Gregorian calendar jitter and lunar calendar in Wikipedia computus

[Tom Peters-6]

Joe Kress and others:
I noticed that in the Wikipedia article on the computus (http://
en.wikipedia.org/wiki/Computus), at some time the explanation has  
been removed how the use of a separate solar and lunar  
"equation" (=correction) prevents introducing the jitter in the  
Gregorian solar calendar into its lunar calendar.  Is that  
intentional?  I make a point of it because some years ago Heiner  
Lichtenberg published some papers on the Lilius lunar calendar, in  
which he promotes the idea that the calendar could be simplified/
improved by distributing the net 43 corrections evenly; which is not  
a bright idea as explained in the deleted paragraph.

--
Tom Peters

[Joe Kress]

Tom:

 

According to the history of Computus, the jitter explanation was removed by Mockingbird0 on 30 October 2008 without explanation. 

 

Joe Kress

On Sun, Mar 8, 2009 at 10:02 AM, Tom Peters <tpeters@...> wrote:

Joe Kress and others:
I noticed that in the Wikipedia article on the computus (http://en.wikipedia.org/wiki/Computus), at some time the explanation has been removed how the use of a separate solar and lunar "equation" (=correction) prevents introducing the jitter in the Gregorian solar calendar into its lunar calendar.  Is that intentional?  I make a point of it because some years ago Heiner Lichtenberg published some papers on the Lilius lunar calendar, in which he promotes the idea that the calendar could be simplified/improved by distributing the net 43 corrections evenly; which is not a bright idea as explained in the deleted paragraph.

--
Tom Peters

[Karl Palmen]

Dear Tom, Joe and Other Calendar People

I've added something to the talk page of Computus. You may wish to
continue the discussion there at
http://en.wikipedia.org/wiki/Talk:Computus#Unified_system_of_corrections
.

Karl

10(06(20

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 08 March 2009 14:02
To: CALNDR-L@...
Subject: Gregorian calendar jitter and lunar calendar in Wikipedia
computus

Joe Kress and others:
I noticed that in the Wikipedia article on the computus (http://
en.wikipedia.org/wiki/Computus), at some time the explanation has  
been removed how the use of a separate solar and lunar  
"equation" (=correction) prevents introducing the jitter in the  
Gregorian solar calendar into its lunar calendar.  Is that  
intentional?  I make a point of it because some years ago Heiner  
Lichtenberg published some papers on the Lilius lunar calendar, in  
which he promotes the idea that the calendar could be simplified/
improved by distributing the net 43 corrections evenly; which is not  
a bright idea as explained in the deleted paragraph.

--
Tom Peters

--
Scanned by iCritical.

[Karl Palmen]

Dear Tom and Calendar People

Putting aside the issue of short-term accuracy, I notice that the 43
corrections in 100 centuries normally follow a 7-century cycle of 3
corrections and once every 14 of these seven-century cycles and a two
century period with once correction is inserted.

Now I look at which of these cycles have exactly the same mean moon
phase as the Gregorian cycle. The Gregorian cycle is symmetrical about
years 1600, 6600, 11600 etc. There are two of the above-mentioned
43-correction cycles that have the same symmetry one of which can be
given exactly the same mean moon phase as the Gregorian.

One of these have corrections at
1400 1600 1800  
2100 2300 2600
2800 3000 3200
3500 3700 3900
and so on every 700 years until
6300 6500 6700 6900
7200 7400 7600
7900 8100 8300
and so on every 700 years to 11400.

The other has corrections at
1300 1500 1700 1900
2200 2400 2600
2900 3100 3300
And so one every 700 years to 11300.

The years (1800, 2100, 2300 and 2600) that Mockingbird picked for his
example belong to the first of these two cycles.
However it has a correction in the symmetry year 1600 in which the
Gregorian has no correction. So it's the other cycle that has the same
mean moon phase as the Gregorian.

This other 43-correction cycle agrees with Gregorian from its start
(1583 or year 900 proleptic) until year 2300. Then 2300-2399 is a day
ahead and 2400-2499 is a day behind then there is no more disagreement
till year 3300. I expect disagreements to become more frequent in later
years.

I notice that the Gregorian and 43-correction cycle almost repeat once
every 28 centuries. The only differences after 28 centuries is one
Gregorian lunar correction per cycle of 8 in 25 centuries is a century
late and four corrections in the 43-correction cycle are a century early
. This suggests 28 centuries could be a good period to do comparisons
over rather than just 800 years or the whole 10,000 years.

Karl

10(06(22




-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 08 March 2009 14:02
To: CALNDR-L@...
Subject: Gregorian calendar jitter and lunar calendar in Wikipedia
computus

Joe Kress and others:
I noticed that in the Wikipedia article on the computus (http://
en.wikipedia.org/wiki/Computus), at some time the explanation has  
been removed how the use of a separate solar and lunar  
"equation" (=correction) prevents introducing the jitter in the  
Gregorian solar calendar into its lunar calendar.  Is that  
intentional?  I make a point of it because some years ago Heiner  
Lichtenberg published some papers on the Lilius lunar calendar, in  
which he promotes the idea that the calendar could be simplified/
improved by distributing the net 43 corrections evenly; which is not  
a bright idea as explained in the deleted paragraph.

--
Tom Peters

--
Scanned by iCritical.

[Karl Palmen]

Dear Tom and Calendar People

Actually proving that an arbitrary uniform correction system (of 43
corrections per 100 centuries) has worse lunar jitter than the Gregorian
computus is not simple and might not be possible.

Perhaps we could find out what Lichtenburg's proposal was.

I've already identified one weak point of a uniform correction system,
which is a leap century year with a correction. This enables a period of
235 lunar months and 19 lunisolar years to have 6941 days which is one
more than maximum of 6940 that can occur in the Gregorian computus.
Mockingbird has pointed out that a uniform correction system need not
have any of its corrections on a leap century year.

I've since identified another weak point of a uniform correction system.
It is two consecutive common century years with no correction. This
leads to six consecutive periods of 235 lunar month and of 19 lunisolar
years having one day less than the minimum that can occur in the
Gregorian computus.

However it is possible to create a uniform correction system free of
both these weaknesses. If there is just one correction between two leap
century years, place it half way in between.

One such system could be defined by starting with the Gregorian and
postponing by one century each lunar equation correction that occurs on
a leap century year. This would differ from Gregorian for 8% of
centuries. However the sequence of corrections would be so complicated
as to have no advantage in simplicity over Gregorian.

Another could be to have corrections on years

0100 0300
0600
0900 1100 1300 1500 1700 1900
2200
2500 2700 2900 3100
3400
3700 3900 4100 4300 4500 4700
5000
5300 5500 5700 5900 6100 6300
6600
6900 7100 7300 7500
7800
8100 8300 8500 8700 8900 9100
9400
9700 9900
and so in every 10,000 years.

To get the same mean moon phase as Gregorian, postpone the cycle by 1600
years.

Karl

10(06(23

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 08 March 2009 14:02
To: CALNDR-L@...
Subject: Gregorian calendar jitter and lunar calendar in Wikipedia
computus

Joe Kress and others:
I noticed that in the Wikipedia article on the computus (http://
en.wikipedia.org/wiki/Computus), at some time the explanation has  
been removed how the use of a separate solar and lunar  
"equation" (=correction) prevents introducing the jitter in the  
Gregorian solar calendar into its lunar calendar.  Is that  
intentional?  I make a point of it because some years ago Heiner  
Lichtenberg published some papers on the Lilius lunar calendar, in  
which he promotes the idea that the calendar could be simplified/
improved by distributing the net 43 corrections evenly; which is not  
a bright idea as explained in the deleted paragraph.

--
Tom Peters

--
Scanned by iCritical.

[Karl Palmen]

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

10(06(23

-----Original Message-----
From: Palmen, KEV (Karl)
Sent: 19 March 2009 13:35
To: 'East Carolina University Calendar discussion List'
Subject: RE: Gregorian calendar jitter and lunar calendar in Wikipedia
computus

Dear Tom and Calendar People

Actually proving that an arbitrary uniform correction system (of 43
corrections per 100 centuries) has worse lunar jitter than the Gregorian
computus is not simple and might not be possible.

Perhaps we could find out what Lichtenburg's proposal was.

I've already identified one weak point of a uniform correction system,
which is a leap century year with a correction. This enables a period of
235 lunar months and 19 lunisolar years to have 6941 days which is one
more than maximum of 6940 that can occur in the Gregorian computus.
Mockingbird has pointed out that a uniform correction system need not
have any of its corrections on a leap century year.

I've since identified another weak point of a uniform correction system.
It is two consecutive common century years with no correction. This
leads to six consecutive periods of 235 lunar month and of 19 lunisolar
years having one day less than the minimum that can occur in the
Gregorian computus.

However it is possible to create a uniform correction system free of
both these weaknesses. If there is just one correction between two leap
century years, place it half way in between.

One such system could be defined by starting with the Gregorian and
postponing by one century each lunar equation correction that occurs on
a leap century year. This would differ from Gregorian for 8% of
centuries. However the sequence of corrections would be so complicated
as to have no advantage in simplicity over Gregorian.

Another could be to have corrections on years

0100 0300
0600
0900 1100 1300 1500 1700 1900
2200
2500 2700 2900 3100
3400
3700 3900 4100 4300 4500 4700
5000
5300 5500 5700 5900 6100 6300
6600
6900 7100 7300 7500
7800
8100 8300 8500 8700 8900 9100
9400
9700 9900
and so in every 10,000 years.

To get the same mean moon phase as Gregorian, postpone the cycle by 1600
years.

Karl

10(06(23

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 08 March 2009 14:02
To: CALNDR-L@...
Subject: Gregorian calendar jitter and lunar calendar in Wikipedia
computus

Joe Kress and others:
I noticed that in the Wikipedia article on the computus (http://
en.wikipedia.org/wiki/Computus), at some time the explanation has  
been removed how the use of a separate solar and lunar  
"equation" (=correction) prevents introducing the jitter in the  
Gregorian solar calendar into its lunar calendar.  Is that  
intentional?  I make a point of it because some years ago Heiner  
Lichtenberg published some papers on the Lilius lunar calendar, in  
which he promotes the idea that the calendar could be simplified/
improved by distributing the net 43 corrections evenly; which is not  
a bright idea as explained in the deleted paragraph.

--
Tom Peters

--
Scanned by iCritical.

[Tom Peters-6]

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

[Karl Palmen]

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.

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

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

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 28 March 2009 01:06
To: CALNDR-L@...
Subject: Metonic-Lunar cycle RE: Gregorian calendar jitter and lunar calendar in Wikipedia computus

 

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 

(MJD 2454919)/1361+D-097W13-05 (G. Friday, 2009 March 27H21:08 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 1(201)675-8548 (M)
001(201)962-3708(R)



 

> 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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---

Scanned by iCritical.

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Brij and Calendar People

 

A look at the attachment shows that Brij has based his supposed Harappan Calendar on a leap week calendar year of 364 days resulting in a lunar year of just 352 days from skipping the 13^th day of each month.  A twelve month lunar year needs 354 or 355 days. I doubt that the Harappan used such a calendar (with a 352-day lunar year). The Hebrew Calendar has a postponement rule whose purpose is to prevent to occurrence of a 352-day year.

 

Karl

 

10(07(05

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 28 March 2009 01:06
To: CALNDR-L@...
Subject: Metonic-Lunar cycle RE: Gregorian calendar jitter and lunar calendar in Wikipedia computus

 

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 

(MJD 2454919)/1361+D-097W13-05 (G. Friday, 2009 March 27H21:08 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 1(201)675-8548 (M)
001(201)962-3708(R)



 

> 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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[Tom Peters-6]

Op 26-mrt-2009, om 14:53 heeft Palmen, KEV (Karl) het volgende  
geschreven:

> 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.

Lichtenberg claims that the Gregorian calendar has adjustable  
parameters.  Apparently the central formulae of his 2003 paper are:

(4) a[trop] = (1461/4 - s/(100*P)) d
(5) m[syn] = a[trop]/(235/19 - e/(3000*Q))

where s=3, P=4, e=43, Q=100 for the current version of the Gregorian  
calendar.

I think that this means that he distributes the net 43 epact  
corrections evenly over 10000 years.

In any case, I think he is misguided on many aspects.
--
Tom Peters

[Karl Palmen]

Dear Tom and Calendar People

Thank you Tom for your reply.

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 30 March 2009 21:37
To: CALNDR-L@...
Subject: Re: Gregorian calendar jitter and lunar calendar in Wikipedia
computus

Op 26-mrt-2009, om 14:53 heeft Palmen, KEV (Karl) het volgende  
geschreven:

> 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.

Lichtenberg claims that the Gregorian calendar has adjustable  
parameters.  Apparently the central formulae of his 2003 paper are:

(4) a[trop] = (1461/4 - s/(100*P)) d
(5) m[syn] = a[trop]/(235/19 - e/(3000*Q))

where s=3, P=4, e=43, Q=100 for the current version of the Gregorian  
calendar.

I think that this means that he distributes the net 43 epact  
corrections evenly over 10000 years

KARL SAYS: They look like formulae for the mean calendar year and lunar
month. The d in the mean year formula is a day. I'd not take this alone
as evidence of even distribution of the net 43 epact corrections.
However the idea of changing the 43 to some other value does hint of a
uniform correction computus.

Not placing the corrections on the century years would allow even more
solar jitter to be transmitted to the lunar calendar.

I've produced a spreadsheet for variations of the Gregorian Calendar and
it's computus. It is at http://www.the-light.com/cal/LuniGreg1.xls The
four parameters are Sn, Sd, Ln and Ld. For the Gregorian Calendar and
Computus they are Sn=3, Sd=4, Ln=8, Ld=25. Sd is the number of centuries
in the solar calendar cycle, Sn is the number of common century years in
the solar calendar cycle. Ld is the number of centuries in the lunar
equation cycle and Ln is the number of lunar equation corrections in the
lunar equation cycle. I make e = 100*(Sn/Sd - Ln/Ld).

Karl

10(07(05 till noon


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[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Brij and Calendar People

 

Brij claims that the calendar he showed is based on the tithi of 2/59 lunar month equated to 966/965 days, giving a mean month of 29.530569948 days. I see no evidence of this.

 

What would a calendar based on this Vij tithi look like?

It could have every 138^th Sunday made into a phantom day without its own date in the calendar. This would provide 965 dates every 966 days and so make each date correspond to a Vij tithi.

 

The lunar calendar would simply have months that alternate between 29 and 30 dates not counting any phantom day.

 

A year of 365.2422 days would have 364.8641 Vij tithis, so the solar calendar would have a mean year about 364.8641 dates. So most years could have 365 dates, while a minority of short years have 364 dates.

If 5 out of 38 years are short, then a 19-year Metonic cycle would result and the mean year would be 365.24652 days.

If 5 out of 37 years are short, then a 2183-year cycle of 27,000 months would result and the mean year would be 365.242963 days.

If 3 out of 22 years are short, then a 649-year cycle of 8027 months would result and the mean year would be 365.241773 days.

If 11 out of 81 years are short, then a 4779-year cycle of 59,108 months would result and the mean year would be 365.242295 days.

 

Note that a solar year has one average 10.8641 more dates than a lunar year of 12 months which has exactly 354 Vij tithis. This difference is not 12.

 

Karl

 

10(07(06

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 28 March 2009 01:06
To: CALNDR-L@...
Subject: Metonic-Lunar cycle RE: Gregorian calendar jitter and lunar calendar in Wikipedia computus

 

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 

(MJD 2454919)/1361+D-097W13-05 (G. Friday, 2009 March 27H21:08 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 1(201)675-8548 (M)
001(201)962-3708(R)

 

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[Karl Palmen]

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Dear Brij and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 31 March 2009 20:23
To: CALNDR-L@...
Subject: Harappan Links RE: A Vij Tithi Calendar RE: Metonic-Lunar cycle RE: ...

 

Karl, Tom Peters & list, sirs:

> Brij claims that the calendar he showed is based on the tithi of 2/59 lunar month equated to 966/965 days, giving a mean month of 29.530569948 days. I see no evidence of this.

 This is NOT a claim but a possibility that I expressed of ‘Harappan knowledge’ of using Luni-Solar compromise for their ‘panchangs, if they had any’. 

It’s a claim that Brij makes about the calendar that he showed in his attachment regardless of whether it was used by the Harappan.

                                                                                                      

> The lunar calendar would simply have months that alternate between 29 and 30 dates not counting any phantom day

Yes, sir. The format was intended to present a calendar with NEVER a date/Tithi with 13^th (as a number). No religious sentiments.

I was writing about a lunar calendar that does use the his tithi, by making every 138^th  Sunday an phantom day.

                 

>  Note that a solar year has one average 10.8641 more dates than a lunar year of 12 months which has exactly 354 Vij tithis. This difference is not 12.

 It was intended to point the ease that 12 lunation make ‘exactly 354 V-tithi’, as you would note (12*29.53058881= 354.36706572)/(138W/965) = 354.00022611 Tithi. The 12 ‘missing 13^th ‘s are TITHIS’s carried over to the next *civil year* as it happen now during 19-year cycle with 235 lunation (5*47-lunar months) and ONE additional lunation once every 138Weeks i.e. 2.654 years  during  1^st,3^rd ,5^th ,8^th,11^th ,13^th, 16^th  & 19^th /1^st – years of 19-year (6939.601603725839 days) cycle. This may NOT be the Indus people calculation BUT 47-lunation could have the groupings of 138-days i.e. 50 such groups during 19-years, leaving 40-days for ONE ‘added lunation’. However!

I was making the point that taking all 12 13ths from the 12 months of a solar year would make the year shorter than the 354 tithis. Brij cannot claim both that the year is both 12 days  or tithis shorter than a solar year and is also equal to 12 lunar months (of 364 tithis).  The difference is 10.8641 tithis or 10.8753 days. There’s more about this later on.

 

A 19-year cycle of 235 lunar months has 6932.5 tithis and so has one intercalary month once every 990 5/14  tithis on average. This about 25 tithis more than the 965 in 138 weeks. This 25-tithi difference would accumulate to almost half a year over one 19-year cycle.

Brij has noted that fifty cycles of 138 days is 40 days short of a long Metonic cycle of 6940 days and has tried to take advantage of this. More important is that 49 cycles of 138 days equal seven cycles of 138 weeks = 965 tithis is 177.5 tithis short of a Metonic cycle. The 50^th period of 138 days reduces this by 137 6/7 tithis to 39 5/14 tithis.

 

 

> A look at the attachment shows that Brij has based his supposed Harappan Calendar on a leap week calendar year of 364 days resulting in a lunar year of just 352 days…..

No, sir. The year that is shown starts at Gregorian YEAR 2005 April 10^th and removing 13^th date from each month would make the year of [12*29.5+12 days] 353/354-days and NOT 352 days.  I counted only 364 days in the attachment not a full Gregorian year of 365 days. Even if it were a full Gregorian year the resulting lunar year would have only 353 days, which is over a day or tithi  short of the 354.3668 days = 354 tithis.

 

Adding 12-Tithis would make the Gregorian Year!

No it would not!

The mean Gregorian year has 365.2425*965/966 = 364.8644… tithis, which is just 10.8644… tithis more than 354 tithis.

 

The point I made was that it reconcile along the duration of lunar year for taking advantage to make luni-solar calendar, such as:  

896-year cycle= (12*19)+1+(12*19)+1+(11*19)+1+(12*19). The 229^th year being the year for adjustment of ‘± Epact left over’. This had been pointed in my earlier mails.

I do not believe that Brij has a workable suggestion here.

 

Likewise, in 834-year cycle= (12*19)+75+(12*19)+75+(12*19), when ‘Epact adjustment’ is suggested during 16^th cycle of 19-years.

I do not believe that Brij has a workable suggestion here.

 

> This implies that the Harappan people anticipated the Julian calendar with its irregular months before it was invented.                                                                            

The point I intend making is “Harappan people possibly had the knowledge” and Meton & Metonic cycle were a later names given with the invention of Julian calendar; like my impressions about physical dimensions of Great-Bath at Mohenjo-Daro!

They would not have known the precise numbers of days in the various Julian Calendar months as defined by Julius Caesar, who lived much later.

                                                                         

My ‘claim, if any’ thus remain to the extant that Indus civilization had the knowhow/knowledge that remain far in EXCESS of our current knowledge & development in Mathematics & Astronomy that present generations talk *pending* decipherment of Indus script

If this were so, I’d expect that used a more sensible calendar than what Brij has suggested.

 

Perhaps, they had a solar calendar with months alternating between 30 and 31 days, with the last month shortened to 30 days in a 365-day year. The lunar calendar has the 13^th day removed from every month of the year except one month of 30 days during the winter. Over a 19-year cycle six months of 30 days and one month of 29 days were added to the lunar years. No tithis would be used in this.

 

If Brij is really interested in calendars that use his tithi of 966/965 day = 2/59 lunar month, he should consider my suggestions below.

A mean year of 364 33/38 tithis would give a 19-year cycle and a mean year of 364 70/81 tithis would be close to a tropical year.

 

Karl

 

10(07(07
 

---

Date: Tue, 31 Mar 2009 12:44:59 +0100
From: karl.palmen@...
Subject: A Vij Tithi Calendar RE: Metonic-Lunar cycle RE: ...
To: CALNDR-L@...

Dear Brij and Calendar People

 

Brij claims that the calendar he showed is based on the tithi of 2/59 lunar month equated to 966/965 days, giving a mean month of 29.530569948 days. I see no evidence of this.

 

What would a calendar based on this Vij tithi look like?

It could have every 138^th Sunday made into a phantom day without its own date in the calendar. This would provide 965 dates every 966 days and so make each date correspond to a Vij tithi.

 

The lunar calendar would simply have months that alternate between 29 and 30 dates not counting any phantom day.

 

A year of 365.2422 days would have 364.8641 Vij tithis, so the solar calendar would have a mean year about 364.8641 dates. So most years could have 365 dates, while a minority of short years have 364 dates.

If 5 out of 38 years are short, then a 19-year Metonic cycle would result and the mean year would be 365.24652 days.

If 5 out of 37 years are short, then a 2183-year cycle of 27,000 months would result and the mean year would be 365.242963 days.

If 3 out of 22 years are short, then a 649-year cycle of 8027 months would result and the mean year would be 365.241773 days.

If 11 out of 81 years are short, then a 4779-year cycle of 59,108 months would result and the mean year would be 365.242295 days.

 

Note that a solar year has one average 10.8641 more dates than a lunar year of 12 months which has exactly 354 Vij tithis. This difference is not 12.

 

Karl

 

10(07(06

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 28 March 2009 01:06
To: CALNDR-L@...
Subject: Metonic-Lunar cycle RE: Gregorian calendar jitter and lunar calendar in Wikipedia computus

 

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 

(MJD 2454919)/1361+D-097W13-05 (G. Friday, 2009 March 27H21:08 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 1(201)675-8548 (M)
001(201)962-3708(R)

 

 

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[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Brij and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 01 April 2009 22:42
To: CALNDR-L@...
Subject: 9405-year cycle RE: Harappan Links RE: A Vij Tithi Calendar RE: Metonic-Lunar cycle RE: ...

 

Karl, sir:
>Perhaps, they had a solar calendar with months alternating between 30 and 31 days, with the last month shortened to 30 days in a 365-day year. The lunar calendar has the 13^th day removed from every month of the year except one month of 30 days during the winter. Over a 19-year cycle six months of 30 days and one month of 29 days were added to the lunar years. No tithis would be used in this.
I thank you for this and your opinion of 834-year cycle that is closest to 'Mean Year' of tropical year.

 

I write to Brij in private to tell him that I discovered that three 834-year cycles each with 148 leap weeks have a whole number (946) of 138-week periods so is a whole number (912890) of Vij tithis of 966/965 days each..

 

 I have some logged up info that make me send the attachment. I do feel sorry since my Home Page 'uploading link' has vanished and I am stuck to update my documents. My appology for this!
It is my belief that the attachment shall prove fruitful in your considered thoughts, and the Era of 9405-year cycle that we discussed long ago.

 

The attachment contain numerous ideas from Brij, but no coherent calendar.

 

It includes a lunar calendar that consists of a solar calendar (similar to the World Calendar), but with the 13^th day removed from every month.

There are two or three  interruptions to the seven day week in this lunar year

 

Thursday 31 March followed by Monday 1 April (Wow that will be popular! L)

Wednesday 30 June followed by leap day followed by Thursday 1 July in a leap year,

Thursday 30 December followed by World day followed by Monday 1 January.

 

The attachment states when the seven leap months would be placed

 

3rd year – 7th month (July) of cycle

6th year – 4th month (April) of cycle

8th year – 12th month(December) of cycle

11th year– 9th month (September)of cycle

14th year – 5th month (May) of cycle

17th year – 2nd month (February) of cycle

19th year – 10th month (October) of cycle

 

The intervals are 33, 32, 33, 32, 33, 32 and 33 months excluding the leap months. So they are spaced as evenly as possible. The attachment does not state how many days these leap months have.

 

If the year that the 13^th days are omitted from is a solar year, then the number of days in the  leap months must equal the number of 13^th days omitted from the other months. If all 12 non-leap months have a 13^th day omitted, then these seven leap months need to have 228 days in total and so 32 4/7 days on average. Indeed the number of days in a leap month can  be equal to the number of non-leap months since the previous leap month.

 

Suppose the 2^nd month (February) does not have its 13^th day removed, then six of the leap months can have 30 days and one 29 days. If the leap months are placed AFTER each of the seven months shown above and the 29-day leap month is the one placed after the 5^th month of the 14^th year, then each leap month has as many days as 13^th days omitted between it and the previous leap month.

 

 

Brij states that the calendar uses his Tithi of 2/59 lunar month = 966/965 days but does not show how this is done in the above-mentioned calendar. I have stated that making every 138^th Sunday into a phantom day is a possible way of implementing this tithi. This would fit in fairly well with Brij’s 834-year leap week cycle, three of which have a whole number (946) of 138-week periods.

 

 

Brij states that his 9405-year cycle has 3556 periods of 138 weeks. This is one week less that the 490729 weeks that he says the period contains. The period with either 490729 or 490728 weeks does not contain a multiple of 12053 days so is not a multiple of the 33-year cycle as claimed. However 490729 weeks and two days is exactly 285 33-year cycles.  So we do not have a consistent cycle. Also it does not have a whole number of lunar months, but is almost one and a half lunar months short of 9405*235/19 = 116325 lunar months.

 

 If Brij is really interested in finding a lunisolar cycle that is a multiple of the 33-year cycle, he could look at http://www.the-light.com/cal/Lunisolar33.html of http://www.the-light.com/cal/kp_Lunisolar_xls.html . Perhaps,  Brij could consider a 3234-year cycle with 39,999 months and also 574 leap weeks or even a 4950-year cycle of 1823 leap months J.

 

 

Karl

 

10(07(08

 

 

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[Karl Palmen]

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Dear Brij and Calendar People

 

Brij said in his attachment

The only cycle that has whole number of 15*19*33-year cycles and can satisfy ratio Tithi norm of 138W/965 is that of − 9405-years

 

Actually, it does not satisfy Tithi norm of 138W/965, if what is meant by this is that it has a whole number of tithis. This requires it to be a multiple of 138 weeks. The only multiples of the 33-year cycles that are a multiple of 138 weeks are a multiples of 966*33 = 31,878 years. However only three 834-year cycles are a multiple  of 138 weeks.

 

Also (and I think I may have pointed this out before), the 9405-year cycle is not the smallest cycle that is a multiple of 33, 15 and 19 years. 33 and 15 have a common divisor of 3, hence one third of a 9405-year cycle is a multiple of 33, 15 and 19 years. This is a 3135-year cycle, which has 1,145,035 days. I think Brij may have chosen 9405 in preference to 3135, because it is just 9 days more than a multiple of 138 weeks.

 

Karl

 

10(07(08

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 01 April 2009 22:42
To: CALNDR-L@...
Subject: 9405-year cycle RE: Harappan Links RE: A Vij Tithi Calendar RE: Metonic-Lunar cycle RE: ...

 

Karl, sir:
>Perhaps, they had a solar calendar with months alternating between 30 and 31 days, with the last month shortened to 30 days in a 365->day year. The lunar calendar has the 13^th day removed from every month of the year except one month of 30 days during the winter. >Over a 19-year cycle six months of 30 days and one month of 29 days were added to the lunar years. No tithis would be used in this.
I thank you for this and your opinion of 834-year cycle that is closest to 'Mean Year' of tropical year. I have some logged up info that make me send the attachment. I do feel sorry since my Home Page 'uploading link' has vanished and I am stuck to update my documents. My appology for this!
It is my belief that the attachment shall prove fruitful in your considered thoughts, and the Era of 9405-year cycle that we discussed long ago.
Regards, 
Brij Bhushan Vij 

(MJD 2454924)/1361+D-102W14-03 (G. Wednesday, 2009 April 01H17:69 (decimal) EST
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda
Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30
Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30
(365th day of Year is World Day)
My Profile:http://www.brijvij.com/bbv_2col-vipBrief.pdf
HOME PAGE: http://www.brijvij.com/
******As per Kali V-GRhymeCalendaar*****
"Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai"
Contact # 1(201)675-8548 (M)
001(201)962-3708 (R)



 

---

Date: Wed, 1 Apr 2009 12:47:28 +0100
From: karl.palmen@...
Subject: Re: Harappan Links RE: A Vij Tithi Calendar RE: Metonic-Lunar cycle RE: ...
To: CALNDR-L@...

Dear Brij and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 31 March 2009 20:23
To: CALNDR-L@...
Subject: Harappan Links RE: A Vij Tithi Calendar RE: Metonic-Lunar cycle RE: ...

 

Karl, Tom Peters & list, sirs:

> Brij claims that the calendar he showed is based on the tithi of 2/59 lunar month equated to 966/965 days, giving a mean month of 29.530569948 days. I see no evidence of this.

 This is NOT a claim but a possibility that I expressed of ‘Harappan knowledge’ of using Luni-Solar compromise for their ‘panchangs, if they had any’. 

It’s a claim that Brij makes about the calendar that he showed in his attachment regardless of whether it was used by the Harappan.

                                                                                                      

> The lunar calendar would simply have months that alternate between 29 and 30 dates not counting any phantom day

Yes, sir. The format was intended to present a calendar with NEVER a date/Tithi with 13^th (as a number). No religious sentiments.

I was writing about a lunar calendar that does use the his tithi, by making every 138^th  Sunday an phantom day.

                 

>  Note that a solar year has one average 10.8641 more dates than a lunar year of 12 months which has exactly 354 Vij tithis. This difference is not 12.

 It was intended to point the ease that 12 lunation make ‘exactly 354 V-tithi’, as you would note (12*29.53058881= 354.36706572)/(138W/965) = 354.00022611 Tithi. The 12 ‘missing 13^th ‘s are TITHIS’s carried over to the next *civil year* as it happen now during 19-year cycle with 235 lunation (5*47-lunar months) and ONE additional lunation once every 138Weeks i.e. 2.654 years  during  1^st,3^rd ,5^th ,8^th,11^th ,13^th, 16^th  & 19^th /1^st – years of 19-year (6939.601603725839 days) cycle. This may NOT be the Indus people calculation BUT 47-lunation could have the groupings of 138-days i.e. 50 such groups during 19-years, leaving 40-days for ONE ‘added lunation’. However!

I was making the point that taking all 12 13ths from the 12 months of a solar year would make the year shorter than the 354 tithis. Brij cannot claim both that the year is both 12 days  or tithis shorter than a solar year and is also equal to 12 lunar months (of 364 tithis).  The difference is 10.8641 tithis or 10.8753 days. There’s more about this later on.

 

A 19-year cycle of 235 lunar months has 6932.5 tithis and so has one intercalary month once every 990 5/14  tithis on average. This about 25 tithis more than the 965 in 138 weeks. This 25-tithi difference would accumulate to almost half a year over one 19-year cycle.

Brij has noted that fifty cycles of 138 days is 40 days short of a long Metonic cycle of 6940 days and has tried to take advantage of this. More important is that 49 cycles of 138 days equal seven cycles of 138 weeks = 965 tithis is 177.5 tithis short of a Metonic cycle. The 50^th period of 138 days reduces this by 137 6/7 tithis to 39 5/14 tithis.

 

 

> A look at the attachment shows that Brij has based his supposed Harappan Calendar on a leap week calendar year of 364 days resulting in a lunar year of just 352 days…..

No, sir. The year that is shown starts at Gregorian YEAR 2005 April 10^th and removing 13^th date from each month would make the year of [12*29.5+12 days] 353/354-days and NOT 352 days.  I counted only 364 days in the attachment not a full Gregorian year of 365 days. Even if it were a full Gregorian year the resulting lunar year would have only 353 days, which is over a day or tithi  short of the 354.3668 days = 354 tithis.

 

Adding 12-Tithis would make the Gregorian Year!

No it would not!

The mean Gregorian year has 365.2425*965/966 = 364.8644… tithis, which is just 10.8644… tithis more than 354 tithis.

 

The point I made was that it reconcile along the duration of lunar year for taking advantage to make luni-solar calendar, such as:  

896-year cycle= (12*19)+1+(12*19)+1+(11*19)+1+(12*19). The 229^th year being the year for adjustment of ‘± Epact left over’. This had been pointed in my earlier mails.

I do not believe that Brij has a workable suggestion here.

 

Likewise, in 834-year cycle= (12*19)+75+(12*19)+75+(12*19), when ‘Epact adjustment’ is suggested during 16^th cycle of 19-years.

I do not believe that Brij has a workable suggestion here.

 

> This implies that the Harappan people anticipated the Julian calendar with its irregular months before it was invented.                                                                            

The point I intend making is “Harappan people possibly had the knowledge” and Meton & Metonic cycle were a later names given with the invention of Julian calendar; like my impressions about physical dimensions of Great-Bath at Mohenjo-Daro!

They would not have known the precise numbers of days in the various Julian Calendar months as defined by Julius Caesar, who lived much later.

                                                                         

My ‘claim, if any’ thus remain to the extant that Indus civilization had the knowhow/knowledge that remain far in EXCESS of our current knowledge & development in Mathematics & Astronomy that present generations talk *pending* decipherment of Indus script

If this were so, I’d expect that used a more sensible calendar than what Brij has suggested.

 

Perhaps, they had a solar calendar with months alternating between 30 and 31 days, with the last month shortened to 30 days in a 365-day year. The lunar calendar has the 13^th day removed from every month of the year except one month of 30 days during the winter. Over a 19-year cycle six months of 30 days and one month of 29 days were added to the lunar years. No tithis would be used in this.

 

If Brij is really interested in calendars that use his tithi of 966/965 day = 2/59 lunar month, he should consider my suggestions below.

A mean year of 364 33/38 tithis would give a 19-year cycle and a mean year of 364 70/81 tithis would be close to a tropical year.

 

Karl

 

10(07(07
 

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Date: Tue, 31 Mar 2009 12:44:59 +0100
From: karl.palmen@...
Subject: A Vij Tithi Calendar RE: Metonic-Lunar cycle RE: ...
To: CALNDR-L@...

Dear Brij and Calendar People

 

Brij claims that the calendar he showed is based on the tithi of 2/59 lunar month equated to 966/965 days, giving a mean month of 29.530569948 days. I see no evidence of this.

 

What would a calendar based on this Vij tithi look like?

It could have every 138^th Sunday made into a phantom day without its own date in the calendar. This would provide 965 dates every 966 days and so make each date correspond to a Vij tithi.

 

The lunar calendar would simply have months that alternate between 29 and 30 dates not counting any phantom day.

 

A year of 365.2422 days would have 364.8641 Vij tithis, so the solar calendar would have a mean year about 364.8641 dates. So most years could have 365 dates, while a minority of short years have 364 dates.

If 5 out of 38 years are short, then a 19-year Metonic cycle would result and the mean year would be 365.24652 days.

If 5 out of 37 years are short, then a 2183-year cycle of 27,000 months would result and the mean year would be 365.242963 days.

If 3 out of 22 years are short, then a 649-year cycle of 8027 months would result and the mean year would be 365.241773 days.

If 11 out of 81 years are short, then a 4779-year cycle of 59,108 months would result and the mean year would be 365.242295 days.

 

Note that a solar year has one average 10.8641 more dates than a lunar year of 12 months which has exactly 354 Vij tithis. This difference is not 12.

 

Karl

 

10(07(06

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 28 March 2009 01:06
To: CALNDR-L@...
Subject: Metonic-Lunar cycle RE: Gregorian calendar jitter and lunar calendar in Wikipedia computus

 

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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