The Hermatic Leap Week Calendar is a leap week calendar with 71 leap weeks per 400 years so having a mean year of 365.2425 days equal to the mean year of the Gregorian calendar. It was proposed by Peter Meyer.
The distinctive feature is that the years are grouped into hexades of six or five years. The third year of each hexade is its only year with a leap week. The length of hexade is determined by the last two digits of its first year's number.
A hexade is short (has five years) if and only if the last two digits of the product of 71 and the last two digits of the first year of the hexade is less than 26. Also a hexade begins at year 1, which began on Monday 25 December 1 BC in the proleptic Gregorian calendar.
This results in the northern winter solstice always occurring in or near the last week of the year.
The Hexade Pattern of the Hermetic Leap Week Calendar[]
This table shows the distribution of short (5-year) and long (6-year) hexades for the years 1 through 400. The year number is the number of the year which begins the hexade. The same pattern is repeated every 400 years, so this is also the pattern for the years 2001 through 2400.
| Hexade number | Year numbers | Hexade type | Hexade number | Year numbers | Hexade type | Hexade number | Year numbers | Hexade type | ||
| 1 | 1-6 | long | 2 | 7-12 | long | 3 | 13-17 | short | ||
| 4 | 18-23 | long | 5 | 24-28 | short | |||||
| 6 | 29-34 | long | 7 | 35-40 | long | 8 | 41-45 | short | ||
| 9 | 46-51 | long | 10 | 52-57 | long | 11 | 58-62 | short | ||
| 12 | 63-68 | long | 13 | 69-74 | long | 14 | 75-79 | short | ||
| 15 | 80-85 | long | 16 | 86-90 | short | |||||
| 17 | 91-96 | long | 18 | 97-102 | long | 19 | 103-107 | short | ||
| 20 | 108-113 | long | 21 | 114-119 | long | 22 | 120-124 | short | ||
| 23 | 125-130 | long | 24 | 131-135 | short | |||||
| 25 | 136-141 | long | 26 | 142-147 | long | 27 | 148-152 | short | ||
| 28 | 153-158 | long | 29 | 159-164 | long | 30 | 165-169 | short | ||
| 31 | 170-175 | long | 32 | 176-181 | long | 33 | 182-186 | short | ||
| 34 | 187-192 | long | 35 | 193-197 | short | |||||
| 36 | 198-203 | long | 37 | 204-209 | long | 38 | 210-214 | short | ||
| 39 | 215-220 | long | 40 | 221-226 | long | 41 | 227-231 | short | ||
| 42 | 232-237 | long | 43 | 238-243 | long | 44 | 244-248 | short | ||
| 45 | 249-254 | long | 46 | 255-259 | short | |||||
| 47 | 260-265 | long | 48 | 266-271 | long | 49 | 272-276 | short | ||
| 50 | 277-282 | long | 51 | 283-288 | long | 52 | 289-293 | short | ||
| 53 | 294-299 | long | 54 | 300-304 | short | |||||
| 55 | 305-310 | long | 56 | 311-316 | long | 57 | 317-321 | short | ||
| 58 | 322-327 | long | 59 | 328-333 | long | 60 | 334-338 | short | ||
| 61 | 339-344 | long | 62 | 345-350 | long | 63 | 351-355 | short | ||
| 64 | 356-361 | long | 65 | 362-366 | short | |||||
| 66 | 367-372 | long | 67 | 373-378 | long | 68 | 379-383 | short | ||
| 69 | 384-389 | long | 70 | 390-395 | long | 71 | 396-400 | short | ||
The 26 short hexades are as evenly spaced in the sequence of 71 hexades as is possible consistent with the properties of the calendar.
Since the pattern is cyclic it may be expressed succinctly as follows, beginning with hexade 17, and with hexade 1 following hexade 71:
(l,l,sh,l,l,sh,l,sh) + 2x(l,l,sh,l,l,sh,l,l,sh,l,sh) + (l,l,sh,l,l,sh,l,sh) + 3x(l,l,sh,l,l,sh,l,l,sh,l,sh) |
Months[]The weeks can be grouped into months of 5, 4, 4 weeks, except that the 12th month has 5 weeks in a year in a year with a leap week. External Links[] |
