48 (in 48-tET). This time, new results indicate an outstanding marksmanship in the contrivance of 79 MOS 159-tET (my 79-tone Qanun tuning) above all others. A “Just Noticeable Difference” (JND) of solely 7-8 cents (¢) unweighted maximum divergence from the histogram peaks – in comparison to the as much as “half a comma” corresponding divergences of the contending 60-tET, 65-tET and 72-tET from the same peaks – enables 79 MOS 159-tET to outclass its competition. When size is an issue however, the “bulk vs. peak-matching performance” of the mentioned three immediate rivals to the 79-tone Qanun tuning are over the top and analogous to each other. All the same, the minimalist Yarman-24 a-b-c-d variants (as direct replacements for Arel-Ezgi-Uzdilek) do, despite being about thrice as sparse, deviate from the measured peak values by only “one comma” at most while performing reasonably. The key question therefore is: “Why triple the number of conventional tones just to gain half a comma finer granularity for makams that would still remain coarse?”. Likewise, one may ask: “Why double the number of tones whilst technically not managing to overcome the need for commatic alterations?” The findings are discussed in terms of which fixed-pitch approach is more optimal for traditional and modern practice in Turkish Classical/Art/Folk music.Keywords:Tuning, temperament, music theory, makam, maqam, pitch measurement, histogram peak, computational musicology