Soviet calendar

[Joe Kress]

Calendar people:

I have rewritten the Wikipedia article on the Soviet calendar to
show via surviving calendars that its five- and six-day weeks were
always used with the Gregorian calendar, not with 30-day months,
based on a large number of sources. Any suggested improvement would
be appreciated.
http://en.wikipedia.org/wiki/Soviet_calendar

Although I cite two Russian language sources, others would be
appreciated, especially if they are online so that I can translate
them using Google translation.

Joe Kress

[Joachim Krueger]

Dear Joe and all,

thank you for this great work particularly with regard to
the images. It is the first time one can see these color-coded
calendars on the web.
The article states very clearly, that the soviet (revolutionary)
calendar was not an independent calendar beside the Gregorian
calendar. It was only a specific work-shift calendar for
industrial purposes based on the Gregorian calendar.

Greetings to all
Joachim Krueger

Joe Kress schrieb:
> Calendar people:
>
> I have rewritten the Wikipedia article on the Soviet calendar to show
> via surviving calendars that its five- and six-day weeks were always
> used with the Gregorian calendar, not with 30-day months, based on a
> large number of sources. Any suggested improvement would be appreciated.
> http://en.wikipedia.org/wiki/Soviet_calendar

[Irv Bromberg]

On 2008.07.24, at 00:22 , Joe Kress wrote:

I have rewritten the Wikipedia article on the Soviet calendar to show via surviving calendars that its five- and six-day weeks were always used with the Gregorian calendar, not with 30-day months, based on a large number of sources. Any suggested improvement would be appreciated.
http://en.wikipedia.org/wiki/Soviet_calendar

Irv replies:  That Soviet calendar was a leap day calendar.  Interestingly, if it had been a leap WEEK calendar with 5-day weeks then the leap year interval would be 20-21 years!

This would happen because the 365-day length of a short year would be much closer to the solar year length than the 370-day length of a long year -- try it on my Fixed Leap Cycle Finder at <http://www.sym454.org/leap/>.

A 6-day leap week calendar is the opposite extreme, as its 360-day short year is much further away from the solar year length than is its 366-day long year, making long years much more common and hence the average leap interval would be just over one year!

-- Irv Bromberg, Toronto, Canada

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

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

 

Examples of such calendars exist on the web.

---

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 24 July 2008 15:13
To: CALNDR-L@...
Subject: Re: Soviet calendar

On 2008.07.24, at 00:22 , Joe Kress wrote:

I have rewritten the Wikipedia article on the Soviet calendar to show via surviving calendars that its five- and six-day weeks were always used with the Gregorian calendar, not with 30-day months, based on a large number of sources. Any suggested improvement would be appreciated.
http://en.wikipedia.org/wiki/Soviet_calendar

Irv replies:  That Soviet calendar was a leap day calendar.  Interestingly, if it had been a leap WEEK calendar with 5-day weeks then the leap year interval would be 20-21 years! 

See http://web.ncf.ca/aa735/new_cal.html . It uses one of two leap week rules suggested by me. The other was a 62-year cycle of 3 leap weeks (21-21-20).

Also see http://www.hermetic.ch/cal_stud/sdwc/sdwc.htm#defn_ifdwc  which uses a 165-year cycle of 8 leap weeks such that every 21st year within a 165-year cycle has a leap week (21-21-21-21-21-21-21-18) 

For mean years of 365.2416 days to 365.2428 days, the mixer cycles are 21 years of one leap week and 41 years of two leap weeks.

This would happen because the 365-day length of a short year would be much closer to the solar year length than the 370-day length of a long year -- try it on my Fixed Leap Cycle Finder at <http://www.sym454.org/leap/>.

A 6-day leap week calendar is the opposite extreme, as its 360-day short year is much further away from the solar year length than is its 366-day long year, making long years much more common and hence the average leap interval would be just over one year! 

See  http://www.hermetic.ch/cal_stud/sdwc/sdwc.htm#defn_isdwc which uses a 198-year cycle of 25 short years such that every 8th year within a 198-year cycle is short.

For mean years of 365.2416 days to 365.2428 days, the mixer cycles are 87 years of 11 short years and 8 years of one short year (8-8-8-...-8-6).

 

Karl

 

09(13(22

[Irv Bromberg]

On 2008.07.24, at 11:06 , Palmen, KEV (Karl) wrote:

>> Irv replies:  That Soviet calendar was a leap day calendar.  
>> Interestingly, if it had been a leap WEEK calendar with 5-day weeks  
>> then the leap year interval would be 20-21 years!
>
> Karl says:  See http://web.ncf.ca/aa735/new_cal.html . It uses one  
> of two leap week rules suggested by me. The other was a 62-year  
> cycle of 3 leap weeks (21-21-20).
> Also see http://www.hermetic.ch/cal_stud/sdwc/sdwc.htm#defn_ifdwc   
> which uses a 165-year cycle of 8 leap weeks such that every 21st  
> year within a 165-year cycle has a leap week (21-21-21-21-21-21-21-18)

>> Irv continued:  A 6-day leap week calendar is the opposite extreme,  
>> as its 360-day short year is much further away from the solar year  
>> length than is its 366-day long year, making long years much more  
>> common and hence the average leap interval would be just over one  
>> year!
>
> Karl says:  See  http://www.hermetic.ch/cal_stud/sdwc/sdwc.htm#defn_isdwc 
>  which uses a 198-year cycle of 25 short years such that every 8th  
> year within a 198-year cycle is short.


Irv replies:

You certainly seem to strongly favor a calendar mean year of 365+8/33  
days!  The simple long year interval repeat patterns outlined above  
are interesting, the tradeoff being more equinox wobble, as the long  
years are not as smoothly spread as possible.  I'm wondering if there  
is a generic calculation for coming up with such simple sequences.  
Would it suffice to make it just the FLOOR of the mean long year  
interval for all intervals except the last?  Hmm, that would sometimes  
make the last interval exceptionally short...

For the northward equinox, I always prefer the slightly shorter  
calendar mean year of 365+71/293 days, which for a 6-day leap week  
would have 256 long years per 293-year cycle, whereas for a 5-day leap  
week it would require a 5 * 293 = 1465 years having 71 long years.

-- Irv Bromberg, Toronto, Canada

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

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

More about calendar cycles like those mentioned like
(21-21-21-21-21-21-21-18).

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 24 July 2008 19:09
To: CALNDR-L@...
Subject: Re: Five and Six day leap week calendars RE: Soviet calendar

On 2008.07.24, at 11:06 , Palmen, KEV (Karl) wrote:

>> Irv replies:  That Soviet calendar was a leap day calendar.  
>> Interestingly, if it had been a leap WEEK calendar with 5-day weeks
>> then the leap year interval would be 20-21 years!
>
> Karl says:  See http://web.ncf.ca/aa735/new_cal.html . It uses one of
> two leap week rules suggested by me. The other was a 62-year cycle of
> 3 leap weeks (21-21-20).
> Also see http://www.hermetic.ch/cal_stud/sdwc/sdwc.htm#defn_ifdwc   
> which uses a 165-year cycle of 8 leap weeks such that every 21st year
> within a 165-year cycle has a leap week (21-21-21-21-21-21-21-18)

>> Irv continued:  A 6-day leap week calendar is the opposite extreme,
>> as its 360-day short year is much further away from the solar year
>> length than is its 366-day long year, making long years much more
>> common and hence the average leap interval would be just over one
>> year!
>
> Karl says:  See  
> http://www.hermetic.ch/cal_stud/sdwc/sdwc.htm#defn_isdwc
>  which uses a 198-year cycle of 25 short years such that every 8th
> year within a 198-year cycle is short.

Irv replies:

You certainly seem to strongly favor a calendar mean year of 365+8/33
days!

KARL SAYS: It was not me who invented those two calendars. It was Peter
Meyer.


IRV CONTINUED:
The simple long year interval repeat patterns outlined above are
interesting, the tradeoff being more equinox wobble, as the long years
are not as smoothly spread as possible.  I'm wondering if there  
is a generic calculation for coming up with such simple sequences.  

KARL SAYS: By such a simple sequence. I take it Irv means a sequence
where the exceptional years are spaced equally within each calendar
cycle, but have a different spacing between cycles.

Let's consider it for leap weeks using a 7-day week. These occur at
intervals of five and six years when spaced as evenly as possible. There
are two approaches:
(1) Have every fifth year in the cycle have a leap week beginning with
the 5th (latest possible) year
(2) Have every sixth year in the cycle have a leap week beginning with
the 1st (earliest possible) year

Either can be done with the 28-year cycle of 5 leap weeks
(1) 05, 10, 15, 20, 25
(2) 01, 07, 13, 19, 25
But only (2) can be done to the 62-year cycle of 11 leap weeks, because
(1) would produce 12 leap weeks.
(2) 01, 07, 13, 19, 25,  31, 37, 43, 49, 55,  61.
The 293-year cycle is too long to be produced by either method.


IRV CONTINUES:
Would it suffice to make it just the FLOOR of the mean long year
interval for all intervals except the last?  Hmm, that would sometimes
make the last interval exceptionally short...

KARL SAY: No. For reasons stated above.

Irv's suggested approach is (1). For a cycle of C years of which L are
exceptional. Then the mean interval between the exceptional years is
C/L. The interval within the cycle is floor(C/L). For this to work I
reckon that
C < (L + 1) * floor(C/L)
For method (2) you use CEILING instead of FLOOR and for it to work I
reckon that
C > (L - 1) * ceiling(C/L)

For the 28-year cycle examples above we have
(1) 28 < 6 * 5  and (2) 28 > 4 * 6.
And the 62-year cycle
(1) 62 !< 12 * 5 and (2) 62 > 10 * 6

IRV CONTINUES:
For the northward equinox, I always prefer the slightly shorter calendar
mean year of 365+71/293 days, which for a 6-day leap week would have 256
long years per 293-year cycle, whereas for a 5-day leap week it would
require a 5 * 293 = 1465 years having 71 long years.

KARL SAYS:
In the examples Irv has just mentioned, only the 6-day week can have its
exceptional years spaced equally within its cycle.

Noting that the 6-day week has 293-256=37 short years per cycle. We have
a mean interval between short years of 7.9189 years, so using (2) to
round up to 8 we get
293 > 36 * 8.

So we can have short years thus: 001, 009, 017, 025, ... , 281, 289.

But for five day weeks the mean interval between long years is 20.6338.
so using (2) to round up to 21 we get
1465 !> 70 * 21.
Nor does it work for (1)
1465 !< 72 * 20.
However the short 165-year cycle of 8 long years works for either
approach
(1) 020, 040, 060, 080, 100, 120, 140, 160
(2) 001, 022, 043, 064, 085, 106, 127, 148.


Methods (1) and (2) always give a jitter less than two weeks.

To get a better idea of the jitter, compare the exceptional interval
over the end of the cycle with the equal interval within the cycle. For
the 165-year cycle, these are 25-20 for (1) and 18-21 for (2), so in
this case the jitter would be well less than two weeks.
Another way of assessing jitter is to ask the question how long would
the cycle need to be extended for correction by adding or removing a
leap week. In this case, it is 660 years for (1) and 1155 years for (2).
These are much longer, so indicate low jitter.
I can now see that the 1465-year cycle failed for (1) because it is
longer than about 660 years and failed for (2) because its longer than
about 1155 years.

Karl

09(13(23

[guvapo]

Dear Calendar People,

Commenting the Hadrian exhibition at the British Museum, there was a  
lenghty article in my newspaper.
The author quotes the belgian writer M. Yourcenar (Mémoires de  
Hadrien) where she writes : "The first day of the month athyr, the  
second year of the 226th Olympiad. It is the birthday of Osiris... ."
 From the context it seems this is the very day Antinous drowned in  
the Nile, the 3th day since the beginning of the Osiris mourning.

I don't have my copy of the Mémoirs at hand to check, but anyway  
Olympiad 226.2 is (225*4)+2 or 902-776 or AD 126. Most people agree  
with 130 AD as date of Antinous's death (probably based on Plutarch).

I thought the (mythical) birthday of Osiris was in one of the 5  
epagomenal days and not on 1 athyr, and the Osiris mystery festival  
started on 17 athyr.

Yourcenar published the famous Memoirs after 15 years of thorough  
research.
Was she misquoted in the newspaper or was she wrong ?

Guido VanPoucke
Brugge

[Irv Bromberg]

On 2008.07.25, at 09:28 , Palmen, KEV (Karl) wrote:

Irv wrote:  The simple long year interval repeat patterns outlined above are
interesting, the tradeoff being more equinox wobble, as the long years
are not as smoothly spread as possible.  I'm wondering if there  
is a generic calculation for coming up with such simple sequences.

KARL SAYS: By such a simple sequence. I take it Irv means a sequence
where the exceptional years are spaced equally within each calendar
cycle, but have a different spacing between cycles.

Let's consider it for leap weeks using a 7-day week. These occur at
intervals of five and six years when spaced as evenly as possible. There
are two approaches:
(1) Have every fifth year in the cycle have a leap week beginning with
the 5th (latest possible) year
(2) Have every sixth year in the cycle have a leap week beginning with
the 1st (earliest possible) year

Irv's suggested approach is (1). For a cycle of C years of which L are
exceptional. Then the mean interval between the exceptional years is
C/L. The interval within the cycle is floor(C/L). For this to work I
reckon that
C < (L + 1) * floor(C/L)
For method (2) you use CEILING instead of FLOOR and for it to work I
reckon that
C > (L - 1) * ceiling(C/L)

<snip> etc., remainder of Karl's comments not quoted, see original message.

I have today posted a new version of my Excel spreadsheet with macro, the Automated Fixed Leap Cycle Finder at <http://www.sym454.org/leap/>.

This version attempts to find such simple leap sequences and lists them at the end of the generated report worksheet.

It tries both of the strategies that Karl outlined above.

It allows the length of the last interval to differ from the repeated interval length by as much as +/- ceiling(C/4).

All cases where the last interval deviates by more than that are ignored, unless its length is a "nice" multiple of the repeated interval length.  For example, where the repeated interval is 21 years, it allows 7 or 14 for the final segment even though those are more than the allowed deviation.  Where the repeated interval is 20 years, it allows the last segment to be 10 or 30 years. This is based on the greatest common divisor (GCD) of the repeated interval and the final segment.  If that GCD divides into the repeated interval no more than 3 times, it is considered a "nice" multiple.

It matches the row color and boldface style to the corresponding row in the main list.

To implement this feature I had to change the logic so that instead of reporting the interval between "long" years, it chooses which is the least common year type.

The chances of finding a simple leap sequence is greater when the average interval between exceptional years is greater, and as Karl pointed out the cycle must be reasonably short.

Thus 2-, 3- or 4- day leap week cycles have no such sequences, generally, if I recall correctly.

7-day leap cycles have such simple sequences only for the 62-year cycle and the short mixers.

Longer weeks generally don't yield simple sequences, or only a few.

The 5- and 6- day leap week cycles have many such sequences.

After the report is generated, to quickly get to the simple sequences at the end of the list, press the Ctrl-End keys and then just the Home key.

This version also removes the checkbox to force each cycle to start at the beginning of a week.  This "feature" frustrated users when it was accidentally left on.  It was redundant anyway, because it happens automatically if generating leap week cycles, and for leap day or leap month calendars it is simple to see only cycles that have days per cycle divisible by days per week by autofiltering for zero in the MODx the column of the report worksheet, where x is the number of days per week.

-- Irv Bromberg, Toronto, Canada

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

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

 

One comment below.

---

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 06 August 2008 15:22
To: CALNDR-L@...
Subject: Re: Five and Six day leap week calendars RE: Soviet calendar

On 2008.07.25, at 09:28 , Palmen, KEV (Karl) wrote:

Irv wrote:  The simple long year interval repeat patterns outlined above are
interesting, the tradeoff being more equinox wobble, as the long years
are not as smoothly spread as possible.  I'm wondering if there  
is a generic calculation for coming up with such simple sequences.

KARL SAYS: By such a simple sequence. I take it Irv means a sequence
where the exceptional years are spaced equally within each calendar
cycle, but have a different spacing between cycles.

Let's consider it for leap weeks using a 7-day week. These occur at
intervals of five and six years when spaced as evenly as possible. There
are two approaches:
(1) Have every fifth year in the cycle have a leap week beginning with
the 5th (latest possible) year
(2) Have every sixth year in the cycle have a leap week beginning with
the 1st (earliest possible) year

Irv's suggested approach is (1). For a cycle of C years of which L are
exceptional. Then the mean interval between the exceptional years is
C/L. The interval within the cycle is floor(C/L). For this to work I
reckon that
C < (L + 1) * floor(C/L)
For method (2) you use CEILING instead of FLOOR and for it to work I
reckon that
C > (L - 1) * ceiling(C/L)

<snip> etc., remainder of Karl's comments not quoted, see original message.

I have today posted a new version of my Excel spreadsheet with macro, the Automated Fixed Leap Cycle Finder at <http://www.sym454.org/leap/>.

This version attempts to find such simple leap sequences and lists them at the end of the generated report worksheet.

It tries both of the strategies that Karl outlined above.

It allows the length of the last interval to differ from the repeated interval length by as much as +/- ceiling(C/4). 

 

KARL ASKS: Why not have the last (cycle end crossing interval) be in the range of 1 to 2*(floor(C/L)-1), which can be accommodated by my two strategies. In terms of the repeated interval length the range is plus or minus that repeated interval length less 1.

 

Note that the repeated interval length is floor(C/L) if the last interval is longer or ceiling(C/L) if the last interval is shorter.

 

Perhaps Irv meant ceiling(C/L) when he stated ceiling(C/4).

 

Karl

 

09(14(05

[Irv Bromberg]

On 2008.08.06, at 11:21 , Palmen, KEV (Karl) wrote:
> Irv Bromberg wrote:

> I have today posted a new version of my Excel spreadsheet with  
> macro, the Automated Fixed Leap Cycle Finder at <http://www.sym454.org/leap/ 
> >.
> This version attempts to find such simple leap sequences and lists  
> them at the end of the generated report worksheet.
> It tries both of the strategies that Karl outlined above.
> It allows the length of the last interval to differ from the  
> repeated interval length by as much as +/- ceiling(C/4).
>
> KARL ASKS: Why not have the last (cycle end crossing interval) be in  
> the range of 1 to 2*(floor(C/L)-1), which can be accommodated by my  
> two strategies. In terms of the repeated interval length the range  
> is plus or minus that repeated interval length less 1.

Irv replies:  I started with allowing that range, but that yielded  
what I thought were unreasonably short or long final segments, which  
would cause appreciably more equinox or solstice wobble.  Instead I  
thought it preferable to have the final segment length "reasonably"  
close to the repeated interval length, or otherwise divide exactly 2  
or 3 times into it.

> Perhaps Irv meant ceiling(C/L) when he stated ceiling(C/4).

Irv replies:  No, my mistake.  I intended to state it as the ceiling  
of one quarter of the repeated leap interval, which is an arbitrary  
range that I considered reasonable.


-- Irv Bromberg, Toronto, Canada

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

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

Comment below.

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 06 August 2008 16:50
To: CALNDR-L@...
Subject: Re: Five and Six day leap week calendars RE: Soviet calendar

On 2008.08.06, at 11:21 , Palmen, KEV (Karl) wrote:
> Irv Bromberg wrote:

> I have today posted a new version of my Excel spreadsheet with macro,
> the Automated Fixed Leap Cycle Finder at <http://www.sym454.org/leap/
> >.
> This version attempts to find such simple leap sequences and lists
> them at the end of the generated report worksheet.
> It tries both of the strategies that Karl outlined above.
> It allows the length of the last interval to differ from the repeated
> interval length by as much as +/- ceiling(C/4).
>
> KARL ASKS: Why not have the last (cycle end crossing interval) be in
> the range of 1 to 2*(floor(C/L)-1), which can be accommodated by my
> two strategies. In terms of the repeated interval length the range is
> plus or minus that repeated interval length less 1.

Irv replies:  I started with allowing that range, but that yielded what
I thought were unreasonably short or long final segments, which would
cause appreciably more equinox or solstice wobble.  Instead I thought it
preferable to have the final segment length "reasonably"  
close to the repeated interval length, or otherwise divide exactly 2 or
3 times into it.

> Perhaps Irv meant ceiling(C/L) when he stated ceiling(C/4).

Irv replies:  No, my mistake.  I intended to state it as the ceiling of
one quarter of the repeated leap interval, which is an arbitrary range
that I considered reasonable.

KARL SAYS: So Irv seems to selected an arbitrary quarter of ceiling(C/L)
(which should be the lesser floor(C/L) when the last interval is
longer).

Perhaps the user could select this limit. One quarter would limit the
jitter to 1+1/4 'weeks'.

Karl

09(14(05

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

Limiting the difference in the interval lengths to 1/4 the normal
interval length is unsound.

If the regular (repeated) interval is 4 (as with leap day calendars),
you'll only get the optimally spaced cycles such as the 33-year cycle.
If the regular interval is 3 or less you won't get any at all.

This can be corrected by using the difference between the actual end
interval and what the end interval would be for an optimally-spaced
cycle. In the case where the end interval is longer (and so the regular
interval is floor(C/L)), the jitter would be limited to 1+r times the
minimum possible, where r is the fraction of the regular interval this
is limited to (e.g. 1/4). I've checked this with the 33-year cycle and
two longer equivalent cycles.

For the case where the end interval is shorter, this is only
approximately true.

I've worked out the following expressions for the jitter, of a C-year
cycle with L exceptional years and an interval of E years over the end.
If the end interval is longer (hence the regular interval is
floor(L/C)), the jitter is (L/C)*(E-1)*d, where d is the difference of
length between an exceptional year and a common year.
E = C - L*floor(C/L)
If the end interval is shorter (hence the regular interval is
ceiling(L/C)), the jitter is (2 - (L/C)*(E+1))*d.
E = C - L*ceiling(C/L).

One could directly limit the jitter via these expressions.

Karl

09(14(06
 

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 06 August 2008 16:50
To: CALNDR-L@...
Subject: Re: Five and Six day leap week calendars RE: Soviet calendar

On 2008.08.06, at 11:21 , Palmen, KEV (Karl) wrote:
> Irv Bromberg wrote:

> I have today posted a new version of my Excel spreadsheet with macro,
> the Automated Fixed Leap Cycle Finder at <http://www.sym454.org/leap/
> >.
> This version attempts to find such simple leap sequences and lists
> them at the end of the generated report worksheet.
> It tries both of the strategies that Karl outlined above.
> It allows the length of the last interval to differ from the repeated
> interval length by as much as +/- ceiling(C/4).
>
> KARL ASKS: Why not have the last (cycle end crossing interval) be in
> the range of 1 to 2*(floor(C/L)-1), which can be accommodated by my
> two strategies. In terms of the repeated interval length the range is
> plus or minus that repeated interval length less 1.

Irv replies:  I started with allowing that range, but that yielded what
I thought were unreasonably short or long final segments, which would
cause appreciably more equinox or solstice wobble.  Instead I thought it
preferable to have the final segment length "reasonably"  
close to the repeated interval length, or otherwise divide exactly 2 or
3 times into it.

> Perhaps Irv meant ceiling(C/L) when he stated ceiling(C/4).

Irv replies:  No, my mistake.  I intended to state it as the ceiling of
one quarter of the repeated leap interval, which is an arbitrary range
that I considered reasonable.


-- Irv Bromberg, Toronto, Canada

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

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

It allows the length of the last interval to differ from the repeated interval length by as much as +/- ceiling(C/4).

All cases where the last interval deviates by more than that are ignored, unless its length is a "nice" multiple of the repeated interval length.  For example, where the repeated interval is 21 years, it allows 7 or 14 for the final segment even though those are more than the allowed deviation.  Where the repeated interval is 20 years, it allows the last segment to be 10 or 30 years. This is based on the greatest common divisor (GCD) of the repeated interval and the final segment.  If that GCD divides into the repeated interval no more than 3 times, it is considered a "nice" multiple.

KARL SAYS: Of particular interest are those cycles where the last interval differs from the regular (repeated) interval by a divisor of the regular interval. Then the cycle is an optimally spaced cycle of a period equal to that difference. For example, a 20-year cycle corrected by an end interval of 30 years, would effectively be an optimally spaced cycle of 10-year periods. A 21-year cycle corrected by an end interval of 14 years, would effectively be an optimally spaced cycle of 7-year periods. Such cycles would be amenable to calendar conversion algorithms.

 

Note that correcting 21-year by a 7-year end cycle is NOT such a cycle, because the difference of 14 is not a divisor of 21 and so the 7-year periods would not be optimally spaced.

 

I have investigated the case for 7-day leap week calendar with a regular interval of 6 years and an end interval of 4 years. I came up with 28-year cycle equivalent to the Julian Calendar and a 34-year cycle. I constructed may longer cycles by alternating the 28-year and 34-year cycles beginning and ending with the 28-year cycle. These include the Gregorian 400-year cycle and  Brij's 834-year cycle and the 896-year cycle. The jitter is just under 8.25 days.

 

Karl

 

09(14(06

[Irv Bromberg]

On 2008.08.07, at 08:10 , Palmen, KEV (Karl) wrote:

I've worked out the following expressions for the jitter, of a C-year
cycle with L exceptional years and an interval of E years over the end.
If the end interval is longer (hence the regular interval is
floor(L/C)), the jitter is (L/C)*(E-1)*d, where d is the difference of
length between an exceptional year and a common year.
E = C - L*floor(C/L)
If the end interval is shorter (hence the regular interval is
ceiling(L/C)), the jitter is (2 - (L/C)*(E+1))*d.
E = C - L*ceiling(C/L).

One could directly limit the jitter via these expressions.

Irv replies:

I had my own expressions for the jitter, they yield the same results, but mine were much more complicated and I needed 4 expressions instead of only 2.

I did further rewrites of my Fixed Leap Cycle Finder (posted at <http://www.sym454.org/leap/> to better generalize short vs. long and leap vs. common years, thus enabling use of Karl's simpler jitter expressions.

I did at first have a user entry field to allow the user to specify the maximum jitter, but it was too easy to accidentally leave it at inappropriate values when changing the leap cycle type.  Anybody who prefers either tighter or more liberal maximum jitter limits can modify the MaxJitter expression accordingly.

I decided to limit based on MaxJitter = DaysPerLeap + ceiling( DaysPerLeap/2 ), where DaysPerLeap is the same as "d" in Karl's expressions quoted above.

The jitter in days is shown in column "A" to the left of the listed simple leap sequences, and the macro boldfaces the jitter if it is less than DaysPerLeap, which only and always occurs if the simple sequence is inherently as uniformly spread as possible.

The GCD criterion for "nice" divisors is gone...

Currently the simple leap sequence list is in descending order of calendar mean year.  I find it useful to alternatively sort the list ascending by the jitter column, especially for the 5-day and 6-day leap week calendars, which generate a lot of simple leap sequences.

On 2008.08.07, at 09:12 , Palmen, KEV (Karl) wrote:

KARL SAYS: Of particular interest are those cycles where the last interval differs from the regular (repeated) interval by a divisor of the regular interval. Then the cycle is an optimally spaced cycle of a period equal to that difference. For example, a 20-year cycle corrected by an end interval of 30 years, would effectively be an optimally spaced cycle of 10-year periods. A 21-year cycle corrected by an end interval of 14 years, would effectively be an optimally spaced cycle of 7-year periods. Such cycles would be amenable to calendar conversion algorithms.

 

Note that correcting 21-year by a 7-year end cycle is NOT such a cycle, because the difference of 14 is not a divisor of 21 and so the 7-year periods would not be optimally spaced.

Irv replies:  OK, the updated version now lists only those cycles that don't exceed MaxJitter as above, or where the difference between the main leap interval and the end interval is a divisor of the main interval.

Karl continued:  I have investigated the case for 7-day leap week calendar with a regular interval of 6 years and an end interval of 4 years. I came up with 28-year cycle equivalent to the Julian Calendar and a 34-year cycle. I constructed may longer cycles by alternating the 28-year and 34-year cycles beginning and ending with the 28-year cycle. These include the Gregorian 400-year cycle and  Brij's 834-year cycle and the 896-year cycle. The jitter is just under 8.25 days.

Irv replies:  This brings up the question about further generalization to allow automatic generation of repeated sequences that add up to a longer cycle without jitter being excessive.  I experimented a bit with allowing repeated cycles and for leap day calendars my macro generates 8/33, 16/66, and 24/99, but in each case it uses only repeated sequences of 4-year intervals with only a single end interval, so the 8/33 has minimal jitter and each of the repeated cycles has greater jitter.  It might be better to either ignore the repeated cycles for the simple repeated sequences, or to copy the repeats from the primary cycle.  That is a trivial example, though.  What Karl described above was implementing some repeated sequences that were short and in fact had to types of cycles in an alternating pattern, considerably more complicated.  Nevertheless, this approach is attractive because without it there are essentially no simple repeat sequences that are useful with leap week calendars having reasonably accurate mean years (there are only the short mixers and the high jitter 62-year cycle).

-- Irv Bromberg, Toronto, Canada

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

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

---

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 12 August 2008 19:23
To: CALNDR-L@...
Subject: Re: Five and Six day leap week calendars RE: Soviet calendar

On 2008.08.07, at 08:10 , Palmen, KEV (Karl) wrote:

I've worked out the following expressions for the jitter, of a C-year
cycle with L exceptional years and an interval of E years over the end.
If the end interval is longer (hence the regular interval is
floor(L/C)), the jitter is (L/C)*(E-1)*d, where d is the difference of
length between an exceptional year and a common year.
E = C - L*floor(C/L)
If the end interval is shorter (hence the regular interval is
ceiling(L/C)), the jitter is (2 - (L/C)*(E+1))*d.
E = C - L*ceiling(C/L).

One could directly limit the jitter via these expressions.

Irv replies:

I had my own expressions for the jitter, they yield the same results, but mine were much more complicated and I needed 4 expressions instead of only 2.

I did further rewrites of my Fixed Leap Cycle Finder (posted at <http://www.sym454.org/leap/> to better generalize short vs. long and leap vs. common years, thus enabling use of Karl's simpler jitter expressions.

I did at first have a user entry field to allow the user to specify the maximum jitter, but it was too easy to accidentally leave it at inappropriate values when changing the leap cycle type.   I.e. value of d. 

 

 Anybody who prefers either tighter or more liberal maximum jitter limits can modify the MaxJitter expression accordingly.

I decided to limit based on MaxJitter = DaysPerLeap + ceiling( DaysPerLeap/2 ), where DaysPerLeap is the same as "d" in Karl's expressions quoted above. 

 

I don't see any need for this, there is an inbuilt maximum jitter just under 2*(DaysPerLeap) = 2*d. This assumes that the end interval E is at least 1 and less than twice the regular interval, which is necessary for the regular interval to apply throughout the whole cycle. Perhaps the jitter could be specified by the user in units of (DaysPerLeap) and then shown in days.

The jitter in days is shown in column "A" to the left of the listed simple leap sequences, and the macro boldfaces the jitter if it is less than DaysPerLeap, which only and always occurs if the simple sequence is inherently as uniformly spread as possible.  This is the case if and only if the end interval differs from the regular interval by 1. 

The GCD criterion for "nice" divisors is gone...

Currently the simple leap sequence list is in descending order of calendar mean year.  I find it useful to alternatively sort the list ascending by the jitter column, especially for the 5-day and 6-day leap week calendars, which generate a lot of simple leap sequences. 

 

Perhaps, one could highlight those cycles where the difference between the end interval and regular interval is a divisor of the regular interval (as described below). 

On 2008.08.07, at 09:12 , Palmen, KEV (Karl) wrote:

KARL SAYS: Of particular interest are those cycles where the last interval differs from the regular (repeated) interval by a divisor of the regular interval. Then the cycle is an optimally spaced cycle of a period equal to that difference. For example, a 20-year cycle corrected by an end interval of 30 years, would effectively be an optimally spaced cycle of 10-year periods. A 21-year cycle corrected by an end interval of 14 years, would effectively be an optimally spaced cycle of 7-year periods. Such cycles would be amenable to calendar conversion algorithms.

 

Note that correcting 21-year by a 7-year end cycle is NOT such a cycle, because the difference of 14 is not a divisor of 21 and so the 7-year periods would not be optimally spaced.

Irv replies:  OK, the updated version now lists only those cycles that don't exceed MaxJitter as above, or where the difference between the main leap interval and the end interval is a divisor of the main interval.

Karl continued:  I have investigated the case for 7-day leap week calendar with a regular interval of 6 years and an end interval of 4 years. I came up with 28-year cycle equivalent to the Julian Calendar and a 34-year cycle. I constructed may longer cycles by alternating the 28-year and 34-year cycles beginning and ending with the 28-year cycle. These include the Gregorian 400-year cycle and  Brij's 834-year cycle and the 896-year cycle. The jitter is just under 8.25 days.

Irv replies:  This brings up the question about further generalization to allow automatic generation of repeated sequences that add up to a longer cycle without jitter being excessive.  I experimented a bit with allowing repeated cycles and for leap day calendars my macro generates 8/33, 16/66, and 24/99, but in each case it uses only repeated sequences of 4-year intervals with only a single end interval, so the 8/33 has minimal jitter and each of the repeated cycles has greater jitter.   

 

I tested my jitter formulae with these particular cases. The length of the end interval is 5, 6 and 7 respectively. Note that we cannot continue this sequence into 32/132, 40/165 etc, because the end interval would be too long to allow the regular interval (of 4)  to apply to the whole cycle.  

 

 It might be better to either ignore the repeated cycles for the simple repeated sequences, or to copy the repeats from the primary cycle.  That is a trivial example, though.  What Karl described above was implementing some repeated sequences that were short and in fact had to types of cycles in an alternating pattern, considerably more complicated.  Nevertheless, this approach is attractive because without it there are essentially no simple repeat sequences that are useful with leap week calendars having reasonably accurate mean years (there are only the short mixers and the high jitter 62-year cycle). 

 

In general, we'd have two types of these cycles spaced as evenly as possible. In the case mentioned, this happens to be alternating as described. Any other arrangement of the two types of cycle would produce more jitter.

 

Just one type of cycle would suffice if long enough. 

 

Karl

 

09(14(11 till noon

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

 

More about Irv's 62-year and 28-year cycle idea.

---

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 12 August 2008 19:23
To: CALNDR-L@...
Subject: Re: Five and Six day leap week calendars RE: Soviet calendar

 

Karl continued:  I have investigated the case for 7-day leap week calendar with a regular interval of 6 years and an end interval of 4 years. I came up with 28-year cycle equivalent to the Julian Calendar and a 34-year cycle. I constructed may longer cycles by alternating the 28-year and 34-year cycles beginning and ending with the 28-year cycle. These include the Gregorian 400-year cycle and  Brij's 834-year cycle and the 896-year cycle. The jitter is just under 8.25 days.

What Karl described above was implementing some repeated sequences that were short and in fact had to types of cycles in an alternating pattern, considerably more complicated.  Nevertheless, this approach is attractive because without it there are essentially no simple repeat sequences that are useful with leap week calendars having reasonably accurate mean years (there are only the short mixers and the high jitter 62-year cycle). 

 

KARL SAYS: I assume by high-jitter 62-year cycle, Irv means the 62-year cycle within which all leap years occur once every 6 years from first or second year and the end interval is two years.

There is also a medium jitter 45-year cycle with an end interval of 3 years. The two types of three-year period are spread as evenly as possible. Estimated jitter is just under 9.5 days. The jitter remains below 9.5 days, if you use a mixer of 51-years mixed as evenly as possible.

The 231-year cycle (equivalent to seven 33-year cycles) can be constructed from four 45-year cycles and one 51-year cycle. Removal of one 45-year cycle from the 231-year cycle creates a 186-year cycle equivalent to three 62-year cycles. Alternating the 231-year and 186-year cycles creates half of Brij's 834-year cycle.

 

The 51-year mixer cycle is equivalent to 1.5 34-year mixer cycles.

 

 

 Karl 

 

09(14(12

[Irv Bromberg]

On 2008.08.13, at 04:22 , Palmen, KEV (Karl) wrote:
>> Irv wrote:  I decided to limit based on MaxJitter = DaysPerLeap +  
>> ceiling( DaysPerLeap/2 ), where DaysPerLeap is the same as "d" in  
>> Karl's expressions quoted above.

> Karl replied:  I don't see any need for this, there is an inbuilt  
> maximum jitter just under 2*(DaysPerLeap) = 2*d. This assumes that  
> the end interval E is at least 1 and less than twice the regular  
> interval, which is necessary for the regular interval to apply  
> throughout the whole cycle. Perhaps the jitter could be specified by  
> the user in units of (DaysPerLeap) and then shown in days.

Irv replies:  I found that if I didn't place some limit on jitter  
range, then simple repeating sequences with end interval markedly  
different from the repeating interval get listed, and I felt they  
wouldn't be of interest.  As it is, some such cycles get listed, but I  
didn't want to trim the limit too tight.  I have placed the idea of  
specifying the jitter in units of DaysPerLeap on the "ToDo" list for  
future consideration, but so far I feel that it would add an obscure  
feature to an increasingly obscure functionality.

>> Irv continued: The jitter in days is shown in column "A" to the  
>> left of the listed simple leap sequences, and the macro boldfaces  
>> the jitter if it is less than DaysPerLeap, which only and always  
>> occurs if the simple sequence is inherently as uniformly spread as  
>> possible.

> Karl replied:  This is the case if and only if the end interval  
> differs from the regular interval by 1.
> Perhaps, one could highlight those cycles where the difference  
> between the end interval and regular interval is a divisor of the  
> regular interval (as described below).

Irv replies:  I've now posted a new version that underscores the  
jitter value when that is the case.  I ignore, however, the trivial  
case where the difference is 1 year, which anyhow gets boldfaced to  
highlight that it is uniformly spread as above.

>> Irv wrote: It might be better to either ignore the repeated cycles  
>> for the simple repeated sequences, or to copy the repeats from the  
>> primary cycle.

Irv adds:  The latest posted version ignores the simple repeated leap  
cycles during generation of the repeated interval sequences at the end  
of the worksheet.

> Karl wrote:  In general, we'd have two types of these cycles spaced  
> as evenly as possible. In the case mentioned, this happens to be  
> alternating as described. Any other arrangement of the two types of  
> cycle would produce more jitter.  Just one type of cycle would  
> suffice if long enough.

Irv replies:  OK, but for now I haven't done anything further about  
that idea...

-- Irv Bromberg, Toronto, Canada

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

[Palmen, KEV (Karl)]

Dear Irv and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Irv Bromberg
Sent: 14 August 2008 04:50
To: CALNDR-L@...
Subject: Re: Five and Six day leap week calendars RE: Soviet calendar

On 2008.08.13, at 04:22 , Palmen, KEV (Karl) wrote:
>> Irv wrote:  I decided to limit based on MaxJitter = DaysPerLeap +
>> ceiling( DaysPerLeap/2 ), where DaysPerLeap is the same as "d" in
>> Karl's expressions quoted above.

> Karl replied:  I don't see any need for this, there is an inbuilt
> maximum jitter just under 2*(DaysPerLeap) = 2*d. This assumes that the

> end interval E is at least 1 and less than twice the regular interval,

> which is necessary for the regular interval to apply throughout the
> whole cycle. Perhaps the jitter could be specified by the user in
> units of (DaysPerLeap) and then shown in days.

Irv replies:  I found that if I didn't place some limit on jitter range,
then simple repeating sequences with end interval markedly different
from the repeating interval get listed, and I felt they wouldn't be of
interest.  As it is, some such cycles get listed, but I didn't want to
trim the limit too tight.  I have placed the idea of specifying the
jitter in units of DaysPerLeap on the "ToDo" list for future
consideration, but so far I feel that it would add an obscure feature to
an increasingly obscure functionality.

KARL SAYS: It seems that Irv hasn't placed any limit on the end
interval.
The end interval MUST be at least 1 and also less than twice the regular
interval. This is necessary and sufficient to ensure that the regular
interval applies within the whole cycle. I made this clear in the
previous note.
I suggest placing such a limit. Then any such cycle can be displayed if
the user allows its jitter and no cycle that fails to have the regular
interval throughout its cycle is ever shown.

In my first note on this topic I gave some inequalities in terms of the
number of years C and number of exceptional years L that ensure this,
thereby removing the need to calculate the regular and end intervals
beforehand.

Karl

[Mikhail Petin]

It is devoted to memory Lance Latham 

 

World Dual Calendar  2009  -  http://mikhlud.narod.ru/WorldCalendar2009.htm

 

World Dual Calendar  2008  -  http://CalendarPetin-Meton.narod.ru/DualCalendar2008.htm

 

Best regards
Mikhail Petin

http://CalendarPetin-Meton.narod.ru 

[Palmen, KEV (Karl)]

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

Dear Brij, Irv and Calendar People

---

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Brij Bhushan Vij
Sent: 15 August 2008 12:10
To: CALNDR-L@...
Subject: 5-d weeks & 896-year cycle RE: Five and Six day leap week calendars RE: Soviet calendar

Karl, Irv sirs:
I pondered over my 'concept' of The Metric Calendar Year (1971-73) to see if I could bring my THINKING in line with *Symmetrical placing of 5-day Leap Weeks*. I assume these shall be within the 'jitter factor Karl & Irv are working'. This can be arranged as:

5-day Leap Weeks: Each Year has (365/5=73 Weeks). In 896-years, we have [65408+43=65451, 5-day Weeks]. Thus, there can be 896-year of (73*5-day weeks) and added 43-five day Additional LWks starting at Y021, [20+(18*21)+(6*20)+(18*21)]=896-years. These can be symmetrically placed, starting at Year ZERO as: 021, 042, 063, 084, 125, 146, 167, 188, 209, 230, 251, 272, 293, 314, 335, 356, 377, 398, 418, 438, 458, 478, 498, 518, 539, 560, 581, 602, 623, 644, 665, 686, 707, 728, 749, 770, 791, 812, 833, 854, 875, 896…..and cycles repeat.  

 

KARL SAYS: Brij's proposed 896-year cycle would have 896*365+43*5=327255 days, which would give a mean year of only  365.23995 days. It is too short.

The 896-year cycle that Brij usually proposes has 7*(128*365+31) = 7*45751 = 327257 days (2 days more). It cannot be divided into a whole number of five-day weeks. Instead you can use the 640-year cycle of 31 leap weeks for a 5 days week. This is done in the proposed Quinta calendar

http://web.ncf.ca/aa735/new_cal.html by Duncan MacGregor.

He use one of two rules that I suggested and has a leap years every 20 years except once every 640 years when a leap week is dropped (rather like the 128-year leap-day cycle). This has a jitter of about two weeks. For less jitter one could have leap weeks in years

021 042 062

083 104 124

and so on every 62 years until

579 600 620 640

661 682 702

and so on every 640 years.

 

These leap years are not as evenly spaced as possible but are almost so spaced.

 

Karl

 

09(14(17