The 33 Varieties of the 33-Year Cycle

There are 33 possible ways of defining a 33-year cycle of eight leap years, so that the eight leap years are as evenly-spaced as possible.

In each such cycle there exists a meridian whose local time is such that the Vernal equinox occurs on the same date each year for a long time. I list estimates of these meridians and corresponding timezones. Each of these 33 varieties of the 33-year cycle has a unique year that is the first of four consecutive common years (non-leap years).

If the leap day occurs before the Vernal equinox in a leap year, then I define the base year as the first of the four consecutive common years.
If the leap day occurs after the Vernal equinox in a leap year, then I define the base year as the second of the four consecutive common years. This makes the base year be the year that in the local time of the calendar's meridian, is the first of four consecutive years where the vernal equinox day occurs 365 days after the previous year's vernal equinox day.

The Dee cycle in which the leap years are those years whose AD number is not divisible by 33 and has a remainder divisible by 4, has year AD 33 as a base year and 1980 is the most recent base year.

Sorted by Meridian

Base Year AD  VE Meridian Timezone
    30         170W       UT-11
    01         159W
    05         148W       UT-10
    09         137W       UT-09
    13         127W
    17         116W       UT-08
    21         105W       UT-07
    25          94W       UT-06
    29          83W
    33          72W       UT-05
    04          61W       UT-04
    08          50W       UT-03
    12          39W
    16          28W       UT-02
    20          17W       UT-01
    24           7W 
    28           4E       UT
    32          15E       UT+01
    03          26E       UT+02
    07          37E       
    11          48E       UT+03
    15          59E       UT+04
    19          70E       UT+05
    23          81E       UT+05:30
    27          92E       UT+06
    31         103E       UT+07
    02         113E       
    06         124E       UT+08
    10         135E       UT+09
    14         146E       UT+10
    18         157E
    22         168E       UT+11
    26         179E       UT+12

Sorted by Base Year

Base Year AD  VE Meridian Timezone
    01         159W
    02         113E       
    03          26E       UT+02
    04          61W       UT-04
    05         148W       UT-10
    06         124E       UT+08
    07          37E       
    08          50W       UT-03
    09         137W       UT-09
    10         135E       UT+09
    11          48E       UT+03
    12          39W
    13         127W
    14         146E       UT+10
    15          59E       UT+04
    16          28W       UT-02
    17         116W       UT-08
    18         157E
    19          70E       UT+05
    20          17W       UT-01
    21         105W       UT-07
    22         168E       UT+11
    23          81E       UT+05:30
    24           7W 
    25          94W       UT-06
    26         179E       UT+12
    27          92E       UT+06
    28           4E       UT
    29          83W
    30         170W       UT-11
    31         103E       UT+07
    32          15E       UT+01
    33          72W       UT-05

Times of Vernal Equinox

The time of day of the Vernal equinox at the local time of the calendar's meridian is approximately determined by the number of years the Vernal equinox occurs after the most recent base year.

The following table gives these approximate Vernal equinox times.

Years after   Approx      1/33s of day
Base Year     VE time      elapsed
    0       05:50-06:32        8
    1       11:39-12:21       16
    2       17:28-18:10       24 
    3       23:17-23:59       32
    4       05:06-05:49        7   
    5       10:55-11:38       15
    6       16:44-17:27       23
    7       22:33-23:16       31
    8       04:22-05:05        6
    9       10:11-10:54       14
   10       16:00-16:43       22
   11       21:50-22:32       30
   12       03:39-04:21        5
   13       09:28-10:10       13
   14       15:17-15:59       21
   15       21:06-21:49       29
   16       02:55-03:38        4
   17       08:44-09:27       12
   18       14:33-15:16       20
   19       20:22-21:05       28
   20       02:11-02:54        3
   21       08:00-08:43       11
   22       13:50-14:32       19
   23       19:39-20:21       27
   24       01:28-02:10        2
   25       07:17-07:59       10
   26       13:06-13:49       18
   27       18:55-19:38       26
   28       00:44-01:27        1
   29       06:33-07:16        9
   30       12:22-13:05       17
   31       18:11-18:54       25
   32       00:00-00:43        0
Karl Palmen June 2004