An analytical method for melodic nuclei based applications in music informatics

Melodic nuclei have a suitable structure for algorithmic approach and mathematical modeling. The melodic nuclei method has taken its place in the literature as a "motif centric-nuclei based" makam analysis method, which is presented as an alternative to "scale-based" methods. A mathematical approach will pave the way for the use of melodic nuclei method in music informatics studies in the future. In this study, a multi-stage analytical method is proposed, which classifies melodic pieces with a mathematical approach and performs pitch function-based analyses. In the first stage of the method, it is defined according to which criteria the makam classes in the literature can be subclassified. In the second stage of the method, the pitch functions which emerge from the the relationship between the pitches within the melodic nuclei are both analyzed mathematically, and the interval and pattern relationships for critical pitches are examined. As a result of applying the proposed method to Hüseyni and Gülizar melodies, a total of 14 maqam subclasses were formed, 6 of them Hüseyni and 8 of them Gülizar. In addition, it was observed that central tendency measures, extremums, inflection points and pitch dominance emerged as pitch function indicators of the melodic nuclei in the relevant makam. Finally, pitch duration, interval and pattern analyses provided significant results on how the pitch functions resemble and differ in subclasses of the same makam and among makams. It is possible to apply this method to other makams, and it is anticipated and hoped that the mathematical approach proposed in this study will be guiding for music informatics studies such as melody generation.