If a year was 13 months not 12
Every month would be exactly 28 days
The 1st would always be a Monday
The 28th would always be a Sunday
13 x 28 = 364
not 365
The 13th month would need a name
There were originally 10 months
That is why October is the tenth month, it was the eighth
November 9th
December 10th
September 7th
January and February were added later
The Gregorian Calendar was finalised in 1582
If the first day of the new year was named Day Zero it would bring the days back to 365
a Leap Year with the extra day would still be needed every four years