General remark

In short, this is the comparison between year, month, week and day. Between the ratio of 4.348125 weeks in a month, there are some steps to go:

((365 x 4 + 1) x 25 - 1) x 4 + 1 = 146,097 days in 400 years is our valid time scheme.

Astronomically, the remaining fault could be 100 times less, when using:

(((365 x 4 + 1) x 25 - 1) x 4 + 1) x 8 - 1 = 1,168,775 days in 3,200 years (3,230 would be right).

The 20,871 weeks in 400 years give us exactly the same weekday to begin all over again! For whoever this is useful ...

To be a little more serious:

If you use the constants in Excel, you are able to ensure both a constant step width and a constant number of events in a period of changing length, as a year or a month. See a matrix of these here. It is different from the month's first!