Year Types

ISO8601:1988 defines that a week begins on Monday. The first week of a year is the one which includes the first Thursday, or equivalently the one which includes January 4.

There are 14 possible year patterns (if one excludes 1752, the year when Great Britain and her colonies switched from the Julian to the Gregorian calendar, when 11 days were 'missed out' from September. However let us ignore such historical problems, otherwise other issues arise - such as before 1751 the New Year began on Lady Day (25 March) rather than 1 January).

The 14 possible year patterns are made from:

7 different days on which the year can start
and for each, 2 ways the year can proceed (Leap Year, or Non-Leap Year).

Whitaker's Almanac refers to these 14 years by year letter, in the range A to N.
Years B*,D*,F*,H*,J*,L*, and N* are Leap Years, '*' indicates a Leap Year in the rest of this page.
Years A,C,E,G,I,K, and M are Non-Leap Years

For the current period of interest:

Year Year Type
1997 G
1998 I
1999 K
2000 N*
2001 C
2002 E
2003 G
2004 J*

Year	Year Type
1997	G
1998	I
1999	K
2000	N*
2001	C
2002	E
2003	G
2004	J*

Year start:

Year Type Jan 1 falls on
A and B* Sunday
C and D* Monday
E and F* Tuesday
G and H* Wednesday
I and J* Thursday
K and L* Friday
M and N* Saturday

Year Type	Jan 1 falls on
A and B*	Sunday
C and D*	Monday
E and F*	Tuesday
G and H*	Wednesday
I and J*	Thursday
K and L*	Friday
M and N*	Saturday

Year end:

Year Type Dec 31 falls on
N* and A Sunday
B* and C Monday
D* and E Tuesday
F* and G Wednesday
H* and I Thursday
J* and K Friday
L* and M Saturday
Year types H*,I, and J* have 53 weeks. All other year types have 52 weeks.

Year Type	Dec 31 falls on
N* and A	Sunday
B* and C	Monday
D* and E	Tuesday
F* and G	Wednesday
H* and I	Thursday
J* and K	Friday
L* and M	Saturday

An examples of each year type is:

A B* C D* E F* G H* I J* K L* M N*
1995 1984 1990 1996 1991 1980 1997 1992 1998 1976 1993 1988 1994 2000

Within my code, the value 'x%7' is used, where 'x' is the day number of the year (1-366) minus the day of the week (1-7).
This is the date of the first Sunday in the year (except that '0' is used instead of '7').
The mapping between 'x%7' and the year type letter is:

x%7 0 1 2 3 4 5 6
Year Letter C/D* A/B* M/N* K/L* I/J* G/H* E/F*
Clearly one cannot tell from the first Sunday in the year whether the year is a Leap Year or not, hence the two possible year type letters in each case.

x%7	0	1	2	3	4	5	6
Year Letter	C/D*	A/B*	M/N*	K/L*	I/J*	G/H*	E/F*

The sequence of year types is:

Year -1 Year Year +1
L*/M A C/D*
M B* E
A/N* C E/F*
A D* G
B*/C E G/H*
C F* I
D*/E G I/J*
E H* K
F*/G I K/L*
G J* M
H*/I K M/N*
I L* A
J*/K M A/B*
K N* C
For each of these transitions, I have produced a snapshot of the week numbers at the year transition

Year -1	Year	Year +1
L*/M	A	C/D*
M	B*	E
A/N*	C	E/F*
A	D*	G
B*/C	E	G/H*
C	F*	I
D*/E	G	I/J*
E	H*	K
F*/G	I	K/L*
G	J*	M
H*/I	K	M/N*
I	L*	A
J*/K	M	A/B*
K	N*	C

This information provided by

Andrew Benham

A	B*	C	D*	E	F*	G	H*	I	J*	K	L*	M	N*
1995	1984	1990	1996	1991	1980	1997	1992	1998	1976	1993	1988	1994	2000