Time in Edo (IMPORTANT)

Years and seasons function differently in Edo than they do in the real world and terminology surrounding time is slightly different as well. In Edo a year is exactly 120 days with four 30 day seasons and no leap years. The seasons themselves are the same as in our world, that being Spring, Summer, Fall, and Winter, but they are much better defined, as you might have snow on the ground half way through spring here, but in Edo that is not the case. Additionally, seasons (referred to interchangeably with months) follow the cycle of the moon, as the moon is always full on the 15th of each season and to reflect that during the 15th the season is at it's most intense, for example in summer there may be a heatwave, in fall the leaves begin to fall, in winter there might be a snowstorm, in spring there might be rain. There is little variance in the overlap of seasons, and within 5 days of a season starting or ending the approximate weather conditions that come with it are in effect.
Weeks do not exist in the traditional sense in this world, and there is no Monday, Tuesday, etc. Instead weeks are a unit of measurement of seven days so you might hear "a week from now" but not "at the end of this week." (hopefully that makes sense)