Weekdate specifies
dates using week numbers rather than months. Monday is day 1 of each sevenday
week, Sunday is day 7. Every year in weekdate begins on Monday of week one.
Common years have 52 weeks, leap years have 53.
The long, thin table at right
represents the current Gregorian year, with weeks
beginning on Monday, and with a column of weekdate week numbers in red.
Below is a comparison of the Gregorian and weekdate dating systems. In the
weekdate system, the weekday is specified first, then the week number, then the year.
The week number should always have two digits; so the year's first weeks should be
represented as 0109. When the weekdate is specified as a string of numbers, the
weekday number can be preceded optionally by a lower case "d" (or the initial of the word for
day in the local language). This is only to distinguish the numerically specified
weekdate from the numerically specified Gregorian date.
The above table
of the current Gregorian month, with Sundays first, presents weekdates in
red, as a supplemental dating system. The week numbers can be seen to change every Monday.
Weekdate Calendar
The weekdate dating system is independent of the Gregorian Calendar,
though the two share an important basis.
Both systems observe the same 400year cycle, called a "quadricentennium."
The cycle contains 146,097 days, which is 20,871 whole weeks. The average
yearlength within the cycle is 365.2425 days. This compares favorably to the
mean tropical year (365.2423 days), providing for a oneday discrepancy in
3,300 years.
The Gregorian year contains 365 days in common years, and 366 days in leap years.
Gregorian years also contain one or two week fragments. In weekdate, common years contain
364 days, or 52 whole weeks, while leap years contain 371 days, or 53 whole weeks.
Weekdate is independent of the Gregorian calendar
precisely because its leapyear rule is different.
For leap years in the Gregorian calendar an extra day is added to February
in each year whose number is divisible by four, unless it is divisible by 100, except if it
is divisible by 400. In weekdate, a 53rd week is added in every year whose number is
divisible by five, with two or three exceptions per century. These are computed using a
leapyear exception matrix.
quarters   exception matrix  
exception years 
2000  +  35 85  =  2035 2085 
2100  25 70  2125 2170 
2200  10 55  2210 2255 
2300  0 45 90  2300 2345 2390 
Centesimal quarters for the 2000 quadricentennium,
when added to the leapyear exception matrix,
generate the nine exception years.
The fiveyear leap rule, with the 9 exceptions generated by
the matrix, provides for 71 leap
weeks in 400 years, and so for a quadricentennium of 20,871 weeks.



Coincidence of Weekdate and Gregorian Systems
The weekdate and Gregorian systems coincide every four hundred years.
Gregorian Jan. 1, 2001 and Jan. 1, 2401 fall on 1/01/2001 and 1/01/2401 in weekdate.
Between these parameters, the two systems coincide on New Year's day in 55 additional
years, and never vary more than six days. Week 01 of the weekdate year can begin as early
as Gregorian Dec. 26, and as late as Jan. 6—a 12day spread. Sixty percent of
weekdate years begin on the five Gregorian dates from Dec. 30 to Jan. 3.
Weekdate and ISO8601
ISO8601 is a dating system comparable to weekdate, but it is not independent
of the Gregorian calendar. It includes no distinct leapyear rule. ISO8601 specifies that the
first week of the year is the week containing the first Thursday of the Gregorian year. So at the
end of the year it is necessary to consult the Gregorian calendar to determine whether the
week number following 52 should be 01, or 53. This is not the case with weekdate. Whether
the year contains a 53rd week in weekdate is determined by an independent leapyear rule. Usually, if
its number ends in 0 or 5, the year contains 53 weeks.
Advantages of the Weekdate System

Fewer data are required to specify dates, compared with the
Gregorian calendar. Weekdate's three data—weekday, week, year—completely specify
each date. Specifying Gregorian dates completely requires four data—weekday, month,
ordinal day, year (e.g., Friday, January 3rd, 2020).

Intervals between dates are easier to calculate, since weekdates are
specified independently of variable monthlengths. How many days from
March 19 to June 10? In weekdate the question would be, How many
days from 1/12 to 7/23? Answer: six days, eleven weeks, obviously. Or
83 days.

Weekdate is compatible with the Gregorian calendar, and can be used
concurrently as an alternative dating system. Most other calendar systems introduce variations
on the Gregorian monthly structure, so implementing them requires abruptly setting that
calendar aside.

No costly software corrections are required for weekdate's
implementation. As it becomes more popular, software developers will choose to
overlay the weekdate on the Gregorian date. As the latter gradually falls out of use,
weekdate will transition to the default calendar. The prospect of vital computer systems
crashing because of outdated calendar programming is nil.

The Weekdate calendar is perennial, apart from the leap week.
The year always begins on the same weekday, so weekday events like
the start of school terms or holidays can be
fixed on the same dates every year. Autumn school terms, in the northern hemisphere, can
begin every year on Monday 34, for example.

There is no interruption of the sevenday cycle of the week, as in
other methods of establishing a perennial calendar. Those methods
designate one or two days each year as falling outside the weekcycle. In weekdate,
every day of the year has a weekday designation consistent with the sevenday cycle.

Weekdate is independent of any other calendar system;
with its own leapyear rule, weekdate is a standalone calendar. Dating by weeks with
ISO8601 depends upon the Gregorian calendar. In order to follow ISO8601
it is necessary to determine the first Thursday of each Gregorian year.
Some Disadvantages

The weekdate leapyear rule is more complicated than
most alternatives. Its quintennial rule—leap years end in 0 or 5—is a bit simpler
than the Gregorian's quadrennial rule. But computing the quintennial rule's exceptions,
2 or 3 per century, is not as easy as computing the Gregorian rule's exceptions.

Seasonal variance of dates is greater, because of the sevenday
leapyear correction. Solstices and equinoxes will fall on a wider range of dates (±11 days)
than in the Gregorian calendar (±3 days).

Leap years do not divide easily into quarters, because of their
inclusion of a 53rd week. Most years, however, break down into 13week regular quarters,
each with the same number of workdays and weekends.

The seven dates in the leap week are not annual occurrences,
whereas only one date, Feb. 29, is like this in the Gregorian calendar. So a larger number
of birthdays and anniversaries must be celebrated on analogous dates.

