Hyperbolic Numbers, Genetics and Musicology

  • Sergey V. PetoukhovEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1126)


The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic extensions in the form of 2n-dimensional hyperbolic numbers in bioinformatics, algebraic biology and musicology. These applications reveal hidden interconnections between structures of different biological phenomena. It helps to understand living bodies as holistic essences, structural organisation of which has relations with musical harmony, first of all, with Pythagorean musical scales on the basis of the quint ratio 3/2. Presented results are connected with a problem of genetic fundamentals of aesthetics and inborn feeling of harmony. On the basis of these and some other results, the author believes that 2n-dimensional hyperbolic numbers and their matrix representations are a key element for effective algebraic modeling many aspects of inherited structural organisation of biological bodies and for developing algebraic biology. The received results lead to new approaches in bioinformatics, musicological analysis, acoustic biotechnologies and artificial intelligence.


Hyperbolic numbers Genetics DNA Tensor product Musical scales Quint ratio 



Some results of this paper have been possible due to a long-term cooperation between Russian and Hungarian Academies of Sciences on the topic “Non-linear models and symmetrologic analysis in biomechanics, bioinformatics, and the theory of self-organizing systems”, where S.V. Petoukhov was a scientific chief from the Russian Academy of Sciences. The author is grateful to participants of this international cooperation and to all the colleagues who discussed the materials of this article with him.


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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Mechanical Engineering Research Institute, Russian Academy of SciencesMoscowRussia

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