A calendar based on the yearly movement of the sun (Ra) was once used in Egypt:

"Nut, whom the Greeks sometimes identified with Rhea, was goddess of the sky, but it was debatable if in historical times she was the object of a genuine cult. She was Geb's twin sister and, it was said, married him secretly and against the will of Ra.

Angered, Ra had the couple brutally separated by Shu and afterwards decreed that Nut could not bear a child in any given month of any year. Thoth, Plutarch tells us, happily had pity on her. Playing draughts with the Moon, he won in the course of several games a seventy-second part of the Moon's light with which he composed five new days.

As these five intercalated days did not belong to the official Egyptian calendar of three hundred and sixty days, Nut was thus able to give birth successively to five children: Osiris, Haroeris (Horus), Set, Isis and Nepthys." (Larousse)