Abstract
This article discusses the mathematical foundations of al - Farabi music, and suggests the main actions of arithmetic operations with Farabi relations to obtain musical intervals. Farabi drew attention to some problems for the study of musical art. This article provides an extensive understanding of how the three main problems are needed to get the ratio. Musical intervals have different values. You can divide them, multiply them, and listen to them. In music theory, you need to be familiar with the mathematical foundations for working with ratios, as well as arithmetic operations like multiplication, division, and addition. Farabi not only gives a scientific idea of the ratio of sounds, but also reveals the mathematical foundations of the emergence of harmony and musical melodies.