Many of the great writers of the Ancient Greece such as Plutarc, Aristoxen, and above all, Plato, wrote about music, and through them we know that music and music education had great importance in their society. On the other hand, we know the various instruments that were used to acompany the songs through their representations in paintings and pottery. We also know that music was essencially vocal and homophonic, and we have the texts of many poems that we know were sung. Even more, there are some documents where above the text, there are signs roughly showing the fluctuation of the tune.
These signs can be observed on the Delphi stone, as shown in the article about the Music of ancient Greece, on the Wikipedia.
However in the performance of this music there are many more subjects unknown than proved, and the different attempts to perform this music in the present days tilt more to the side of intuition and assumption, or directly of a risky invention, than to that of certainty. Next, we include links to some of these sound examples: