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?
- with the year being 365.24219 days you don’t get a lot of factors to work with (365 ⇒ 1, 5, 73, 365)
- there have been various proposals for perennial calendars – in a perennial calendar, months always start on the same day, have the same number of days, no worries about “last Thursday of the month” calculations for holidays
- if you deal with the year as 364 days + filler, you get more factors to work with (364 ⇒ 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364)
- fiscal quarters are always the same length and you get an extra day during the winter holidays
- the easiest being something like a 13 month calendar (each month being exactly 4 weeks, 28 days) = 364 days + 1 year day + 1 leap day – this gets a lot of flack from religious groups because they don’t like the extra days messing with a 7 day week cycle
- this keeps the 365 day year and uses the same calculations for adding in leap days
- leap week calendars get around that by doing a 364 day year and then adding in a whole leap week to bring things back into alignment (you can do this yourself using ISO week dates and looking for week 53)
- calculations for leap years are a bit more elaborate and don’t fit as easily into a simple mnemonic
- if you deal with the year as 364 days + filler, you get more factors to work with (364 ⇒ 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364)
Woah, those bullets. I didn’t know you could do that.
Great post too!
