Фрактальная геометрия Сонаты № 10 А. Н. Скрябина

Abstract

The physical-mathematical concept of the “fractal,” which has determined the formation of the contemporary paradigm of natural science, has initiated new perspectives of research of biological systems, informational technologies, society, the history of culture, religion and art. The article is devoted to revealing the psychological premises of fractal modeling in the late music of Alexander Scriabin and the description of its algorithm in the spatial-temporal organization of Sonata No. 10 for piano. The personal myth of the composer’s life was realized in the mystical actualization of the archetype of God (the Highest Selfhood), becoming the key towards the interpretation of its artistic content. The composition’s conception is connected with the cognition of the Divine genesis of Nature. The sound code of the fractal as “an imprint of God’s thumb” is presented by archaic migrating musical-lexical formulas of the signal and the invocation. The intertext of the culture is demonstrated by “pantheistic signs” together with echo effects. The reminiscence of archetypical geometric figures of the circle, the triangle, the square and the cross in the semantic fractal Universe are identified with segments of the mandala. In the spatial-temporal construction it is possible to discover the mythologemes of: the Divine score, the number, Apollo, Dionysus, Zephyr. Having reconstructed in the Piano Sonata opus 70 the universal mythopoetic model of the Divine Creation of the world, common for European and Eastern cultures, Scriabin has revived the celebrated Pythagorean triad of “mathematics – music – cosmos.” The artistic picture of the Sonata has reflected the mythical cosmogenesis and the mechanism of “the expanding Universe,” the crucial aspect of which is the conceptual fractal. Keywords: the fractal, Alexander Scriabin, mysticism, Being in myth, archetypes of God and mandalas, Sonata No. 10 for piano by Scriabin, mythologemes, pastoral topics, geometric figures in music, symbolism of the universe.