Analysis of the vertical structures in the context of set theory in Ivan Wyschnegrasky's 24 Preludes in Quarter Tone System for Two Pianos, Op. 22

In this study, the vertical structures in the work 24 Preludes in Quarter Tone for Two Pianos, which is important in terms of applying the principles of diatonic chromatism, ultrachromatism and quarter tone system by composer Ivan Wyschnegradsky, who made many theoretical and practical contributions to microtonal music in the twentieth century, were tried to be analyzed in the context of set theory adapted to quarter tone system. The vertical structures in the work, which was designed in the mathematics-based quarter tone and diatonic chromatism systems devised by the composer, were tried to be made more understandable with the set theory, which is also a mathematical system. In this context, this study is formatted within the framework of five main headings: In the first part, the concept of microtonality, the historical development of microtonal music, types of microtonal structures and the quarter tone system are explained, while in the second part, Wyschnegradsky's life story, his approach to the concept of microtonality and the way it is used in his works are mentioned. In the third chapter, the transfer of set theory and its adaptation to the quarter tone system was attempted, and in the fourth chapter, the analysis of the vertical structures in the work in the context of set theory was included. Finally, in the fifth chapter, the findings in the context of the analysis are presented and the conclusions reached based on the findings are tried to be evaluated.