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88 LEONARDO, Vol. 53, No. 1, pp. 000–000, 2020 doi:10.1162/leon_a_01840 © ISAST cairotronica [C G A T] EPITA MATRIX GENETICS: TOWARD A VISUALIZATION OF GENETIC CODES VIA “GENETIC MUSIC” Renate C.-Z. Quehenberger, Ziegelofengasse 6, 1040 Vienna, Austria. Email: Ivan Stepanyan, Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4, M. Kharitonyevskiy Pereulok, 101990 Moscow, and Tchaikovsky Moscow State Conservatory, 22/24 Malaya Gruzinskaya Street, Moscow, 123557, Russian Federation . Email: Benjamin Skepper, 1-15-10 DAC Building 2F, Shinkiba, Koto-ku Tokyo, 136-0082 Japan and Center for Interdisciplinary Research of Musical Creativity, Moscow State Conservatory, 13/6 Bolshaya Nikitskaya Street, Moscow 125009, Russia. Email: See for supplemental files associated with this issue. Submitted: 15 January 2017 Abstract The authors describe the scientific background and technical details of the visualization of the mathematics underlying genetic codes applied to musical scales. “Genetic Music” provides audible access to genetic structures that become visible based on the fundamental level of nature as permutations of space itself. The carriers of genetic information characteristically possess hydrogen bonds in quantities 2 and 3 in complementary pairs of nitrogenous bases [GACT] in DNA and [GACU] in RNA. Since hydrogen is observed to expose the symmetries of the Penrose Patterns, visual access is achieved by means of a 3D representation of Penrose kites and darts named “epitahedron.” Those pyramid-shaped polyhedra represent the numbers of hydrogen bonds (C=G=3, A=T=2) that generate musical equivalence between the genetic alphabet and the 7 notes of the Pythagorean scale, as well as further and distinct correlations with “Fibonacci stage” “Genetic Music” scales. The visualization must be played synchronously with the musical performance. “Genetic Music” scales (so named by the Russian biophysicists who invented them) are an alternative microtonal system of musical notation [1–4] and provide audible access to genetic structures where hydrogen bonds with quantities 2 and 3 are characteristics of complementary letters of the genetic alphabet , the pairs of nitrogenous bases (C=G=3, A=T=2). Hydrogen is not only an element of the basic building blocks of genetic codes and therefore used as the fundamental principle of “genetic music”: It also plays an important role in the composition of our universe, where hydrogen atoms make up 87% of all atoms, and the “chemical influence of omnipresent hydrogen is the defining factor” [5]. The genetic matrix of the varying hydrogen bonds [3 2; 2 3](n) generates a musical equivalence between the genetic alphabet and a new system of “Genetic Music” scales. Visualization of Genetic Music Our visualization concept is based on the fact that hydrogen atoms , which serve as bonds in genetic molecules, are observed to expose the 5-fold symmetries of the Penrose Patterns [6,7], a visual pattern of the golden ratio, φ = 1⁄2(1±√5), whereas the Genetic and Pythagorean music scales are also based on the golden number. Therefore musical notes shall provide audible access to the underlying abstract mathematical structures of the genetic code that finds their visual expression in the 3D representation of the Penrose kites and darts tiles named epitahedra (E±) [8]. This shape of the 5D-space cell provides a glimpse of the transcendent events inherent in genetic codes: The musical harmonies reflect the wavelike behavior of matter and epitahedra as unit cells of the 5D space allow us to see the permutations of the hyperspace elements that subscend—as David Bohm would say instead of underlie—all matter and, therefore, the structures of DNA. Thus the visionary Austrian physicist Erwin Schrödinger (1887–1961), inventor of wave mechanics, named living substances “aperiodic crystal” and coined the terms code and chromosome code [9]. Finally, aperiodic crystals in materials were discovered in 1982 and named Quasi-crystals [10]. This is a synchronic visualization grammar matching the acoustic patterns according to the “Genetic Music” scale, whereby for each note a distinct movie with a certain number of epitahedra is designed: The pentagonal symmetries provide the dynamics required for a stable and uniform helical structure and contain ten bases within a single turn of the helix...


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