The notions of harmony and symmetry played a pivotal role in early Greek mathematics as well as in philosophy, science, religion and art. Since all these areas of intellect were not sharply divided and separated in ancient Greece as they are today, their meanings and connotations tended to overlap and intersect. The essay offers a brief historical-philological examination of the terms \emph{harmonía} and \emph{symmetría} in ancient Greek thought, with a comparative look at some cognate terms such as \emph{métron}, \emph{lógos} and \emph{analogía}. By examining these terms from the vantage point of etymology, semantics and intellectual history, it is possible to acquire a more comprehensive understanding of their multilayered meanings in different fields, from mathematics to art. The analysis focuses more closely on the concept of harmony in the Pythagoreans and Plato, who applied this term in their doctrines of the harmony of the spheres.