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.