Which day of the week a particular day falls on can be determined by charts that operate like the following one:
1) Sun Mon Tue Wed Thu Fri Sat
2) Mon Tue Wed Thu Fri Sat Sun
3) Tue Wed Thu Fri Sat Sun Mon
4) Wed Thu Fri Sat Sun Mon Tue
5) Thu Fri Sat Sun Mon Tue Wed
6) Fri Sat Sun Mon Tue Wed Thu
7) Sat Sun Mon Tue Wed Thu Fri
MAR 1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31
APR 1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30
MAY 1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31
JUN 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30
JUL 1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31
AUG 1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31
SEP 1 2 3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30
OCT 1 2 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31
NOV 1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30
DEC 1 2 3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31
JAN 1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31
FEB 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 (29)
where the row in which to find the days of the week is found by looking up the year (because a day is added to February in a leap year, January and February are considered to be part of the previous year to make the table simpler in its form) in a table like the following:
00 01 02 03 04 05
06 07 08 09 10 11
12 13 14 15 16
17 18 19 20 21 22
23 24 25 26 27
28 29 30 31 32 33
34 35 36 37 38 39
40 41 42 43 44
45 46 47 48 49 50
51 52 53 54 55
56 57 58 59 60 61
62 63 64 65 66 67
68 69 70 71 72
73 74 75 76 77 78
79 80 81 82 83
84 85 86 87 88 89
90 91 92 93 94 95
96 97 98 99
GREG
4 5 6 7 1 2 3 1600 2000 2400
2 3 4 5 6 7 1 1700 2100 2500
7 1 2 3 4 5 6 1800 2200 2600
5 6 7 1 2 3 4 1500 1900 2300 2700
JUL
5 6 7 1 2 3 4 400 1100
4 5 6 7 1 2 3 500 1200
3 4 5 6 7 1 2 600 1300
2 3 4 5 6 7 1 700 1400
1 2 3 4 5 6 7 800 1500
7 1 2 3 4 5 6 900 1600
6 7 1 2 3 4 5 1000 1700
The Gregorian calendar, which the top section of the bottom half of this table within this calendar reflects, was only adopted in the English-speaking countries in 1752. However, it was first put into practice in 1582 in countries where the Roman Catholic Church was generally followed.
Note that the Julian calendar repeats in a cycle of 700 years, while the Gregorian calendar repeats in a cycle of only 400 years, since the number of days in four centuries, 146,097 days, happens to be an exact multiple of seven. (20,871 times 7.)
The reason why the second table is so neat and tidy is that the number of days in a year is 365, which is just one more than a multiple of 7. Similar tables can be made for other kinds of "week", but they will have a somewhat different form, as we will see below. And in some of these cases, the table will have a somewhat more elaborate form.
For example, in the traditional Chinese calendar, days as well as years belong to a succession of 10 Heavenly stems and of 12 Earthly branches. Let us first consider the case of the 12 Earthly branches.
Setting up the first part of the chart is as straightforwards as for the days of the seven-day week:
1) Tzu Ch'ou Yin Mao Ch'en Szu Wu Wei Shen Yu Hsu Hai
2) Ch'ou Yin Mao Ch'en Szu Wu Wei Shen Yu Hsu Hai Tzu
3) Yin Mao Ch'en Szu Wu Wei Shen Yu Hsu Hai Tzu Ch'ou
4) Mao Ch'en Szu Wu Wei Shen Yu Hsu Hai Tzu Ch'ou Yin
5) Ch'en Szu Wu Wei Shen Yu Hsu Hai Tzu Ch'ou Yin Mao
6) Szu Wu Wei Shen Yu Hsu Hai Tzu Ch'ou Yin Mao Ch'en
7) Wu Wei Shen Yu Hsu Hai Tzu Ch'ou Yin Mao Ch'en Szu
8) Wei Shen Yu Hsu Hai Tzu Ch'ou Yin Mao Ch'en Szu Wu
9) Shen Yu Hsu Hai Tzu Ch'ou Yin Mao Ch'en Szu Wu Wei
10) Yu Hsu Hai Tzu Ch'ou Yin Mao Ch'en Szu Wu Wei Shen
11) Hsu Hai Tzu Ch'ou Yin Mao Ch'en Szu Wu Wei Shen Yu
12) Hai Tzu Ch'ou Yin Mao Ch'en Szu Wu Wei Shen Yu Hsu
MAR 1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31
APR 1 2 3 4 5
6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29
30
MAY 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31
JUN 1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28
29 30
JUL 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22
23 24 25 26 27 28 29 30 31
AUG 1 2 3
4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27
28 29 30 31
SEP 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
OCT 1 2
3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26
27 28 29 30 31
NOV 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30
DEC 1
2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23 24 25
26 27 28 29 30 31
JAN 1 2 3 4 5 6
7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30
31
FEB 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 (29)
But since there are five days left over in a year of 365 days, rather than just 1, the chart for the years looks somewhat different. To allow successive years, when they are not leap years, to be contiguous, the sequence below of displacements for the years is decimated in fives. But then one extra day no longer produces a gap of one space in the series of years, but a longer gap. (This would be true even if we did not also have the fact that 366, the number of days in a leap year, being divisible by 6, is not relatively prime to 12.)
00 01 02 03 04 05 06
07 08 09 10 11
12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27
28 29 30 31
32 33 34 35 36 37 38
39 40 41 42 43
44 45 46 47
48 49 50 51 52 53 54
55 56 57 58 59
60 61 62 63
64 65 66 67 68 69 70
71 72 73 74 75
76 77 78 79
80 81 82 83 84 85 86
87 88 89 90 91
92 93 94 95
96 97 98 99
GREG
5 10 3 8 1 6 11 4 9 2 7 12 1600 1900
1 6 11 4 9 2 7 12 5 10 3 8 1700
9 2 7 12 5 10 3 8 1 6 11 4 1800
2 7 12 5 10 3 8 1 6 11 4 9 2000 2300
10 3 8 1 6 11 4 9 2 7 12 5 2100
6 11 4 9 2 7 12 5 10 3 8 1 2200
11 4 9 2 7 12 5 10 3 8 1 6 2400 2700
7 12 5 10 3 8 1 6 11 4 9 2 2500
3 8 1 6 11 4 9 2 7 12 5 10 2600
8 1 6 11 4 9 2 7 12 5 10 3 1500 2800 3100
4 9 2 7 12 5 10 3 8 1 6 11 2900
12 5 10 3 8 1 6 11 4 9 2 7 3000
JUL
9 2 7 12 5 10 3 8 1 6 11 4 600 1000 1400
6 11 4 9 2 7 12 5 10 3 8 1 700 1100 1500
3 8 1 6 11 4 9 2 7 12 5 10 800 1200 1600
12 5 10 3 8 1 6 11 4 9 2 7 900 1300 1700
In this perpetual calendar, the Gregorian calendar repeats with a cycle of 1600 years, and the Julian calendar repeats in 400 years.
Next, we have a table for the Ten Heavenly Stems. Again, the first table is straightforwards; a calendar with a longer week, with a set of scales at the top with the day names in all their possible displacements.
To make the table below smaller, it relates directly to a Western cycle of ten days, the last digit of the Julian Day number. Since the Julian Day begins, or at least began, at noon, the digits are shown between the days of the calendar; thus, the digit in the column between March 1st and 2nd refers to the number of the Julian Day beginning at noon (UT, or GMT) March 1st and ending at noon March 2nd.
1) 0 1 2 3 4 5 6 7 8 9 0
2) 1 2 3 4 5 6 7 8 9 0 1
3) 2 3 4 5 6 7 8 9 0 1 2
4) 3 4 5 6 7 8 9 0 1 2 3
5) 4 5 6 7 8 9 0 1 2 3 4
6) 5 6 7 8 9 0 1 2 3 4 5
7) 6 7 8 9 0 1 2 3 4 5 6
8) 7 8 9 0 1 2 3 4 5 6 7
9) 8 9 0 1 2 3 4 5 6 7 8
10) 9 0 1 2 3 4 5 6 7 8 9
MAR 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31
APR 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30
MAY 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31
JUN 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28
29 30
JUL 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28
29 30 31
AUG 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27
28 29 30 31
SEP 1 2 3 4 5 6
7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26
27 28 29 30
OCT 1 2 3 4 5 6
7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26
27 28 29 30 31
NOV 1 2 3 4 5
6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25
26 27 28 29 30
DEC 1 2 3 4 5
6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25
26 27 28 29 30 31
JAN 1 2 3 4
5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31
FEB 1 2 3
4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29
These digits relate to the Ten Heavenly Stems as shown in the table below:
0 Chia 1 I 2 Ping 3 Ting 4 Wu 5 5 Chi 6 Keng 7 Hsin 8 Jen 9 Kuei 0
thus, by a coincidence, both series begin on the same days.
But because a year has 365 days normally, and 365 is not relatively prime to 10, the second chart takes a complicated form indeed. With care, it can still be made reasonably compact, however: but in this case, one cannot merely read across to see the years in order, but must bounce up and down within a group of two or three rows.
00 01|04 05|08 09|12 13|16 17
02 03|06 07|10 11|14 15|18 19
-----------------------------
20| 24| 28| 32| 36
21 22|25 26|29 30|33 34|37 38
23 |27 |31 |35 |39
-----------------------------
40 41|44 45|48 49|52 53|56 57
42 43|46 47|50 51|54 55|58 59
-----------------------------
60| 64| 68| 72| 76
61 62|65 66|69 70|73 74|77 78
63 |67 |71 |75 |79
-----------------------------
80 81|84 85|88 89|92 93|96 97
82 83|86 87|90 91|94 95|98 99
GREG
3 8 4 9 5 0 6 1 7 2 1600 3500 4200 4900
7 2 8 3 9 4 0 5 1 6 1700 2400 4300 5000
1 6 2 7 3 8 4 9 5 0 1800 2500 3200 5100
5 0 6 1 7 2 8 3 9 4 1900 2600 3300 4000
9 4 0 5 1 6 2 7 3 8 2700 3400 4100 4800
0 5 1 6 2 7 3 8 4 9 2000 3900 4600 5300
4 9 5 0 6 1 7 2 8 3 2100 2800 4700 5400
8 3 9 4 0 5 1 6 2 7 1500 2200 2900 3600 5500
2 7 3 8 4 9 5 0 6 1 2300 3000 3700 4400
6 1 7 2 8 3 9 4 0 5 3100 3800 4500 5200
JUL
3 8 4 9 5 0 6 1 7 2 1000 1200 1400 1600
8 3 9 4 0 5 1 6 2 7 1100 1300 1500 1700
Note that in this case the Julian calendar has a cycle of only 200 years, while the Gregorian calendar repeats in a cycle of 4000 years.
Thus, this illustrates the possible difficulties one might encounter producing perpetual calendars for different lengths of week. It is just fortunate that the seven-day week produces the simplest possible type of perpetual calendar.
The Tzolkin component of the Mayan calendar lends itself to treatment by perpetual calendars of this type as well.
Thus, the 20-day cycle is indicated as follows:
1) Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha
2) Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi
3) Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix
4) Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb
5) Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan
6) Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi
7) Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim
8) Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man
9) Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam
10) Oc Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul
11) Chu Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc
12) Eb Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu
13) Ben Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb
14) Ix Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben
15) Men Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix
16) Cib Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men
17) Cab Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib
18) Etz Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab
19) Cau Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz
20) Aha Imi Ix Akb Kan Chi Cim Man Lam Mul Oc Chu Eb Ben Ix Men Cib Cab Etz Cau
MAR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31
APR 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
30
MAY 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31
JUN 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
29 30
JUL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31
AUG 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
28 29 30 31
SEP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28 29 30
OCT 1 2 3 4 5 6
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27 28 29 30 31
NOV 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
DEC 1 2 3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
26 27 28 29 30 31
JAN 1 2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
FEB 1 2 3
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29
Imi: Imix Cim: Cimi Chu: Chuen Cib
Ix Man: Manik Eb Cab: Caban
Akb: Akbal Lam: Lamat Ben Etz: Etznab
Kan Mul: Muluc Ix Cau: Cauac
Chi: Chicchan Oc Men Aha: Ahau
For this cycle, in four years we have 21 excess days, not 20, so we don't quite have the overlap problem we did for the 10 day cycle, but we still have to put the years out of order:
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19
-----------------------------------------------------------
20 21 22| 24 25 26| 28 29 30| 32 33 34| 36 37 38
23 |27 |31 |35 |39
-----------------------------------------------------------
40 41| 44 45| 48 49| 52 53| 56 57
42 43 |46 47 |50 51 |54 55 |58 59
-----------------------------------------------------------
60| 64| 68| 72| 76
61 62 63 |65 66 67 |69 70 71 |73 74 75 |77 78 79
-----------------------------------------------------------
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
GREG
5 10 15 20 6 11 16 1 7 12 17 2 8 13 18 3 9 14 19 4 1600 3500 4900 8200
9 14 19 4 10 15 20 5 11 16 1 6 12 17 2 7 13 18 3 8 1700 5000 6400 8300
13 18 3 8 14 19 4 9 15 20 5 10 16 1 6 11 17 2 7 12 1800 3200 5100 6500
17 2 7 12 18 3 8 13 19 4 9 14 20 5 10 15 1 6 11 16 1900 3300 6600 8000
1 6 11 16 2 7 12 17 3 8 13 18 4 9 14 19 5 10 15 20 3400 4800 6700 8100
2 7 12 17 3 8 13 18 4 9 14 19 5 10 15 20 6 11 16 1 2000 3900 5300 8600
6 11 16 1 7 12 17 2 8 13 18 3 9 14 19 4 10 15 20 5 2100 5400 6800 8700
10 15 20 5 11 16 1 6 12 17 2 7 13 18 3 8 14 19 4 9 2200 3600 5500 6900
14 19 4 9 15 20 5 10 16 1 6 11 17 2 7 12 18 3 8 13 2300 3700 7000 8400
18 3 8 13 19 4 9 14 20 5 10 15 1 6 11 16 2 7 12 17 3800 5200 7100 8500
19 4 9 14 20 5 10 15 1 6 11 16 2 7 12 17 3 8 13 18 2400 4300 5700 9000
3 8 13 18 4 9 14 19 5 10 15 20 6 11 16 21 7 12 17 2 2500 5800 7200 9100
7 12 17 2 8 13 18 3 9 14 19 4 10 15 20 5 11 16 1 6 2600 4000 5900 7300
11 16 1 6 12 17 2 7 13 18 3 8 14 19 4 9 15 20 5 10 2700 4100 7400 8800
15 20 5 10 16 1 6 11 17 2 7 12 18 3 8 13 19 4 9 14 4200 5600 7500 8900
16 1 6 11 17 2 7 12 18 3 8 13 19 4 9 14 20 5 10 15 2800 4700 6100 9400
20 5 10 15 1 6 11 16 2 7 12 17 3 8 13 18 4 9 14 19 1500 2900 6200 7600 9500
4 9 14 19 5 10 15 20 6 11 16 1 7 12 17 2 8 13 18 3 3000 4400 6300 7700
8 13 18 3 9 14 19 4 10 15 20 5 11 16 1 6 12 17 2 7 3100 4500 7800 9200
12 17 2 7 13 18 3 8 14 19 4 9 15 20 5 10 16 1 6 11 4600 6000 7900 9300
JUL
5 10 15 20 6 11 16 1 7 12 17 2 8 13 18 3 9 14 19 4 1000 1400
10 15 20 5 11 16 1 6 12 17 2 7 13 18 3 8 14 19 4 9 1100 1500
15 20 5 10 16 1 6 11 17 2 7 12 18 3 8 13 19 4 9 14 1200 1600
20 5 10 15 1 6 11 16 2 7 12 17 3 8 13 18 4 9 14 19 1300 1700
The length of the cycle for the Gregorian calender has doubled, to 8000 years. For the Julian calendar, the century contains 25 leap years, and so the cycle doubles for it as well, to 400 years, since 5 days repeat four times in 20.
For the 13-day cycle, the perpetual calendar will look like this:
1) 1 2 3 4 5 6 7 8 9 10 11 12 13
2) 2 3 4 5 6 7 8 9 10 11 12 13 1
3) 3 4 5 6 7 8 9 10 11 12 13 1 2
4) 4 5 6 7 8 9 10 11 12 13 1 2 3
5) 5 6 7 8 9 10 11 12 13 1 2 3 4
6) 6 7 8 9 10 11 12 13 1 2 3 4 5
7) 7 8 9 10 11 12 13 1 2 3 4 5 6
8) 8 9 10 11 12 13 1 2 3 4 5 6 7
9) 9 10 11 12 13 1 2 3 4 5 6 7 8
10) 10 11 12 13 1 2 3 4 5 6 7 8 9
11) 11 12 13 1 2 3 4 5 6 7 8 9 10
12) 12 13 1 2 3 4 5 6 7 8 9 10 11
13) 13 1 2 3 4 5 6 7 8 9 10 11 12
MAR 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23 24 25 26
27 28 29 30 31
APR 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30
MAY 1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30
31
JUN 1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24 25
26 27 28 29 30
JUL 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31
AUG 1 2 3
4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26 27 28 29
30 31
SEP 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30
OCT 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31
NOV 1 2
3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28
29 30
DEC 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31
JAN 1 2 3 4 5 6
7 8 9 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29 30 31
FEB 1
2 3 4 5 6 7 8 9 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27
28 29
Because there are 52 weeks in a year, with one extra day, the cycle of years in a century takes the same simple form it did for the perpetual calendar for the 7-day week.
00 01 02 03 04 05 06 07 08 09 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39 40 41
42 43 44 45 46 47 48 49 50 51
52 53 54 55 56 57 58 59 60 61 62
63 64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 81 82 83
84 85 86 87 88 89 90 91 92 93
94 95 96 97 98 99
GREG
3 4 5 6 7 8 9 10 11 12 13 1 2 1600 2600
10 11 12 13 1 2 3 4 5 6 7 8 9 1700 2700 4400
4 5 6 7 8 9 10 11 12 13 1 2 3 1800 3600 4500
11 12 13 1 2 3 4 5 6 7 8 9 10 1900 2800 3700 4600
5 6 7 8 9 10 11 12 13 1 2 3 4 2900 3800 4700
12 13 1 2 3 4 5 6 7 8 9 10 11 3000 3900
6 7 8 9 10 11 12 13 1 2 3 4 5 2000 3100
13 1 2 3 4 5 6 7 8 9 10 11 12 2100 4800
7 8 9 10 11 12 13 1 2 3 4 5 6 2200 4000 4900
1 2 3 4 5 6 7 8 9 10 11 12 13 2300 3200 4100 5000
8 9 10 11 12 13 1 2 3 4 5 6 7 1500 3300 4200 5100
2 3 4 5 6 7 8 9 10 11 12 13 1 2400 3400 4300
9 10 11 12 13 1 2 3 4 5 6 7 8 2500 3500
JUL
6 7 8 9 10 11 12 13 1 2 3 4 5 500
13 1 2 3 4 5 6 7 8 9 10 11 12 600
7 8 9 10 11 12 13 1 2 3 4 5 6 700
1 2 3 4 5 6 7 8 9 10 11 12 13 800
8 9 10 11 12 13 1 2 3 4 5 6 7 900
2 3 4 5 6 7 8 9 10 11 12 13 1 1000
9 10 11 12 13 1 2 3 4 5 6 7 8 1100
3 4 5 6 7 8 9 10 11 12 13 1 2 1200
10 11 12 13 1 2 3 4 5 6 7 8 9 1300
4 5 6 7 8 9 10 11 12 13 1 2 3 1400
11 12 13 1 2 3 4 5 6 7 8 9 10 1500
5 6 7 8 9 10 11 12 13 1 2 3 4 1600
12 13 1 2 3 4 5 6 7 8 9 10 11 1700