Мова теорії множин у сучасних музикознавчих та культурологічних дослідженнях
The language of the set theory in modern musicology and cultural studies

Summary/Abstract: The article considers the trends in modern musicology and cultural studies, related to the set-theoretic laws, extrapolated to the mechanisms of artistic thinking, composer creativity, structural analysis of music. The purpose of the study is to analyse the spheres of application of set theory in modern musicological and cultural studies. Methodology. The methodology of the study is to use the musicological, cultural, set-theoretic and system-structural methods. The noted methodological approach allows us to analyze the harmonic language of Scriabin’s piano works on the example of the late period, the logic-design principles of his musical thinking, artistic thinking processes. Scientific Novelty. The scientific novelty of the research consists in extrapolating the principles of set theory on the piano work of Scriabin’s late period. The determining factor of the set theory is the principle of affiliation, which allows to analyze different cultural events and expose logical laws in thinking mechanisms in the context of humanitarian studies. For example, in the analysis of mythical plots it is important to study the internal correlations. In the study of the problem of "meaning" in a literary text, which is correlated with the concept of sign and sign system, "meaning" is formed by internal and external recoding of semiotic system. In musicology set-theoretic principles as the intersection operations are manifested in heterophonic type of texture, folklore samples, early professional music; operations of complementarity can be traced as far back as the Renaissance polyphony. In the B.Bartok’s work the language of set theory manifests itself in the form of chromatic complementarity of high pitch structures. In the work of J. Xenakis the organization of sound phenomena is represented in the form of "sound clouds". The sound intersection of "Promethean structures" (the preservation of common tones at varying of identical harmonic formations) is peculiar to the harmonic language of the late period of A. Scriabin’s creativity. The analysis revealed that the association of a number of defined sets (chord structures), can be made by means of different operations on them: addition of a certain set of new elements; using of one or more elements according to the principle of intersection; possibly full integration of elements and their equivalence. Conclusions. Thus, the new properties of the harmonic language are responsible for a significant upgrade of the logic of "harmonic events" sequences, indicating the operation of logical thinking mechanisms in musical thinking of the composer.

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