Mean Year of 353-year lunisolar cycle

[Helios]

I've found one more lunisolar cycle made up of the same repetition of one lunar calendar cycle listed in
Karl P,'s "Lunar Calendar Cycles less than 1885 Months"

This is the case of the 43 yerm era with 703 months with
mean month = 29 & 373 / 703 days
that factors into
-----------------------------------

6707 years = ( 2*59 )*2*2*2*3*5*173 = 82954 months

-----------------------------------
This is 19 repeats of the 353-year cycle of 4366 months. This scheme allows us to write

mean year of 353-year cycle = 365 & 1625 / 6707 days

mean year of 3-year cycle = 364 & 4 / 19 days

I think the 3-year cycle's new year drifts through the seasons 19 times in 6707 years, that is once every 353 years

[Karl Palmen]

Dear Helios and Calendar People

The 6707-year cycle is a multiple of 19-years and is listed in
http://www.the-light.com/cal/Lunisolar19.html of
http://www.the-light.com/cal/kp_Lunisolar_xls.html . It is equivalent to
353 19-year cycles with one lunar month returned.

Thanks for noticing that the 82954 months are a multiple of 703 months.
For this to be a multiple of the 703-month lunar cycle its number of
yerms (5074) must be the same multiple of the number of yerms (43) in
the 703-month cycle.

We have 82954 = 703*118 and 5074 = 43*118. So this 19-multiple of the
353-year cycle is indeed a multiple of the 703-month lunar cycle. It is
another good example of a lunisolar cycle that is a multiple of a short
lunar calendar cycle (besides 5515-year and 725-year cycles).

See http://www.hermetic.ch/cal_stud/lunarcal/lunacycl.htm for the
703-month cycle.

The spreadsheet gives a mean year of 365.24228 days and a mean month of
29.5305832 days.
The mean year and month are a little shorter than in Irv's 13-multiple
of the 353-year cycle. Intermediary multiples exist of 15 and 17
353-year cycles of which the 17-multiple has a whole number of weeks and
also has 6001 years.

The 19-multiple is special in that it is a multiple of a lunar calendar
cycle less than 1000-months long, each consisting of a single year era
(of 43 yerms).

Irv has pointed out that the number of months in this 6707-year cycle is
a multiple of 37. This 37 is a multiple of the 703-month cycle 703=37*19
and so if you (as suggested by Helios) defined a short year, so that 3
short years equal 37 months, the 703-month cycle would have 57 short
years in it. The whole 6707-year cycle so has 118*57=6726 short years,
so the short year would drift 19 times through the 6707-year cycle,
which is indeed once every 353-year cycle as Helios thinks.

The number of months in the 6707-year cycle is also divisible by 59 and
so a 2-month cycle of 59 days would drift a whole number of months with
respect to the 6707-year cycle and this number of months is the number
of yerms divided by 59, which is 86. So the 2-month cycle drifts a whole
month once every 964 25/43 lunar months or 965 50/86 2-month cycle
months.

Karl

10(08(17

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 09 May 2009 10:41
To: CALNDR-L@...
Subject: Mean Year of 353-year lunisolar cycle

I've found one more lunisolar cycle made up of the same repetition of
one
lunar calendar cycle listed in
Karl P,'s "Lunar Calendar Cycles less than 1885 Months"

This is the case of the 43 yerm era with 703 months with
mean month = 29 & 373 / 703 days
that factors into
-----------------------------------

6707 years = ( 2*59 )*2*2*2*3*5*173 = 82954 months

-----------------------------------
This is 19 repeats of the 353-year cycle of 4366 months. This scheme
allows
us to write

mean year of 353-year cycle = 365 & 1625 / 6707 days

mean year of 3-year cycle = 364 & 4 / 19 days

I think the 3-year cycle's new year drifts through the seasons 19 times
in
6707 years, that is once every 353 years

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[Helios]

There is one more lunisolar cycle made up of the same repetition of
one lunar calendar cycle listed in Karl P,'s "Lunar Calendar Cycles less than 1885 Months"

This is the case of the 55 yerm era with 899 months with
mean month = 29 & 477 / 899 days
mean year = 365 & 1513 / 6251 days

6251 years = [ 2*43 | 2*2*6637 ] = 77314 months

The 6251-year cycle is also a multiple of 19-years but not listed in
http://www.the-light.com/cal/Lunisolar19.html of
http://www.the-light.com/cal/kp_Lunisolar_xls.html .

[Karl Palmen]

Dear Helios and Calendar People

I didn't put this cycle into
http://www.the-light.com/cal/Lunisolar19.html because the mean number of
years per truncation of the Metonic cycle (329) is less than that for
the 334-year cycle (334).

The number of 55-yerm 899-month cycles in one 6251-year cycle is 86.

In my lunisolar spreadsheets, the cycle is obtained by setting A=6251
(years), B=2302 (leap months) and C=1214 (abundant years). It shows mean
year of 365.24204 days and a mean month of 29.5305895 days.

Karl

10(08(17

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 11 May 2009 14:18
To: CALNDR-L@...
Subject: Re: Mean Year of 353-year lunisolar cycle

There is one more lunisolar cycle made up of the same repetition of
one lunar calendar cycle listed in Karl P,'s "Lunar Calendar Cycles less
than 1885 Months"

This is the case of the 55 yerm era with 899 months with
mean month = 29 & 477 / 899 days
mean year = 365 & 1513 / 6251 days

6251 years = [ 2*43 | 2*2*6637 ] = 77314 months

The 6251-year cycle is also a multiple of 19-years but not listed in
http://www.the-light.com/cal/Lunisolar19.html of
http://www.the-light.com/cal/kp_Lunisolar_xls.html .


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[Karl Palmen]

Dear Helios and Calendar People

Now that Helios has found a lunisolar multiple of the 899-month cycle of
55 yerms, could we find a similar lunisolar multiple of the 850-month
cycle of 52 yerms as in my Yerm Lunar Calendar
http://www.hermetic.ch/cal_stud/palmen/yerm1.htm ?

I'm ware that the 334-year cycle has 4131=17*243 months and the
850-month cycle has 17*50 months and so we can construct 50 334-year
cycles with 243 850-month cycles. The resulting mean year is about
365.2420958 days. The resulting cycle of 16,700 years is rather long, so
how could I find a shorter cycle?

Using http://the-light.com/cal/converter/ , I found that 29 850-month
cycles is within a day or two of 1993 years.
 21-01(01(01 = 11 Nov 1996
 50-01(01(01 = 12 Nov 3989
 79-01(01(01 = 13 Nov 5982
108-01(01(01 = 14 Nov 7975.
Can we get a shorter cycle by adding this rough 1993-year cycle to the
16,700-year cycle and divide out a common divisor?
The answer is in the determinant of the two cycles, which is 29*16,700 -
243*1993 = 1.
The answer is no, because the determinant of 1 indicates that no common
divisor can occur and that the 16,700-year and 1993-year cycles are
mixer cycles for all cycles whose mean year lies in between.

Can we get a much shorter cycle by subtracting this rough 1993-year
cycle to the 16,700-year cycle and divide out a common divisor?
The resulting mean year would be less than the 365.2420958 days of the
16,700-year cycle.
I think the determinant of 1 indicates an answer no, but I'm not yet so
sure.

So it seems that the 16,700-year cycle is the best multiple of the
850-month cycle you can get. I investigate this further:

I think the determinant of 1 indicates that the 16,700-year cycle is
made up of a number of 1993-year cycles and just one other shorter
cycle, such that both cycles are mixer cycles. I also think the shorter
cycle is 756 years of 11 859-month cycles.
Indeed, 16,700 = 8*1993 + 756 and 243 = 8*29 + 11, so confirming what I
also think. Also 29*756 - 11*1993 = 1 and so the 1993-year and 756-year
cycles are indeed mixers. The mix needs to be close to 8 to 1 for an
accurate cycles and therefore an accurate cycle cannot be much shorter
than 16,700 years.

Similar work could be done to see if the 6707-year, 6251-year or
5515-year cycles can be shortened much while keeping them as multiples
of the same lunar calendar cycle without much loss of accuracy. I expect
the answer is no in all three cases.

Karl

10(08(18

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 11 May 2009 14:18
To: CALNDR-L@...
Subject: Re: Mean Year of 353-year lunisolar cycle

There is one more lunisolar cycle made up of the same repetition of
one lunar calendar cycle listed in Karl P,'s "Lunar Calendar Cycles less
than 1885 Months"

This is the case of the 55 yerm era with 899 months with
mean month = 29 & 477 / 899 days
mean year = 365 & 1513 / 6251 days

6251 years = [ 2*43 | 2*2*6637 ] = 77314 months

The 6251-year cycle is also a multiple of 19-years but not listed in
http://www.the-light.com/cal/Lunisolar19.html of
http://www.the-light.com/cal/kp_Lunisolar_xls.html .


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[Karl Palmen]

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Dear Brij, Helios and Calendar People

 

Brij has created a tithi of 2/59 lunar months equated to 966/965 days. This follows a 965-month cycle of 4071 weeks = 28497 days, which has a mean month of about 29.53057 days and is about 8.1 days more than 78 years .  Any accurate lunisolar multiple of this lunar 965-month cycle would be useful for a calendar really based on this Vij tithi and also would have a whole number of weeks. I’ve found that 45 of these lunar 965-month cycles make a 3511-year cycle with a mean year of about 365.242096 days.

 

In my lunisolar spreadsheets http://www.the-light.com/cal/kp_Lunisolar_xls.html , this cycle can be made up from A=3511 (years), B=1293 (leap months), C=681(abundant years). The equivalent solar calendar has 850 leap days in a 3511-year cycle. The equivalent leap week solar calendar has (850+3511)/7 = 623 leap weeks in 3511 years.

 

 

Brij said that the 1749-year cycle is equal to (d) (88*19)+(7*11) years, which is correct and so shows that this cycle would have 7 corrections of the 19-year cycle by truncating to 11 years. This is one truncation per 1749/7 = 249 6/7 years (just under 250 years), which is a bit too frequent. The cycle has (88*235) + (7*136) = 21632 lunar months. So for an accurate lunar month of 29.530588 days, it would give a mean year of about 365.240526 days, which is rather short. For Vij tithis the mean year would be 21632*29.5/1749 tithis = 364.8622 tithis = 365.2403 days.  The other sums for the 1749-year cycle are of little use for calendars, so won’t be commented on any further.

 

The main point of my note is that there is no accurate lunisolar multiple of the 850-month lunar cycle much shorter than 50 334-year cycles lasting 16,700 years. This arises the approximation of 29 850-month cycles to 1993 years being much better than any other approximation of similar size. Helios has found that 86 899-month cycles of 55 yerms are 6251 years and 118 703-month cycles of 43 yerms are 6707 years equal to 19 353-year cycles.

 

More important than Brij’s lunisolar 1749-year cycle is Helios’s lunar 1749-month cycle. 39 of these make up a lunisolar 5515-year cycle.

 

Karl

 

10(08(19

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 12 May 2009 20:00
To: CALNDR-L@...
Subject: 78-yr & 1749-yrs cycle RE: Lunisolar multiples of the 850-month cycle RE: Mean Year of 353-year lunisolar cycle

 

Karl, Helios & CC:
>.....could we find a similar lunisolar multiple of the 850-month
>cycle of 52 yerms as in my Yerm Lunar Calendar.....
From old memory, a yerm is around 483/484 days i.e. 52*483.5 =25142 days. This is 2 lunation short of 69-years, approximately 853 lunation. 853-lunation = 25189.59225493 days =68.96681974-years
69-yrs =25201.7111 days =853.41 lunation; and 850-lunation = 25101.0004885 days.
78-years =28497 days = 4071 weeks fit my Lunar Tithi 'Harappan) calendar 28497 tithi/59 =28526.53057/59 =483.50052 days. Also, please see: http://www.brijvij.com/XorT-units-5x47lunation.doc.
In my previous post, there was a slight 'mis-conveyed thought' about 1749-year cycle. This may be corrected as:

"My 1749-years is ONE year short of (896+19+834)-yrs, make ninty-two cycles of 19-years=(92*19)=1748-years i.e. ONE year short of 1749-years;  having 638808.5897 days in (91258Weeks+2days); & (21632.0979525 Lunation).  1749-year cycle is a combination of (896+19+834)-years. This cycle can be made out of:   

      (a) (13*128)+19+(6*11) years;       (b) (5*334)+(3*19)+(2*11) years;        (c) (50*33)+(9*11) years; 
(d) (88*19)+(7*11) years; & (e) [(92*19)+1]-years. This cycle is also (22 cycles of 78-years + 33-year solar cycle).
Regards,
Brij Bhushan Vij 
2009 May 12H14:99(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 # 001 [phone]


 
> Date: Tue, 12 May 2009 13:01:17 +0100
> From: karl.palmen@...
> Subject: Lunisolar multiples of the 850-month cycle RE: Mean Year of 353-year lunisolar cycle
> To: CALNDR-L@...
>
> Dear Helios and Calendar People
>
> Now that Helios has found a lunisolar multiple of the 899-month cycle of
> 55 yerms, could we find a similar lunisolar multiple of the 850-month
> cycle of 52 yerms as in my Yerm Lunar Calendar
> http://www.hermetic.ch/cal_stud/palmen/yerm1.htm ?
>
> I'm ware that the 334-year cycle has 4131=17*243 months and the
> 850-month cycle has 17*50 months and so we can construct 50 334-year
> cycles with 243 850-month cycles. The resulting mean year is about
> 365.2420958 days. The resulting cycle of 16,700 years is rather long, so
> how could I find a shorter cycle?
>
> Using http://the-light.com/cal/converter/ , I found that 29 850-month
> cycles is within a day or two of 1993 years.
> 21-01(01(01 = 11 Nov 1996
> 50-01(01(01 = 12 Nov 3989
> 79-01(01(01 = 13 Nov 5982
> 108-01(01(01 = 14 Nov 7975.
> Can we get a shorter cycle by adding this rough 1993-year cycle to the
> 16,700-year cycle and divide out a common divisor?
> The answer is in the determinant of the two cycles, which is 29*16,700 -
> 243*1993 = 1.
> The answer is no, because the determinant of 1 indicates that no common
> divisor can occur and that the 16,700-year and 1993-year cycles are
> mixer cycles for all cycles whose mean year lies in between.
>
> Can we get a much shorter cycle by subtracting this rough 1993-year
> cycle to the 16,700-year cycle and divide out a common divisor?
> The resulting mean year would be less than the 365.2420958 days of the
> 16,700-year cycle.
> I think the determinant of 1 indicates an answer no, but I'm not yet so
> sure.
>
> So it seems that the 16,700-year cycle is the best multiple of the
> 850-month cycle you can get. I investigate this further:
>
> I think the determinant of 1 indicates that the 16,700-year cycle is
> made up of a number of 1993-year cycles and just one other shorter
> cycle, such that both cycles are mixer cycles. I also think the shorter
> cycle is 756 years of 11 859-month cycles.
> Indeed, 16,700 = 8*1993 + 756 and 243 = 8*29 + 11, so confirming what I
> also think. Also 29*756 - 11*1993 = 1 and so the 1993-year and 756-year
> cycles are indeed mixers. The mix needs to be close to 8 to 1 for an
> accurate cycles and therefore an accurate cycle cannot be much shorter
> than 16,700 years.
>
> Similar work could be done to see if the 6707-year, 6251-year or
> 5515-year cycles can be shortened much while keeping them as multiples
> of the same lunar calendar cycle without much loss of accuracy. I expect
> the answer is no in all three cases.
>
> Karl
>
> 10(08(18
>

 

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[Karl Palmen]

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Dear Brij, Helios and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 13 May 2009 18:23
To: CALNDR-L@...
Subject: Re: 3511-yr cycle RE: 78-yr & 1749-yrs cycle RE: Lunisolar multiples of the 850-month cycle RE: ...

 

Brij said:

3511-years =1282365.327930601091 days (183195 weeks) =43424.9833683 lunation 

 

Comparing the cycle with today’s values of the mean tropical year and lunation is meaningless, because these values would change significantly over 3511 years. It is better (but not so easy) to use predicted equinoxes, solstices and moon phases. That is why I only give the mean year and mean month.

 

Brij continued:

with Mean Year =365.2420962689 days; and Mean Lunation =29.5305699482 days.

 

This is for exactly 1,282,365 days divided into 3511 years or 43425 lunar months.

 

The mean year is also exactly 365 850/3511 days and also exactly 52 623/3511 weeks.

 

The mean month  is exactly what one gets by approximating a tithi  of2/59 month to 966/965 days. This is the important point about this cycle. It is a multiple (45) of the lunar 965-month cycle formed by approximating 2/59 month to 966/965 days. It is also shorter than any other accurate lunisolar cycle found so far that is a multiple of a lunar calendar cycle less than 1885 months (others being 5515, 6707, 6251 and 16,700 years).

 

The 3511-year cycle is thus a very good cycle for any calendar that is based strictly on the Vij tithi of 2/59 month equated to 966/965 days. Brij does not seem to have appreciated this point yet.

 

3511 is a prime number.

 

 

Karl

 

10(08(19 till noon
 

---

Date: Wed, 13 May 2009 13:57:05 +0100
From: karl.palmen@...
Subject: 3511-yr cycle RE: 78-yr & 1749-yrs cycle RE: Lunisolar multiples of the 850-month cycle RE: ...
To: CALNDR-L@...

Dear Brij, Helios and Calendar People

 

Brij has created a tithi of 2/59 lunar months equated to 966/965 days. This follows a 965-month cycle of 4071 weeks = 28497 days, which has a mean month of about 29.53057 days and is about 8.1 days more than 78 years .  Any accurate lunisolar multiple of this lunar 965-month cycle would be useful for a calendar really based on this Vij tithi and also would have a whole number of weeks. I’ve found that 45 of these lunar 965-month cycles make a 3511-year cycle with a mean year of about 365.242096 days.

 

In my lunisolar spreadsheets http://www.the-light.com/cal/kp_Lunisolar_xls.html , this cycle can be made up from A=3511 (years), B=1293 (leap months), C=681(abundant years). The equivalent solar calendar has 850 leap days in a 3511-year cycle. The equivalent leap week solar calendar has (850+3511)/7 = 623 leap weeks in 3511 years.

 

 

Brij said that the 1749-year cycle is equal to (d) (88*19)+(7*11) years, which is correct and so shows that this cycle would have 7 corrections of the 19-year cycle by truncating to 11 years. This is one truncation per 1749/7 = 249 6/7 years (just under 250 years), which is a bit too frequent. The cycle has (88*235) + (7*136) = 21632 lunar months. So for an accurate lunar month of 29.530588 days, it would give a mean year of about 365.240526 days, which is rather short. For Vij tithis the mean year would be 21632*29.5/1749 tithis = 364.8622 tithis = 365.2403 days.  The other sums for the 1749-year cycle are of little use for calendars, so won’t be commented on any further.

 

The main point of my note is that there is no accurate lunisolar multiple of the 850-month lunar cycle much shorter than 50 334-year cycles lasting 16,700 years. This arises the approximation of 29 850-month cycles to 1993 years being much better than any other approximation of similar size. Helios has found that 86 899-month cycles of 55 yerms are 6251 years and 118 703-month cycles of 43 yerms are 6707 years equal to 19 353-year cycles.

 

More important than Brij’s lunisolar 1749-year cycle is Helios’s lunar 1749-month cycle. 39 of these make up a lunisolar 5515-year cycle.

 

Karl

 

10(08(19

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 12 May 2009 20:00
To: CALNDR-L@...
Subject: 78-yr & 1749-yrs cycle RE: Lunisolar multiples of the 850-month cycle RE: Mean Year of 353-year lunisolar cycle

 

Karl, Helios & CC:
>.....could we find a similar lunisolar multiple of the 850-month
>cycle of 52 yerms as in my Yerm Lunar Calendar.....
From old memory, a yerm is around 483/484 days i.e. 52*483.5 =25142 days. This is 2 lunation short of 69-years, approximately 853 lunation. 853-lunation = 25189.59225493 days =68.96681974-years
69-yrs =25201.7111 days =853.41 lunation; and 850-lunation = 25101.0004885 days.
78-years =28497 days = 4071 weeks fit my Lunar Tithi 'Harappan) calendar 28497 tithi/59 =28526.53057/59 =483.50052 days. Also, please see: http://www.brijvij.com/XorT-units-5x47lunation.doc.
In my previous post, there was a slight 'mis-conveyed thought' about 1749-year cycle. This may be corrected as:

"My 1749-years is ONE year short of (896+19+834)-yrs, make ninty-two cycles of 19-years=(92*19)=1748-years i.e. ONE year short of 1749-years;  having 638808.5897 days in (91258Weeks+2days); & (21632.0979525 Lunation).  1749-year cycle is a combination of (896+19+834)-years. This cycle can be made out of:   

      (a) (13*128)+19+(6*11) years;       (b) (5*334)+(3*19)+(2*11) years;        (c) (50*33)+(9*11) years; 
(d) (88*19)+(7*11) years; & (e) [(92*19)+1]-years. This cycle is also (22 cycles of 78-years + 33-year solar cycle).
Regards,
Brij Bhushan Vij 
2009 May 12H14:99(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 # 001 [phone]


 
> Date: Tue, 12 May 2009 13:01:17 +0100
> From: karl.palmen@...
> Subject: Lunisolar multiples of the 850-month cycle RE: Mean Year of 353-year lunisolar cycle
> To: CALNDR-L@...
>
> Dear Helios and Calendar People
>
> Now that Helios has found a lunisolar multiple of the 899-month cycle of
> 55 yerms, could we find a similar lunisolar multiple of the 850-month
> cycle of 52 yerms as in my Yerm Lunar Calendar
> http://www.hermetic.ch/cal_stud/palmen/yerm1.htm ?
>
> I'm ware that the 334-year cycle has 4131=17*243 months and the
> 850-month cycle has 17*50 months and so we can construct 50 334-year
> cycles with 243 850-month cycles. The resulting mean year is about
> 365.2420958 days. The resulting cycle of 16,700 years is rather long, so
> how could I find a shorter cycle?
>
> Using http://the-light.com/cal/converter/ , I found that 29 850-month
> cycles is within a day or two of 1993 years.
> 21-01(01(01 = 11 Nov 1996
> 50-01(01(01 = 12 Nov 3989
> 79-01(01(01 = 13 Nov 5982
> 108-01(01(01 = 14 Nov 7975.
> Can we get a shorter cycle by adding this rough 1993-year cycle to the
> 16,700-year cycle and divide out a common divisor?
> The answer is in the determinant of the two cycles, which is 29*16,700 -
> 243*1993 = 1.
> The answer is no, because the determinant of 1 indicates that no common
> divisor can occur and that the 16,700-year and 1993-year cycles are
> mixer cycles for all cycles whose mean year lies in between.
>
> Can we get a much shorter cycle by subtracting this rough 1993-year
> cycle to the 16,700-year cycle and divide out a common divisor?
> The resulting mean year would be less than the 365.2420958 days of the
> 16,700-year cycle.
> I think the determinant of 1 indicates an answer no, but I'm not yet so
> sure.
>
> So it seems that the 16,700-year cycle is the best multiple of the
> 850-month cycle you can get. I investigate this further:
>
> I think the determinant of 1 indicates that the 16,700-year cycle is
> made up of a number of 1993-year cycles and just one other shorter
> cycle, such that both cycles are mixer cycles. I also think the shorter
> cycle is 756 years of 11 859-month cycles.
> Indeed, 16,700 = 8*1993 + 756 and 243 = 8*29 + 11, so confirming what I
> also think. Also 29*756 - 11*1993 = 1 and so the 1993-year and 756-year
> cycles are indeed mixers. The mix needs to be close to 8 to 1 for an
> accurate cycles and therefore an accurate cycle cannot be much shorter
> than 16,700 years.
>
> Similar work could be done to see if the 6707-year, 6251-year or
> 5515-year cycles can be shortened much while keeping them as multiples
> of the same lunar calendar cycle without much loss of accuracy. I expect
> the answer is no in all three cases.
>
> Karl
>
> 10(08(18
>

 

 

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