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Hermetic Leap Week Calendar

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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 Edit

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)

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