Intercalary Month in Balinese Calendar

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Intercalary Month in Balinese Calendar

Walter J Ziobro
Dear Calendar List:

      I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary month.  According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar – as happens with the Islamic calendar, an extra month, known as an intercalary month, is added after the 11th month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule.  Thus, I am uncertain as to which years the extra month is added, and as to why in some years it is added after Jiyestha, and in other years it is added after Sadha.  As best as I can determine from the on-line Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as
Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro

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Re: Intercalary Month in Balinese Calendar

Karl Palmen

Dear Walter and Calendar People

 

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

 

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

 

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037 inclusive would be

 

2000  2003 2005  2008  2011  2014 2016  

2019  2022 2024  2027  2030  2033 2035

 

Karl

 

16(11(27

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: [hidden email]
Subject: Intercalary Month in Balinese Calendar

 

Dear Calendar List:

      I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary month.  According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar – as happens with the Islamic calendar, an extra month, known as an intercalary month, is added after the 11th month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule.  Thus, I am uncertain as to which years the extra month is added, and as to why in some years it is added after Jiyestha, and in other years it is added after Sadha.  As best as I can determine from the on-line Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro

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Re: Intercalary Month in Balinese Calendar

Walter J Ziobro
Dear Karl:

Thank you for your response.   Since I posted this question yesterday, I found two sources that, indeed, indicated that the current version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKmGIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

 the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980,  the Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People
 
The number of months in the year matches the number of new moons in the corresponding Gregorian year.
 
I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.
 
This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037 inclusive would be
 
2000  2003 2005  2008  2011  2014 2016  
2019  2022 2024  2027  2030  2033 2035
 
Karl
 
16(11(27
 
From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: CALNDR-[hidden email]
Subject: Intercalary Month in Balinese Calendar
 
Dear Calendar List:

      I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary month.  According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar – as happens with the Islamic calendar, an extra month, known as an intercalary month, is added after the 11th month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule.  Thus, I am uncertain as to which years the extra month is added, and as to why in some years it is added after Jiyestha, and in other years it is added after Sadha.  As best as I can determine from the on-line Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro
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Re: Intercalary Month in Balinese Calendar

Amos Shapir-2
It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month).  This suggestion was rejected as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SVK_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro <[hidden email]> wrote:
Dear Karl:

Thank you for your response.   Since I posted this question yesterday, I found two sources that, indeed, indicated that the current version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKmGIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

 the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980,  the Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People
 
The number of months in the year matches the number of new moons in the corresponding Gregorian year.
 
I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.
 
This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037 inclusive would be
 
2000  2003 2005  2008  2011  2014 2016  
2019  2022 2024  2027  2030  2033 2035
 
Karl
 
16(11(27
 
From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: CALNDR-[hidden email]
Subject: Intercalary Month in Balinese Calendar
 
Dear Calendar List:

      I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary month.  According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar – as happens with the Islamic calendar, an extra month, known as an intercalary month, is added after the 11th month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule.  Thus, I am uncertain as to which years the extra month is added, and as to why in some years it is added after Jiyestha, and in other years it is added after Sadha.  As best as I can determine from the on-line Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir
 
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Re: Intercalary Month in Balinese Calendar

Karl Palmen
Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Amos Shapir [[hidden email]]
Sent: 21 July 2017 07:06
To: [hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month).  This suggestion was rejected as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SVK_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro <[hidden email]<mailto:[hidden email]>> wrote:
Dear Karl:

Thank you for your response.   Since I posted this question yesterday, I found two sources that, indeed, indicated that the current version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKmGIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

 the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980,  the Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<mailto:[hidden email]>>
To: CALNDR-L <[hidden email]<mailto:[hidden email]>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037 inclusive would be

2000  2003 2005  2008  2011  2014 2016
2019  2022 2024  2027  2030  2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [mailto:[hidden email]<mailto:[hidden email]?>] On Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: [hidden email]<mailto:[hidden email]>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

      I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary month.  According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar – as happens with the Islamic calendar<https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule.  Thus, I am uncertain as to which years the extra month is added, and as to why in some years it is added after Jiyestha, and in other years it is added after Sadha.  As best as I can determine from the on-line Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir
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Re: Intercalary Month in Balinese Calendar

Takashi SUGA
Dear Walter, Karl, Amos and Calendar People,

According to the explanation written on a published Balinese calendar over a decade ago,
the intercalary rule of the Balinese saka calendar was as follows:

CE 1965 - CE 1992 : Pattern 1

If the remainder after dividing the Saka era by 19 is

 0,  6, 11 then Jiyestha is repeated,
 3,  8, 14, 16 then Sadha is repeated.


CE 1993 - CE 2003/2004 :  Pattern 2

If the remainder after dividing the Saka era by 19 is

13 then Kadasa is repeated,
 2, 10 then Jiyestha is repeated,
18 then Sadha is repeated,
 7 then Kasa is repeated,
15 then Karo is repeated,
 4 then Katiga is repeated.


CE 2003/2004 - :  Pattern 1

 The rule was returned to the pattern 1 adopted during the period of CE 1965 to CE 1992.

Let's check with when.exe( https://rubygems.org/gems/when_exe ) which uses the intercalary pattern 1 and 2.

=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=
#!/usr/bin/env ruby
require 'when_exe'
include When

(1924..2049).each do |year|
  bdate = tm_pos('BalineseLuniSolar::SE', year, 8, 1) - 1
  gdate = When::Gregorian ^ bdate
  p [bdate, gdate] unless gdate.month == 1
end
=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=

Result:
 [SE1924(2002).07<15., 2003-02-01]
 [SE2049(2127).07<15., 2128-02-01]

It means that
the situation that the new moon at the end of 7th month of the Balinese saka Calendar is not included in January of Gregorian
calendar
occurred in the year 2003, and it will not occur until the year 2128 in the future if the intercalary pattern is the pattern 1.
In the year 2003, the arrangement of the new moon was out of the principle.

I heard that two types of calendars were actually published and confused in the year 2003.
It seems that the intercalary pattern was modified because the displacement was regarded as a problem of departure from the
principle.

--
Takashi SUGA, Ph.D.
Wiki: http://www2u.biglobe.ne.jp/~suchowan/when_exe_wiki.html

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Karl Palmen
Sent: Friday, July 21, 2017 11:51 PM
To: [hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year
is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the
postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan
has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may
give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Amos Shapir [[hidden email]]
Sent: 21 July 2017 07:06
To: [hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way
to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month).  This suggestion was rejected
as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SV
K_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro
<[hidden email]<mailto:[hidden email]>> wrote:
Dear Karl:

Thank you for your response.   Since I posted this question yesterday, I found two sources that, indeed, indicated that the current
version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the
Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKm
GIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

 the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980,  the
Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall
in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would
otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<mailto:[hidden email]>>
To: CALNDR-L <[hidden email]<mailto:[hidden email]>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037
inclusive would be

2000  2003 2005  2008  2011  2014 2016
2019  2022 2024  2027  2030  2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [mailto:[hidden email]<mailto:[hidden email]?>] On
Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: [hidden email]<mailto:[hidden email]>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

      I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary
month.  According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar - as happens with the Islamic
calendar<https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th
month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule.  Thus, I am uncertain as to which years the extra month is added, and as to why
in some years it is added after Jiyestha, and in other years it is added after Sadha.  As best as I can determine from the on-line
Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no
ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir
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Re: Intercalary Month in Balinese Calendar

Walter J Ziobro
Dear Takashi Suga:

I thank you for that information.

I have been studying the interactive Balinese Calendar located at:

http://www.kalenderbali.info/?month=1&year=2004&submit=Tampilkan

It appears that Pattern 1 has been followed from 2005 (Saka 1927) to 2027 (Saka 1949)

Mala Jiyestha occurs in the following years:

2008 (Saka 1928, year 11 of 19 year cycle)
2016 (Saka 1937, year 0 of 19 year cycle)
2022 (Saka 1944, year 6 of 19 year cycle)

Mala Sadha occurs in the following years:

2005 (Saka 1927, year 8 of 19 year cycle)
2011 (Saka 1933, year 14 of 19 year cycle)
2013 (Saka 1935, year 16 of 19 year cycle)
2019 (Saka 1941, year 3 of 19 year cycle)

Prior to 2005, and beyond 2027, the intercalary month does not appear, and there are discontinuities from some of the last dates of December to the first dates of the following January.  For instance, in December of 2003, Tilem Kapitu appears on the 23rd, and in January of 2004, it also appears on the 21st. So, one would presume that 2003 should have an intercalary month, but, for some reason it was not added.  I presume that, either the program used requires an occasional manual adjustment, or there is some disagreement as to when the intercalary month is to be added.

-Walter Ziobro 


-----Original Message-----
From: Takashi SUGA <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Wed, Jul 26, 2017 7:07 pm
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter, Karl, Amos and Calendar People,

According to the explanation written on a published Balinese calendar over a decade ago,
the intercalary rule of the Balinese saka calendar was as follows:

CE 1965 - CE 1992 : Pattern 1

If the remainder after dividing the Saka era by 19 is

0, 6, 11 then Jiyestha is repeated,
3, 8, 14, 16 then Sadha is repeated.


CE 1993 - CE 2003/2004 : Pattern 2

If the remainder after dividing the Saka era by 19 is

13 then Kadasa is repeated,
2, 10 then Jiyestha is repeated,
18 then Sadha is repeated,
7 then Kasa is repeated,
15 then Karo is repeated,
4 then Katiga is repeated.


CE 2003/2004 - : Pattern 1

The rule was returned to the pattern 1 adopted during the period of CE 1965 to CE 1992.

Let's check with when.exe( https://rubygems.org/gems/when_exe ) which uses the intercalary pattern 1 and 2.

=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=
#!/usr/bin/env ruby
require 'when_exe'
include When

(1924..2049).each do |year|
bdate = tm_pos('BalineseLuniSolar::SE', year, 8, 1) - 1
gdate = When::Gregorian ^ bdate
p [bdate, gdate] unless gdate.month == 1
end
=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=

Result:
[SE1924(2002).07<15., 2003-02-01]
[SE2049(2127).07<15., 2128-02-01]

It means that
the situation that the new moon at the end of 7th month of the Balinese saka Calendar is not included in January of Gregorian
calendar
occurred in the year 2003, and it will not occur until the year 2128 in the future if the intercalary pattern is the pattern 1.
In the year 2003, the arrangement of the new moon was out of the principle.

I heard that two types of calendars were actually published and confused in the year 2003.
It seems that the intercalary pattern was modified because the displacement was regarded as a problem of departure from the
principle.

--
Takashi SUGA, Ph.D.
Wiki: http://www2u.biglobe.ne.jp/~suchowan/when_exe_wiki.html

-----Original Message-----
From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Karl Palmen
Sent: Friday, July 21, 2017 11:51 PM
To: CALNDR-[hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year
is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the
postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan
has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may
give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Amos Shapir [[hidden email]]
Sent: 21 July 2017 07:06
To: CALNDR-[hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way
to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month). This suggestion was rejected
as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SV
K_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro
<000000080342b460-dmarc-[hidden email]<[hidden email]>> wrote:
Dear Karl:

Thank you for your response. Since I posted this question yesterday, I found two sources that, indeed, indicated that the current
version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the
Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKm
GIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980, the
Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall
in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would
otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<[hidden email]>>
To: CALNDR-L <CALNDR-[hidden email]<[hidden email]>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037
inclusive would be

2000 2003 2005 2008 2011 2014 2016
2019 2022 2024 2027 2030 2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [mailto:[hidden email]<mailto:[hidden email]?>] On
Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: CALNDR-[hidden email]<[hidden email]>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary
month. According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar - as happens with the Islamic
calendar<<a href="https://en.wikipedia.org/wiki/Islamic_calendar>," target="_blank">https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th
month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule. Thus, I am uncertain as to which years the extra month is added, and as to why
in some years it is added after Jiyestha, and in other years it is added after Sadha. As best as I can determine from the on-line
Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no
ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir
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Re: Intercalary Month in Balinese Calendar

Karl Palmen
Dear Walter Takashi and Calendar People

Thank you for the information. It looks like Takashi's pattern 2 looks like Walter's intervals of 33 & 34, but this is hard to determine without being told which position in the numbered year each doubled month occurs.

The 7 years Walter listed match the number of new moons in the Gregorian year, except that it has 2013 instead of 2014. 2014 has its first new moon at 11:13 UT on Jan 1 and so could be counted as belonging to the previous year.


The other interesting issue is which of the two months is doubled (ignoring the more complex pattern 2). If this is selected to ensure that the leap month always has 30 days, then I'd expect it to normally alternate (as I have observed). This is because the interval between two successive leap months would then have an even number of months and last approximately one 32-month cycle.

Deviation from the alternation would be expected because the actual intervals are 24, 26, 36 or 38 months, which deviate from 4 to 8 months from the 32-month cycle. The average interval is between 33 and 34 months One important point is that this pattern would NOT follow a 19-year cycle and so pattern 1 if strictly followed would NOT ensure that the leap months have 30 days.

Karl

16(12(05

________________________________
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Walter J Ziobro [[hidden email]]
Sent: 27 July 2017 01:24
To: [hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

Dear Takashi Suga:

I thank you for that information.

I have been studying the interactive Balinese Calendar located at:

http://www.kalenderbali.info/?month=1&year=2004&submit=Tampilkan

It appears that Pattern 1 has been followed from 2005 (Saka 1927) to 2027 (Saka 1949)

Mala Jiyestha occurs in the following years:

2008 (Saka 1928, year 11 of 19 year cycle)
2016 (Saka 1937, year 0 of 19 year cycle)
2022 (Saka 1944, year 6 of 19 year cycle)

Mala Sadha occurs in the following years:

2005 (Saka 1927, year 8 of 19 year cycle)
2011 (Saka 1933, year 14 of 19 year cycle)
2013 (Saka 1935, year 16 of 19 year cycle)
2019 (Saka 1941, year 3 of 19 year cycle)

Prior to 2005, and beyond 2027, the intercalary month does not appear, and there are discontinuities from some of the last dates of December to the first dates of the following January.  For instance, in December of 2003, Tilem Kapitu appears on the 23rd, and in January of 2004, it also appears on the 21st. So, one would presume that 2003 should have an intercalary month, but, for some reason it was not added.  I presume that, either the program used requires an occasional manual adjustment, or there is some disagreement as to when the intercalary month is to be added.

-Walter Ziobro


-----Original Message-----
From: Takashi SUGA <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Wed, Jul 26, 2017 7:07 pm
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter, Karl, Amos and Calendar People,

According to the explanation written on a published Balinese calendar over a decade ago,
the intercalary rule of the Balinese saka calendar was as follows:

CE 1965 - CE 1992 : Pattern 1

If the remainder after dividing the Saka era by 19 is

0, 6, 11 then Jiyestha is repeated,
3, 8, 14, 16 then Sadha is repeated.


CE 1993 - CE 2003/2004 : Pattern 2

If the remainder after dividing the Saka era by 19 is

13 then Kadasa is repeated,
2, 10 then Jiyestha is repeated,
18 then Sadha is repeated,
7 then Kasa is repeated,
15 then Karo is repeated,
4 then Katiga is repeated.


CE 2003/2004 - : Pattern 1

The rule was returned to the pattern 1 adopted during the period of CE 1965 to CE 1992.

Let's check with when.exe( https://rubygems.org/gems/when_exe ) which uses the intercalary pattern 1 and 2.

=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=
#!/usr/bin/env ruby
require 'when_exe'
include When

(1924..2049).each do |year|
bdate = tm_pos('BalineseLuniSolar::SE', year, 8, 1) - 1
gdate = When::Gregorian ^ bdate
p [bdate, gdate] unless gdate.month == 1
end
=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=

Result:
[SE1924(2002).07<15., 2003-02-01]
[SE2049(2127).07<15., 2128-02-01]

It means that
the situation that the new moon at the end of 7th month of the Balinese saka Calendar is not included in January of Gregorian
calendar
occurred in the year 2003, and it will not occur until the year 2128 in the future if the intercalary pattern is the pattern 1.
In the year 2003, the arrangement of the new moon was out of the principle.

I heard that two types of calendars were actually published and confused in the year 2003.
It seems that the intercalary pattern was modified because the displacement was regarded as a problem of departure from the
principle.

--
Takashi SUGA, Ph.D.
Wiki: http://www2u.biglobe.ne.jp/~suchowan/when_exe_wiki.html

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]<mailto:[hidden email]?>] On Behalf Of Karl Palmen
Sent: Friday, July 21, 2017 11:51 PM
To: [hidden email]<mailto:[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year
is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the
postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan
has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may
give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [[hidden email]<mailto:[hidden email]>] on behalf of Amos Shapir [[hidden email]<mailto:[hidden email]>]
Sent: 21 July 2017 07:06
To: [hidden email]<mailto:[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way
to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month). This suggestion was rejected
as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SV
K_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro
<[hidden email]<mailto:[hidden email]><mailto:[hidden email]<mailto:[hidden email]?>>> wrote:
Dear Karl:

Thank you for your response. Since I posted this question yesterday, I found two sources that, indeed, indicated that the current
version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the
Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKm
GIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980, the
Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall
in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would
otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<mailto:[hidden email]><mailto:[hidden email]<mailto:[hidden email]?>>>
To: CALNDR-L <[hidden email]<mailto:[hidden email]><mailto:[hidden email]<mailto:[hidden email]?>>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037
inclusive would be

2000 2003 2005 2008 2011 2014 2016
2019 2022 2024 2027 2030 2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [mailto:[hidden email]<mailto:[hidden email]<mailto:[hidden email]<mailto:[hidden email]?>?>] On
Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: [hidden email]<mailto:[hidden email]><mailto:[hidden email]<mailto:[hidden email]?>>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary
month. According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar - as happens with the Islamic
calendar<https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th
month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule. Thus, I am uncertain as to which years the extra month is added, and as to why
in some years it is added after Jiyestha, and in other years it is added after Sadha. As best as I can determine from the on-line
Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no
ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir
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Re: Intercalary Month in Balinese Calendar

Brij Bhushan metric VIJ
Karl, Takeshi, Walter all sirs:
>The 7 years Walter listed match the >number of new moons in the Gregorian >year, except that it has 2013 instead of >2014.
Perhaps I am butting in un-necessarily, as my WIFE (SNEH) fights her last battle, I wish to add the start of my Brij-Gregorian Modified

image1.JPG (396K) Download Attachment
ATT00001.txt (178 bytes) Download Attachment
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ATT00002.txt (1K) Download Attachment
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Re: Intercalary Month in Balinese Calendar

Walter J Ziobro
In reply to this post by Karl Palmen
Dear Karl:

Thank you for your thoughts.

In the 19 year cycle that I reported, 5 of 7 intercalary months have 30 days.  2 of them have only 29, both of them Mala Sadha, in 2011 (Saka 1933) and in 2013 (Saka 1935).  So the theory that a month with 30 days is chosen is not so..

With regard to Pattern 2, the months cited by Takashi fall at intervals of 16, 34. 46, 35, 16, 46, and 35 months. I don't know the reason for this, but I suspect that it is done to arrange some convenient placement of certain festivals.

For the intercalary months to fall in a pattern of 33-32-33-32-33-32-33 months (not counting the intercalary month itself), they could fall, (for instance) after the following months in a 19 year cycle:

Year 2: Jyestha (11th month)
Year 5: Kapitu (7th)
Year 8: Kapat (4th)
Year 10 Sadha (12th)
Year 13: Kasanga (9th)
Year 16: Kalima (5th)
Year 19: Kara (2th)

This is just one possibility. There could be other arrangements that could maintain the same interval. I offer it as an example.

-Walter Ziobro





-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Fri, Jul 28, 2017 11:56 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter Takashi and Calendar People

Thank you for the information. It looks like Takashi's pattern 2 looks like Walter's intervals of 33 & 34, but this is hard to determine without being told which position in the numbered year each doubled month occurs.

The 7 years Walter listed match the number of new moons in the Gregorian year, except that it has 2013 instead of 2014. 2014 has its first new moon at 11:13 UT on Jan 1 and so could be counted as belonging to the previous year.


The other interesting issue is which of the two months is doubled (ignoring the more complex pattern 2). If this is selected to ensure that the leap month always has 30 days, then I'd expect it to normally alternate (as I have observed). This is because the interval between two successive leap months would then have an even number of months and last approximately one 32-month cycle.

Deviation from the alternation would be expected because the actual intervals are 24, 26, 36 or 38 months, which deviate from 4 to 8 months from the 32-month cycle. The average interval is between 33 and 34 months One important point is that this pattern would NOT follow a 19-year cycle and so pattern 1 if strictly followed would NOT ensure that the leap months have 30 days.

Karl

16(12(05

________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Walter J Ziobro [000000080342b460-dmarc-[hidden email]]
Sent: 27 July 2017 01:24
To: CALNDR-[hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

Dear Takashi Suga:

I thank you for that information.

I have been studying the interactive Balinese Calendar located at:

http://www.kalenderbali.info/?month=1&year=2004&submit=Tampilkan

It appears that Pattern 1 has been followed from 2005 (Saka 1927) to 2027 (Saka 1949)

Mala Jiyestha occurs in the following years:

2008 (Saka 1928, year 11 of 19 year cycle)
2016 (Saka 1937, year 0 of 19 year cycle)
2022 (Saka 1944, year 6 of 19 year cycle)

Mala Sadha occurs in the following years:

2005 (Saka 1927, year 8 of 19 year cycle)
2011 (Saka 1933, year 14 of 19 year cycle)
2013 (Saka 1935, year 16 of 19 year cycle)
2019 (Saka 1941, year 3 of 19 year cycle)

Prior to 2005, and beyond 2027, the intercalary month does not appear, and there are discontinuities from some of the last dates of December to the first dates of the following January. For instance, in December of 2003, Tilem Kapitu appears on the 23rd, and in January of 2004, it also appears on the 21st. So, one would presume that 2003 should have an intercalary month, but, for some reason it was not added. I presume that, either the program used requires an occasional manual adjustment, or there is some disagreement as to when the intercalary month is to be added.

-Walter Ziobro


-----Original Message-----
From: Takashi SUGA <[hidden email]>
To: CALNDR-L <CALNDR-[hidden email]>
Sent: Wed, Jul 26, 2017 7:07 pm
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter, Karl, Amos and Calendar People,

According to the explanation written on a published Balinese calendar over a decade ago,
the intercalary rule of the Balinese saka calendar was as follows:

CE 1965 - CE 1992 : Pattern 1

If the remainder after dividing the Saka era by 19 is

0, 6, 11 then Jiyestha is repeated,
3, 8, 14, 16 then Sadha is repeated.


CE 1993 - CE 2003/2004 : Pattern 2

If the remainder after dividing the Saka era by 19 is

13 then Kadasa is repeated,
2, 10 then Jiyestha is repeated,
18 then Sadha is repeated,
7 then Kasa is repeated,
15 then Karo is repeated,
4 then Katiga is repeated.


CE 2003/2004 - : Pattern 1

The rule was returned to the pattern 1 adopted during the period of CE 1965 to CE 1992.

Let's check with when.exe( https://rubygems.org/gems/when_exe ) which uses the intercalary pattern 1 and 2.

=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=
#!/usr/bin/env ruby
require 'when_exe'
include When

(1924..2049).each do |year|
bdate = tm_pos('BalineseLuniSolar::SE', year, 8, 1) - 1
gdate = When::Gregorian ^ bdate
p [bdate, gdate] unless gdate.month == 1
end
=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=

Result:
[SE1924(2002).07<15., 2003-02-01]
[SE2049(2127).07<15., 2128-02-01]

It means that
the situation that the new moon at the end of 7th month of the Balinese saka Calendar is not included in January of Gregorian
calendar
occurred in the year 2003, and it will not occur until the year 2128 in the future if the intercalary pattern is the pattern 1.
In the year 2003, the arrangement of the new moon was out of the principle.

I heard that two types of calendars were actually published and confused in the year 2003.
It seems that the intercalary pattern was modified because the displacement was regarded as a problem of departure from the
principle.

--
Takashi SUGA, Ph.D.
Wiki: http://www2u.biglobe.ne.jp/~suchowan/when_exe_wiki.html

-----Original Message-----
From: East Carolina University Calendar discussion List [[hidden email]?>] On Behalf Of Karl Palmen
Sent: Friday, July 21, 2017 11:51 PM
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year
is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the
postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan
has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may
give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]<[hidden email]>] on behalf of Amos Shapir [[hidden email]<[hidden email]>]
Sent: 21 July 2017 07:06
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way
to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month). This suggestion was rejected
as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SV
K_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro
<000000080342b460-dmarc-[hidden email]<[hidden email]?>>> wrote:
Dear Karl:

Thank you for your response. Since I posted this question yesterday, I found two sources that, indeed, indicated that the current
version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the
Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKm
GIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980, the
Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall
in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would
otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<[hidden email]?>>>
To: CALNDR-L <CALNDR-[hidden email]<[hidden email]?>>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037
inclusive would be

2000 2003 2005 2008 2011 2014 2016
2019 2022 2024 2027 2030 2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [[hidden email]?>?>] On
Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: CALNDR-[hidden email]<[hidden email]?>>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary
month. According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar - as happens with the Islamic
calendar<https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th
month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule. Thus, I am uncertain as to which years the extra month is added, and as to why
in some years it is added after Jiyestha, and in other years it is added after Sadha. As best as I can determine from the on-line
Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no
ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir
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Re: Intercalary Month in Balinese Calendar

Karl Palmen

Dear Walter and Calendar People

 

Thank you Walter for your reply.

 

Walter refuted the theory that the intercalary months were chosen to always have 30 days.

 

However I did investigate this idea further and found that the following six intervals would occur:

 

24 months, 11 ngunalatri, increment = +16

25 months, 12 ngunalatri, increment = -18

26 months, 12 ngunalatri, increment = +12

 

36 months, 17 ngunalatri, increment = -8

37 months, 17 ngunalatri, increment = +22

38 months, 18 ngunalatri, increment = -12

 

Each increment have +1 added, if a correction of the 32-month cycle occurs within the interval.

 

The increment is the change in position in the 63-day cycle of 64 lunar days, numbered as follows:

The 2nd lunar day of a ngunalatri is numbered 0, the next 62 lunar days, which are also days are numbered 1 to 62 and the 1st lunar day of a ngunalatri is numbered 63. A month has 30 days if it begins on lunar days 0 to 33, and 29 days if it begins on lunar days 34 to 63. A leap month was assumed to have 30 days and if so, the increment must be in the range -33 to +33, so excluding certain intervals.

 

If the intercalary months don’t always have 30 days, then what is the rule for choosing which of the two months has an intercalary month?

One must bear in mind that the 19-year cycle would be broken occasionally, if fixed relative to the Gregorian calendar, by truncating to either 8 or 11 months.

 

Pattern 2 would also need to have its rules form intercalary month selection explained. Does the pattern repeat every 19-year cycle?

If so, how would it cope with a truncation?

I notice that the intervals in pattern 2, are near a multiple of 16 months and so near a whole number of yerms, if the number of months and yerms are both odd or both even, then the number of days in the leap month probably won’t change, otherwise it would probably change.

16 months 1 yerm

34 months 2 yerms

35 months 2 yerms

46 months 3 yerms

Therefore every interval except the 34-month interval probably has a change of length of the leap month. I’d suggest checking the number of days in each leap month.

 

Karl

 

16(12(08

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 31 July 2017 01:27
To: [hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

 

Dear Karl:

Thank you for your thoughts.

In the 19 year cycle that I reported, 5 of 7 intercalary months have 30 days.  2 of them have only 29, both of them Mala Sadha, in 2011 (Saka 1933) and in 2013 (Saka 1935).  So the theory that a month with 30 days is chosen is not so..

With regard to Pattern 2, the months cited by Takashi fall at intervals of 16, 34. 46, 35, 16, 46, and 35 months. I don't know the reason for this, but I suspect that it is done to arrange some convenient placement of certain festivals.

For the intercalary months to fall in a pattern of 33-32-33-32-33-32-33 months (not counting the intercalary month itself), they could fall, (for instance) after the following months in a 19 year cycle:

Year 2: Jyestha (11th month)
Year 5: Kapitu (7th)
Year 8: Kapat (4th)
Year 10 Sadha (12th)
Year 13: Kasanga (9th)
Year 16: Kalima (5th)
Year 19: Kara (2th)

This is just one possibility. There could be other arrangements that could maintain the same interval. I offer it as an example.

-Walter Ziobro

 

 

 

-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Fri, Jul 28, 2017 11:56 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter Takashi and Calendar People

Thank you for the information. It looks like Takashi's pattern 2 looks like Walter's intervals of 33 & 34, but this is hard to determine without being told which position in the numbered year each doubled month occurs.

The 7 years Walter listed match the number of new moons in the Gregorian year, except that it has 2013 instead of 2014. 2014 has its first new moon at 11:13 UT on Jan 1 and so could be counted as belonging to the previous year.


The other interesting issue is which of the two months is doubled (ignoring the more complex pattern 2). If this is selected to ensure that the leap month always has 30 days, then I'd expect it to normally alternate (as I have observed). This is because the interval between two successive leap months would then have an even number of months and last approximately one 32-month cycle.

Deviation from the alternation would be expected because the actual intervals are 24, 26, 36 or 38 months, which deviate from 4 to 8 months from the 32-month cycle. The average interval is between 33 and 34 months One important point is that this pattern would NOT follow a 19-year cycle and so pattern 1 if strictly followed would NOT ensure that the leap months have 30 days.

Karl

16(12(05

________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Walter J Ziobro [000000080342b460-dmarc-[hidden email]]
Sent: 27 July 2017 01:24
To: CALNDR-[hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

Dear Takashi Suga:

I thank you for that information.

I have been studying the interactive Balinese Calendar located at:

http://www.kalenderbali.info/?month=1&year=2004&submit=Tampilkan

It appears that Pattern 1 has been followed from 2005 (Saka 1927) to 2027 (Saka 1949)

Mala Jiyestha occurs in the following years:

2008 (Saka 1928, year 11 of 19 year cycle)
2016 (Saka 1937, year 0 of 19 year cycle)
2022 (Saka 1944, year 6 of 19 year cycle)

Mala Sadha occurs in the following years:

2005 (Saka 1927, year 8 of 19 year cycle)
2011 (Saka 1933, year 14 of 19 year cycle)
2013 (Saka 1935, year 16 of 19 year cycle)
2019 (Saka 1941, year 3 of 19 year cycle)

Prior to 2005, and beyond 2027, the intercalary month does not appear, and there are discontinuities from some of the last dates of December to the first dates of the following January. For instance, in December of 2003, Tilem Kapitu appears on the 23rd, and in January of 2004, it also appears on the 21st. So, one would presume that 2003 should have an intercalary month, but, for some reason it was not added. I presume that, either the program used requires an occasional manual adjustment, or there is some disagreement as to when the intercalary month is to be added.

-Walter Ziobro


-----Original Message-----
From: Takashi SUGA <[hidden email]>
To: CALNDR-L <CALNDR-[hidden email]>
Sent: Wed, Jul 26, 2017 7:07 pm
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter, Karl, Amos and Calendar People,

According to the explanation written on a published Balinese calendar over a decade ago,
the intercalary rule of the Balinese saka calendar was as follows:

CE 1965 - CE 1992 : Pattern 1

If the remainder after dividing the Saka era by 19 is

0, 6, 11 then Jiyestha is repeated,
3, 8, 14, 16 then Sadha is repeated.


CE 1993 - CE 2003/2004 : Pattern 2

If the remainder after dividing the Saka era by 19 is

13 then Kadasa is repeated,
2, 10 then Jiyestha is repeated,
18 then Sadha is repeated,
7 then Kasa is repeated,
15 then Karo is repeated,
4 then Katiga is repeated.


CE 2003/2004 - : Pattern 1

The rule was returned to the pattern 1 adopted during the period of CE 1965 to CE 1992.

Let's check with when.exe( https://rubygems.org/gems/when_exe ) which uses the intercalary pattern 1 and 2.

=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=
#!/usr/bin/env ruby
require 'when_exe'
include When

(1924..2049).each do |year|
bdate = tm_pos('BalineseLuniSolar::SE', year, 8, 1) - 1
gdate = When::Gregorian ^ bdate
p [bdate, gdate] unless gdate.month == 1
end
=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=

Result:
[SE1924(2002).07<15., 2003-02-01]
[SE2049(2127).07<15., 2128-02-01]

It means that
the situation that the new moon at the end of 7th month of the Balinese saka Calendar is not included in January of Gregorian
calendar
occurred in the year 2003, and it will not occur until the year 2128 in the future if the intercalary pattern is the pattern 1.
In the year 2003, the arrangement of the new moon was out of the principle.

I heard that two types of calendars were actually published and confused in the year 2003.
It seems that the intercalary pattern was modified because the displacement was regarded as a problem of departure from the
principle.

--
Takashi SUGA, Ph.D.
Wiki: http://www2u.biglobe.ne.jp/~suchowan/when_exe_wiki.html

-----Original Message-----
From: East Carolina University Calendar discussion List [[hidden email]?>] On Behalf Of Karl Palmen
Sent: Friday, July 21, 2017 11:51 PM
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year
is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the
postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan
has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may
give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]<[hidden email]>] on behalf of Amos Shapir [[hidden email]<[hidden email]>]
Sent: 21 July 2017 07:06
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way
to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month). This suggestion was rejected
as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
<a href="https://books.google.co.il/books?id=f5VUAAAAYAAJ&amp;pg=PA266&amp;lpg=PA266&amp;dq=rav&#43;ada&#43;calendar&amp;source=bl&amp;ots=TPCq1NqGj9&amp;sig=PVWIqjj1R8R29SV" target="_blank">https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SV
K_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro
<000000080342b460-dmarc-[hidden email]<[hidden email]?>>> wrote:
Dear Karl:

Thank you for your response. Since I posted this question yesterday, I found two sources that, indeed, indicated that the current
version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the
Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

<a href="https://books.google.com/books?id=WoLQAgAAQBAJ&amp;pg=PT204&amp;lpg=PT204&amp;dq=eiseman&#43;indonesian&#43;calendar&amp;source=bl&amp;ots=2SwKC-54w5&amp;sig=s_kZKm" target="_blank">https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKm
GIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980, the
Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall
in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would
otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<[hidden email]?>>>
To: CALNDR-L <CALNDR-[hidden email]<[hidden email]?>>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037
inclusive would be

2000 2003 2005 2008 2011 2014 2016
2019 2022 2024 2027 2030 2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [[hidden email]?>?>] On
Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: CALNDR-[hidden email]<[hidden email]?>>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary
month. According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar - as happens with the Islamic
calendar<https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th
month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule. Thus, I am uncertain as to which years the extra month is added, and as to why
in some years it is added after Jiyestha, and in other years it is added after Sadha. As best as I can determine from the on-line
Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no
ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir

Reply | Threaded
Open this post in threaded view
|  
Report Content as Inappropriate

Re: Intercalary Month in Balinese Calendar

Karl Palmen
In reply to this post by Walter J Ziobro

Dear Walter and Calendar People

 

Another idea occurred to me and this is to have a leap month, whenever the lunar month does not contain the first day of a month of the Indian National Calendar (or similar), which is fixed to the Gregorian calendar. This would also be similar to the Chinese calendar.

 

See https://en.wikipedia.org/wiki/Indian_national_calendar for Indian National Calendar.

 

Karl

 

16(12(08

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 31 July 2017 01:27
To: [hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

 

Dear Karl:

Thank you for your thoughts.

In the 19 year cycle that I reported, 5 of 7 intercalary months have 30 days.  2 of them have only 29, both of them Mala Sadha, in 2011 (Saka 1933) and in 2013 (Saka 1935).  So the theory that a month with 30 days is chosen is not so..

With regard to Pattern 2, the months cited by Takashi fall at intervals of 16, 34. 46, 35, 16, 46, and 35 months. I don't know the reason for this, but I suspect that it is done to arrange some convenient placement of certain festivals.

For the intercalary months to fall in a pattern of 33-32-33-32-33-32-33 months (not counting the intercalary month itself), they could fall, (for instance) after the following months in a 19 year cycle:

Year 2: Jyestha (11th month)
Year 5: Kapitu (7th)
Year 8: Kapat (4th)
Year 10 Sadha (12th)
Year 13: Kasanga (9th)
Year 16: Kalima (5th)
Year 19: Kara (2th)

This is just one possibility. There could be other arrangements that could maintain the same interval. I offer it as an example.

-Walter Ziobro

 

 

 

-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Fri, Jul 28, 2017 11:56 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter Takashi and Calendar People

Thank you for the information. It looks like Takashi's pattern 2 looks like Walter's intervals of 33 & 34, but this is hard to determine without being told which position in the numbered year each doubled month occurs.

The 7 years Walter listed match the number of new moons in the Gregorian year, except that it has 2013 instead of 2014. 2014 has its first new moon at 11:13 UT on Jan 1 and so could be counted as belonging to the previous year.


The other interesting issue is which of the two months is doubled (ignoring the more complex pattern 2). If this is selected to ensure that the leap month always has 30 days, then I'd expect it to normally alternate (as I have observed). This is because the interval between two successive leap months would then have an even number of months and last approximately one 32-month cycle.

Deviation from the alternation would be expected because the actual intervals are 24, 26, 36 or 38 months, which deviate from 4 to 8 months from the 32-month cycle. The average interval is between 33 and 34 months One important point is that this pattern would NOT follow a 19-year cycle and so pattern 1 if strictly followed would NOT ensure that the leap months have 30 days.

Karl

16(12(05

________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Walter J Ziobro [000000080342b460-dmarc-[hidden email]]
Sent: 27 July 2017 01:24
To: CALNDR-[hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

Dear Takashi Suga:

I thank you for that information.

I have been studying the interactive Balinese Calendar located at:

http://www.kalenderbali.info/?month=1&year=2004&submit=Tampilkan

It appears that Pattern 1 has been followed from 2005 (Saka 1927) to 2027 (Saka 1949)

Mala Jiyestha occurs in the following years:

2008 (Saka 1928, year 11 of 19 year cycle)
2016 (Saka 1937, year 0 of 19 year cycle)
2022 (Saka 1944, year 6 of 19 year cycle)

Mala Sadha occurs in the following years:

2005 (Saka 1927, year 8 of 19 year cycle)
2011 (Saka 1933, year 14 of 19 year cycle)
2013 (Saka 1935, year 16 of 19 year cycle)
2019 (Saka 1941, year 3 of 19 year cycle)

Prior to 2005, and beyond 2027, the intercalary month does not appear, and there are discontinuities from some of the last dates of December to the first dates of the following January. For instance, in December of 2003, Tilem Kapitu appears on the 23rd, and in January of 2004, it also appears on the 21st. So, one would presume that 2003 should have an intercalary month, but, for some reason it was not added. I presume that, either the program used requires an occasional manual adjustment, or there is some disagreement as to when the intercalary month is to be added.

-Walter Ziobro


-----Original Message-----
From: Takashi SUGA <[hidden email]>
To: CALNDR-L <CALNDR-[hidden email]>
Sent: Wed, Jul 26, 2017 7:07 pm
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter, Karl, Amos and Calendar People,

According to the explanation written on a published Balinese calendar over a decade ago,
the intercalary rule of the Balinese saka calendar was as follows:

CE 1965 - CE 1992 : Pattern 1

If the remainder after dividing the Saka era by 19 is

0, 6, 11 then Jiyestha is repeated,
3, 8, 14, 16 then Sadha is repeated.


CE 1993 - CE 2003/2004 : Pattern 2

If the remainder after dividing the Saka era by 19 is

13 then Kadasa is repeated,
2, 10 then Jiyestha is repeated,
18 then Sadha is repeated,
7 then Kasa is repeated,
15 then Karo is repeated,
4 then Katiga is repeated.


CE 2003/2004 - : Pattern 1

The rule was returned to the pattern 1 adopted during the period of CE 1965 to CE 1992.

Let's check with when.exe( https://rubygems.org/gems/when_exe ) which uses the intercalary pattern 1 and 2.

=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=
#!/usr/bin/env ruby
require 'when_exe'
include When

(1924..2049).each do |year|
bdate = tm_pos('BalineseLuniSolar::SE', year, 8, 1) - 1
gdate = When::Gregorian ^ bdate
p [bdate, gdate] unless gdate.month == 1
end
=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=

Result:
[SE1924(2002).07<15., 2003-02-01]
[SE2049(2127).07<15., 2128-02-01]

It means that
the situation that the new moon at the end of 7th month of the Balinese saka Calendar is not included in January of Gregorian
calendar
occurred in the year 2003, and it will not occur until the year 2128 in the future if the intercalary pattern is the pattern 1.
In the year 2003, the arrangement of the new moon was out of the principle.

I heard that two types of calendars were actually published and confused in the year 2003.
It seems that the intercalary pattern was modified because the displacement was regarded as a problem of departure from the
principle.

--
Takashi SUGA, Ph.D.
Wiki: http://www2u.biglobe.ne.jp/~suchowan/when_exe_wiki.html

-----Original Message-----
From: East Carolina University Calendar discussion List [[hidden email]?>] On Behalf Of Karl Palmen
Sent: Friday, July 21, 2017 11:51 PM
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year
is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the
postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan
has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may
give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]<[hidden email]>] on behalf of Amos Shapir [[hidden email]<[hidden email]>]
Sent: 21 July 2017 07:06
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way
to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month). This suggestion was rejected
as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
<a href="https://books.google.co.il/books?id=f5VUAAAAYAAJ&amp;pg=PA266&amp;lpg=PA266&amp;dq=rav&#43;ada&#43;calendar&amp;source=bl&amp;ots=TPCq1NqGj9&amp;sig=PVWIqjj1R8R29SV" target="_blank">https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SV
K_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro
<000000080342b460-dmarc-[hidden email]<[hidden email]?>>> wrote:
Dear Karl:

Thank you for your response. Since I posted this question yesterday, I found two sources that, indeed, indicated that the current
version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the
Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

<a href="https://books.google.com/books?id=WoLQAgAAQBAJ&amp;pg=PT204&amp;lpg=PT204&amp;dq=eiseman&#43;indonesian&#43;calendar&amp;source=bl&amp;ots=2SwKC-54w5&amp;sig=s_kZKm" target="_blank">https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKm
GIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980, the
Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall
in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would
otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<[hidden email]?>>>
To: CALNDR-L <CALNDR-[hidden email]<[hidden email]?>>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037
inclusive would be

2000 2003 2005 2008 2011 2014 2016
2019 2022 2024 2027 2030 2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [[hidden email]?>?>] On
Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: CALNDR-[hidden email]<[hidden email]?>>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary
month. According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar - as happens with the Islamic
calendar<https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th
month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule. Thus, I am uncertain as to which years the extra month is added, and as to why
in some years it is added after Jiyestha, and in other years it is added after Sadha. As best as I can determine from the on-line
Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no
ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir

Reply | Threaded
Open this post in threaded view
|  
Report Content as Inappropriate

Re: Intercalary Month in Balinese Calendar

Walter J Ziobro

Dear Karl et al

According to Takashi's post, the intercalary rule was apparently changed from Pattern 2 to Pattern 1 because Pattern 2 caused Tilem Kapitu to Fall in December in 2003 He stated that his source was a Balinese calendar published some years ago It would be good to see that particular calendar to see if it could provide clarification of the current rule

Walter Ziobro

Sent from AOL Mobile Mail




On Monday, July 31, 2017 Karl Palmen <[hidden email]> wrote:

Dear Walter and Calendar People

 

Another idea occurred to me and this is to have a leap month, whenever the lunar month does not contain the first day of a month of the Indian National Calendar (or similar), which is fixed to the Gregorian calendar. This would also be similar to the Chinese calendar.

 

See https://en.wikipedia.org/wiki/Indian_national_calendar for Indian National Calendar.

 

Karl

 

16(12(08

 

From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Walter J Ziobro
Sent: 31 July 2017 01:27
To: CALNDR-L@...
Subject: Re: Intercalary Month in Balinese Calendar

 

Dear Karl:

Thank you for your thoughts.

In the 19 year cycle that I reported, 5 of 7 intercalary months have 30 days.  2 of them have only 29, both of them Mala Sadha, in 2011 (Saka 1933) and in 2013 (Saka 1935).  So the theory that a month with 30 days is chosen is not so..

With regard to Pattern 2, the months cited by Takashi fall at intervals of 16, 34. 46, 35, 16, 46, and 35 months. I don't know the reason for this, but I suspect that it is done to arrange some convenient placement of certain festivals.

For the intercalary months to fall in a pattern of 33-32-33-32-33-32-33 months (not counting the intercalary month itself), they could fall, (for instance) after the following months in a 19 year cycle:

Year 2: Jyestha (11th month)
Year 5: Kapitu (7th)
Year 8: Kapat (4th)
Year 10 Sadha (12th)
Year 13: Kasanga (9th)
Year 16: Kalima (5th)
Year 19: Kara (2th)

This is just one possibility. There could be other arrangements that could maintain the same interval. I offer it as an example.

-Walter Ziobro

 

 

 

-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Fri, Jul 28, 2017 11:56 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter Takashi and Calendar People

Thank you for the information. It looks like Takashi's pattern 2 looks like Walter's intervals of 33 & 34, but this is hard to determine without being told which position in the numbered year each doubled month occurs.

The 7 years Walter listed match the number of new moons in the Gregorian year, except that it has 2013 instead of 2014. 2014 has its first new moon at 11:13 UT on Jan 1 and so could be counted as belonging to the previous year.


The other interesting issue is which of the two months is doubled (ignoring the more complex pattern 2). If this is selected to ensure that the leap month always has 30 days, then I'd expect it to normally alternate (as I have observed). This is because the interval between two successive leap months would then have an even number of months and last approximately one 32-month cycle.

Deviation from the alternation would be expected because the actual intervals are 24, 26, 36 or 38 months, which deviate from 4 to 8 months from the 32-month cycle. The average interval is between 33 and 34 months One important point is that this pattern would NOT follow a 19-year cycle and so pattern 1 if strictly followed would NOT ensure that the leap months have 30 days.

Karl

16(12(05

________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Walter J Ziobro [000000080342b460-dmarc-[hidden email]]
Sent: 27 July 2017 01:24
To: CALNDR-[hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

Dear Takashi Suga:

I thank you for that information.

I have been studying the interactive Balinese Calendar located at:

http://www.kalenderbali.info/?month=1&year=2004&submit=Tampilkan

It appears that Pattern 1 has been followed from 2005 (Saka 1927) to 2027 (Saka 1949)

Mala Jiyestha occurs in the following years:

2008 (Saka 1928, year 11 of 19 year cycle)
2016 (Saka 1937, year 0 of 19 year cycle)
2022 (Saka 1944, year 6 of 19 year cycle)

Mala Sadha occurs in the following years:

2005 (Saka 1927, year 8 of 19 year cycle)
2011 (Saka 1933, year 14 of 19 year cycle)
2013 (Saka 1935, year 16 of 19 year cycle)
2019 (Saka 1941, year 3 of 19 year cycle)

Prior to 2005, and beyond 2027, the intercalary month does not appear, and there are discontinuities from some of the last dates of December to the first dates of the following January. For instance, in December of 2003, Tilem Kapitu appears on the 23rd, and in January of 2004, it also appears on the 21st. So, one would presume that 2003 should have an intercalary month, but, for some reason it was not added. I presume that, either the program used requires an occasional manual adjustment, or there is some disagreement as to when the intercalary month is to be added.

-Walter Ziobro


-----Original Message-----
From: Takashi SUGA <[hidden email]>
To: CALNDR-L <CALNDR-[hidden email]>
Sent: Wed, Jul 26, 2017 7:07 pm
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter, Karl, Amos and Calendar People,

According to the explanation written on a published Balinese calendar over a decade ago,
the intercalary rule of the Balinese saka calendar was as follows:

CE 1965 - CE 1992 : Pattern 1

If the remainder after dividing the Saka era by 19 is

0, 6, 11 then Jiyestha is repeated,
3, 8, 14, 16 then Sadha is repeated.


CE 1993 - CE 2003/2004 : Pattern 2

If the remainder after dividing the Saka era by 19 is

13 then Kadasa is repeated,
2, 10 then Jiyestha is repeated,
18 then Sadha is repeated,
7 then Kasa is repeated,
15 then Karo is repeated,
4 then Katiga is repeated.


CE 2003/2004 - : Pattern 1

The rule was returned to the pattern 1 adopted during the period of CE 1965 to CE 1992.

Let's check with when.exe( https://rubygems.org/gems/when_exe ) which uses the intercalary pattern 1 and 2.

=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=
#!/usr/bin/env ruby
require 'when_exe'
include When

(1924..2049).each do |year|
bdate = tm_pos('BalineseLuniSolar::SE', year, 8, 1) - 1
gdate = When::Gregorian ^ bdate
p [bdate, gdate] unless gdate.month == 1
end
=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=

Result:
[SE1924(2002).07<15., 2003-02-01]
[SE2049(2127).07<15., 2128-02-01]

It means that
the situation that the new moon at the end of 7th month of the Balinese saka Calendar is not included in January of Gregorian
calendar
occurred in the year 2003, and it will not occur until the year 2128 in the future if the intercalary pattern is the pattern 1.
In the year 2003, the arrangement of the new moon was out of the principle.

I heard that two types of calendars were actually published and confused in the year 2003.
It seems that the intercalary pattern was modified because the displacement was regarded as a problem of departure from the
principle.

--
Takashi SUGA, Ph.D.
Wiki: http://www2u.biglobe.ne.jp/~suchowan/when_exe_wiki.html

-----Original Message-----
From: East Carolina University Calendar discussion List [[hidden email]?>] On Behalf Of Karl Palmen
Sent: Friday, July 21, 2017 11:51 PM
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year
is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the
postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan
has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may
give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]<[hidden email]>] on behalf of Amos Shapir [[hidden email]<[hidden email]>]
Sent: 21 July 2017 07:06
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way
to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month). This suggestion was rejected
as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SV
K_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro
<000000080342b460-dmarc-[hidden email]<[hidden email]?>>> wrote:
Dear Karl:

Thank you for your response. Since I posted this question yesterday, I found two sources that, indeed, indicated that the current
version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the
Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKm
GIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980, the
Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall
in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would
otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<[hidden email]?>>>
To: CALNDR-L <CALNDR-[hidden email]<[hidden email]?>>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037
inclusive would be

2000 2003 2005 2008 2011 2014 2016
2019 2022 2024 2027 2030 2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [[hidden email]?>?>] On
Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: CALNDR-[hidden email]<[hidden email]?>>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary
month. According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar - as happens with the Islamic
calendar<https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th
month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule. Thus, I am uncertain as to which years the extra month is added, and as to why
in some years it is added after Jiyestha, and in other years it is added after Sadha. As best as I can determine from the on-line
Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no
ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir

Reply | Threaded
Open this post in threaded view
|  
Report Content as Inappropriate

Re: Intercalary Month in Balinese Calendar

Karl Palmen

Dear Walter and Calendar People

 

Both patterns 1 & 2 follow the 19-year cycle, which would need correcting occasionally. Defining a leap month rule so that a particular lunisolar date occurs within a given range of Gregorian dates, would ensure that such a correction automatically occurs. However with a calendar as jittery as the Gregorian, these automatic corrections would be quite complicated.

 

Also the 32-month cycle arising from the 63-day cycle rule needs correcting and this can be done by removing one day = one lunar day around once every 120 years.

 

If the 19-year cycle were run with the 32-month cycle without any corrections at all, the mean year would be (235/19)*29.53125 = 365.2549342… days.

 

One possibility is  to fix the leap month rule to the Gregorian Calendar and correct the 32-month cycle whenever the Gregorian Calendar drop as leap day, which is a little less often than needed.  The calendar would then follow a 315-year cycle of 3896 months. I think Walter has considered this.

The mean month would then be (315/3896)*365.2425 = 29.5306436… days.

 

If the leap day were dropped once every 128 years, the mean month would be (315/3896)*365.2421875 = 29.5306183… days.

If it were dropped once every 124 years (whole number of weeks), the mean month would be (315/3896)*(365 + 15/62) = 29.5305980… days.

 

Karl

 

16(12(09

 

 

From: Walter J Ziobro [mailto:[hidden email]]
Sent: 01 August 2017 12:03
To: [hidden email]; Palmen, Karl (STFC,RAL,ISIS)
Subject: Re: Intercalary Month in Balinese Calendar

 

Dear Karl et al

According to Takashi's post, the intercalary rule was apparently changed from Pattern 2 to Pattern 1 because Pattern 2 caused Tilem Kapitu to Fall in December in 2003 He stated that his source was a Balinese calendar published some years ago It would be good to see that particular calendar to see if it could provide clarification of the current rule

Walter Ziobro

Sent from AOL Mobile Mail

 


On Monday, July 31, 2017 Karl Palmen <[hidden email]> wrote:

Dear Walter and Calendar People

 

Another idea occurred to me and this is to have a leap month, whenever the lunar month does not contain the first day of a month of the Indian National Calendar (or similar), which is fixed to the Gregorian calendar. This would also be similar to the Chinese calendar.

 

See https://en.wikipedia.org/wiki/Indian_national_calendar for Indian National Calendar.

 

Karl

 

16(12(08

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Walter J Ziobro
Sent: 31 July 2017 01:27
To: CALNDR-[hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

 

Dear Karl:

Thank you for your thoughts.

In the 19 year cycle that I reported, 5 of 7 intercalary months have 30 days.  2 of them have only 29, both of them Mala Sadha, in 2011 (Saka 1933) and in 2013 (Saka 1935).  So the theory that a month with 30 days is chosen is not so..

With regard to Pattern 2, the months cited by Takashi fall at intervals of 16, 34. 46, 35, 16, 46, and 35 months. I don't know the reason for this, but I suspect that it is done to arrange some convenient placement of certain festivals.

For the intercalary months to fall in a pattern of 33-32-33-32-33-32-33 months (not counting the intercalary month itself), they could fall, (for instance) after the following months in a 19 year cycle:

Year 2: Jyestha (11th month)
Year 5: Kapitu (7th)
Year 8: Kapat (4th)
Year 10 Sadha (12th)
Year 13: Kasanga (9th)
Year 16: Kalima (5th)
Year 19: Kara (2th)

This is just one possibility. There could be other arrangements that could maintain the same interval. I offer it as an example.

-Walter Ziobro

 

 

 

-----Original Message-----
From: Karl Palmen <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Fri, Jul 28, 2017 11:56 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter Takashi and Calendar People

Thank you for the information. It looks like Takashi's pattern 2 looks like Walter's intervals of 33 & 34, but this is hard to determine without being told which position in the numbered year each doubled month occurs.

The 7 years Walter listed match the number of new moons in the Gregorian year, except that it has 2013 instead of 2014. 2014 has its first new moon at 11:13 UT on Jan 1 and so could be counted as belonging to the previous year.


The other interesting issue is which of the two months is doubled (ignoring the more complex pattern 2). If this is selected to ensure that the leap month always has 30 days, then I'd expect it to normally alternate (as I have observed). This is because the interval between two successive leap months would then have an even number of months and last approximately one 32-month cycle.

Deviation from the alternation would be expected because the actual intervals are 24, 26, 36 or 38 months, which deviate from 4 to 8 months from the 32-month cycle. The average interval is between 33 and 34 months One important point is that this pattern would NOT follow a 19-year cycle and so pattern 1 if strictly followed would NOT ensure that the leap months have 30 days.

Karl

16(12(05

________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]] on behalf of Walter J Ziobro [000000080342b460-dmarc-[hidden email]]
Sent: 27 July 2017 01:24
To: CALNDR-[hidden email]
Subject: Re: Intercalary Month in Balinese Calendar

Dear Takashi Suga:

I thank you for that information.

I have been studying the interactive Balinese Calendar located at:

http://www.kalenderbali.info/?month=1&year=2004&submit=Tampilkan

It appears that Pattern 1 has been followed from 2005 (Saka 1927) to 2027 (Saka 1949)

Mala Jiyestha occurs in the following years:

2008 (Saka 1928, year 11 of 19 year cycle)
2016 (Saka 1937, year 0 of 19 year cycle)
2022 (Saka 1944, year 6 of 19 year cycle)

Mala Sadha occurs in the following years:

2005 (Saka 1927, year 8 of 19 year cycle)
2011 (Saka 1933, year 14 of 19 year cycle)
2013 (Saka 1935, year 16 of 19 year cycle)
2019 (Saka 1941, year 3 of 19 year cycle)

Prior to 2005, and beyond 2027, the intercalary month does not appear, and there are discontinuities from some of the last dates of December to the first dates of the following January. For instance, in December of 2003, Tilem Kapitu appears on the 23rd, and in January of 2004, it also appears on the 21st. So, one would presume that 2003 should have an intercalary month, but, for some reason it was not added. I presume that, either the program used requires an occasional manual adjustment, or there is some disagreement as to when the intercalary month is to be added.

-Walter Ziobro


-----Original Message-----
From: Takashi SUGA <[hidden email]>
To: CALNDR-L <CALNDR-[hidden email]>
Sent: Wed, Jul 26, 2017 7:07 pm
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter, Karl, Amos and Calendar People,

According to the explanation written on a published Balinese calendar over a decade ago,
the intercalary rule of the Balinese saka calendar was as follows:

CE 1965 - CE 1992 : Pattern 1

If the remainder after dividing the Saka era by 19 is

0, 6, 11 then Jiyestha is repeated,
3, 8, 14, 16 then Sadha is repeated.


CE 1993 - CE 2003/2004 : Pattern 2

If the remainder after dividing the Saka era by 19 is

13 then Kadasa is repeated,
2, 10 then Jiyestha is repeated,
18 then Sadha is repeated,
7 then Kasa is repeated,
15 then Karo is repeated,
4 then Katiga is repeated.


CE 2003/2004 - : Pattern 1

The rule was returned to the pattern 1 adopted during the period of CE 1965 to CE 1992.

Let's check with when.exe( https://rubygems.org/gems/when_exe ) which uses the intercalary pattern 1 and 2.

=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=
#!/usr/bin/env ruby
require 'when_exe'
include When

(1924..2049).each do |year|
bdate = tm_pos('BalineseLuniSolar::SE', year, 8, 1) - 1
gdate = When::Gregorian ^ bdate
p [bdate, gdate] unless gdate.month == 1
end
=-=-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-==-=-=-=

Result:
[SE1924(2002).07<15., 2003-02-01]
[SE2049(2127).07<15., 2128-02-01]

It means that
the situation that the new moon at the end of 7th month of the Balinese saka Calendar is not included in January of Gregorian
calendar
occurred in the year 2003, and it will not occur until the year 2128 in the future if the intercalary pattern is the pattern 1.
In the year 2003, the arrangement of the new moon was out of the principle.

I heard that two types of calendars were actually published and confused in the year 2003.
It seems that the intercalary pattern was modified because the displacement was regarded as a problem of departure from the
principle.

--
Takashi SUGA, Ph.D.
Wiki: http://www2u.biglobe.ne.jp/~suchowan/when_exe_wiki.html

-----Original Message-----
From: East Carolina University Calendar discussion List [[hidden email]?>] On Behalf Of Karl Palmen
Sent: Friday, July 21, 2017 11:51 PM
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

Dear Amos and Calendar People

The suggestion may not just be hard to calculate, but impossible to calculate.

It has a rule that if the March equinox (referred to as Tekufat Nisan) occurs after the 15th, then the month is Adar II and the year
is a leap (month) year, else it is in Nisan of a 12-month year. However to work out the day of the equinox one has to calculate the
postponement. To calculate the postponement one needs to know whether the year is a leap year.

An alternative is to replace the 15th day of the month in the leap year rule with a fixed time after the molad. If the Tekufat Nisan
has a constant interval like the molad, then one can modify the formula for which month is Tishri, by a small correction term. I may
give this in detail in a later note.

Karl

16(11(27
________________________________
From: East Carolina University Calendar discussion List [CALNDR-[hidden email]<[hidden email]>] on behalf of Amos Shapir [[hidden email]<[hidden email]>]
Sent: 21 July 2017 07:06
To: CALNDR-[hidden email]<[hidden email]>
Subject: Re: Intercalary Month in Balinese Calendar

It's interesting to note that this method is similar to the one which had been suggested in the 2nd century AD by Rav Ada as a way
to fix the Jewish calendar (in which the moment of new moon also occurs on the last day of the month). This suggestion was rejected
as being too complicated.

See http://www.youngisrael-stl.org/articles/shulman/Calendar/Hebrew%20Calendar%20-%20Lecture%201.pdf and
<a href="https://books.google.co.il/books?id=f5VUAAAAYAAJ&amp;pg=PA266&amp;lpg=PA266&amp;dq=rav&#43;ada&#43;calendar&amp;source=bl&amp;ots=TPCq1NqGj9&amp;sig=PVWIqjj1R8R29SV" target="_blank">https://books.google.co.il/books?id=f5VUAAAAYAAJ&pg=PA266&lpg=PA266&dq=rav+ada+calendar&source=bl&ots=TPCq1NqGj9&sig=PVWIqjj1R8R29SV
K_tUJ1rH1LmE&hl=iw&sa=X&ved=0ahUKEwj0xOaP2JnVAhWDuBQKHavAANcQ6AEIJTAA#v=onepage&q=rav%20ada%20calendar&f=false
(top right of page)

On Thu, Jul 20, 2017 at 9:01 PM, Walter J Ziobro
<000000080342b460-dmarc-[hidden email]<[hidden email]?>>> wrote:
Dear Karl:

Thank you for your response. Since I posted this question yesterday, I found two sources that, indeed, indicated that the current
version of the Balinese Calendar is linked to the Gregorian Calendar:

According to:

http://www.visionbali.net/calendar/balinese_calendar.html

under the heading "Adjustments", the new moon of the 7th month (which, interestingly, is the LAST day of a given month in the
Balinese Calendar, and is called the "tilem" day) must fall in January.


And, more definitely, according to Fred B Eiseman in the following reference:

<a href="https://books.google.com/books?id=WoLQAgAAQBAJ&amp;pg=PT204&amp;lpg=PT204&amp;dq=eiseman&#43;indonesian&#43;calendar&amp;source=bl&amp;ots=2SwKC-54w5&amp;sig=s_kZKm" target="_blank">https://books.google.com/books?id=WoLQAgAAQBAJ&pg=PT204&lpg=PT204&dq=eiseman+indonesian+calendar&source=bl&ots=2SwKC-54w5&sig=s_kZKm
GIznEYfkz7xp-tPpFMIVo&hl=en&sa=X&ei=5Gg-VfCeGOKasQSkn4DoAg&ved=0CEAQ6AEwBA#v=onepage&q=eiseman%20indonesian%20calendar&f=false

the placement of the intercalary month in the Balinese Calendar had been arbitrary until quite recently, when, about 1980, the
Department of Religion on Bali established the rule that Tilem Kepitu, the last day (also the new moon) of the 7th month would fall
in the Gregorian month of January, and that, to effect this, the intercalary month must be added prior to Tilem Kepitu if it would
otherwise fall in December.

-Walter Ziobro



-----Original Message-----
From: Karl Palmen <[hidden email]<[hidden email]?>>>
To: CALNDR-L <CALNDR-[hidden email]<[hidden email]?>>>
Sent: Thu, Jul 20, 2017 8:02 am
Subject: Re: Intercalary Month in Balinese Calendar

Dear Walter and Calendar People

The number of months in the year matches the number of new moons in the corresponding Gregorian year.

I checked this with https://stellafane.org/observing/moon_phase.html for all 5 of the intercalary years.

This suggests that the month intercalation is regulated by the Gregorian calendar. If so, the intercalary years from 2000 to 2037
inclusive would be

2000 2003 2005 2008 2011 2014 2016
2019 2022 2024 2027 2030 2033 2035

Karl

16(11(27

From: East Carolina University Calendar discussion List [[hidden email]?>?>] On
Behalf Of Walter J Ziobro
Sent: 20 July 2017 06:31
To: CALNDR-[hidden email]<[hidden email]?>>
Subject: Intercalary Month in Balinese Calendar

Dear Calendar List:

I have been studying the Balinese Calendar for some time, but I am uncertain as to the rule when they add the intercalary
month. According to the Wikipedia article at:

https://en.wikipedia.org/wiki/Balinese_saka_calendar


"To stop the Saka from lagging behind the Gregorian calendar - as happens with the Islamic
calendar<https://en.wikipedia.org/wiki/Islamic_calendar>, an extra month, known as an intercalary month, is added after the 11th
month (when it is known as Mala Jiyestha), or after the 12th month (Mala Sadha)"

The article is not any more specific about the rule. Thus, I am uncertain as to which years the extra month is added, and as to why
in some years it is added after Jiyestha, and in other years it is added after Sadha. As best as I can determine from the on-line
Balinese Calendar at:

http://www.kalenderbali.info/?month=6&year=2024&submit=Tampilkan

The extra month is added in the following years:

2016 (Saka 1938) as Mala Jiyestha, with 30 days
2019 (Saka 1941) as Mala Sadha, with 30 days
2022 (Saka 1944) as Mala Jiyestha, with 30 days
2024 (Saka 1946) as Mala Sadha, with 30 days
2027 (Saka 1949) as Mala Jiyestha, with 30 days

(after 2027, this program does not show the intercalary month reliably.)

As best as I can determine, the month is chosen as either Jiyestha or Sadha based on whether or not that month has 30 days (no
ngunalatri, according to the 63 day rule), but I still am uncertain as to why any particular year has the intercalary month.

Does anyone have a clue?

-Walter Ziobro



--
Amos Shapir

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315-yr vs 448-years Re: Intercalary Month in Balinese Calendar

Brij Bhushan metric VIJ
Karl, cc sirs:
>If the leap day were dropped once every >128 years, the mean month would be
>(315/3896)*365.2421875 = 29.5306183… >days.
For 315-years/3896 moons is good for Mean Moon=29d12h44m5s.42112.
This indeed is a good attempt, against my calculation for 448-years/5541 moons, the result of what is placed, close to current values of 'Lunation period' of Mean Moon=
29d12h44m2s.877594 on extending
 just ONE Tithi
(from 1/2 to (0.5+0.49287326 day =0.99287336) day - in 5541 moons; which is still lesser than my regular Tithi of 1 338/326819 day). Moreso, this extended duration CONSUMES one full moon over about a cycle of precession, as discussed and demonstrated in my calculations.
Thus, Mean Moon=(448-years+ 0.49287326) day/5541 moons=29.5305888 6 days =29d12h44 m2s.877594.
Regards,
Ex-Flt.Lt. Brij Bhushan VIJ, Author
Brij-Gregorian Modified Caldndar
Wednesday, 2017 August02H16:67)decimal)
 
Sent from my iPhone

> On Aug 1, 2017, at 6:00 AM, Karl Palmen <[hidden email]> wrote:
>
> If the leap day were dropped once every 128 years, the mean month would be (315/3896)*365.2421875 = 29.5306183… days
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Re: 315-yr vs 448-years Re: Intercalary Month in Balinese Calendar

Karl Palmen
Dear Brij and Calendar People

(448/5541)*365.2421875 = 29.5304999... days = 29d12h43m55.1922... s.

Brij corrects this by adding a period of time of just under half a day to the 5541 months, but not to the 448 years. Then we no longer have  5541 months = 448 years. So why have 5541/448 at all?
It seems pointless to me.

The (315/3896) arises from a calendar explained in my previous note.
This calendar runs to a 32-month cycle of 945 days, from which one day is removed whenever the solar calendar drops a leap day. This causes the lunar calendar months to remain aligned to the solar calendar years, as if the 32-month cycle were never corrected and no leap days were dropped.

(315/3896) = 29.53125/365.25

Karl

16(12(11


-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Brij Bhushan metric VIJ
Sent: 03 August 2017 00:41
To: [hidden email]
Subject: 315-yr vs 448-years Re: Intercalary Month in Balinese Calendar

Karl, cc sirs:
>If the leap day were dropped once every 128 years, the mean month would be
>(315/3896)*365.2421875 = 29.5306183… days.
For 315-years/3896 moons is good for Mean Moon=29d12h44m5s.42112.
This indeed is a good attempt, against my calculation for 448-years/5541 moons, the result of what is placed, close to current values of 'Lunation period' of Mean Moon=
29d12h44m2s.877594 on extending
 just ONE Tithi
(from 1/2 to (0.5+0.49287326 day =0.99287336) day - in 5541 moons; which is still lesser than my regular Tithi of 1 338/326819 day). Moreso, this extended duration CONSUMES one full moon over about a cycle of precession, as discussed and demonstrated in my calculations.
Thus, Mean Moon=(448-years+ 0.49287326) day/5541 moons=29.5305888 6 days =29d12h44 m2s.877594.
Regards,
Ex-Flt.Lt. Brij Bhushan VIJ, Author
Brij-Gregorian Modified Caldndar
Wednesday, 2017 August02H16:67)decimal)
 
Sent from my iPhone

> On Aug 1, 2017, at 6:00 AM, Karl Palmen <[hidden email]> wrote:
>
> If the leap day were dropped once every 128 years, the mean month would be (315/3896)*365.2421875 = 29.5306183… days
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Indirect Adjustments Re: 315-yr vs 448-years Re: Intercalary Month in Balinese Calendar

Brij Bhushan metric VIJ
Karl, Walter, listserv sirs:
>The (315/3896) arises from a calendar >explained in my previous note.
>This calendar runs to a 32-month cycle of >945 days, from which one day is removed >whenever the solar calendar drops a leap >day.
Karl has a right to say my calculations as 'pointless' to consider their calendaric worth.
His own 32-month calculation bases duration of Mean Moon=29d12h45m i.e. 29.53125x32=945 days; while 32 Lunation x29.53058886=944.97884352 days  or 2-years 214.49446852 days!
(5541/32)x944.97884352 days =163628.99287326 days; which is
448-years+0.49287326 days, the figure I used in reaching my shown/demonstrated calculations.
This is 5541-Lunation x 29.53058886= 163628.99287326 days demonstrated in my calculated results (already with Karl)! What new is being shown by Karl an Astro-mathematician?
My regards to him and the list, for examining my calculations. I thank you all,
Ex-Flt.Lt. Brij Bhushan VIJ (Retd.), Author
Brij-Gregorian Modified Calendar
Thursday, 2017 August 03H07:34 (decimal)

Sent from my iPhone

> On Aug 3, 2017, at 5:08 AM, Karl Palmen <[hidden email]> wrote:
>
> The (315/3896) arises from a calendar explained in my previous note.
> This calendar runs to a 32-month cycle of 945 days, from which one day is removed whenever the solar calendar drops a leap day.
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