Earlier Saltus Lunae instead of Lunar Equation Corrections RE: Dee-Cecil Calendar and Simon Cassidy's Epacts

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Earlier Saltus Lunae instead of Lunar Equation Corrections RE: Dee-Cecil Calendar and Simon Cassidy's Epacts

Karl Palmen

Dear Amos, Walter and Calendar People

 

Amos’s remark “The only way to improve the Easter computus would require fixing the lunar cycle algorithm, within the 400-year Gregorian solar cycle.” Reminded me of the idea of replacing the lunar equation corrections with a shift of the saltus lunae while keeping the solar equation corrections as they are.

 

The saltus lunae is when the epact increments by 12 or decrements by 18, instead of the usual 11 and 19 respectively. If this occurs once every 19 years, we get the 19-year cycle. The Gregorian computus places the saltus lunae at years of golden number 1 as does the Julian calendar computus.

 

Suppose each century the saltus lunae were moved 6 years earlier and if this results in the first saltus lunae of the century moving into the previous century, it is held at the year with number ending with 00. Suppose also for every 25th century, the saltus lunae are moved 2 more years earlier, then the mean lunar month would be exactly equal to that of the existing computus. The lunar jitter would be reduced a little, but the main advantage of such a system like this is that it can be adapted to any lunisolar cycle a multiple of 400 years and not just those also a multiple of 19 years, including those I’ve listed in

http://the-light.com/cal/Lunisolar400.html

 

Suppose instead of moving the saltus lunae 2 more years earlier once every 25 centuries, we instead move them 1 more year earlier once every 12 centuries (3 Gregorian 400-year cycles). Then one would get the 18,000-year cycle. Over 1200 years, the saltus lunae would have moved at total of 11*6 + 7 = 73 years earlier and so those 1200 years have 1273/19 = 67 saltus lunae. Then the whole 18,000-year cycle has 1005 saltus lunae. The spreadsheet I linked in this note indicates that 870 saltus lunae are needed, but we need 135 more to compensate for the 135 solar equation corrections and so this 1005 is the number of saltus lunae corrections needed here .  Suppose the saltus lunae began at golden number 1, then after 18,000 years they would be at golden number 1 + (15*(4*19 - 73) mod 19) = 1 + (45 mod 19) = 8, which is the golden number of the first year of the second 18,000-year cycle.

 

Amos. Is this the kind of thing you meant by the remark I quote in this note?

I show the whole note in which this occurs below.

 

Karl

 

16(07(27

 

Friday Queen of Clubs 2017, ISO deck

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 24 March 2017 02:26
To: [hidden email]
Subject: Re: Dee-Cecil Calendar and Simon Cassidy's Epacts

 

Dear Karl:

Your post reminded me of a thought that have had, for which I cannot think of any answer:

Is there any record of when Dee and Cecil  proposed their calendars with the 33 year leap day rule, whether they themselves proposed how Easter should be determined by their calendars?   It seems from what I have seen that Simon Cassidy was actually the first person to devise a lunar equation rule for any 33 year calendar.

-Walter Ziobro

 

 

 

-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Wed, Mar 22, 2017 9:04 am
Subject: Re: Dee-Cecil Calendar and Simon Cassidy's Epacts

Dear Amos, Walter and Calendar People

 

I looked back at some old notes and wonder what Amos meant by

fixing the lunar cycle algorithm, within the 400-year Gregorian solar cycle

 

It could mean fixing Easter date to something like the 2nd Sunday in April.

It could mean making Easter repeat on a 400-year cycle.

In neither case would Easter be lunar.

 

Perhaps it just means fixing the equinox date to Gregorian 21 March.

Actually I think the underlying issue is what day do we count the epacts relative to.  The number of days that the paschal full moon occurs after the ecclesiastical equinox day is determined in a simple manner from the epact. I think Walter wants to preserve that, but vary the ecclesiastical equinox date so that it jitters less. Then a method such as Simon Cassidy’s Moonkey epacts could be applied.

 

If we both fix the ecclesiastical epact date and preserve the simple relationship between the number of days that the paschal full moon occurs after the ecclesiastical equinox day and the epact, then the choice of good epact rules available is seriously constrained. This arises from the jitter of the Gregorian calendar of 2.1975 days, we don’t want all the jitter to be transferred to the Paschal full moon. One way of reducing the transfer of jitter is to have every correction of the 19-year cycle at a year ending in 00, which include the dropped leap years. Better still, decrement the epact by 1 at every dropped leap year (solar equation) and increment by 1 once every 300 or 400 years (lunar equation). This is what the Gregorian computus does.

 

The Gregorian computus corrects the 19-year cycle by simply decrementing or incrementing the epacts by 1. One could also correct by changing the Golden Number of the Saltus Lunae.  This offers finer control of 1/570 month instead of 1/30 month and allows the Easter days to follow a shorter cycle such as the 18,000-year cycle.

 

Karl

 

16(07(25

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Amos Shapir
Sent: 20 July 2015 07:31
To: CALNDR-[hidden email]
Subject: Re: Dee-Cecil Calendar and Simon Cassidy's Epacts

 

Hi Walter and Calendar people,

I don't think there's any chance of making the Church adopt any alternative way of computing the vernal equinox.  Keep in mind that the very purpose of the gregorian reform was to make the vernal equinox fall on a fixed date.

The only way to improve the Easter computus would require fixing the lunar cycle algorithm, within the 400-year Gregorian solar cycle.

 

On Mon, Jul 20, 2015 at 5:56 AM, Walter J Ziobro <[hidden email]> wrote:

Dear  Mr Otero:

Your reference to the Sacraffia article in which the Pope offered to standardize the date of Easter, got me thinking about how this could be done.  If the Lunisolar method of determining Easter is to be retained, but improved, two standing proposals could be used to facilitate this.

The first could be to determine the Ecclesiastical Vernal Equinox according to the Dee-Cecil Calendar, or some calendar with a variant of the 33 year leap day rule.   This would cause the Ecclesiastical Vernal Equinox to fall on a narrower range of dates, and,more often on the date of the astronomical northward equinox.  An exposition of the Dee-Cecil Calendar can be found here:    

http://www.hermetic.ch/cal_stud/dee-cecil-calendar.htm

An alternative to adopting the Dee-Cecil Calendar might be simply to have the Ecclesiastical Vernal Equinox determined solely by a 33 year rule, independently of any specific calendar.

The second could be to change the rules whereby the lunar epacts are shifted.  Simon Cassidy has proposed alternative rules whereby the epacts are adjusted gradually every twelfth year, instead of all at once on certain century years, thereby minimizing lunar jitter, and maximizing correspondence with the astronomical lunar phases.  An abstract outlining his proposals can be found here:

      http://www.hermetic.ch/cal_stud/cassidy/metonic_epacts.htm

Again, if it is decided that the Ecclesiastical Vernal Equinox is to be determined independently of any specific calendar, and a 33 year rule is chosen, the system of epacts could be applied to the Ecclesiastical Vernal Equinox (EVE) itself.  That is to say, an alternative table of epacts  showing the age of the moon on the EVE could be generated, with the next 14th day of a lunation determined to be the Paschal Full Moon for that year.


-Walter Ziobro




--

Amos Shapir

 

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Tithi & 19-year/33-year cycle Re: Earlier Saltus Lunae instead of Lunar Equation Corrections RE: Dee-Cecil Calendar and Simon Cassidy's Epacts

Brij Bhushan metric VIJ
Simon, Karl sirs:
>Reform was to make the vernal equinox fall >on a fixed date.

The only way to improve the Easter computus would require fixing the lunar cycle algorithm, within the 400-year Gregorian solar cycle.

Some aspects of this were discussed by list during 2010 thro 2014....when I pointed to my Tithi values worked as:
ONE Tithi =1 335/326919 day to exactly fit
19-years/6932.5 Tithi (235*29.5 moons). Also, good for 896-years/327257 days with Tithi=1 338/326919 day; needing an EXTRA Tithi during 11082nd Lunation.
       "....I provide a brief over view, for easy grasp: http://www.brijvij.com/bb_AltWrldcal-OverView.pdf. My drawing attention of Calndr-L on (21*19)=399-yrs/4935 lunation with TWO 'tithi' removed - adjusts ONE lunation over 15 such cycles i.e. {15*[(399-yrs/4935 lunation)]-1 lunation} result in a cycle of

5985-yrs (2185974.5 days)/74024 lunation (over accounting 'only' 1.787246882289 hour). This gives:
Mean Lunation =29.530618448071 days (29d 12h 44m 5s.4339).
Incidentally, (9*1730)=15570-years =[(630*19)+(60*60)]-years, the cycle that I calculated earlier with almost current values for Mean Year & Mean lunation.
mEtric100
(BRIJ BHUSHAN VIJ) 20100126H1053(decimal)"

    It is easy to see that using TITHI=No.of days in 896-years/No. of (11082x29.5) tithi make the right fit, even when used for 'controlling epact' in 400-years , since 400-years={(19x21)+1} or 1200-years to choose 1-day correction of Julian/Gregorian dates of past or future historical events. 

Larger cycles, however, can be controlled for synchronizing Solar and/or Lunar events for fixing 'religious dates of significance'. 

I recall, this had come up during some clarifications on Stone Henge/Harappa phase/ tithi 19-year cycle with Simon Cassidy, in some e-Mails that were exchanged, sir.

True, my working had been to point the Lunation interval equated to 29 1/2 tithi, which led me to the values pointed above. 896-years={27*33+5} years; and also, {47*19+3} years.

Regards, 

Brij Bhushan metric VIJ

Author, Brij-Gregorian Modified calendar.                   Saturday, 2017March24H03:33 (decimal)


Sent from my iPhone

On Mar 24, 2017, at 9:02 AM, Karl Palmen <[hidden email]> wrote:

eform was to make the vernal equinox fall on a fixed date.

The only way to improve the Easter computus would require fixing the lunar cycle algorithm, within the 400-year Gregorian solar cycle.

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