(Πυθοκλείδης), a celebrated musician of the time of Pericles, was a native of Ceos (Plat. Protag. 316, e.), and flourished at Athens, under the patronage of Pericles, whom he instructed in his art. (Plut. Per. 4; Pseudo_Plat. Alcib. i. p. 118c.). The Scholiast on the passage last cited states that Pythocleides was also a Pythagorean philosopher, and that Agathocles was his disciple. Pythocleides was one of those musicians to whom some writers ascribed the invention of the Mixolydian mode of music. (Plut. de Mus. 16, p. 1136d.).
[P.S]A Dictionary of Greek and Roman biography and mythology
Smith, William
A Dictionary of Greek and Roman biography and mythology. William Smith, LLD, ed. 1890