Mixing the Primary Lunisolar Cycles
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Mixing the Primary Lunisolar Cycles
by Karl Palmen
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11,15,19,33 & 128-year cycles RE: Mixing the Primary Lunisolar Cycles
by Brij Bhushan Vij
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I had an interesting inter-action with Karl, who may not be convinced with my calculations on SEVERAL solar and/or luni-solar cycles that were discussed some time in 2006-2007 and later. As far me I am convined that Harappan Lunar-Tithi (as I call) had been in vogue during their flourishing days. I attempted to provide format of such a lunar calendar by *deleting 13th from every Gregorian month* to have the lunar year of 354 Tithi making 19-year cycle of 6932.5 Tithi. Please see: http://www.brijvij.com/bb-kp_count-by-week.cycles.doc I have my doubt's if Karl really ment he was NOT interested in several of my 'discussed cycles'. Primary Lunisolar cycles, now pointed are really built up from smaller cycles that I place at: http://www.brijvij.com/bb_harappaTithi-cycles.pdf showing their mixing of cycles, as I hope Karl expects. 429-years =11*39 =13*33; 462-years =(11*33)+(9*11); 627-years =33*19 =57*11 and 649-years =(4*128)+(2*19)+(9*11) 2502-year cycle is in fact: 3*834-year cycle; 3234-year cycle = (3*896)+(3*128)+19+(13*11). It is my opinion that ANY cycle could be attempted to become useful with smaller cycles that I have shown in the link, to satisfy requirements of an accurate calendar format. 293-year cycle that was discussed is in fact 294-years of sidreal day calendar that I mentioned earlier - some members may recall introducing a 'Brahaspati Leap Year'; which may be un-realistic in Earth calendars that man-on-street would like to have for daily activity. Brij Bhushan Vij (MJD 2454941)/1361+D-120W17-00 (G. Sunday, 2009 April 19H23:28 (decimal) EST Date: Fri, 17 Apr 2009 14:10:04 +0100 From: karl.palmen@... Subject: Mixing the Primary Lunisolar Cycles To: CALNDR-L@... Dear Calendar People Some time ago I stated to the list that all accurate lunisolar calendar cycles can be made up three of three primary lunisolar cycles: (1) 391 years, 4836 months, 142,810 days (2) 334 years, 4131 months, 121,991 days (3) 315 years, 3896 months, 115,051 days
For examples of lunisolar cycles see http://www.the-light.com/cal/kp_Lunisolar_xls.html some of which are shown as a mixture of primary cycles in http://www.the-light.com/cal/Lunisolar_333.html .
I’ve found a way of deriving a equation that the numbers of each type of primary cycle must satisfy for a given mean year or for a given mean month. Suppose a given lunisolar cycle has P 391-year cycles (1), Q 334-year cycles (2) and R 315-year cycles (3), then for a mean year of 365 + E/A days P*(E*391 – A*95) + Q*(E*334 – A*81) + R*(E*315 – A*76) = 0 This gives rise to examples such as Mean year 365 8/33 days: 12*R = 7*P + Q Mean year 365 31/128 days: 37*R = 39*P + 14*Q Mean year 365 39/161 days: 49*R = 46*P + 15*Q
Note that the third equation is the sum of the first two. This applies in general whenever the numerator and denominator of the fractional part of the mean year both add up (as in this case). Other examples are Mean year 365 71/293 days: 97*R = 74*P + 19*Q Mean year 365 97/400 days: 155*R = 73*P + 2*Q Mean year 365 25/103 days: 47*R = 10*P – 7*Q
Similarly, for a mean lunar month of (59 + F/J)/2 days: P*(F*4836 – J*296)/2 + Q*(F*4131 – J*253)/2 + R*(F*3896 – J*238)/2 = 0 This gives rise to examples such as
Mean month 29 451/850 days (F=52, J=850): 146*R = 64*P + 119*Q Mean month 29 512/965 days (F=59, J=965): 97*R = 158*P + 208*Q
The latter equation arises from the Vij tithi of 2/59 lunation equated to 966/965 days. Every lunisolar cycle based strictly on this tithi is made up of primary lunisolar cycles whose numbers (P, Q and R) satisfy this latter equation. The lunar equations add up in a similar manner to the solar equations. The following equation is useful in this adding. Mean month 29 26/49 days (F=3, J=49): 13*R = 2*P - 2*Q
One can find a lunisolar cycle with a desired mean year and mean month by solving the corresponding solar and lunar equations as simultaneous equations. The resulting cycle is unique when common divisors have been cancelled out, but probably very long (perhaps millions of years).
Karl 10(07(23 Scanned by iCritical. Rediscover Hotmail®: Get quick friend updates right in your inbox. Check it out. |
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