Dualitätsprinzip und musikalische Interpretation der komplexen zahlen


Although expressed in the same way in different sciences and arts and in the case of nature, the principle of duality resumes various phenomenological forms. That fact is demonstrated in this paper by a comparative consideration of complex numbers and their conjugate values in mathematics and of big and small terza and the relation ``major-minor'' in music, including also the teachings about Jin and Jang which represent the formulation of the ancient Chinese ``Book of Change -- Jih Djing''. Using Weber-Fechner's Law, a musical interpretation of complex numbers and operations with them is developed, particularly observing musical chords. On the other hand, chords of classic tonality (dyatonal quadritones) correspond to the eight trigrams in the Book of Change. Finally, without entering some deeper area of mathematics, elements of combinatorics and interpretations by means of regular polygons can be applied to the whole Book of Change, what closes this sort of considerations.