Re: 3511-yr cycle RE: 78-yr & 1749-yrs cycle RE: Lunisolar multiples of the 850-month cycle RE: ...

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

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 
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> 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
>