Pawukon Lunisolar Cycles

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Pawukon Lunisolar Cycles

Karl Palmen

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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Re: Pawukon Lunisolar Cycles

Karl Palmen

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: [hidden email]
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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Re: Pawukon Lunisolar Cycles

Walter J Ziobro

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