Буччо Даниэле — аспирант, Ph.D., пианист
Казанская государственная консерватория им. Н. Г. Жиганова, Казань, Россия
E-mail: danielebuccio@yahoo.it,
ORCID: https://orcid.org/0009-0005-8371-1258
В данной статье теоретически обоснована звуковысотная организация 72‑ступенной микротоновой (шестинатонововой) системы. Автор опирается на оригинальные разработки в области микрохроматики Ивана Александровича Вышнеградского, а также теоретиков второй половины XX века, аргументируя перспективность шестинатонового деления октавы математически — ее внутренними связями с числовыми последовательностями и геометрическими фигурами.
The present article examines the procedure of reducing sequences of natural numbers modulo 72 in order to define specific pitch class sets within the tempered system of twelfths of tone. The specific properties of number sequences are reflected and manifested in interval relationships highlighted by the characteristic
structure of the system. The study starts from the reduction of polygonal, polytopic, and non-figural number sequences and is based on a rethinking of positions on cyclical techniques developed by 20th-century theorists and, after World War II, by Ivan Aleksandrovich Wyshnegradsky in the ultrachromatic field. I. A. Wyshnegradsky
considered the system in twelfths of tone as the limit of his theoretical reflections and compositional goals, in reason of its aptitude for containing all the intervallic relationships observed in the domains of the quarter tones, sixth tones, and the traditional system. The representation of intervals formed by sequences within
the heptacontakaidigon (hebdomecontadigon) correlates with the blurring of the opposition between melodic and harmonic intervals. This extractive process represents a pre-compositional plan aimed at the conscious organisation of intervallic qualities, which are subsequently made available for creative purposes.
Ключевые слова: ультрахроматизм, микрохроматика, двенадцатая доля тона, 72‑ступенная равномерная темперация, интервальные циклы, последовательности натуральных чисел, Иван Александрович Вышнеградский
Keywords: Ultrachromatism, Microchromatics, Twelfth Tone, 72-EDO, Interval Cycles, Sequences of Natural Numbers, Ivan Aleksandrovitch Wyschnegradsky
