“Etudes by Chopin in the Light of the Golden Section Law (Experience of the Laws of Form Positive Justification)
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Abstract
In the article, the beginning of which was published in 1925 [1, 2], but the ending – in 1927, Sabaneev gives the mathematical justification of the “golden section” law universality “as something normative, not accidental, perhaps even intuitively postulated as a certain norm of creativity, a norm of the aesthetic construction of the whole and parts” not only in spatial arts, where its role was already known, but also in musical works. It is noted the role of all means of musical expressiveness, which “divide time spans into separate parts that bear on the “golden division”. By analyzing all Chopin՚s etudes, Sabaneev proves the deep interdependence of the concepts: golden section and harmony (“harmony intuition”). At the same time, the researcher discovers the phenomenon of the “golden section” at the different structural levels: parts of the form (code), the form in general, its texture part (“melodic formations”) as well as in other developments: modal, structural, dynamic culminations. Сабанеев раскрывает значение темповых изменений в «уклонении от закона». Включенные в текст таблицы вычислений золотого сечения делают наглядным ход мысли автора. Sabaneev reveals the meaning of tempo changes in “evading the law.” Included in the text the golden section calculation tables make the author’s thought process clear.
The published text retains the stylistics of the original, however, punctuation and the spelling are given in accordance with the modern Russian language rules.
Keywords: “golden section,” aesthetic “milestone,” mathematical essence, sense of harmony, Chopin’s etudes, metric coordinates.
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