The Ides of March was originally a full moon and the Nones was a first quarter. The Roman calendar is a moon calendar with the Moon taken out.

Kalends meant the new moon and the day the month's debts were called. It is where the word calendar comes from. Nones fell at first quarter, Ides at full. Long before Caesar the dates had been frozen to fixed numbers and drifted off the sky entirely, but the names stayed. Shakespeare's most famous date is a fossil of a lunar month.