Dear Walter & Calendar People Some time ago (29 May 2014) I found some lunisolar cycles than are a multiple of the 210-day Pawukon cycle. They are a mix of two such cycles I had known of beforehand. Mix Years Months 210-day cycles mean year mean month (1,0) 2930 36239 5096 365.24232 29.530616 (1,1) 3302 40840 5743 365.24228 29.530607 (1,2) 3674 45441 6390 365.24224 29.530600 (1,3) 4046 50042 7037 365.24221 29.530594 (1,4) 4418 54643 7684 365.24219 29.530589 (1,5) 4790 59244 8331 365.24217 29.530585 (0,1) 372 4601 647 365.24194 29.530537 Of these, the 4790-year cycle is also a whole number (4937) of lunar twelve-month years (with 147 drift cycles). Twice the 3674-year cycle (7348 years) is a multiple of twelve Pawukon cycles and so 2520 days. 4000 Gregorian years is also equal to 6957 Pawukon cycles. It is about 3 days too long to be a lunisolar cycle, but is formed from the mix (2,-5). 4000 = 2*2930 - 5*372 49473 = 2*36239 – 5*4601
6957 = 2*5096 - 5*647 These mixes do not exhaust all lunisolar Pawukon cycles. There must exist one (perhaps very long), which is independent of these mixes. Karl 16(13(24 |
Dear Calendar People I’m looking for a lunisolar calendar cycle that is a multiple of 210 days and is independent of those listed in the previous note below. By independent, I mean it can’t be made up of a mix of those even with
negative or non-integer numbers. In those cycles listed in the note below the number of months M is determined by the number of years Y and the number of 210-day cycles (Pawukon) P as follows: M = 31.5*Y – 11*P I’d expect an accurate independent cycle would have a number of months differing from this (31.5*Y – 11*P) by 0.5.
I decide to start with a very short, but inaccurate cycle 19 years = 235 months = 33 Pawukon, which is nearly 10 days short of a Metonic cycle. This has (31.5*Y – 11*P) = 31.5*19 – 11*33 = 598.5 – 363 = 235.5 and this differs from the number of months by 0.5. This cycle is nearly 10 days short and the 4000-year cycle is 3 days too long. This suggests adding three 4000-year cycles to one of these cycles and we get: Years Months 210-day cycles mean year mean month 12019 148654 20904 365.24170… 29.5305878… Other such cycles can be found by adding or subtracting cycles listed below. If you want a longer mean year one can subtract this cycle from a sufficiently long mix of the cycles below. If you want a shorter accurate cycle, then one can only use those listed below. Karl 16(13(25 From: Palmen,
Karl (STFC,RAL,ISIS) Dear Walter & Calendar People Some time ago (29 May 2014) I found some lunisolar cycles than are a multiple of the 210-day Pawukon cycle. They are a mix of two such cycles I had known of beforehand. Mix Years Months 210-day cycles mean year mean month (1,0) 2930 36239 5096 365.24232 29.530616 (1,1) 3302 40840 5743 365.24228 29.530607 (1,2) 3674 45441 6390 365.24224 29.530600 (1,3) 4046 50042 7037 365.24221 29.530594 (1,4) 4418 54643 7684 365.24219 29.530589 (1,5) 4790 59244 8331 365.24217 29.530585 (0,1) 372 4601 647 365.24194 29.530537 Of these, the 4790-year cycle is also a whole number (4937) of lunar twelve-month years (with 147 drift cycles). Twice the 3674-year cycle (7348 years) is a multiple of twelve Pawukon cycles and so 2520 days. 4000 Gregorian years is also equal to 6957 Pawukon cycles. It is about 3 days too long to be a lunisolar cycle, but is formed from the mix (2,-5). 4000 = 2*2930 - 5*372 49473 = 2*36239 – 5*4601
6957 = 2*5096 - 5*647 These mixes do not exhaust all lunisolar Pawukon cycles. There must exist one (perhaps very long), which is independent of these mixes. Karl 16(13(24 |
Dear Karl I don't know if this is helpful, but there are about 64 lunar months in 9 puwakons of 210 days each for a total of 1890 days So presumably a lunisolar cycle that contains a multiple of 1890 could work Walter Ziobro Sent from AOL Mobile Mail On Friday, September 15, 2017 Karl Palmen <[hidden email]> wrote: Dear Calendar People
I’m looking for a lunisolar calendar cycle that is a multiple of 210 days and is independent of those listed in the previous note below. By independent, I mean it can’t be made up of a mix of those even with negative or non-integer numbers.
In those cycles listed in the note below the number of months M is determined by the number of years Y and the number of 210-day cycles (Pawukon) P as follows:
M = 31.5*Y – 11*P
I’d expect an accurate independent cycle would have a number of months differing from this (31.5*Y – 11*P) by 0.5.
I decide to start with a very short, but inaccurate cycle 19 years = 235 months = 33 Pawukon, which is nearly 10 days short of a Metonic cycle. This has (31.5*Y – 11*P) = 31.5*19 – 11*33 = 598.5 – 363 = 235.5 and this differs from the number of months by 0.5.
This cycle is nearly 10 days short and the 4000-year cycle is 3 days too long. This suggests adding three 4000-year cycles to one of these cycles and we get:
Years Months 210-day cycles mean year mean month 12019 148654 20904 365.24170… 29.5305878…
Other such cycles can be found by adding or subtracting cycles listed below.
If you want a longer mean year one can subtract this cycle from a sufficiently long mix of the cycles below.
If you want a shorter accurate cycle, then one can only use those listed below.
Karl
16(13(25
From: Palmen, Karl (STFC,RAL,ISIS) Sent: 14 September 2017 13:19 To: CALNDR-L@... Subject: Pawukon Lunisolar Cycles
Dear Walter & Calendar People
Some time ago (29 May 2014) I found some lunisolar cycles than are a multiple of the 210-day Pawukon cycle. They are a mix of two such cycles I had known of beforehand.
Mix Years Months 210-day cycles mean year mean month (1,0) 2930 36239 5096 365.24232 29.530616 (1,1) 3302 40840 5743 365.24228 29.530607 (1,2) 3674 45441 6390 365.24224 29.530600 (1,3) 4046 50042 7037 365.24221 29.530594 (1,4) 4418 54643 7684 365.24219 29.530589 (1,5) 4790 59244 8331 365.24217 29.530585 (0,1) 372 4601 647 365.24194 29.530537
Of these, the 4790-year cycle is also a whole number (4937) of lunar twelve-month years (with 147 drift cycles).
Twice the 3674-year cycle (7348 years) is a multiple of twelve Pawukon cycles and so 2520 days.
4000 Gregorian years is also equal to 6957 Pawukon cycles. It is about 3 days too long to be a lunisolar cycle, but is formed from the mix (2,-5). 4000 = 2*2930 - 5*372 49473 = 2*36239 – 5*4601 6957 = 2*5096 - 5*647
These mixes do not exhaust all lunisolar Pawukon cycles. There must exist one (perhaps very long), which is independent of these mixes.
Karl
16(13(24 |
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