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He started playing violin when he was ten years old. It is known that when he was in the elementary school, he was usually playing his violin with his cousin, Manolis Katsonakis, another popular Cretan musician. He and Manolis Kartsonakis were one of the most popular musical duets during the 1950s in Chania. They were also known as "Kounelakia" which in Greek means "little bunnies" (as "Kounelis" means "bunny" in Greek).
In 1957, Kounelis went to Athens and stayed there until 1982 where he played in numerous Cretan folk music festivals. In Athens, he recorded his first and only album with his friend, Panagiotis Kastanis. He also recorded several audio cassettes in the town of Kissamos in Ioannis Stamatakis' studio that contributed significantly to the propagation of Cretan music.
In 1981, he traveled to the United States, invited by the Pancretan Association of America. He stayed there for one year and he performed in several festivals throughout United States and Canada. He also performed in many cities in Greece and Europe.