An Investigation of the Role of Diatonic Functions in the Seyir Phenomenon of Turkish Makam Music: Case of ‘Hicaz Family’
An Investigation of the Role of Diatonic Functions in the Seyir Phenomenon of Turkish Makam Music: Case of ‘Hicaz Family’ Ozan Yarman 1, William A. Sethares 2, M. Kemal Karaosmanoğlu 3, Mehtap Demir 4, Tolga Yarman 5. Abstract This paper presents a novel mathematical approach – originally framed by the first co-author and systematized afterwards by the second and last co-authors – that extracts sets of features related to diatonic functions out of a large collection of pieces in Turkish music. Pitch histograms, which are so far commonly used as a surrogate for the “perde” (variable pitch), customarily represent the proportion of time that a melody rests on each visited frequency. Contour histograms, introduced herein as a surrogate for the “seyir” (thematic flow), display the proportion of time the melody is “ascending” (e.g., Do-Re-Mi), reaches a “peak” (e.g., Re-Fa-Re), is “descending” (e.g., Sol-Fa-Mi), or remains in a “valley” (e.g., La-Do-Mi). It is possible to conceive these sets of mathematical properties in terms of a scale-degree vector analysis of a trigram chain of musical notes that demarcates both perde and seyir elements of Turkish makam scales. Using such computational surrogates, it becomes viable to examine the balance between the two elements (perde vs seyir) in a different light, and to identify, with respect to the established Arel-Ezgi-Uzdilek (AEU) theory, the prominent features of makam scale degrees that other pitches ‘gravitate towards’. The proposed method is first concretized by the popular children’s song commonly known as “Twinkle Twinkle Little Star” to show, in a familiar context, some of the interpretations that are suitable.
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