A full Gregorian cycle lasts 400 years, and interestingly, common years (i.e. those with 365 days) beginning on a Tuesday or Thursday are slightly more frequent than common years beginning in other weekdays. (44 vs. 43 for other weekdays) In leap years, 15 begin on a Sunday or on a Friday, 14 begin on Tuesday or Wednesday and 13 begin on a Saturday, Monday or Thursday.
And if you are wanting to know the frequency of specific days falling on a certain weekday: it’s between 56 and 58 times on a full cycle, depending of the year type. E.g. October 19 falls on a Saturday in 57 years of a full calendar cycle, but 58 years have it falling on a Monday and 56 years have it falling on a Tuesday.
It’s just me or is the Gregorian calendar very weird?
In the Gregorian Calendar, the year is 365.2425 days.
https://astronomy.stackexchange.com/questions/21182/to-several-decimal-places-how-many-days-are-in-one-year
The reason is basically that the Earth doesn’t spin at an integer rate daily compared to the yearly revolution around the sun. The leap year rules mostly accommodate for this offset.
The 7 days per week thing is purely a human invention, and basically means squat in the bigger mathematical picture of timekeeping. Except that the 7 day week closely aligns with the phases of the moon.
The moon cycle is approximately 29.5 days, which is pretty close to a 28 day, 7 days 4 weeks cycle, as I can only assume some ancient astronomers estimated before they got their numbers right.
Edited more than once, apologies.