Olympic Calendar

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Olympic Calendar

Helios
The Olympic Calendar is a very simple luni-solar calendar.

There are three kinds of years: red, green, and blue. Red years are years divisable by four and can be called Olympic years. The first month of every year is called Primember.

Rules

1) Red and Green years have 12 months. Blue years have 13 months.
2) Green and Blue years always have Primember fixed to 30 days. Red or Olympic Primember is never fixed and can have either 29 or 30 days.
3) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... ) unless a fixed Primember ( Green and Blue years ) is encountered, in which case the pattern is interrupted, but resumes on the second month of the year.
4) Very rarely one 29-day month is removed from a blue year ( embolistic year ). With the 1040 year luni-solar cycle, these 7 corrective years are 73, 225, 369, 521, 673, 817, 969.

After designing this calendar, I searched these forums to find that Karl recognized the utility of removing a 29-day month from the double octaeteris, in his discourse with Lance L. in 2006.

mean year = 5847/16 - 29*(7/1040) = 365 & 63/260 days


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Re: Olympic Calendar

Walter J Ziobro

When does the year start?
Are all subsequent months -embers ?

Walter Ziobro

Sent from AOL Mobile Mail




On Friday, December 30, 2016 Helios <[hidden email]> wrote:

The Olympic Calendar is a very simple luni-solar calendar.

There are three kinds of years: red, green, and blue. Red years are years
divisable by four and can be called Olympic years. The first month of every
year is called Primember.

Rules

1) Red and Green years have 12 months. Blue years have 13 months.
2) Green and Blue years always have Primember fixed to 30 days. Red or
Olympic Primember is never fixed and can have either 29 or 30 days.
3) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember ( Green and Blue years ) is encountered, in which
case the pattern is interrupted, but resumes on the second month of the
year.
4) Very rarely one 29-day month is removed from a blue year ( embolistic
year ). With the 1040 year luni-solar cycle, these 7 corrective years are
73, 225, 369, 521, 673, 817, 969.

After designing this calendar, I searched these forums to find that Karl
recognized the utility of removing a 29-day month from the double
octaeteris, in his discourse with Lance L. in 2006.

mean year = 5847/16 - 29*(7/1040) = 365 & 63/260 days

<http://calndr-l.10958.n7.nabble.com/file/n17384/oly01.jpg>




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Re: Olympic Calendar

Karl Palmen
Dear Helios and Calendar People

The rule specifying, which years are blue and which years are green is not found. Context suggests its an 8-year cycle with three blue years, so green and blue years may simply alternate within the non-red years. Such a calendar with have a solar jitter of about 2 months rather than 1 month in existing lunisolar calendars.

Karl

16(05(05 till noon
________________________________
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Walter J Ziobro [[hidden email]]
Sent: 30 December 2016 17:14
To: [hidden email]
Subject: Re: Olympic Calendar


When does the year start?
Are all subsequent months -embers ?

Walter Ziobro

Sent from AOL Mobile Mail


________________________________
On Friday, December 30, 2016 Helios <[hidden email]> wrote:

The Olympic Calendar is a very simple luni-solar calendar.

There are three kinds of years: red, green, and blue. Red years are years
divisable by four and can be called Olympic years. The first month of every
year is called Primember.

Rules

1) Red and Green years have 12 months. Blue years have 13 months.
2) Green and Blue years always have Primember fixed to 30 days. Red or
Olympic Primember is never fixed and can have either 29 or 30 days.
3) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember ( Green and Blue years ) is encountered, in which
case the pattern is interrupted, but resumes on the second month of the
year.
4) Very rarely one 29-day month is removed from a blue year ( embolistic
year ). With the 1040 year luni-solar cycle, these 7 corrective years are
73, 225, 369, 521, 673, 817, 969.

After designing this calendar, I searched these forums to find that Karl
recognized the utility of removing a 29-day month from the double
octaeteris, in his discourse with Lance L. in 2006.

mean year = 5847/16 - 29*(7/1040) = 365 & 63/260 days

<http://calndr-l.10958.n7.nabble.com/file/n17384/oly01.jpg>




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Re: Olympic Calendar

Walter J Ziobro

Dear Karl

Perhaps solar jitter could be minimized by shifting the blue years in the 8 year cycle according to some schedule

Walter Ziobro

Sent from AOL Mobile Mail




On Tuesday, January 3, 2017 Karl Palmen <[hidden email]> wrote:

Dear Helios and Calendar People

The rule specifying, which years are blue and which years are green is not found. Context suggests its an 8-year cycle with three blue years, so green and blue years may simply alternate within the non-red years. Such a calendar with have a solar jitter of about 2 months rather than 1 month in existing lunisolar calendars.

Karl

16(05(05 till noon
________________________________
From: East Carolina University Calendar discussion List [CALNDR-L@...] on behalf of Walter J Ziobro [000000080342b460-dmarc-request@...]
Sent: 30 December 2016 17:14
To: CALNDR-L@...
Subject: Re: Olympic Calendar


When does the year start?
Are all subsequent months -embers ?

Walter Ziobro

Sent from AOL Mobile Mail


________________________________
On Friday, December 30, 2016 Helios <000000050d08d56e-dmarc-request@...> wrote:

The Olympic Calendar is a very simple luni-solar calendar.

There are three kinds of years: red, green, and blue. Red years are years
divisable by four and can be called Olympic years. The first month of every
year is called Primember.

Rules

1) Red and Green years have 12 months. Blue years have 13 months.
2) Green and Blue years always have Primember fixed to 30 days. Red or
Olympic Primember is never fixed and can have either 29 or 30 days.
3) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember ( Green and Blue years ) is encountered, in which
case the pattern is interrupted, but resumes on the second month of the
year.
4) Very rarely one 29-day month is removed from a blue year ( embolistic
year ). With the 1040 year luni-solar cycle, these 7 corrective years are
73, 225, 369, 521, 673, 817, 969.

After designing this calendar, I searched these forums to find that Karl
recognized the utility of removing a 29-day month from the double
octaeteris, in his discourse with Lance L. in 2006.

mean year = 5847/16 - 29*(7/1040) = 365 & 63/260 days

<http://calndr-l.10958.n7.nabble.com/file/n17384/oly01.jpg>




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Re: Olympic Calendar

Karl Palmen

Dear Helios, Walter and Calendar People

 

I looked more into Helios’s idea. I realise there are at least 5 types of year rather than 3 types. They can be specified by the colour and how many days are in the 2nd month. Red and Green years with the second month having 29 days are identical so there are 5 types rather than 6.  The months can be thought of as being organised in yerms like in my yerm calendar, then every green & blue year has a yerm starting with its 1st or 2nd month and a red year continues an already started yerm. So there are 3 yerms every 4 years, except when a 29-day month is removed from a blue year, in which case 1 more yerm occurs.

 

Now I consider the removal of 29-day month from blue year to correct the calendar. A blue year has either the 2nd month with 29 days or the last (13th) month with 29 days. If this month is removed, one gets a green year whose 2nd month has 30 days, but there is an additional interruption of the alternating months, a yerm starts with the 1st month (as well as the 2nd month), if the 2nd month was removed or a year later if the last month was removed. Because of this difference from ordinary green years, I refer to such years as special green years. Helios refers to them as corrective years.

 

Helios has not stated which of the non-red years are green or blue. I  guess he intends year 1 to be blue and alternates all non-red years between blue & green treating the special green years as blue years. This leads to an 8-year cycle for the years according to their colour and to a 16-year cycle for the 5 year types, except when a special green year occurs. I note that all the special green years have numbers with a remainder of 1 when divided by 8 and all such years are blue or treated as blue. 

 

I reckon the solar jitter of this calendar, which I guess Helios is suggesting is just over 1.8 months. I found a way of rearranging the blue and green years, that reduces the jitter to just over 1.3 months.  The red years remain in the same places. This I define next.

 

The blue and green years alternate within the years, excluding the red years, the special green years (73, 225, 369, 521, 673, 817, 969),  and the years (1, 149, 297, 445, 587, 745, 893 ) half-way between, which are ordinary green years, referred to as intermediary green years. It would be nice if every Olympiad was either (blue, green, blue, red) or (green, blue, green, red) and this can be achieved if every interval between the intermediary green years and the special green years has an odd number of Olympiads so that the two types of Olympiad form a yerm pattern. To obtain this I move three of the seven intermediary green years by 4 years to (149, 301, 445, 587, 741, 893, 1037) and make year 1 blue.

 

To completely specify either of the two calendars defined here, one needs to start the number of days in the second month of year 1.

 

 

I also thought of an alternative rule for determining the number of days in each month, which resembles Walter’s Olympiad calendar. Every year has the first 11 months alternate between 30 and 29 days so the 1st and 11th months have 30 days. Every red year has 12th month with 30 days, so is like Tabular Islamic leap year and every green year has the 12th month with 29 days , so is like a tabular Islamic common year. The blue years have the 1st to 12th months the same as for a green year and also have a 13th month. There are two types a blue year. Ordinary blue years, which always have 30 days in the 13th month and special blue years, in which the number of days in the 13th month alternates between 29 and 30 days for successive special blue years. The special blue years are those years that are the second blue year in an Olympiad, but not the last such year before a special green year (which is otherwise just like an ordinary green year).

 

In Walter’s Olympiad calendar, I suggested yerms the for two types of Olympiad of 49 or 50 months and the number of days in the 50th month. The Olympiad yerms usually have 19 Olympiads, but may have 17 Olympiads. The yerms for the 50th month are approximately twice as long. The 6840-year cycle has 92 Olympiad yerms and 45 50th month yerms. The 1040-year cycle has 14 Olympiad yerms and 7 50th month yerms.

When there are exactly twice as many Olympiad yerms as 50th month yerms, the  calendar cycle is equal to one got by correcting the 16-year double Octaeteris of 5847 days, by occasionally removing a 29-day month. Therefore, I’d suggest a 1040-year cycle rather than 6849-year cycle, because of the greater structural simplicity that would result in such a calendar.

 

Karl

 

16(05(12

 

From: Walter J Ziobro [mailto:[hidden email]]
Sent: 03 January 2017 15:03
To: [hidden email]; Palmen, Karl (STFC,RAL,ISIS)
Subject: Re: Olympic Calendar

 

Dear Karl

Perhaps solar jitter could be minimized by shifting the blue years in the 8 year cycle according to some schedule

Walter Ziobro

Sent from AOL Mobile Mail

 


On Tuesday, January 3, 2017 Karl Palmen <[hidden email]> wrote:

Dear Helios and Calendar People

The rule specifying, which years are blue and which years are green is not found. Context suggests its an 8-year cycle with three blue years, so green and blue years may simply alternate within the non-red years. Such a calendar with have a solar jitter of about 2 months rather than 1 month in existing lunisolar calendars.

Karl

16(05(05 till noon
________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Walter J Ziobro [000000080342b460-dmarc-[hidden email]]
Sent: 30 December 2016 17:14
To: CALNDR-[hidden email]
Subject: Re: Olympic Calendar


When does the year start?
Are all subsequent months -embers ?

Walter Ziobro

Sent from AOL Mobile Mail


________________________________

On Friday, December 30, 2016 Helios <000000050d08d56e-dmarc-[hidden email]> wrote:

The Olympic Calendar is a very simple luni-solar calendar.

There are three kinds of years: red, green, and blue. Red years are years
divisable by four and can be called Olympic years. The first month of every
year is called Primember.

Rules

1) Red and Green years have 12 months. Blue years have 13 months.
2) Green and Blue years always have Primember fixed to 30 days. Red or
Olympic Primember is never fixed and can have either 29 or 30 days.
3) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember ( Green and Blue years ) is encountered, in which
case the pattern is interrupted, but resumes on the second month of the
year.
4) Very rarely one 29-day month is removed from a blue year ( embolistic
year ). With the 1040 year luni-solar cycle, these 7 corrective years are
73, 225, 369, 521, 673, 817, 969.

After designing this calendar, I searched these forums to find that Karl
recognized the utility of removing a 29-day month from the double
octaeteris, in his discourse with Lance L. in 2006.

mean year = 5847/16 - 29*(7/1040) = 365 & 63/260 days

<http://calndr-l.10958.n7.nabble.com/file/n17384/oly01.jpg>




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Re: Olympic Calendar

Karl Palmen
In reply to this post by Helios
Dear Helios, Walter and Calendar People

I stated in a note that this calendar really has 5 types of year rather than 3, because of rule 3.

Each of these year types can be specified by it colour and the number of days in its last month. If the last month has 29 days, I put '-' after the colour and if the last month has 30 days, I put '+' after the colour.

We then get the following 5 types:

30 29 30 29 ... 30 29    354 days Red- = Green-
29 30 29 30 ... 29 30    354 days Red+
30 30 29 30 ... 29 30    355 days Green+
30 29 30 29 ... 30 29 30 384 days Blue+
30 30 29 30 ... 29 30 29 384 days Blue-

Then we get
the sign of a red or blue year is the same as for last year and
the sign of a green year is the opposite to the sign of a previous year.

Helios has not stated, which month of a blue year is the intercalary month. If this is made the 2nd month (month after Primember), then the sign of the year type indicates, which months after Primember and any intercalary month have 29 or 30 days.

If a Blue+ year has its 2nd month removed, it becomes a Green+ year, even though the previous year is also a + year.
If a Blue- year has its last month removed, the names of the months after Primember shift one month back to remove the intercalary month name and it also becomes a green+ year, but the following year will disobey the sign rule (i.e. behave as if preceded by a blue- year).

Then the calendar begins with a 16-year cycle as follows:

1 Blue+
2 Green-
3 Blue-
4 Red-
5 Green+
6 Blue+
7 Green-
8 Red-
9 Blue-
10 Green+
11 Blue+
12 Red+
13 Green-
14 Blue-
15 Green+
16 Red+

Or the same with the signs interchanged or equivalently shifted by 8 years.

Karl

16(05(16

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 30 December 2016 04:58
To: [hidden email]
Subject: Olympic Calendar

The Olympic Calendar is a very simple luni-solar calendar.

There are three kinds of years: red, green, and blue. Red years are years
divisable by four and can be called Olympic years. The first month of every
year is called Primember.

Rules

1) Red and Green years have 12 months. Blue years have 13 months.
2) Green and Blue years always have Primember fixed to 30 days. Red or
Olympic Primember is never fixed and can have either 29 or 30 days.
3) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember ( Green and Blue years ) is encountered, in which
case the pattern is interrupted, but resumes on the second month of the
year.
4) Very rarely one 29-day month is removed from a blue year ( embolistic
year ). With the 1040 year luni-solar cycle, these 7 corrective years are
73, 225, 369, 521, 673, 817, 969.

After designing this calendar, I searched these forums to find that Karl
recognized the utility of removing a 29-day month from the double
octaeteris, in his discourse with Lance L. in 2006.

mean year = 5847/16 - 29*(7/1040) = 365 & 63/260 days

<http://calndr-l.10958.n7.nabble.com/file/n17384/oly01.jpg>




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Re: Olympic Calendar: polyoid variant

Helios
In reply to this post by Helios
Dear Karl, Walter, and Calendar People,

I've developed a "polyoid" variant that's more complicated, but may jitter less based on Karl's alternating olympiad idea. There's still some arrangments I must manage.

Rules;
1) Red and Green years have 12 months. Blue years have 13 months and 384 days.
2) Green and Blue years always have Primember fixed to 30 days. Red or Olympic Primember is never fixed and can have either 29 or 30 days.
3) Red years are years divisable by four and can be called Olympic years. Because its Primember is never fixed and no leap months are added, so red years always have 354 days, except for very infrequent years [ 148, 444, 744, 1040, 1336, 1636, 1932 ] of a 2080 year cycle when a leap day is added.
4) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... ) unless a fixed Primember ( Green and Blue years ) is encountered, in which case the pattern is interrupted, but resumes on the second month of the year.
5) Olympiads are grouped into long series of 17 and 19 olympiads or 68 and 76 years. I call these groupings "polyoids". Olympiads alternate between 49 and 50 months. Polyoids began and end with 49 month olympiads. Given olympiads O: compute M and D
M = ( 99*O - 1 )/2
D = [ 5847*O  - 59 ] /4
----------------------------------------------------------------
compute M and D for the 17 and 19 olympiad polyoid
17-polyoid= 841 months = 24835 days
19-polyoid= 940 months = 27758.5 days
----------------------------------------------------------------
The 2080 year cycle has 759704 days. Without the 7 leap days, there are 759697 days.

759697 days = 6*( 24835 days ) + 22*( 27758.5 days )
260 olympiads = 3*( 17 olympiads ) + 11*( 19 olympiads )

There are 14 polyoids in 1040 years and it takes two to have the same effect of removing a month from the octaeteris regime, which in 1040 years takes seven.
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Re: Olympic Calendar: polyoid variant

Karl Palmen
Dear Helios and Calendar People

Comments below:

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 16 January 2017 08:07
To: [hidden email]
Subject: Re: Olympic Calendar: polyoid variant

Dear Karl, Walter, and Calendar People,

I've developed a "polyoid" variant that's more complicated, but may jitter
less based on Karl's alternating olympiad idea. There's still some
arrangments I must manage.

Rules;
1) Red and Green years have 12 months. Blue years have 13 months and 384
days.
KARL SUGGESTS: and the month after Primember is the intercalary month.
This way, it is the green years that interchange the 29-day and 30-day months as explained in an earlier note.


HELIOS CONTINUED:
2) Green and Blue years always have Primember fixed to 30 days. Red or
Olympic Primember is never fixed and can have either 29 or 30 days.
3) Red years are years divisable by four and can be called Olympic years.
Because its Primember is never fixed and no leap months are added, so red
years always have 354 days, except for very infrequent years [ 148, 444,
744, 1040, 1336, 1636, 1932 ] of a 2080 year cycle when a leap day is added.

KARL REPLIES: This rule negates much of the benefit of having the alternating months by adding lunar jitter.
I suggest instead that the last Olympic (red) year of every other polyoid has its Primember fixed to 30 days like a green year.
One could call such years, Olympic green years. There would be 7 every 1040 years, given there a 14 polyoids every 1040 years.

Two polyoids with one Olympic green year is equivalent to a number of Octaeterides with a 29-day month removed.


HELIOS CONTINUED:
4) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember ( Green and Blue years ) is encountered, in which
case the pattern is interrupted, but resumes on the second month of the
year.
5) Olympiads are grouped into long series of 17 and 19 olympiads or 68 and
76 years. I call these groupings "polyoids". Olympiads alternate between 49
and 50 months. Polyoids began and end with 49 month olympiads. Given
olympiads O: compute M and D
M = ( 99*O - 1 )/2
D = [ 5847*O  - 59 ] /4

KARL REPLIES: Helios needs to also mention something like
a 49-month Olympiad has (green, blue, green, red) years and
a 50-month Olympiad has (blue, green, blue, red) years.
to indicate which years are green and blue.


HELIOS CONTINUED:
----------------------------------------------------------------
compute M and D for the 17 and 19 olympiad polyoid
17-polyoid= 841 months = 24835 days
19-polyoid= 940 months = 27758.5 days
----------------------------------------------------------------
The 2080 year cycle has 759704 days. Without the 7 leap days, there are
759697 days.

759697 days = 6*( 24835 days ) + 22*( 27758.5 days )
260 olympiads = 3*( 17 olympiads ) + 11*( 19 olympiads )

There are 14 polyoids in 1040 years and it takes two to have the same effect
of removing a month from the octaeteris regime, which in 1040 years takes
seven.

KARL REPLIES: These Polyoids could have

19, 19, 17, 19, 19
19, 19, 17, 19, 19
19, 19, 17, 19  olympiads.

Karl

16(05(19

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Re: Olympic Calendar: polyoid variant

Helios
In reply to this post by Helios
Dear Karl, Walter, and Calendar People,

I've polished up these calendar axioms implementing the red year fixed Primember feature. Thanks to Karl for his advisement. I've attached a graphic which depicts the polyoids in braid form in three colors.

Rules for 260 Olympiad luni-solar calendar
1) Red and Green years have 12 months. Blue years have 384 days and 13 months with an intercalary month after Primember called Second Primember.
2) Green and Blue years have Primember fixed to 30 days. Second Primember is not fixed and can have either 29 or 30 days.
3) Red years are divisible by four and are called Olympic years. These years usually have 354 days because this Primember is usually left unfixed, but rarely Primember is fixed to 30 days. These Primember-fixed Olympic years are [ 76, 220, 372, 524, 668, 820, 964 ] in a 1040 cycle. These are half of the Great Olympic 1040-year series [ 76, 152, 220, 296, 372, 448, 524, 592, 668, 744, 820, 896, 964, 1040 ]
4) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... ) unless a fixed Primember is encountered, in which case the pattern is interrupted, but resumes on the second month of the year.
5) Olympiads alternate between 49 and 50 months. They come in two patterns; a 49-month Olympiad with (green, blue, green, red) years and a 50-month Olympiad with (blue, green, blue, red) years. Olympiads are grouped into long series of 17 and 19 olympiads or 68 and 76 years called polyoids which span between the Great Olympic years. Polyoids contain an odd number of olympiads , beginning and ending with 49 month olympiads. New polyoids begin after the Great Olympic years with a green year and the penultimate year is also green.

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Re: Olympic Calendar: polyoid variant

Karl Palmen
Dear Helios, Walter and Calendar People

I see all the necessary information is now in the rules except the number of days in the second month of year 1, but 30 days may be implied.

There is a redundancy of terminology Olympic year and red year mean the same thing.
So it occurred to me that we could have every 4th year an Olympic year, but if Primember is fixed to 30 days it is a green year, just like in the Gregorian calendar not every 4th year is a leap year. This however may spoil the braiding.

Curiously the frequency of these Green Olympic years is almost the same as for dropped leap years, but slightly less, so that if a solar calendar were to drop a leap day every Green Olympic year, it's 1040-year cycle would have one day more than that of the Olympic Polyoid Calendar.

Also, I think it would be useful to introduce the polyoid earlier on after rule 2.
Then after this introduction, one can simply say that a Green Olympic year occurs on the last Olympic year of every other polyoid starting with the first polyoid.

I see in rule 3 that the "Great Olympic 1040-year series" is simply the last year of each polyoid. Why not introduce it as such?

Karl

16(05(22

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 18 January 2017 08:30
To: [hidden email]
Subject: Re: Olympic Calendar: polyoid variant

Dear Karl, Walter, and Calendar People,

I've polished up these calendar axioms implementing the red year fixed
Primember feature. Thanks to Karl for his advisement. I've attached a
graphic which depicts the polyoids in braid form in three colors.

Rules for 260 Olympiad luni-solar calendar
1) Red and Green years have 12 months. Blue years have 384 days and 13
months with an intercalary month after Primember called Second Primember.
2) Green and Blue years have Primember fixed to 30 days. Second Primember is
not fixed and can have either 29 or 30 days.
3) Red years are divisible by four and are called Olympic years. These years
usually have 354 days because this Primember is usually left unfixed, but
rarely Primember is fixed to 30 days. These Primember-fixed Olympic years
are [ 76, 220, 372, 524, 668, 820, 964 ] in a 1040 cycle. These are half of
the Great Olympic 1040-year series [ 76, 152, 220, 296, 372, 448, 524, 592,
668, 744, 820, 896, 964, 1040 ]
4) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember is encountered, in which case the pattern is
interrupted, but resumes on the second month of the year.
5) Olympiads alternate between 49 and 50 months. They come in two patterns;
a 49-month Olympiad with (green, blue, green, red) years and a 50-month
Olympiad with (blue, green, blue, red) years. Olympiads are grouped into
long series of 17 and 19 olympiads or 68 and 76 years called polyoids which
span between the Great Olympic years. Polyoids contain an odd number of
olympiads , beginning and ending with 49 month olympiads. New polyoids begin
after the Great Olympic years with a green year and the penultimate year is
also green.
<http://calndr-l.10958.n7.nabble.com/file/n17473/poly01.jpg>




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Re: Olympic Calendar: polyoid variant

Karl Palmen
In reply to this post by Helios
Dear Walter, Helios and Calendar People

Here is an alternative Olympic Polyoid calendar. The rules for determining the number of months in a year are unchanged, but the rules for determining the number of days in a month are changed so that each of the first 11 months of the year has the same number of days every year. The price for this desirable simplicity is greater lunar jitter. The resulting calendar resembles an Olympiad calendar suggested by Walter.

Rules for 260-Olympiad Fixed-Month lunisolar calendar
1) Red and Green years have 12 months. Blue years have 13
months with an intercalary month added to the end of the year.
2) Every 4th year is a red year and the other years are either green or blue.
3) Olympiads alternate between 49 and 50 months. They come in two patterns;
a 49-month Olympiad with (green, blue, green, red) years and a 50-month
Olympiad with (blue, green, blue, red) years. Olympiads are grouped into
long series of 17 and 19 Olympiads or 68 and 76 years called polyoids.
The last year of a polyoid is called a Great Olympic year.
Polyoids contain an odd number of Olympiads ,
beginning and ending with 49 month Olympiads. New polyoids begin
after the Great Olympic years with a green year and the penultimate year is
also green.
4) The Polyoids end on years [ 76, 152, 220, 296, 372, 448, 524, 592,
668, 744, 820, 896, 964, 1040 ] of a 1040-year cycle.
These are the great Olympic years. Each 1040-year cycle has 14 polyoids
of which 11 have 76 years and three (ending at 220, 592 & 964) have 68 years.

5) The 1st, 3rd, 5th, 7th, 9th and 11th months of a year have 30 days
and the 2nd, 4th, 6th, 8th and 10th months of a year have 29 days.
6) The 12th month has 30 days in a red year or 29 days in a green or blue year.
7) The 13th month of a blue year has 30 days, unless it is a special blue year.
8) A blue year is special if it is the 2nd blue year of an Olympiad and is not
The seventh year of an even-numbered Polyoid,
(i.e. not year 83, 227, 379, 531, 675, 827, 971 of a 1040-year cycle).
9) The number of days in the 13th month of the special blue years alternate between
30 and 29 days starting with 30 days in year 7.  

For Helios's alternating month calendar I suggest the following redraft of his rules.
Note that the first rule that refers to the number of days in a month is rule 5.
So the first 4 rules are the same, except for the positioning of the intercalary month.

Rules for 260-Olympiad Alternating-Month lunisolar calendar
1) Red and Green years have 12 months. Blue years have 13 months
with an intercalary month after Primember called Second Primember.
2) Every 4th year is a red year and the other years are either green or blue.
3) Olympiads alternate between 49 and 50 months. They come in two patterns;
a 49-month Olympiad with (green, blue, green, red) years and a 50-month
Olympiad with (blue, green, blue, red) years. Olympiads are grouped into
long series of 17 and 19 Olympiads or 68 and 76 years called polyoids.
The last year of a polyoid is called a Great Olympic year.
Polyoids contain an odd number of Olympiads ,
beginning and ending with 49 month Olympiads. New polyoids begin
after the Great Olympic years with a green year and the penultimate year is
also green.
4) The Polyoids end on years [ 76, 152, 220, 296, 372, 448, 524, 592,
668, 744, 820, 896, 964, 1040 ] of a 1040-year cycle.
These are the great Olympic years. Each 1040-year cycle has 14 polyoids
of which 11 have 76 years and three (ending at 220, 592 & 964) have 68 years.

5) Green and Blue years have Primember fixed to 30 days. Second Primember is
not fixed and can have either 29 or 30 days.
6) Red years do not have Primember fixed,
except the last red year of every odd-numbered polyoid
(i.e.  years 76, 220, 372, 524, 668, 820, 964 of the 1040-year cycle).
7) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember is encountered, in which case the pattern is
interrupted, but resumes on the second month of the year. This alternating pattern
starts with a 30-day month, which is the second month of year 1.

Only when doing this redrafting did I notice that Helios called the last year of each Polyoid a "Great Olympic year".
I had suggested that the red years with fixed Primember be called Olympic green years, but have not done so in this redraft.
Helios originally defined the Great Olympic years obliquely before defining the polyoids.
In the redraft, the polyoids come first and then the Great Olympic years are defined in terms of the polyoids.

I have reckoned the solar jitter to be about 1.3 months, compared to 1 month for every lunisolar calendar used today.

Karl

16(05(29

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 18 January 2017 08:30
To: [hidden email]
Subject: Re: Olympic Calendar: polyoid variant

Dear Karl, Walter, and Calendar People,

I've polished up these calendar axioms implementing the red year fixed
Primember feature. Thanks to Karl for his advisement. I've attached a
graphic which depicts the polyoids in braid form in three colors.

Rules for 260 Olympiad luni-solar calendar
1) Red and Green years have 12 months. Blue years have 384 days and 13
months with an intercalary month after Primember called Second Primember.
2) Green and Blue years have Primember fixed to 30 days. Second Primember is
not fixed and can have either 29 or 30 days.
3) Red years are divisible by four and are called Olympic years. These years
usually have 354 days because this Primember is usually left unfixed, but
rarely Primember is fixed to 30 days. These Primember-fixed Olympic years
are [ 76, 220, 372, 524, 668, 820, 964 ] in a 1040 cycle. These are half of
the Great Olympic 1040-year series [ 76, 152, 220, 296, 372, 448, 524, 592,
668, 744, 820, 896, 964, 1040 ]
4) Months stream in a continuous alternating pattern ( 30, 29, 30, 29, ... )
unless a fixed Primember is encountered, in which case the pattern is
interrupted, but resumes on the second month of the year.
5) Olympiads alternate between 49 and 50 months. They come in two patterns;
a 49-month Olympiad with (green, blue, green, red) years and a 50-month
Olympiad with (blue, green, blue, red) years. Olympiads are grouped into
long series of 17 and 19 olympiads or 68 and 76 years called polyoids which
span between the Great Olympic years. Polyoids contain an odd number of
olympiads , beginning and ending with 49 month olympiads. New polyoids begin
after the Great Olympic years with a green year and the penultimate year is
also green.
<http://calndr-l.10958.n7.nabble.com/file/n17473/poly01.jpg>




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