Philosophy of music in the context of mathematics

In the philosophy of mathematics, two opposing trends have historically developed: apriorism (Pythagoras) and empiricism (Aristotle) and both of them have had their impact on the development of music. Philosophers of Ancient Greece and the East noted the important role of music; it was used in religious rites, which served as the basis for social and state relations. The article presents a joint panorama of the development (by historical eras) of the philosophy of mathematics and music and notes their close relationship. But if the Philosophy of Mathematics has long been included in the section of sciences «Philosophical Questions of Science», the Philosophy of Music has not yet acquired such a full-fledged status, although philosophers, specialists in aesthetics, art criticism, composers and musicians have dedicated their works to it. This can be attributed to the fact that since the time of Pythagoras, science has not advanced much in explaining the phenomenon of music. The article attempts to explain this paradox and offer as a hypothesis possible options for studying this topic «Mathematics and Music». The development of brain sciences, high technologies and cognitive sciences can contribute to the success in the development of the Philosophy of Music. The philosophy of music explores ontological, epistemological and axiological problems, the essence, historical and social existence of music, as well as the features of its interaction with art, literature, mathematics, natural and humanitarian sciences. Applied issues of the philosophy of music are the formation of ethical and cognitive guidelines for life and ideological ideals in humans. Music finds its practical embodiment in medicine, psychology, education and various means of communication. The latter is becoming the most important direction of modern philosophy and science. At present, mathematics contributes to the development of new integral directions in music associated with light, color and many other characteristics.