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Musica Mathematica

Traditions and Innovations in Contemporary Music

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Rima Povilionienė

The concept of «musica mathematica» seeks to accurately examine the intersection of two seemingly radically different subject areas. From the perspective of a European perception, the definition of the science of music was a result of the Pythagorean concept of universal harmony. The Pythagoreans were the first in European culture to raise the issue of uniting music and mathematics, sound and number.

In the three parts of the monograph, versatile cases of the intersection of music and mathematics are displayed, moving from philosophical and aesthetic considerations about mathesis to practical studies, discussing the interaction between music and other kinds of art (architecture, painting, poetry and literature), and providing a practical research of contemporary music compositions.

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The investigations of musical compositions considered in this book determine the original forms of mathematical influence on the art of sounds and on compositional possibilities. These investigations reveal the phenomenon of the renewal of mathematical traditions of earlier epochs, as well as the original trend representing the process of rendering contemporary music mathematically. However, the diversity presented here enables me to state that the original/universal system of composing, created by a composer,187 manifests itself quite rarely. More often contemporary composers experiment with individual concepts within the framework of one composition. They individually choose traditionally defined ways, or elements of mathematical innovations, and adapt their chaotic combinations.

The following statement from Leibniz emphasizes the intuitive process of musical creation: “The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.”188 Meanwhile, the composing practice of contemporary music demonstrates a high degree of consciousness, internal logic, and a solidly created structure, or measures of proportions of certain parameters. These are usually determined in the advance sketches, pre-compositional plans and graphs.

Knowledge of the initial idea is often the only key to the correct analysis of a musical composition of the 20th–21st centuries, as well as an inseparable knowledge of other scientific fields that are closely related to the theories of advanced mathematics, fractals, chaos, etc. On the other hand, the practice of the computerized composing of music, which has recently accelerated, has opened the way for...

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