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Musica Mathematica

Traditions and Innovations in Contemporary Music

Series:

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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Foreword:Mathesis as a Philosophy of the Beauty of Music

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Most likely, one of the answers to the question where the vitality of the idea of the interaction between music and mathematics – which can be traced for more than two thousand years and which has been developed in the modern world – lies in the perception that mathematics is the principal cause and source of an all-embracing beauty. The idea of a mathematically substantiated world was developed as far back as Antiquity, and through its expression has attracted thinkers of this epoch. The idea was in line with the worldview of the later epochs as well: Galileo Galilei (1564–1642) called mathematics the alphabet by means of which God describes the world.3 The Hungarian mathematician Paul Erdős (1913–1996) spoke about the imaginary divine book that contained the most beautiful mathematical proofs. The following utterance is attributed to Erdős:

[When asked why numbers are beautiful?] It’s like asking why Ludwig van Beethoven’s Ninth Symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.4

The Russian philosopher Alexei Losev (Алексeй Фёдорович Лoсев, 1893–1988) related the definition of beauty to numbers as well. He stated that beauty was something “impersonal” that was neither spirit nor personality, but an impersonal, non-qualitative structure. He cited, as examples, numbers (or an atom, the initial←15 | 16→ structure, “the primary kernel”, “the clasp of the entire construction”; see Losev 1963: 506–7 & 1999).

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