If we followed nature and the moon cycle we would have 13 perfect months that equal 28 days each.
28 x 13 = 364 days
There are 365 days in a year, and this left over day actually has a name and purpose.
I found this cool calendar that proposes a 13th month abbreviated 'Sol' set between June and July.
Here I imagine is where the summer solstice would be.
"If, for instance, we wish to keep Independence Day in July, then it will cease to be the fourth of July but become the second of July. If, however, we wish to keep it on virtually the same day of the year. Independence Day will fall into the new month. As July 4 will become Sol 17 and thus fall on Tuesday, Independence Day will then be shifted one day earlier and become Sol 16."
The single left over day is meant to be the day out of space and time, a day for reflection and understanding.
