A need for the use of arithmetic in explanations of musical phenomena has arisen as a consequence of the discovery of early Pythagoreans that some harmonic musical intervals can be ``explained'' by ratios of small positive integers. Following their steps, Euclid in his {ı Sectio Canonis} examines numerical ratios of concords. Using the language of music theory, at the beginning of the treatise he proved a few general arithmetical propositions that are proved in the {ı Elements} in a purely arithmetical manner. He continues with the propositions that are not of the general character since they are related to concrete intervals. The influence of arithmetic to the musical theory is obvious and dominant in the {ı Sectio Canonis}, but the influence of one of these two theories to the other was not only one-way. It is not possible to understand clearly the definitions of some arithmetical notions without understanding of Pythagorean music theory.