Re: Metonic-Lunar cycle RE: Gregorian calendar jitter and lunar calendar in Wikipedia computus

Dear Tom, Brij  and Calendar People

The example of 12 Metonic cycles is simpler (than 11), because it always has the same number of years divisible by 4.

In the Gregorian Computus, a  period of 12 Metonic cycles of 228 lunisolar years of 2820 lunar months is 83277 days if it has no lunar equation correction and 83276 days if it does have a lunar equation correction. It is not long enough to have two or more lunar equation corrections.

In a uniform correction system, it has 83277 days if it has the same number of common century years as corrections, 83276 days if it has one more common century year than corrections and 83275 days if it has two more common century years than corrections. The third case (or a fourth case of 83274 days) occurs in every possible uniform correction computus, because such a computus does not provide at least two corrections to every triplet of consecutive common century years, hence the 228 years may contain three common century years with fewer than two corrections.

Note that I’ve specified the number of lunisolar years in the 228-year period as well as the number of lunar months (2820). Specifying the number of lunar months alone is not sufficient, because over the 2820 lunar months the corrections could cause the epact to jump 25, thereby adding or removing a lunar month from the 228 lunisolar years. This causes the 2820 lunar month not to be a whole number of lunisolar years and so brings in an additional term for within-year fluctuation of lunar months between 29 and 30 days, which would complicate the example.

Brij’s attachment showed a lunar or lunisolar calendar, which he believes may have been used by the Harappan civilisation. It’s months are the same as Brij’s slight modified  Julian/Gregorian months but the 13^th day has been omitted. This implies that the Harappan people anticipated the Julian calendar with its irregular months before it was invented.

To form a 19-year  Metonic cycle, seven intercalary months totalling 19*12=228 days would need to be added.  Three would have 32 days and four would have 33 days.

If one month per year (say February) did not have its 13^th day omitted, then the 228 days would be reduced to 209 leading to six intercalary months of 30 days and one of 29 days as in the Julian Computus.

If the calendar were based on the Tithi of 2/59 lunations equated to 966/965 days, the months would have to follow a 965-month cycle of 966*29.5=28497 days = 4071 weeks, or a multiple thereof. This cannot be easily arranged by a calendar of the type just described in the previous paragraph.

Karl

10(07(05

Karl & list, sirs:
>> This causes the minimum number of days in 11 consecutive Metonic
> cycles
> (of 235 lunar months equal to 19 lunisolar years) to be one less than
> for the Gregorian system.
 I had dispaled some of my working on Tithi value=138W/965 and my interpretation of Harappan calendar to be in link with 'TITHI INTERVAL' rather than solar day. I presnt the possible Harappan calendar (also SKIPPING the date 13th in every month). This make the Lunar Year (format - attached) of [12*29.5+12 days] BUT marked to Gregorian months LESS 13th Tithi. Please see:
http://www.brijvij.com/XorT-units-5x47lunation.doc
 http://www.brijvij.com/bb-kp_count-by-week.cycles.doc
Regards,
Brij Bhushan Vij 

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> Date: Thu, 26 Mar 2009 13:53:38 +0000
> From: karl.palmen@...
> Subject: Re: Gregorian calendar jitter and lunar calendar in Wikipedia computus
> To: CALNDR-L@...
>
> Dear Tom and Calendar People
>
> On the Wikipedia talk page of Computus
> http://en.wikipedia.org/wiki/Talk:Computus#Unified_system_of_corrections
>
>
> Mockingbird said:
>
> "I have always held that the Gregorian scheme is more accurate than a
> unified scheme. See my post at the beginning of this section. What I
> disagree with is the claim that "jitter" from the solar side is being
> "transmitted" to the lunar side by a unified scheme. The "jitter" on the
> solar side is the motion of the mean and true equinoxes relative to
> midnight (beginning of day) March 21 Gregorian. On the lunar side the
> difference between a fixed date and a fixed annual event is of no
> consequence. The important difference is between the beginning of a
> lunation and the mean and true conjunctions. So nothing is "transmitted"
> from one side to the other."
>
> The first two sentences are clear and important.
>
> Tom later gave a reply that did not seem to address these two sentences,
> but got bogged down in the unclear terminology that followed.
>
> Mockingbird seems to be unaware that the lunar calendar piggy backs on
> the solar calendar and that the scheduling of the tabular lunar months
> and the tabular conjunctions does depend on the scheduling of the solar
> year. If the solar year is a day late, so are the lunar months (which
> Mockingbird refers to as Tabular lunations or lunations). Therefore the
> difference between a fixed date and an annual event such as an equinox
> is of consequence to the lunar calendar. It does affect the difference
> between the beginning of a lunar month and a mean or true conjunction.
> So the jitter is transmitted.
>
> Such a transmission does not occur completely, if there is any
> correlation between the leap years in the solar calendar and the
> corrections in the lunar calendar. The corrections in the lunar calendar
> include the saltus lunae corrections, but these follow a strict 19-year
> cycle so have no correlation with the leap years and so only the
> correlations of corrections to the 19-year cycle need be considered. The
> examples of the uniform corrections systems that Mockingbird provided do
> have considerable correlation. This results in only a partial
> transmission of the jitter and can make it appear that no transmission
> occurs at all.
>
> We do not seem to know which uniform correction computus was proposed by
> Lichtenberg. It may have been one that has the 43 correction centuries
> spaced as evenly as possible. If so, the correlation would be low (but
> never completely absent) and so transmission of jitter would be evident.
>
> Also I want to make it clear that the jitter that is transmitted if the
> motion of a mean equinox placed exactly once every mean calendar year
> and (beginning of day) March 21 in the solar calendar. This is only
> slightly different from the jitter defined by Mockingbird above.
>
> Karl
>
> 10(07(01
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:CALNDR-L@...] On Behalf Of Tom Peters
> Sent: 20 March 2009 00:20
> To: CALNDR-L@...
> Subject: Re: Gregorian calendar jitter and lunar calendar in Wikipedia
> computus
>
> Op 19-mrt-2009, om 16:26 heeft Palmen, KEV (Karl) het volgende
> geschreven:
>
> > Dear Tom and Calendar People
> >
> > I've found a weakness that occurs in EVERY uniform correction
> > system. It
> > is three consecutive common century years with only one correction.
> > The
> > Gregorian System makes at least two corrections in any three
> > consecutive
> > common century years.
> > This causes the minimum number of days in 11 consecutive Metonic
> > cycles
> > (of 235 lunar months equal to 19 lunisolar years) to be one less than
> > for the Gregorian system.
> >
>
> Karl,
> thank you for your investigations. I do not have the time now to
> study this issue as thorough as is necessary. Maybe at some later time.
>
> --
> Tom Peters
>
> --
> Scanned by iCritical.
>

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