The ONE DAY BEFORE Lunar Calendar

Date: Thu, 1 Oct 1998
To: East Carolina University Calendar discussion List 
From: Karl Palmen 
Subject: The ONE DAY BEFORE Lunar Calendar on the Gregorian Calendar

Dear Calendar People

Making use of the fact that a mean Gregorian Month is about one day longer
than a lunar month, I came up with the following.

ONE DAY BEFORE LUNAR CALENDAR on the Gregorian Calendar

Each month of the Gregorian calendar is usually given one Lunarday, which
corresponds to a full moon night.

They are defined by the following rules:

(1) The Lunarday of each month is ONE DAY BEFORE the Lunarday of the
previous month, except for March and 28 day February.

(2) Any month that has a Lunarday on the 1st also has one on the 30th,
except February of course.

(3) 28 day February has its Lunarday TWO DAYS BEFORE the Lunarday of January
and January 31st counts as February 0th.

(4) Any year that is either 7 or 360 years after a year divisible by 725
(e.g.. 1457, 1810, 2182) has its March Lunarday on the 19th.

(5) All other years have their March Lunarday 11 DAYS BEFORE that of last
year if possible, otherwise 19 DAYS AFTER.


Rules (4) and (5) generate a 19 year Metonic Cycle that is occasionally
truncated to 11 years.
In analogy to Easter Metonic cycle being defined by Golden numbers, this
Metonic Cycle can be defined by Platinum numbers.
Any year for which the March Lunarday is the 19th has a Platinum number of 1
and other years have a Platinum number one greater than that of the year
before.

For years between 1810 and 2181 inclusive the Platinum number is obtained by
subtracting either 100 or 2000 and then as for Golden numbers taking the
remainder from dividing by 19 and adding 1.

The March Lunarday(s) for a year is the remainder of 19 times the Platinum
number divided by 30. Giving rise to the following table.

Pt#   Years       March Lunarday
 1    1981/2000   Mar 19
 2    1982/2001   Mar  8
 3    1983/2002   Mar 27
 4    1984/2003   Mar 16
 5    1985/2004   Mar  5
 6    1986/2005   Mar 24
 7    1987/2006   Mar 13
 8    1988/2007   Mar  2
 9    1989/2008   Mar 21
10    1990/2009   Mar 10
11    1991/2010   Mar 29
12    1992/2011   Mar 18
13    1993/2012   Mar  7
14    1994/2013   Mar 26
15    1995/2014   Mar 15
16    1996/2015   Mar  4
17    1997/2016   Mar 23
18    1998/2017   Mar 12
19    1999/2018   Mar 1,30 (NB: Rule (2) )

Lunardays 1998-2000

    1998  1999 2000
Jan  13   2,31  20
Feb  11     0   19
Mar  12   1,30  19
Apr  11    29   18
May  10    28   17
Jun   9    27   16
Jul   8    26   15
Aug   7    25   14
Sep   6    24   13
Oct   5    23   12
Nov   4    22   11
Dec   3    21   10

The 725 year cycle has 37 full Metonic cycles with 235 Lunardays each and 2
truncated Metonic cycles with 136 Lunardays each. This gives a mean interval
between Lunardays of

365.2425*725/(37*235+2*136) = 365.2425*725/8967 = 29.530591

which is more accurate than the Hebrew Calendar.


Karl Palmen


Wensnight 2 Month 7 Yerm 2


Date: Sun, 4 Oct 1998 To: East Carolina University Calendar discussion List From: Simon Cassidy Subject: Re: The ONE DAY BEFORE Lunar Calendar on the Gregorian Calendar I like the simple algorithm for finding a night of full moon in March, given the year# AD (Y): (19 x Platinum#)mod 30 where Platinum# is (Y+6)mod19 +1 (1457-1809AD) (Y-5)mod19 +1 (1810-2181AD) (Y+3)mod19 +1 (2182-2535AD) etc. I also like the simple way of deriving a full moon night in the following months by subtracting a day per month (and 2 for Jan-Feb). A couple of small points about the posting: Karl Palmen wrote: > ....... > (3) 28 day February has its Lunarday TWO DAYS BEFORE the Lunarday of January > and January 31st counts as February 0th. > .... > .... > Lunardays 1998-2000 > > 1998 1999 2000 > Jan 13 2,31 20 > Feb 11 0 19 > .... Simon notes: A February Lunarday on the 19th. after a January Lunarday on the 20th. in the year 2000 seems to contradict Karl's rule (3). I will assume he means Feb 18. Karl concluded: > The 725 year cycle has 37 full Metonic cycles with 235 Lunardays each and 2 > truncated Metonic cycles with 136 Lunardays each. This gives a mean interval > between Lunardays of > > 365.2425*725/(37*235+2*136) = 365.2425*725/8967 = 29.530591 > > which is more accurate than the Hebrew Calendar. Simon notes: But less accurate than the Gregorian Ecclesiastical Lunar Calendar which (unintentionally) averages 29.530587 days per ecclesiastical month. I am assuming the comparison is with 29.530588 or 29.530589 days per (current?) astronomical synodical month. I think this is currently decreasing when measured in Universal days (as opposed to Atomic or Ephemeris days). --- Dee's Y'rs, Simon Cassidy


Date: Mon, 5 Oct 1998 To: East Carolina University Calendar discussion List From: Karl Palmen Subject: Re: The ONE DAY BEFORE Lunar Calendar on the Gregorian Calendar Dear Simon > ---------- > From: Simon Cassidy > Reply To: East Carolina University Calendar discussion List > Sent: 04 October 1998 > To: CALNDR-L > Subject: Re: The ONE DAY BEFORE Lunar Calendar on the Gregorian > Calendar > > I like the simple algorithm for finding a night of full moon in March, > given the year# AD (Y): (19 x Platinum#)mod 30 > where Platinum# is (Y+6)mod19 +1 (1457-1809AD) > (Y-5)mod19 +1 (1810-2181AD) > (Y+3)mod19 +1 (2182-2535AD) etc. > > I also like the simple way of deriving a full moon night in the following > months by subtracting a day per month (and 2 for Jan-Feb). > > A couple of small points about the posting: > > Karl Palmen wrote: > > ....... > > (3) 28 day February has its Lunarday TWO DAYS BEFORE the Lunarday of > January > > and January 31st counts as February 0th. > > .... > > .... > > Lunardays 1998-2000 > > > > 1998 1999 2000 > > Jan 13 2,31 20 > > Feb 11 0 19 > > .... > > Simon notes: > A February Lunarday on the 19th. after a January Lunarday on the 20th. in > the > year 2000 seems to contradict Karl's rule (3). I will assume he means Feb > 18. > Rule (3) Applies only to 28 day February. In 2000 February has 29 days and so is ONE DAY BEFORE as in rule (1). I put in this variation as a buffer to ensure the interval from one Lunarday to the next is either 29 or 30 days. > Karl concluded: > > The 725 year cycle has 37 full Metonic cycles with 235 Lunardays each > and 2 > > truncated Metonic cycles with 136 Lunardays each. This gives a mean > interval > > between Lunardays of > > > > 365.2425*725/(37*235+2*136) = 365.2425*725/8967 = 29.530591 > > > > which is more accurate than the Hebrew Calendar. > > Simon notes: > But less accurate than the Gregorian Ecclesiastical Lunar Calendar > which (unintentionally) averages 29.530587 days per ecclesiastical > month. It could be made more accurate with a longer and more accurate cycle. But I chose to stop there. The 725 year cycle is a 50% mix of the 353 year cycle which gives 29.530601 and the 372 year cycle which gives 29.520582 . The 334 year cycle that I have mentioned in earlier notes is meant for a mean tropical year and is unsuitable for a Gregorian or Vernal Equinox year. > I am assuming the comparison is with 29.530588 or 29.530589 days > per (current?) astronomical synodical month. I think this is currently > decreasing when measured in Universal days (as opposed to Atomic or > Ephemeris days). I wonder. Karl Palmen Soonnight 2 Month 7 Yerm 2 [ 02(07(2(7] Last of a series that began on Apr4, May 5, June 4, July 5, Aug 4, Sept 4 and Oct 4


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