Damon in arpers Dictionary of Classical Antiquities
An Athenian sophist, the teacher of Pericles and perhaps of Socrates (Diog. Laert. ii. 19).
Damon of Athens in Wikipedia
Damon, son of Damonides, was a Greek musicologist of the fifth century BC. He belonged to the Athenian deme of Oē (sometimes spelled "Oa"). He is credited as teacher and advisor of Pericles.
Damon's expertise was supposed to be musicology, though some believed this was a cover for a broader influence over Pericles' political policy. For instance, Damon is said to have been responsible for advising Pericles to institute the policy of paying jurors for their service; this policy was widely criticized, and Damon is said to have been ostracized for it (see the Aristotelian Athenaion Poleteia), probably sometime in last third of the 5th century BCE.
Plato invokes Damon many times in the Republic as the musical expert to be deferred to concerning the details of musical education. In Plato's Laches, Damon is said to have been a student of Prodicus and of Agathocles. The former was an unabashed sophist, while the latter is said (in Plato's Protagoras) to have used musical expertise as a front for being a sophist.
Some of Damon's research was regarding harmoniai, classifying and describing the various harmonies. He is credited by some scholars as the creator of the hyper and hypo categories (as in Hypophrygian). He did the same with poetic meter. Beyond this technical aspect his work also focused on the social and political consequences of music, through what came to be called the ethos theory. He is the first one to study the effects of different types on music on people's mood. According to Robert Wallace it was Pericles' interest in using this research for controlling the people that lead to Damon's ostracism (Robert W. Wallace, The Sophists in Athens, Harvard University Press, 1998).
The extant texts of the Aristotelian Athenaion Poleteia mention Damonides as an advisor to Pericles. The mention there of "Damonides" is now almost universally considered an editorial slip of pen, where the original text read "Damon, son of Damonides" instead (P. Rhodes, 1981, Commentary on the Aristotelian "Athenaion Politeia", p. 341). This seems to be confirmed by ostraka that have been recovered and that bear the name "Damon son of Damonides".