13-Month Leap Week Calendar

[Irv Bromberg]

Dear Kalendarists:

The 13-Month Calendar implemented with a Leap Week at the end of the year has the disadvantage that it can't be divided into quarters having whole months, but it has many very attractive advantages:

• perpetual, conserves the traditional 7-day weekly cycle
• every month has the same length = 28 days = 4 weeks
• every month starts on the same weekday
• exactly matches the ISO leap week calendar if weeks start on Monday, the same leap rule is employed, and if the ISO week counts are grouped by 4s.

The historical records says that the League of Nations rejected the 13-Month Calendar in favour of The World Calendar because the former couldn't be divided into quarters whereas the latter can be.  Neither the original 13-month nor conserved the 7-day week, but either can easily be implemented as a leap week calendar.  A leap week version of the World Calendar lacks the last 3 advantages listed above, as is the case for my Symmetry010 calendar as well as 100 and 001 variants of it.

How big a deal is division into 4 equal quarters containing only whole months?  Is this really essential?  Is division into quarters as important for businesses as conservation of the 7-day sabbatical cycle is to the major religions?  I have been given to understand that indeed it is truly the "deal breaker", and that is why my Sym454 and Sym010 calendars are divisible into quarters.  On the other hand, the uniform simplicity and consistency of the 13-month calendar layout are very, very attractive.

Some considerations for a 13-Month calendar:

• What should be the name of the extra month, and where should it be positioned in the year?  Americans objected to "Sol" being inserted between June and July because it meant that American Independence Day would fall in Sol instead of July.  If the extra month goes at the end of the year then Christmas won't be in December!
• It is one thing to lay out a 13-month calendar, but it is quite another matter to account for all the holidays and events that need to be adapted to it.  What should be the rules for fixed holidays and events within months?  For events falling within the first 4 weeks of a Gregorian month, it would seem easy to assign them corresponding dates, depending on where the extra month goes.  For events falling from the 29th to 31st day of a Gregorian month, they could be reassigned to a date that is an equal number of days from the end of the corresponding 28-day month.  These rules come close to the Gregorian dates near the beginning of the year, but as the shorter months pass, events on the 13-month calendar will fall out earlier.  If the extra month is not at the end of the year then events will suddenly be "late" by 28 days after the inserted extra month.  These are not insurmountable problems, they just require some sensible rules.
• By the term "fixed holidays", I am excluding Easter and related days counted before and after Easter.  These could be reckoned according to a computus or astronomically or could also be fixed.  For example if the extra month comes somewhere later in the year then the median date for an astronomical Easter would be Sunday, April 14th so that could be proposed as the fixed date for Easter.  (This is the same as Sunday, April 7th on my Symmetry454 or Symmetry010 calendars when the ISO leap rule is employed.  Here you see that already after the first 1/4 of the year the 13-month day number is 7 days later.)
• A different way to assign holidays and events could be to examine the ISO and 13-Month calendars running in parallel to the Gregorian calendar, picking the closest permanent dates that way.  This might mean that an event that in the Gregorian calendar falls on the nth k-day of the mth month might fall on a different k-day or perhaps in a different month.

Although my freeware calendrical calculator Kalendis does offer a leap week variant of the 13-month calendar, it calls the month between June and July "Sol" and it makes no attempt to reckon or report any holidays or events on that calendar.  (The code is actually written, but suppressed during compilation, and subject to revision depending on what others think in regard to the above.)

-- Dr. Irv Bromberg, University of Toronto, Canada

<http://www.sym454.org/>

[Karl Palmen]

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Dear Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 25 January 2012 03:56
To: CALNDR-L@...
Subject: 13-Month Leap Week Calendar

 

Dear Kalendarists:

 

The 13-Month Calendar implemented with a Leap Week at the end of the year has the disadvantage that it can't be divided into quarters having whole months, but it has many very attractive advantages:

 

• perpetual, conserves the traditional 7-day weekly cycle
• every month has the same length = 28 days = 4 weeks

KARL SAYS:  Only if  the days of the leap week are not counted as belonging to a month. Having days not belonging to a month would itself be a problem. Which month’s pay would working on a leap week day count towards?

For that reason and the quarters I’d prefer Symmetry454 months. However I would like 13-months in a leap day calendar.

Karl

12(08(02 till noon

 

--
Scanned by iCritical.

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 25 January 2012 03:56
To: CALNDR-L@...
Subject: 13-Month Leap Week Calendar

 

Dear Kalendarists:

 

The 13-Month Calendar implemented with a Leap Week at the end of the year has the disadvantage that it can't be divided into quarters having whole months, but it has many very attractive advantages:

 

• perpetual, conserves the traditional 7-day weekly cycle
• every month has the same length = 28 days = 4 weeks
• every month starts on the same weekday

KARL SAYS: The only way of ensuring every month has 28 days and every day belongs to a month, is to have a leap month calendar. This works nicely with the 293-year cycle which would have 13 leap months. Symmetrically distributed they would occur in the  12^th , 34^th, 57^th, 79^th, 102^nd, 124^th, 147^th, 170^th,  192^nd, 215^th, 237^th, 260^th & 282^nd   years of the 293-year cycle. Intervals alternate between 22 and 23 years, except around the middle (147th) year which has intervals of 23 years both sides.

 

The drawback is the jitter, but this is no higher than the solar jitter in a lunisolar calendar.

 

Karl

 

12(08(03

--
Scanned by iCritical.

[Irv Bromberg]

On 2012 Jan 24, at 22:55 , Irv Bromberg wrote:

The 13-Month Calendar implemented with a Leap Week at the end of the year has the disadvantage that it can't be divided into quarters having whole months, but it has many very attractive advantages:

• perpetual, conserves the traditional 7-day weekly cycle
• every month has the same length = 28 days = 4 weeks
• every month starts on the same weekday

On 2012 Jan 25, at 04:02 , Karl Palmen wrote:

KARL SAYS:  Only if  the days of the leap week are not counted as belonging to a month. Having days not belonging to a month would itself be a problem. Which month’s pay would working on a leap week day count towards?

For that reason and the quarters I’d prefer Symmetry454 months. However I would like 13-months in a leap day calendar.

Irv replies:  I was continuing to conceive of a separately running 2-week cycle for salaries, and a 4-week cycle for rentals and similar payments.  However Karl is right in pointing out the simplicity of a calendar where all months have 28 days, in that it allows regular monthly or semi-monthly transactions to be on fixed dates.  What about the leap week?  It would occur only once in 6 or 5 years.  Choices are to have it stand-alone as a 7-day "mini-month", or to append it to the last month of the year, which has 35 days in leap years.  Either way it is an "extra" week, but occurs at rare intervals averaging 294 weeks.

On 2012 Jan 25, at 08:10 , Karl Palmen wrote:

The only way of ensuring every month has 28 days and every day belongs to a month, is to have a leap month calendar. This works nicely with the 293-year cycle which would have 13 leap months. Symmetrically distributed they would occur in the  12th , 34th, 57th, 79th, 102nd, 124th, 147th, 170th,  192nd, 215th, 237th, 260th & 282nd   years of the 293-year cycle. Intervals alternate between 22 and 23 years, except around the middle (147th) year which has intervals of 23 years both sides.

 
The drawback is the jitter, but this is no higher than the solar jitter in a lunisolar calendar.

Irv replies:  In a lunisolar calendar the jitter is almost 31 days (lunar jitter added to solar jitter), but here it would be slightly less than 28 days.

My freeware Ford Circles spreadsheet can list cycles and draw Ford circles for "Solar 28-day Leap Month" calendars.

The 293-year cycle is interesting in that most years have 13 months and there are 13 leap months in the cycle, as Karl pointed out above.

The average leap interval is 22+7/13 years.

Primary sub-cycle: •••••••••••|•••••••••••••••••••••|••••••••••• = 45 years with 2 long, mean year 365+11/45 days = 365 days 5h 52m 0s = about 365.244444444444444 days
Second sub-cycle: •••••••••••|••••••••••• = 23 years with 1 long, mean year 365+5/23 days = 365 days 5h 13m 2+14/23s = about 365.217391304347826 days

The overall symmetrical sub-cycle pattern is:
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••

Another attractive cycle is the 1803-year cycle with 80 leap months.  Its average leap interval is 22+43/80 years.

It could be used with an exceptionally short but accurate 1803-year Easter computus having a mean month of 29+2958/5575 days (25-saros cycle x 4 = 1803 years).

Its symmetrical sub-cycle pattern contains 4 repeats of the 293-year cycle, and in the middle contains a 631-year cycle, which has a longer mean year:

Cycle Mean Year = 365+153/631 days = 365 days 5h 49m 9+381/631s = about 365.242472266244057 days = about 365 days 5:49:09.604

The 631-year cycle equals 293 + 45 + 293.

So altogether the 1803-year cycle can be viewed as (3 x 293 + 45 + 293 x 3).

For the north solstice my favorite leap week cycles are the 389- and 327-year cycles, but they have to be multiplied to work with a 28-day leap month:

389 x 4 = 1556 years with 69 leap months.

327 x 2 = 654 years with 29 leap months.

In both cases, therefore, they end up with an even number of years per cycle, so can only be made almost symmetrical.

The 654-year cycle = (203 + 45 + 203 + 203) years, or it could be (203 + 203 + 45 + 203) years.

where the 203-year sub-cycle has  a Cycle Mean Year = 365+7/29 days = 365 days 5h 47m 35+5/29s = about 365.241379310344828 days = about 365 days 5:47:35.172 and its symmetrical sub-cycle pattern is:

•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••

which is similar to the above 293-year cycle pattern except for the removal of the first and last 45-year sub-cycles.

The 1556-year cycle = (203 + 45 + 203 + 203 + 45 + 203 + 203 + 203 + 45 + 203), or it could be (203 + 45 + 203 + 203 + 203 + 45 + 203 + 203 + 45 + 203).

-- Dr. Irv Bromberg, University of Toronto, Canada

<http://www.sym454.org/>

[Irv Bromberg]

On 2012 Jan 25, at 11:41 , Sonny Pondrom wrote:

The leap week question goes away with a leap day at the end of a 13 month layout shown below.  Also "Nova" would be a good name for the first month in a new year.  

It can never go away because proposing a null weekday calendar reform is hopelessly futile, even though Sonny is obviously pinning all of his hopes on it.

"Nova" sounds too much like "November" and would make it impossible to use the "Nov" abbreviation unambiguously.

[Peace Crusader]

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20120126.0815

Dear Calendar People,

A 13-month calendar may have the following disadvantages:

1.      It is not divisible by four which is equal to four quarters a year.  The quarters approximate the seasons.

2.      There are many days that are affected.  If we presently  have 31 days in one month, then three days will be lost and disenfranchised; 30 days, two days lost; 29 days like in Febraury during a leap year, one day lost.

3.      The same number of days every month maybe monotonous.  A 12-month calendar is varied with 91 days per quarter starting on three different days of the week.

Best regards.
Aristeo Canlas Fernando, Peace Crusader and Echo of the Holy Spirit
Motto: pro aris et focis (for the sake of, or defense of, religion and home)
http://aristean.org/ and http://peacecrusader.wordpress.com/
"The Internet is mightier than the sword."

From: Karl Palmen <karl.palmen@...>
To: CALNDR-L@...
Sent: Wednesday, January 25, 2012 7:02 PM
Subject: Re: 13-Month Leap Week Calendar

Dear Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 25 January 2012 03:56
To: CALNDR-L@...
Subject: 13-Month Leap Week Calendar

 

Dear Kalendarists:

 

The 13-Month Calendar implemented with a Leap Week at the end of the year has the disadvantage that it can't be divided into quarters having whole months, but it has many very attractive advantages:

 

• perpetual, conserves the traditional 7-day weekly cycle
• every month has the same length = 28 days = 4 weeks

KARL SAYS:  Only if  the days of the leap week are not counted as belonging to a month. Having days not belonging to a month would itself be a problem. Which month’s pay would working on a leap week day count towards?

For that reason and the quarters I’d prefer Symmetry454 months. However I would like 13-months in a leap day calendar.

Karl

12(08(02 till noon

 

--
Scanned by iCritical.

[Irv Bromberg]

On 2012 Jan 25, at 17:47 , Aristeo Fernando wrote:

A 13-month calendar may have the following disadvantages:
1.      It is not divisible by four which is equal to four quarters a year.  The quarters approximate the seasons.

Victor just explained how easy it is to divide into 4 equal quarters.

2.      There are many days that are affected.  If we presently  have 31 days in one month, then three days will be lost and disenfranchised; 30 days, two days lost; 29 days like in Febraury during a leap year, one day lost.

What the <beep> is a disenfranchised day?  Day numbers are just labels for dates.  All dates are convertible, they don't disappear into "limbo".

If somebody was born on the 30th day of March then their birthday converts to the corresponding day on the 13-month calendar.

There is no reason why this would be any more exceptional than converting anybody else's birthday.

It is true that somebody born on the 17th of March may choose to retain their birthday on that day, but the government would most likely want the official birthday to be the actual date of the proleptic calendar on the true date of their birth.  Fair to everybody.

The only concern is regarding to what I asked about previously, and is easy to resolve by deciding on the rules:  what should be the rule if a holiday or event falls in the 29th, 30th, or 31st day of the Gregorian month?  How should that be converted?  One could go back to the original event or observance and see what the 13-month date was then, and carry that forward.  Or one could do a from-the-end-of-the-month count -- if the event occurred on the last day of the month, then observe it on the last day of the 28-day month.  And so on.  If an event was observed on the nth weekday of a month, then that will always work in a 28-day month, as nth=5th is never used because it won't always work.  Likewise the last such-and-such weekday of the month is not a problem.

3.      The same number of days every month maybe monotonous.  A 12-month calendar is varied with 91 days per quarter starting on three different days of the week.

This "monotonous" attribute is by design -- "it is a feature not a bug".  Eliminate all month-to-month variations to make every month identical and fair, equal numbers of workdays and weekend days, consistent like clockwork.  Like I asked before, would you consider it acceptable if your clock used variable number of hours per day, or minutes per hour, or seconds per minute (well OK, we rarely do have a leap second)?  A calendar is likewise a time-keeping device.  It should keep regular, consistent time.  No excitement, no fun, no variations.  You want those then go to a party.  Or buy a calendar with wonderful pictures on it.

-- Dr. Irv Bromberg, University of Toronto, Canada

<http://www.sym454.org/>

[Karl Palmen]

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Dear Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 25 January 2012 15:29
To: CALNDR-L@...
Subject: Re: 13-Month Leap Week Calendar

 

On 2012 Jan 24, at 22:55 , Irv Bromberg wrote:

The 13-Month Calendar implemented with a Leap Week at the end of the year has the disadvantage that it can't be divided into quarters having whole months, but it has many very attractive advantages:

• perpetual, conserves the traditional 7-day weekly cycle
• every month has the same length = 28 days = 4 weeks
• every month starts on the same weekday

 

On 2012 Jan 25, at 04:02 , Karl Palmen wrote:

KARL SAYS:  Only if  the days of the leap week are not counted as belonging to a month. Having days not belonging to a month would itself be a problem. Which month’s pay would working on a leap week day count towards?

For that reason and the quarters I’d prefer Symmetry454 months. However I would like 13-months in a leap day calendar.

 

Irv replies:  I was continuing to conceive of a separately running 2-week cycle for salaries, and a 4-week cycle for rentals and similar payments.  However Karl is right in pointing out the simplicity of a calendar where all months have 28 days, in that it allows regular monthly or semi-monthly transactions to be on fixed dates.  What about the leap week?  It would occur only once in 6 or 5 years.  Choices are to have it stand-alone as a 7-day "mini-month", or to append it to the last month of the year, which has 35 days in leap years.  Either way it is an "extra" week, but occurs at rare intervals averaging 294 weeks.

 

KARL SAYS: This leads to the idea of a fortnight calendar in which each year has 26 fortnights and a leap week is inserted once every 147 fortnights (5 years and 17 fortnights).

 

On 2012 Jan 25, at 08:10 , Karl Palmen wrote:

The only way of ensuring every month has 28 days and every day belongs to a month, is to have a leap month calendar. This works nicely with the 293-year cycle which would have 13 leap months. Symmetrically distributed they would occur in the  12th , 34th, 57th, 79th, 102nd, 124th, 147th, 170th,  192nd, 215th, 237th, 260th & 282nd   years of the 293-year cycle. Intervals alternate between 22 and 23 years, except around the middle (147th) year which has intervals of 23 years both sides.

 
The drawback is the jitter, but this is no higher than the solar jitter in a lunisolar calendar.

 

Irv replies:  In a lunisolar calendar the jitter is almost 31 days (lunar jitter added to solar jitter), but here it would be slightly less than 28 days.

 

KARL SAYS: Solar and lunar jitter are separate and make no sense to add them. A lunisolar calendar has a solar jitter that can be as little as one lunar month 29 or 30 days and a lunar jitter as little as 1 day, but the jitters can each be a day or two higher to make the calendar simpler (e.g. make most months of the year the same length every year) or accommodate postponement rules.

 

 

My freeware Ford Circles spreadsheet can list cycles and draw Ford circles for "Solar 28-day Leap Month" calendars.

 

The 293-year cycle is interesting in that most years have 13 months and there are 13 leap months in the cycle, as Karl pointed out above.

The average leap interval is 22+7/13 years.

 

Primary sub-cycle: •••••••••••|•••••••••••••••••••••|••••••••••• = 45 years with 2 long, mean year 365+11/45 days = 365 days 5h 52m 0s = about 365.244444444444444 days
Second sub-cycle: •••••••••••|••••••••••• = 23 years with 1 long, mean year 365+5/23 days = 365 days 5h 13m 2+14/23s = about 365.217391304347826 days

 

KARL SAYS: These are the two periods that arise from the first level of the cutting algorithm. The number of weeks in the 23-years is exactly 1200.

 

The overall symmetrical sub-cycle pattern is:
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••

KARL SAYS:  (45+45+45+23+45+45+45). This shows that the 293-year cycle has no further non-trivial levels of the cutting algorithm. This applies to all cycles of forms

(a)    248*N + 45 years and 11*N + 2 leap months

(b)   338*N – 45 years and 15*N – 2 leap months

(c)    248*N – 45 years and 11*N – 2 leap months

The 293-year cycle belongs to both classes (a) and (b) with N=1.

 

Another attractive cycle is the 1803-year cycle with 80 leap months.  Its average leap interval is 22+43/80 years.

It could be used with an exceptionally short but accurate 1803-year Easter computus having a mean month of 29+2958/5575 days (25-saros cycle x 4 = 1803 years).

 

KARL SAYS: The 1803-year cycle has six 23s and thirty-seven 45s ( 6*23+37*45=1803 & 6*1+37*2=80). This makes it equivalent to six 293-year cycles plus a 45. Irv confirms this next.

 

Its symmetrical sub-cycle pattern contains 4 repeats of the 293-year cycle, and in the middle contains a 631-year cycle, which has a longer mean year:

Cycle Mean Year = 365+153/631 days = 365 days 5h 49m 9+381/631s = about 365.242472266244057 days = about 365 days 5:49:09.604

The 631-year cycle equals 293 + 45 + 293.

So altogether the 1803-year cycle can be viewed as (3 x 293 + 45 + 293 x 3).

 

KARL SAYS: The cutting algorithm produces a second level of cutting which is the (293, 293, 631, 293, 293) that Irv has described. The 631 like the 293 is of the form (b) 338*N – 45 years and 15*N – 2 leap months (for N=2) and so has only one level of cutting (23s and 45s) in the cutting algorithm. The cutting algorithm has only one second level cut in any run of 45s and this cut must be in exactly the middle of the run of 45s. This is not possible for the run of seven 45s in the middle of the 631. For the 1803-year leap week cycle there is no second level of cutting (only the 1^st level which is 11s and 17s).

 

As a leap week cycle, the 631-year cycle can be formed from a Gregorian 400-year cycle of 71 leap weeks plus a 231-year cycle of 41 leap weeks made from the 33-year cycle.

 

 

For the north solstice my favorite leap week cycles are the 389- and 327-year cycles, but they have to be multiplied to work with a 28-day leap month:

389 x 4 = 1556 years with 69 leap months.

327 x 2 = 654 years with 29 leap months.

In both cases, therefore, they end up with an even number of years per cycle, so can only be made almost symmetrical.

 

KARL SAYS: 389+389+327 produces a 1105-year cycle with 49 leap months. The cutting algorithm would produce a second level of (451, 203, 451).

 

 

The 654-year cycle = (203 + 45 + 203 + 203) years, or it could be (203 + 203 + 45 + 203) years.

where the 203-year sub-cycle has  a Cycle Mean Year = 365+7/29 days = 365 days 5h 47m 35+5/29s = about 365.241379310344828 days = about 365 days 5:47:35.172 and its symmetrical sub-cycle pattern is:

 

•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••
•••••••••••|•••••••••••••••••••••|•••••••••••

which is similar to the above 293-year cycle pattern except for the removal of the first and last 45-year sub-cycles.

 

KARL SAYS: The cutting algorithm would produce a second level of (203, 451) or (451, 203), which are trivially almost symmetrical. The 451 is of form (c) 248*N – 45 years and 11*N – 2 leap months (for N=2).

 

 

The 1556-year cycle = (203 + 45 + 203 + 203 + 45 + 203 + 203 + 203 + 45 + 203), or it could be (203 + 45 + 203 + 203 + 203 + 45 + 203 + 203 + 45 + 203).

 

KARL SAYS: The cutting algorithm would produce (451, 451, 203, 451) at the second level or its reverse.  Looking at (451, 203) and (451, 451, 203, 451) suggests the symmetrical (451, 203, 451), which is the 1105-year cycle already mentioned.

 

Karl

 

12(08(04

 

--
Scanned by iCritical.

[Irv Bromberg]

On 2012 Jan 26, at 08:37 , Karl Palmen wrote:

This leads to the idea of a fortnight calendar in which each year has 26 fortnights and a leap week is inserted once every 147 fortnights (5 years and 17 fortnights).

Hours after Karl's suggestion, I'm still liking it, and want to pursue it further...

I just fired off a message to another fellow in England who suggested a fortnight calendar to me several years ago, to find out what were the details of his design.

The leap year list could show the year number with a lowercase letter suffix that indicates which fortnight the leap week will follow.

Got any ideas for the calendrical calculation algorithms for that calendar?

Is the symmetrical arithmetic leap rule always going to correctly identify that a year contains a leap week (somewhere)?

If so then the symmetrical arithmetic for the New Year Day will still work with that calendar.

If we calculate the number of weeks since the epoch then the week number that is zero MOD 294 shall be a leap week.

Oh wait, do we need (week + 147) MOD 294 to get the proper symmetry?

All fortnights starting after that week are delayed by one week from their normal position.

-- Dr. Irv Bromberg, University of Toronto, Canada

<http://www.sym454.org/>

[Brillig]

Dear Irv, Karl, and Calendar People,

Karl and I exchanged emails with each other regarding calculations pertaining to a fortnight calendar 5 or 6 years ago. There have also been occasional posts regarding fortnight calendars here on the list from time to time. I'll go back into my email archives and see if there is anything worth posting.

I'm not sure I care for the idea of having a fortnight calendar withe a leap week. I think I'd prefer either leap fortnights or leap days or no leap at all.

Victor

On Thu, Jan 26, 2012 at 4:41 PM, Irv Bromberg <irv.bromberg@...> wrote:

On 2012 Jan 26, at 08:37 , Karl Palmen wrote:

This leads to the idea of a fortnight calendar in which each year has 26 fortnights and a leap week is inserted once every 147 fortnights (5 years and 17 fortnights).

Hours after Karl's suggestion, I'm still liking it, and want to pursue it further...

I just fired off a message to another fellow in England who suggested a fortnight calendar to me several years ago, to find out what were the details of his design.

The leap year list could show the year number with a lowercase letter suffix that indicates which fortnight the leap week will follow.

Got any ideas for the calendrical calculation algorithms for that calendar?

Is the symmetrical arithmetic leap rule always going to correctly identify that a year contains a leap week (somewhere)?

If so then the symmetrical arithmetic for the New Year Day will still work with that calendar.

If we calculate the number of weeks since the epoch then the week number that is zero MOD 294 shall be a leap week.

Oh wait, do we need (week + 147) MOD 294 to get the proper symmetry?

All fortnights starting after that week are delayed by one week from their normal position.

-- Dr. Irv Bromberg, University of Toronto, Canada

<http://www.sym454.org/>

[Irv Bromberg]

On 2012 Jan 26, at 08:37 , Karl Palmen wrote:

On 2012 Jan 25, at 08:10 , Karl Palmen wrote:The only way of ensuring every month has 28 days and every day belongs to a month, is to have a leap month calendar. This works nicely with the 293-year cycle which would have 13 leap months. Symmetrically distributed they would occur in the  12th , 34th, 57th, 79th, 102nd, 124th, 147th, 170th,  192nd, 215th, 237th, 260th & 282nd   years of the 293-year cycle. Intervals alternate between 22 and 23 years, except around the middle (147th) year which has intervals of 23 years both sides. The drawback is the jitter, but this is no higher than the solar jitter in a lunisolar calendar.

Irv replies:  In a lunisolar calendar the jitter is almost 31 days (lunar jitter added to solar jitter), but here it would be slightly less than 28 days.

KARL SAYS: Solar and lunar jitter are separate and make no sense to add them. A lunisolar calendar has a solar jitter that can be as little as one lunar month 29 or 30 days and a lunar jitter as little as 1 day, but the jitters can each be a day or two higher to make the calendar simpler (e.g. make most months of the year the same length every year) or accommodate postponement rules.

 

Irv replies:  Perhaps it was not clear what I meant.  In a lunisolar calendar months can be 29 or 30 days.  This adds to the equinox jitter -- if you take the worse cases then the jitter span is 31 days, but it takes at least 3+1/2 centuries to see this.  This has nothing to do with the jitter of the months relative to the lunar cycle.

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Irv and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 27 January 2012 13:59
To: CALNDR-L@...
Subject: Re: 13-Month Leap Week Calendar

 

On 2012 Jan 26, at 08:37 , Karl Palmen wrote:

On 2012 Jan 25, at 08:10 , Karl Palmen wrote:The only way of ensuring every month has 28 days and every day belongs to a month, is to have a leap month calendar. This works nicely with the 293-year cycle which would have 13 leap months. Symmetrically distributed they would occur in the  12th , 34th, 57th, 79th, 102nd, 124th, 147th, 170th,  192nd, 215th, 237th, 260th & 282nd   years of the 293-year cycle. Intervals alternate between 22 and 23 years, except around the middle (147th) year which has intervals of 23 years both sides. The drawback is the jitter, but this is no higher than the solar jitter in a lunisolar calendar.

Irv replies:  In a lunisolar calendar the jitter is almost 31 days (lunar jitter added to solar jitter), but here it would be slightly less than 28 days.

 

KARL SAYS: Solar and lunar jitter are separate and make no sense to add them. A lunisolar calendar has a solar jitter that can be as little as one lunar month 29 or 30 days and a lunar jitter as little as 1 day, but the jitters can each be a day or two higher to make the calendar simpler (e.g. make most months of the year the same length every year) or accommodate postponement rules.

 

Irv replies:  Perhaps it was not clear what I meant.  In a lunisolar calendar months can be 29 or 30 days.  This adds to the equinox jitter -- if you take the worse cases then the jitter span is 31 days, but it takes at least 3+1/2 centuries to see this.  This has nothing to do with the jitter of the months relative to the lunar cycle.

 

KARL SAYS: I’m not convinced about this at all. A lunisolar calendar can in principle choose its new year to be the closest month start to the equinox and in so doing limit the jitter to one month.

 

Karl

 

12(08(14 till noon

--
Scanned by iCritical.

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Calendar People

 

I realise that the fortnight calendar I hastily suggested would not have the desired mean year. Instead one would require leap weeks alternating every 146 and 147 fortnights. Alternatively, one could have a leap fortnight every 293 ordinary fortnights, which is 11 years and 7 fortnights.

 

Such a calendar requires an additional rule, such as the first fortnight of the year cannot be a leap fortnight, else the calendar rules would not define the year of all fortnights.

If the above-mentioned rule is included, a symmetrical distribution of leap years (but not leap fortnights), would result if the first leap fortnight were to occur after the 17^th fortnight of year 6 (i.e. is the 148^th fortnight). Although the distribution of the leap fortnights is not symmetrical, the distribution of the pairs of fortnights consisting of a leap fortnight and the preceding fortnight are symmetrical. Both fortnights of such a pair would have the same letter or number (similar to Chinese calendar months).

 

Karl

 

12(08(14 till noon

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 26 January 2012 22:59
To: CALNDR-L@...
Subject: Re: 13-Month Leap Week Calendar

 

Dear Irv, Karl, and Calendar People,

Karl and I exchanged emails with each other regarding calculations pertaining to a fortnight calendar 5 or 6 years ago. There have also been occasional posts regarding fortnight calendars here on the list from time to time. I'll go back into my email archives and see if there is anything worth posting.

I'm not sure I care for the idea of having a fortnight calendar withe a leap week. I think I'd prefer either leap fortnights or leap days or no leap at all.

Victor

On Thu, Jan 26, 2012 at 4:41 PM, Irv Bromberg <irv.bromberg@...> wrote:

On 2012 Jan 26, at 08:37 , Karl Palmen wrote:

This leads to the idea of a fortnight calendar in which each year has 26 fortnights and a leap week is inserted once every 147 fortnights (5 years and 17 fortnights).

 

Hours after Karl's suggestion, I'm still liking it, and want to pursue it further...

 

I just fired off a message to another fellow in England who suggested a fortnight calendar to me several years ago, to find out what were the details of his design.

 

The leap year list could show the year number with a lowercase letter suffix that indicates which fortnight the leap week will follow.

 

Got any ideas for the calendrical calculation algorithms for that calendar?

Is the symmetrical arithmetic leap rule always going to correctly identify that a year contains a leap week (somewhere)?

If so then the symmetrical arithmetic for the New Year Day will still work with that calendar.

 

If we calculate the number of weeks since the epoch then the week number that is zero MOD 294 shall be a leap week.

Oh wait, do we need (week + 147) MOD 294 to get the proper symmetry?

All fortnights starting after that week are delayed by one week from their normal position.

 

-- Dr. Irv Bromberg, University of Toronto, Canada

 

<http://www.sym454.org/>

 

--
Scanned by iCritical.

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Victor and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 26 January 2012 22:59
To: CALNDR-L@...
Subject: Re: 13-Month Leap Week Calendar

 

Dear Irv, Karl, and Calendar People,

Karl and I exchanged emails with each other regarding calculations pertaining to a fortnight calendar 5 or 6 years ago. There have also been occasional posts regarding fortnight calendars here on the list from time to time. I'll go back into my email archives and see if there is anything worth posting.

I'm not sure I care for the idea of having a fortnight calendar withe a leap week. I think I'd prefer either leap fortnights or leap days or no leap at all.

KARL SAYS: The hastily suggested fortnight calendar with leap weeks every 147 fortnights is not correct. One would need to alternate between 147 and 146 fortnights for it to work, making it a lot less attractive. The leap fortnight calendar would have a leap fortnight once every 293 ordinary fortnights (11 years 7 fortnights).

Karl

 

12(08(15

Victor

On Thu, Jan 26, 2012 at 4:41 PM, Irv Bromberg <irv.bromberg@...> wrote:

On 2012 Jan 26, at 08:37 , Karl Palmen wrote:

This leads to the idea of a fortnight calendar in which each year has 26 fortnights and a leap week is inserted once every 147 fortnights (5 years and 17 fortnights).

 

Hours after Karl's suggestion, I'm still liking it, and want to pursue it further...

 

I just fired off a message to another fellow in England who suggested a fortnight calendar to me several years ago, to find out what were the details of his design.

 

The leap year list could show the year number with a lowercase letter suffix that indicates which fortnight the leap week will follow.

 

Got any ideas for the calendrical calculation algorithms for that calendar?

Is the symmetrical arithmetic leap rule always going to correctly identify that a year contains a leap week (somewhere)?

If so then the symmetrical arithmetic for the New Year Day will still work with that calendar.

 

If we calculate the number of weeks since the epoch then the week number that is zero MOD 294 shall be a leap week.

Oh wait, do we need (week + 147) MOD 294 to get the proper symmetry?

All fortnights starting after that week are delayed by one week from their normal position.

 

-- Dr. Irv Bromberg, University of Toronto, Canada

 

<http://www.sym454.org/>

 

--
Scanned by iCritical.

[Brillig]

Hmmm. It's a little long, but I note that a solar cycle is about 11 years.

On Mon, Feb 6, 2012 at 9:31 AM, Karl Palmen <karl.palmen@...> wrote:

Dear Victor and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 26 January 2012 22:59
To: CALNDR-L@...
Subject: Re: 13-Month Leap Week Calendar

 

Dear Irv, Karl, and Calendar People,

Karl and I exchanged emails with each other regarding calculations pertaining to a fortnight calendar 5 or 6 years ago. There have also been occasional posts regarding fortnight calendars here on the list from time to time. I'll go back into my email archives and see if there is anything worth posting.

I'm not sure I care for the idea of having a fortnight calendar withe a leap week. I think I'd prefer either leap fortnights or leap days or no leap at all.

KARL SAYS: The hastily suggested fortnight calendar with leap weeks every 147 fortnights is not correct. One would need to alternate between 147 and 146 fortnights for it to work, making it a lot less attractive. The leap fortnight calendar would have a leap fortnight once every 293 ordinary fortnights (11 years 7 fortnights).

Karl

 

12(08(15

Victor

On Thu, Jan 26, 2012 at 4:41 PM, Irv Bromberg <irv.bromberg@...> wrote:

On 2012 Jan 26, at 08:37 , Karl Palmen wrote:

This leads to the idea of a fortnight calendar in which each year has 26 fortnights and a leap week is inserted once every 147 fortnights (5 years and 17 fortnights).

 

Hours after Karl's suggestion, I'm still liking it, and want to pursue it further...

 

I just fired off a message to another fellow in England who suggested a fortnight calendar to me several years ago, to find out what were the details of his design.

 

The leap year list could show the year number with a lowercase letter suffix that indicates which fortnight the leap week will follow.

 

Got any ideas for the calendrical calculation algorithms for that calendar?

Is the symmetrical arithmetic leap rule always going to correctly identify that a year contains a leap week (somewhere)?

If so then the symmetrical arithmetic for the New Year Day will still work with that calendar.

 

If we calculate the number of weeks since the epoch then the week number that is zero MOD 294 shall be a leap week.

Oh wait, do we need (week + 147) MOD 294 to get the proper symmetry?

All fortnights starting after that week are delayed by one week from their normal position.

 

-- Dr. Irv Bromberg, University of Toronto, Canada

 

<http://www.sym454.org/>

 

--
Scanned by iCritical.

[Karl Palmen]

Some parts of this message have been removed. Learn more about Nabble's security policy.

Dear Victor, Irv and Calendar People

 

The leap years symmetrically arranged (in Helios cycle) would be

 

006  

017 029 (2)

040

051

062 074 (5)

085

096 108 (7)

119

130

141 153 (10)

164

175

186 198 (13)

209

220 232 (15)

243

254

265 277 (18)

288

 

I’ve arranged the leap years are in rows of even and odd year numbers. There are 19 rows and the rows of two correspond to the leap years of a symmetrical Metonic cycle (2,5,7,10,13,15,18).

 

Karl

 

12(08(15

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 06 February 2012 16:01
To: CALNDR-L@...
Subject: Re: 13-Month Leap Week Calendar

 

Hmmm. It's a little long, but I note that a solar cycle is about 11 years.

On Mon, Feb 6, 2012 at 9:31 AM, Karl Palmen <karl.palmen@...> wrote:

Dear Victor and Calendar People

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Victor Engel
Sent: 26 January 2012 22:59
To: CALNDR-L@...
Subject: Re: 13-Month Leap Week Calendar

 

Dear Irv, Karl, and Calendar People,

Karl and I exchanged emails with each other regarding calculations pertaining to a fortnight calendar 5 or 6 years ago. There have also been occasional posts regarding fortnight calendars here on the list from time to time. I'll go back into my email archives and see if there is anything worth posting.

I'm not sure I care for the idea of having a fortnight calendar withe a leap week. I think I'd prefer either leap fortnights or leap days or no leap at all.

KARL SAYS: The hastily suggested fortnight calendar with leap weeks every 147 fortnights is not correct. One would need to alternate between 147 and 146 fortnights for it to work, making it a lot less attractive. The leap fortnight calendar would have a leap fortnight once every 293 ordinary fortnights (11 years 7 fortnights).

Karl

 

12(08(15

Victor

On Thu, Jan 26, 2012 at 4:41 PM, Irv Bromberg <irv.bromberg@...> wrote:

On 2012 Jan 26, at 08:37 , Karl Palmen wrote:

This leads to the idea of a fortnight calendar in which each year has 26 fortnights and a leap week is inserted once every 147 fortnights (5 years and 17 fortnights).

 

Hours after Karl's suggestion, I'm still liking it, and want to pursue it further...

 

I just fired off a message to another fellow in England who suggested a fortnight calendar to me several years ago, to find out what were the details of his design.

 

The leap year list could show the year number with a lowercase letter suffix that indicates which fortnight the leap week will follow.

 

Got any ideas for the calendrical calculation algorithms for that calendar?

Is the symmetrical arithmetic leap rule always going to correctly identify that a year contains a leap week (somewhere)?

If so then the symmetrical arithmetic for the New Year Day will still work with that calendar.

 

If we calculate the number of weeks since the epoch then the week number that is zero MOD 294 shall be a leap week.

Oh wait, do we need (week + 147) MOD 294 to get the proper symmetry?

All fortnights starting after that week are delayed by one week from their normal position.

 

-- Dr. Irv Bromberg, University of Toronto, Canada

 

<http://www.sym454.org/>

 

 

--
Scanned by iCritical.

 

 

--
Scanned by iCritical.

[Irv Bromberg]

On 2012 Feb 6, at 11:00 , Victor Engel wrote:

Hmmm. It's a little long, but I note that a solar cycle is about 11 years.

It's about 11  years per half-cycle.  It is true that the sunspots wax and wane over a cycle of roughly 11 years, but more precisely they alternate in magnetic polarity every 11 years.  So the actual cycle is about 22 years.  Although the fact that the magnetic polarity alternates may not have any effectual importance, nevertheless solar sunspot theory will eventually need to explain why the cycle behaves that way.

-- Irv

[Brillig]

Irv,

I realize that. For normal observations of sunspots, the cycle is 11 years. I almost posted that the absolute value of the solar cycle has a period of about 11 years, but I figured that would be too confusing.

Victor

On Mon, Feb 6, 2012 at 11:28 AM, Irv Bromberg <irv.bromberg@...> wrote:

On 2012 Feb 6, at 11:00 , Victor Engel wrote:

Hmmm. It's a little long, but I note that a solar cycle is about 11 years.

It's about 11  years per half-cycle.  It is true that the sunspots wax and wane over a cycle of roughly 11 years, but more precisely they alternate in magnetic polarity every 11 years.  So the actual cycle is about 22 years.  Although the fact that the magnetic polarity alternates may not have any effectual importance, nevertheless solar sunspot theory will eventually need to explain why the cycle behaves that way.

-- Irv