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# Musica Mathematica

## 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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# 4. Musica Mathematica in Practice: Aspects of Analysis

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4. Musica Mathematica in Practice: Aspects of Analysis

In the 20th–21st centuries, the practice of the constructive composing of music is a diverse result in which mathematical manipulations of earlier epochs and modern innovations coexist. Therefore, a wide range of analytical procedures are applied in the analysis of a contemporary musical score, beginning with the universal methods, for example of Renaissance, Baroque or Classicism, to a search for new approaches. Apart from the traditional approach to pitch, rhythmic pattern, musical time, duration, dynamics, timbre, and sonic parameters of a musical composition, we may analyze the arsenal of a sonic expression, which is obviously supplemented with a variety of articulation, scales of dynamics, groups, layers, polytempo and other aspects.

Purely mathematical procedures, which create the possibility to determine and derive, for example, primary numbers, which generate a certain meaning or organize the structure of a composition, are proposed to be employed in the investigations. Therefore: deriving the digital root (the compound number is reduced to a single digit), diminution and augmentation actions, etc. These mathematical actions, such as the reduction of initial compound numeral to its root – a single digit result. For example, in Christian semantics the number 10 can be adapted to the results of its digital augmentation – 10, 30, 100, 1,000, and so on. Therefore, 1,000 can be interpreted as number 10 with exaggerated significance, because 1,000 is the cube of 10. In other words, it is a strengthening of the...

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