YANUS Calendar

Described is a solunar calendar with optimal leap year rule for the solar year and some interesting fixed dates.
Unusual features of YANUS that I hope will survive in other calendars:

This calendar tries to have "the best of both worlds" and leaves the Moon nearly entirely floating ...

Design Principles

Following the design principle of "coincidentia oppositorum" (coincidence of opposites), the polarity of Sun and Moon qualities shall be kept. While Sun is associated with "bright" qualities like predictability, hierarchy, and regularity, many of Moon's characteristics seem to be "dark" - like nonconformity, anarchy, and obscurity.
Janus was the two-faced Roman god who "looked in both directions", unifying polar opposites, hence the name YANUS (Yet Another Never-Used System); capitals denote the acronym.

These objectives guided design:

The last design principle is reflected in "early" beginnings of day, week, lunar month, solar year and lunar year (see below).


The day has the traditional 24 hours of mean solar time, but starts at 18:00 common time (about dusk). The reason for this is the idea that things begin long before they get obvious; you don't see the germination process of a seed until the green sprout appears - yet something is happening while you can't watch.
     time conversion table
    night               day
common  YANUS      common  YANUS
18:00   00:00      06:00   12:00
19:00   01:00      07:00   13:00
20:00   02:00      08:00   14:00
21:00   03:00      09:00   15:00
22:00   04:00      10:00   16:00
23:00   05:00      11:00   17:00
00:00   06:00      12:00   18:00
01:00   07:00      13:00   19:00
02:00   08:00      14:00   20:00
03:00   09:00      15:00   21:00
04:00   10:00      16:00   22:00
05:00   11:00      17:00   23:00
06:00   12:00      18:00   00:00

This is a means to direct attention. When work is over, "at days end", be aware that immediately something new starts - there seems no way to avoid this. Even "taking a break" is a choice for the new start.

As usual, an hour has 60 minutes, a minute has 60 seconds. For no particular reason but to keep the tradition of easy divisibility into 2, 3, 4, 6, 8 and 12 parts.

The 24 hour scheme may be replaced by the system of the Seven Space Calendar (7 "hours" of 7 "hafs" each, where each haf is about half a common hour).

For purposes of assigning a certain lunar phase to a solar day, use local mean solar time (e.g. MET).


The seven weekdays are named just like before, referring to the qualities of the old Roman gods. Week numbering is similar to the ISO norm but slightly differing from the ISO week numbering scheme.

The ISO weekday starts on midnight. The ISO week starts on Monday, 00:00 common time. However, similar to the YANUS day, the YANUS week starts on Sunday 00:00 (i.e. Saturday 18:00, common time). Since Sunday is the first day of the week, the ISO numbering is modified accordingly: Sunday is already the "next" week.

YANUS weeks start 30 hours earlier than ISO weeks. In the table below, n indicates the week number.

YANUS  n        n      n        n+1    n+1    n+1     n+1
day    Thursday Friday Saturday Sunday Monday Tuesday Wednesday
ISO    n        n      n        n      n+1    n+1     n+1 
The ISO week numbering starts at 1 again if its Thursday is in the new year. In YANUS, week count starts again at 1 if its Wednesday is in the new year.

Lunar and Solar Year

Contrary to the common Gregorian calendar, the YANUS solar year starts on Autumn Equinox (fixed at September 23rd, Gregorian). The argument for this is similar to the reasoning that lets the day start at dusk and the week on "Saturday night" (Gregorian calendar).

Consequences of the shifted begin of the year may be felt in banking, accounting and trade. Actually, autumn is generally a phase of fermentation and re-assessment (e.g. autumn stock market panics) and it only has to be perceived as the beginning of the new year.

To start the year on September 23rd is not less reasonable than to start it on Spring Equinox or January 1. In the YANUS view, it is most desirable.

The YANUS lunar year begins on the last Third Quarter (= Waning Half Moon) of the YANUS solar year. As everything in YANUS, the lunar year starts early; to start on New Moon, or even September 23rd, would be too regular and "solar". Lunar years have 12 or 13 months and vary in length.

The number of the lunar year is the same as the number of the solar year most of the time, although it starts a little earlier. For example, on Spring Equinox the year numbers are the same. But at the start of the lunar year, the lunar year number is one ahead in counting.

Since the solar year is rule-based in this calendar, its dates are paradoxically less exact than the moon phases computed from the latest astronomical measurements (e.g. from U.S. Naval Observatory). Since the basic unit of this calendar is the day (and not the second), it does not matter much.

Because of differences in local time, the lunar year may start on different days for different longitudes on the Earth.

Leap Year Rule

Use a "reasonable" value for the tropical year in the next millennium (alternative below): 365.24219 days; a precision of eight digits. Now approximate this value by an integer fraction N/D (N = nominator, D = denominator):
N       D       N/D             rel.err
365     1       365.0000000000  -6.6309e-04 
1096    3       365.3333333333  +2.4954e-04
1461    4       365.2500000000  +2.1383e-05 the Julian cycle
6209    17      365.2352941176  -1.8880e-05
7670    21      365.2380952381  -1.1211e-05
9131    25      365.2400000000  -5.9960e-06
10592   29      365.2413793103  -2.2196e-06
146097  400     365.2425        +8.4875e-07 Gregorian          
12053   33      365.2424242424  +6.4133e-07 alternative YANUS
34698   95      365.2421052632  -2.3200e-07
46751   128     365.2421875000  -6.8448e-09 <-- YANUS (nautical)
The YANUS error is "one day error after 146 million years" (grin) and surely to be corrected after another 1000 years because of changes in earth rotational period due to human influences and celestial mechanics.

LEAP RULE: Each year with a number divisible by 4 is a leap year, except those divisible by 128 (e.g. 2048, 2176, 2304 etc).

Therefore a YANUS period of D = 128 years has 31 leap years of 366 days and 97 normal years of 365 days. 31*366 + 97*365 = 46751 days (the N in the above table).

This is the analog computation for the Gregorian calendar (period 400 years):

leap years 24+24+24+25 = 97
303*365 + 97*366 = 146097 days
146097 / 400 = 365.2425 days per year 
relative accuracy = (365.2425 - 365.24219) / 365.24219 = +8.4875e-07
and it is less exact than the result of YANUS leap rule, if you accept the value for the tropical year given above (see below for alternative).

Thus the YANUS leap rule

If the alternative tropical year of 365.2424 shall be used, the leap rule changes to: Each year with a number divisible by 4 is a leap year, except those divisible by 33 (e.g. 2013, 2046, 2079 etc). This is simpler than Gregorian and more accurate, too (YANUS : +6.6257e-08, Gregorian: +2.7379e-07).

Lunar Months

A rule-based month scheme is ruled out - it would be too "solar" (more on approximations of the lunar month). This viable approximations are eschewed in YANUS, because, being rule-systems, they do not show the Moon's fundamental irregularity.

Instead, to bring out the Moon's qualities, the Moon phases are computed from the latest astronomical measurements (current values see U.S. Naval Observatory, for instance).

The lunar months starts on Third Quarter (day 1). The days are counted to 29 or 30. The months of the next lunar year are predicted on the base of observations after the last Full Moon of the current lunar year. Thus, until after the last Full Moon in the lunar year, especially if Third Quarters are predicted near 18:00 common time, nobody knows the exact beginning days of the lunar months of the next lunar year. Very seldom are cases where the end of the last lunar month (and hence the lunar year) is uncertain until after the Full Moon of that month.

Lunar months are named after regional custom. Here we selected translated Old German month names.

The moon cycle of the lunar year starts with Fall Moon on the Third Quarter directly before September 23rd.

"August/September"   Fall Moon     ("Scheiding")
"September/October"  Wine Moon     ("Gilbhard")
"October/November"   Foggy Moon    ("Nebelung")
"November/December"  Snow Moon (*) 
"December"           Light Moon    ("Julmond, Christmond")
"January"            Hard Moon     ("Hartung")
"February"           Horn Moon     ("Hornung")
"March"              Spring Moon   ("Lenzing")
"April"              Easter Moon   
"May"                Joy Moon      ("Wonnemonat")
"June"               Fallow Moon   ("Brachet")
"July"               Hay Moon      ("Heuert")
"August"             Harvest Moon  ("Ernting")

(*) If the last Third Quarter before September 23rd lies before or on September 9th, it may be appropriate to insert a Snow Moon. In other cases omit the Snow Moon or use an other name.

To keep the playfulness in the month names, no hard rules are given here. The month names for the next lunar year are set together with the month start dates after the observation of the last Full Moon of the ending YANUS year. The names may vary from year to year according to taste and could each be taken from different traditions each year. It may be desirable to arrange Light Moon around the winter solstice.

Because of differences in local time, the lunar months may start on different days for different longitudes on the Earth. This is the same situation as with the current calendar: generally two weekdays exist simultaneously except for noon, GMT, when it is midnight on the international date line.

Solar Months

The solar months are the same as in the Gregorian calendar, with leap day on February 29th as usual.

Solstices and equinoxes are fixed by a rule on the same solar date each year (although they shift a day or so in astronomical reality) to enforce the solar "ruling" quality of this part of YANUS.

In analogy to the qualities of the weekdays, seven periods can be identified within a year. These can be named SaturdaY, MondaY and so on.

The names of the seven weekday periods are deliberately like the weekday names to remind of the weekday qualities; many people "know how a Monday feels", and the names shall reflect that. To make things clear typographically, weekday period names end with a capital Y (for year or YANUS). The order of the weekday periods is not arbitrary (as explained below).

Each of these periods has approximately 52 days. The same can be done with your birthday as start date for the SundaY period.

The SaturdaY period always has 53 days. The YANUS TuesdaY (Gregorian: WednesdaY) period has 52 days normally and 53 days in leap years. All other weekday periods have 52 days.

Note that a different weekday order is used to convey the character of time for the "year-weekdaYs":

  1. SaturdaY - ending, parting, darkening, final settlement and limitation, a seed resting in the earth, relaxation, waiting, old age, death
  2. MondaY - new beginning, cool, insecurity, first steps, infancy
  3. WednesdaY - begin of flow, perception, sowing
  4. TuesdaY - action, power, first attainments, growing, teenage
  5. FridaY - love, arousal, harmony, sweetness, blossoming, youth
  6. SundaY - warmth, shining, opulence, fullness expressed, maturity, ripening
  7. ThursdaY - decision, calm, ratio, harvest, re-assessment, creation of the seed, seniority

Solstice, equinox and Earth orbit data are approximated (Details see Zodiacal Calendar).

Exemplary Calendar 1999

Most dates in the calendar below remain fixed - solar leap years do not change this. Note that YANUS year 1999 (YC : YANUS count) begins in 1998 (CE) Gregorian.

Lunar month beginnings and Easter are different each year and are marked with a * in the table. The lunar months are set for MET (not MEDST). Spring and Easter Moon have switched places because of the Easter date.

Note that the YANUS dates begin the previous Gregorian day, as shown in the first and last entry of the table. For all other YANUS entries in the table the next Gregorian day is given, since 3/4 of the YANUS day falls on that date.

Gregorian    special day
(ISO date)
1998-09-12,18:00 * Lunar Year 1998 YC ends
1998-09-13 * Lunar Year 1999 YC begins
1998-09-13 * Fall Moon (1) begins
1008-09-22   Solar Year's End (1998 YC)
1998-09-23   Autumn Equinox
1998-09-23   Solar Year begins
1998-09-23   New Year (1999 YC)
1998-09-23   SaturdaY begins
1998-10-11 * Fall Moon ends
1998-10-12 * Wine Moon (2) begins
1998-11-08   Gregorian ThursdaY ends
1998-11-09   Gregorian SaturdaY begins 
1998-11-10 * Wine Moon ends 
1998-11-11 * Foggy Moon (3) begins 
1998-11-14   SaturdaY ends    
1998-11-15   MondaY begins
1998-12-10 * Foggy Moon ends (about 18:54 MET)
1998-12-11 * Light Moon (4) begins
1998-12-22   Winter Solstice
1998-12-31   Gregorian SaturdaY ends
1998-12-31   Gregorian Year's End
1999-01-01   Gregorian New Year
1999-01-01   Gregorian MondaY begins
1999-01-03   Earth Perihelion
1999-01-05   MondaY ends
1999-01-06   WednesdaY begins
1999-01-08 * Light Moon ends
1999-01-09 * Hard Moon (5) begins
1999-02-07 * Hard Moon ends
1999-02-08 * Horn Moon (6) begins
1999-02-21   Gregorian MondaY ends
1999-02-22   Gregorian WednesdaY begins
1999-02-26   WednesdaY ends 
1999-02-27   TuesdaY begins
1999-03-09 * Horn Moon ends
1999-03-10 * Easter Moon (7) begins
1999-03-20   Spring Equinox
1999-03-23   Midyear
1999-04-04 * Easter Sunday
1999-04-08 * Easter Moon ends
1999-04-09 * Spring Moon (8) begins
1999-04-14   Gregorian WednesdaY ends
1999-04-15   Gregorian TuesdaY begins
1999-04-19   TuesdaY ends
1999-04-20   FridaY begins
1999-05-01   May day
1999-05-08 * Spring Moon ends (about 18:29 MET)
1999-05-09 * Joy Moon (9) begins
1999-06-05   Gregorian TuesdaY ends
1999-06-06   Gregorian FridaY begins
1999-06-06 * Joy Moon ends
1999-06-07 * Fallow Moon (10) begins
1999-06-10   FridaY ends
1999-06-11   SundaY begins
1999-06-21   Summer Solstice
1999-07-02   Gregorian Midyear  
1999-07-05   Earth Aphelion
1999-07-05 * Fallow Moon ends
1999-07-06 * Hay Moon (11) begins
1999-07-27   Gregorian FridaY ends
1999-07-28   Gregorian SundaY begins
1999-08-01   SundaY ends
1999-08-02   ThursdaY begins
1999-08-04 * Hay Moon ends (about 18:27 MET)
1999-08-05 * Harvest Moon (12) begins
1999-09-01 * Harvest Moon ends 
1999-09-02 * Lunar Year 2000 YC begins
1999-09-02 * Fall Moon (1) begins
1999-09-09   end date for some computers
1999-09-17   Gregorian SundaY ends
1999-09-18   Gregorian ThursdaY begins
1999-09-22   Solar Year's End (1999 YC)
1999-09-22   ThursdaY ends
1999-09-22,18:00 Solar Year 2000 YC begins (leap year)

Date Examples

Full YANUS dates should be written the following way (from left to right, separated by comma): {Name} Moon {day}, {weekday}, {solar date} YC, {weekday period} {day number in weekday period}, {time}. All info should be given, to emphasize the various rhythms.
Time may be omitted, but remember the date shift at dusk.

The week number is normally not given. If the YANUS week number is given, it should be inserted after the solar date and before the weekday period and marked Yw (YANUS week, pronounced "why we").

Some prefer to give the solar or lunar date only, omitting the "other face of YANUS". Sometimes the weekday is omitted, too, resulting in dates like "Fall Moon 8, 1999 YC" (most of 1999-09-09 Gregorian). Here are some examples:

Friday, 1998-09-25, 14:00, Gregorian is
Fall Moon 13, Friday, 1999-09-25 YC, Yw 39, SaturdaY 3, 20:00
The YANUS year has begun on SaturdaY 1 (1998-09-23 Gregorian). The YANUS solar date does not look much different than the ISO date, except for the advanced year. The example date is the third day in the SaturdaY period.

Saturday, 1998-10-17, 18:30, Gregorian is
Wine Moon 7, Sunday, 1999 YC, SaturdaY 26, 00:30
Of note here is the begin of the YANUS day at 18:00 hours common reckoning. The solar date can be abbreviated, if the reference to the Gregorian system is not desired - the Gregorian date can be computed from the day number in the weekday period.

Saturday, 1999-03-20, Gregorian may be written as
Easter Moon 2, 1999 YC, Spring Equinox
because it is on the same date every year. We can omit the weekday period and day number, because it can be inferred: no leap year, therefore TuesdaY 22. In leap years, Spring Equinox falls on TuesdaY 23. Similarly, other fixed dates (like Midyear, Perihelion etc) can replace their solar dates.
Naturally, the lunar date is different from year to year.

Acceptability and End Remarks

Probably the "early start" of the fundamental calendar periods will not be accepted, because it is against tradition. But the unusual features of YANUS, especially the precise and simple leap year rule, may be used elsewhere and become incorporated into other calendric systems.

There are already totally observation-based calendars. And one might call the present calendar still observation-based (although mostly hidden). But the important point is: a modern calendar should reflect that there is unpredictability in heaven. And therefore uncertainty should be introduced into calendars, even in a slightly stronger fashion than is actually the case.

And the observation of "holy", "important", and "national" special days is also nothing new. I tried to share my thoughts, give some new angles and food for your thought. That is all. Thanks for reading thus far, I hope you liked something you found here.

"Now that I know that ... ," you may think, "but this in in principle the calendar we already have!" Certainly. The only thing I did was balance the solar and lunar aspects and change the point of view. For now, feel free to expand or overthrow this and make your own calendar.

Calendrics at this site

Essays on mathematical themes

© Copyright 1998, Mario Hilgemeier, email: contact
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