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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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1. The Constructive Relationships between Music and Mathematics: The Pythagorean Conception of Universal Music and its Spread in the Worldview of Later Periods

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1. The Constructive Relationships between Music and Mathematics: The Pythagorean Conception of Universal Music and its Spread in the Worldview of Later Periods

The popular concept that “there is geometry in the humming of strings, there is music in the spacing of the spheres” is attributed to Pythagoras (Πυθαγόρας, c. 570–497/6 B.C.).15 The name of Aristotle (Άριστοτέλης, 384–322 B.C.) is related to a scholastic definition of beauty: the criteria of beauty, “orderly arrangement, proportion, and definiteness”, are “especially manifested by the mathematical sciences.”16 The last of the three most famous authors of Greek tragedy, Euripides (Ευριπίδης, c. 480–406 B.C.), said that “mighty is geometry; joined with art, resistless.”17

Statements made by the polymaths of Antiquity testify to the fact that the fundamental principles of the philosophic idea about the interaction between music and mathematics were formed as far back as ancient Greece. This idea naturally resulted from the perception of the all-surrounding environment that was made mathematical, and its materialistic substantiation, which dominated in the antique world outlook and which was given special significance in the works of the philosophers of the 6th–4th centuries B.C., underlying “perfect knowledge of canonical rules and the ability to base oneself on them in one’s creative work” (Andrijauskas 1996: 294). The physical sensual experiences of an antique man, a material comparison or contrasting of things, was adapted to getting to know the environment – the cosmos using human’s senses united into ratio.18 This concept gave rise to...

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