Karl Palmen's Yerm Calendar

I've constructed a simple rule-based lunar calendar. It's simplicity arises partly from the abandonment of any pretence to follow the seasons allowing the length of the 'year' to be modified to suit a simple and accurate tracking of the lunar month.

This 'year', which I hence refer to as a 'yerm' (YEaR Moon) has an odd number of months in it and has months of alternating lengths 30 and 29 'days'. The first and last months have 30 days. Each new yerm occurs when there are two consecutive months of 30 days.

A 3 yerm cycle of two 17 month yerms and a 15 month yerm produces a mean month of 29.530612 days. This I call the 'Basic Yerm Calendar'. It is accurate within an hour per century. The three yerm cycle of this calendar is exactly 14 days short of four years with a leap day.

For better accuracy an additional 17 month yerm is inserted after every 17 three yerm cycles. This is done by counting the yerms from 1 to 52 in a cycle and making those yerms whose number is divisible by 3 (digits add up to 3, 6, 9 or 12) have 15 months (also divisible by 3) and all others 17 months. This gives a cycle of 52 yerms, 850 months and 25101 days. The average month length is 29.5305882 days. This is more accurate than the Hebrew calendar.

The 'days' of the calendar begin at 12 midday clock time, so that the night is not interrupted by a date change. I chose yerm 1 of the present cycle to begin on November 11th 1996. This puts the mean 'dark moon' (when the moon is closest to the sun in the sky) near 11pm UT (or GMT) of the last night of the month.

The motion of the moon is very complex and can not be reflected by a simple rule-based calendar. Hence no simple rule-based lunar calendar can predict the exact date of a given phase of the moon.


Correlation with the Moon

Below I give you the start dates of some of the Months in my Yerm Calendar and how many hours (h) the month starts after the 'dark moon' in UT (or GMT). Also I give the number of 'days' (d) that the calendar is late.
  30 'day' Yerm months                   29 'day' Yerm months
ye(mo  begins noon  (h)   (d)      ye(mo  begins noon  (h)   (d)
01(01  1996-11-11   +08    0       01(02  1996-12-11   +19    0
01(03  1997-01-09   +08    0       01(04  1997-02-08   +21    0
01(05  1997-03-09   +11    0       01(06  1997-04-08   +24   +1
01(07  1997-05-07   +14    0       01(08  1997-06-06   +28   +1
01(09  1997-07-05   +16    0       01(10  1997-08-04   +27   +1
01(11  1997-09-02   +11    0       01(12  1997-10-02   +18    0
01(13  1997-10-31   +02    0       01(14  1997-11-30   +10    0
01(15  1997-12-29   -05   -1       01(16  1998-01-28   +06    0
01(17  1998-02-26   -05   -1

  30 'day' Yerm months                   29 'day' Yerm months
ye(mo  begins noon  (h)   (d)      ye(mo  begins noon  (h)   (d)
02(01  1998-03-28   +09    0       02(02  1998-04-27   +23    0
02(03  1998-05-26   +16    0       02(04  1998-06-25   +31   +1
02(05  1998-07-24   +21    0       02(06  1998-08-23   +33   +1
02(07  1998-09-21   +18    0       02(08  1998-10-21   +25   +1
02(09  1998-11-19   +08    0       02(10  1998-12-19   +13    0
02(11  1999-01-17   -04   -1       02(12  1999-02-16   +05    0
02(13  1999-03-17   -07   -1       02(14  1999-04-16   +08    0
02(15  1999-05-15   +00    0       02(16  1999-06-14   +17    0
02(17  1999-07-13   +10    0

  30 'day' Yerm months                   29 'day' Yerm months
ye(mo  begins noon  (h)   (d)      ye(mo  begins noon  (h)   (d)
03(01  1999-08-12   +25   +1       03(02  1999-09-11   +38   +1
03(03  1999-10-10   +24   +1       03(04  1999-11-09   +32   +1
03(05  1999-12-08   +13    0       03(06  2000-01-07   +18    0
03(07  2000-02-05   -01   -1       03(08  2000-03-06   +07    0
03(09  2000-04-04   -06   -1       03(10  2000-05-04   +08    0
03(11  2000-06-02   -00   -1       03(12  2000-07-02   +17    0
03(13  2000-07-31   +10    0       03(14  2000-08-30   +26   +1
03(15  2000-09-28   +16    0

  30 'day' Yerm months                   29 'day' Yerm months
ye(mo  begins noon  (h)   (d)      ye(mo  begins noon  (h)   (d)
04(01  2000-10-28   +28   +1       04(02  2000-11-27   +37   +1
04(03  2000-12-26   +19    0       04(04  2001-01-25   +23    0
It will be easy to work out the starts of later Yerm months, because the basic 3 yerm cycle is exactly 14 days short of the Julian 4 year cycle.

I got the times of the 'dark' moons up to Jan 1999 from my Lunar Tree Calendar produced by William Morris. The others I got from Mario's table.


Challenge

Find a 'dark' moon (astronomical new moon) that does not occur on the penultimate, last or first date of a Yerm calendar month in UT (i.e. (d) in the table is not 1, 0 or -1). Remember that Yerm Calendar dates begin and end at noon.

Hint1: The 'dark' moon at the end of the first month of a yerm or the one at the beginning of the last month of a yerm are good ones to try.

Hint2: Any 49 yerm month period lasts 14 days less than 4 Julian years, except one beginning on 52(02.
This includes any 3 yerm period with a 15 month yerm ending in it.

You may wish to consult http://www.is-bremen.de/~mhi/moontabl.htm

Would it be honest to wish you good luck!


The Lunar Week

The days of the month can be numbered from 1 to 29 or 30 as is conventional in most calendars. But I use a lunar week whose weekends occur around the principal phases of the moon.

The 1st, 8th, 15th, 22nd and 29th 'nights' of the month are called 'Moonnight'. The first four of these form the start of a lunar week, whose 'nights' are

Moonnight, Tuesnight, Wensnight, Thursnight, Frinight, Saturnight and Soonnight (soon to be Moonnight).

For example, the 10th 'night' is referred to as the Second Wensnight.

This fixes the lunar week in relation to the standard 7 day week for the first four weeks of the month.

The 30th 'night' is a Soonnight, but the last night of any month can be referred to just as 'Lastnight' rather than 'Fifth Soonnight' or 'Fifth Moonnight'.

I've also considered making the second lunar week have 8 days, but haven't decided how to name the 'nights' so I stick with the above scheme.

With the help of someone else on the CALNDR-L list, I found out an interesting way of defining full moon weekends. If you define a full moon weekend to have 3 nights (say '2(7' to '3(2'), except in the last month of a yerm, when an extra night is added to the end. Then each such weekend begins on the same day of the week as the one two months ago ended.


Short Dates

Dates can in shorthand be expressed with numbers. The crescent-like brackets used as delimiters.

For example, 'Fourth Frinight Month 3 Yerm 2' can be written as '5)4)03)02' or '02(03(4(5' or even '02(03(26'.


Other Things

Conversion between Yerm and Julian Date


First published Thursday Six of Diamonds, Deck 1998 (Playing Card Calendar)


The above is a merger of emails sent on Thu, 07 May 1998 (Second Thursnight Month 2 Yerm 2 [ 02(02(2(4 ]) and Thu, 24 Sep 1998 (First Thursnight Month 7 Yerm 2 [ 02(07(1(4 ]) and has been faithfully edited without loss of relevant information. Headings have been added for clarity - refer to the CALNDR-L archive for original emails


Karl Palmen's Calendars

Calendrics

Justin White's Calendar Links

Essays on mathematical themes


Copyright 1998, Karl Palmen, (contact info) . Published with permission.
© HTML Copyright 1998, Mario Hilgemeier, email: contact
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