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)
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
Easiest maybe but no way, 13 is an eyesore of a prime number that works with nothing. No quarters, no semesters. Feels icky just thinking about such an idea!
Very interesting points otherwise.
Woah, those bullets. I didn’t know you could do that.
Great post too!
In the Gregorian Calendar, the year is 365.2425 days.
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.
Have you been listening to the podcast A Problem Squared? This was a topic of the most recent episode (095 = Friday Fears and Disco Spheres). Friday the 13th is very slightly more common than other weekdays for the 13th.
