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Nota bene that in the Roman lunar solar calendar the year begins with the first new moon after the winter solstice: Jan. 11, 2013; Dec 22,[2014] for 2015, Jan 6 in 2019.

Nota bene that in the Athenian lunar solar calendar the year begins with the first new moon after the summer solstice: Jul 8,2013; Jun 27,2014; Jul 15, 2015, Jul 2, 2019.

In 432 BC Meton set up a parapegma in the Agora to coordinate the various Athenian calendars. NEW VERSION

If you want more, go here for the full calendars, or here (no password) for Greek quote with each date, or here for an overview.
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