## The ONE DAY BEFORE Lunar Calendar

This version of my ONE DAY BEFORE calendar is obselete and has been replaced by a

new version, which follows the full moon more closely. It also has has a lunar week defined.

## See the New Version

The old version is kept below as a calendar study. Clever people could work out why the new version is better than the old version at predicting the full moon.

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

The above emails have been subject to editing - refer to the CALNDR-L archive for full text

Copyright 1998 Simon Cassidy and Karl Palmen

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