REFORMED INDIAN SOLAR CALENDAR
The socalled Indian National Calendar is a solar calendar adopted for use in India in 1957. It is a solar calendar in which the month lengths are distributed in such a manner as to cause the beginnings of each season to fall on or near the first of four months. The months, beginning with the first month Chaitra, which begins at, or near, the northward equinox, follow the sequence of monthlengths of 30 (31 in leap years)  3131313131303030303030 days. It is described in detail here: https://en.wikipedia.org/wiki/Indian_national_calendar This interesting {to me, anyway} calendar has some good points, and a couple of flaws. The major good point, IMO, is that it attempts to reflect the actual, relative lengths of the seasons in a rule based calendar. It uses a leap day rule that is identical to the 400 year rule of the Gregorian Calendar, with which it is in sync, by design. However, the Gregorian leap day rule is somewhat jittery, with the start dates of each season moving over a range of several days, and the calendar has no rule to adjust for the precession of the equinoxes relative to the apsides (perihelion and aphelion). My proposal attempts to remedy these two problems. The first reform would be to adopt a truncated 900 year, 33year leap day rule. What that means is that the leap year would follow the leap day rule of the Dee calendar, with a leap day every fourth year of a 33 year cycle (with a gap of 5 years from the 32nd year of one cycle until the 4th year of the following) , which would continue for 27 cycles of 891 years. This would be followed by a short period of 9 years, with leap days falling in the 4th and 8th years, after which a new cycle of 900 years would begin. . The total period of 900 years would thus have (((32 x 365.25) + 365) x 27) + ((8 x 365.25) +365) = (12,053 x 27) +3,287 = 328,718 days, which would give an average year length of 365.24222.., which is the exact average year length of the Reformed Julian calendar, and very close to the length of the mean tropical year at this time. Over a period of 3,600 years, it would be exactly one day shorter than the Gregorian Calendar. The use of the 33 year rule would also reduce the jitteriness of the start dates of each quarter relative to the seasonal points. The second reform would be to shift the month lengths by one month every 1800 years (once every 2900 year cycles), to reflect the gradual precession of the equinoxes relative to the apsides. Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 328,718 days later on JD 3064866.5, or 21 March 3679 AD/CE. The months in the 1st 1800 year period of the Saka Era of this proleptic calendar would have the lengths of: 313131313130303030303030/31 days each, which, in the current period would have shifted to: 30/313131313131303030303030 days each, which in the next Saka period commencing in 3601 (3679 AD/CE), will shift to: 3030/3131313131313030303030 days. Walter Ziobro 
Hi Walter and calendar people, The trouble with this calendar  as well as the Reformed Julian (Greek Orthodox) calendar which inspired its 900 year cycle  is that there's no such thing as THE mean tropical year. A tropical year's length depends on which point on the Earth's orbit it's measured from. The Gregorian calendar tries to match the northward (northern spring) equinox year, though currently and for the near future the northern solstice year may be more stable  see Irv Bromberg's posts about this.On Tue, Jan 31, 2017 at 7:10 AM, Walter J Ziobro <[hidden email]> wrote: REFORMED INDIAN SOLAR CALENDAR  Amos Shapir

Dear Amos, Walter, Michael and Calendar People From: East Carolina University Calendar discussion List [mailto:[hidden email]]
On Behalf Of Amos Shapir Hi Walter and calendar people, The trouble with this calendar  as well as the
Reformed Julian (Greek Orthodox) calendar which inspired its 900 year cycle  is that there's no such thing as THE mean tropical year. A tropical year's length depends on which point
on the Earth's orbit it's measured from. The Gregorian calendar tries to match the northward (northern spring) equinox year, though currently and for the near future the northern solstice year may be more stable  see Irv Bromberg's posts about this. KARL REPLIES: The shifting of the month lengths would cause the mean length of the year to depend on which month it begins, to
approximate the tropical years that begin at the start of the month. Hence (assuming the month shifts take effect at a new year), the northward equinox year would be appropriate, which can be approximated by a simple 33year cycle. This calendar has well defined ‘desired dates’ of 12 ecliptic longitudes each at the start of a month and so my definition of yearround
accuracy can be applied and this calendar would have a much better yearround accuracy than any calendar than any calendar Michael Ossipoff has proposed, but would be more complicated. Michael’s definition of yearround accuracy would be grossly misleading. Karl 16(06(04 On Tue, Jan 31, 2017 at 7:10 AM, Walter J Ziobro <[hidden email]> wrote: REFORMED INDIAN SOLAR CALENDAR
Amos Shapir 
In reply to this post by Walter J Ziobro
Dear Walter, Amos and Calendar People In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do
one of my own Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would
be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE. Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error. Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for
the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days
and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox. Karl 16(06(04 From: East Carolina University Calendar discussion List [mailto:[hidden email]]
On Behalf Of Walter J Ziobro REFORMED INDIAN SOLAR CALENDAR 
Dear Karl For the average length of the southward equinox year, wouldn't you have to compare the start dates of the 7th month, Ashwin? Walter Ziobro Sent from AOL Mobile Mail On Tuesday, January 31, 2017 Karl Palmen <[hidden email]> wrote: Dear Walter, Amos and Calendar People
In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do one of my own
Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would
be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE. Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error.
Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox.
Karl
16(06(04
From: East Carolina University Calendar discussion List [mailto:CALNDRL@...] On Behalf Of Walter J Ziobro Sent: 31 January 2017 05:10 To: CALNDRL@... Subject: REFORMED INDIAN SOLAR CALENDAR
REFORMED INDIAN SOLAR CALENDAR 
In reply to this post by Karl Palmen
Dear Karl and Calendar List:
In order to see how the seasonal tropical year lengths determined by my Reformed Indian Solar Calendar compare to known seasonal year lengths, I have computed the seasonal year lengths at the beginning of the months of Caithra, Asadha, Asvina, and Pausa (months 1,4,7,and 10, which correspond respectively to the equinox and solstices, for 2  1800 year periods of the calendar, Saka 11800 (AD/CE 791878), and Saka 18013600 (AD/CE 18793678), and compared them to calculations given by Meeus and Savoie, for year 0, and year 2000, per Wikipedia: 1 Caithra 1, JD 174994.5 to 1801 Caithra 1, JD 2407430.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242137, var = 0.0000852 1 Asadha 1, JD 1750087.5 to 1801 Caithra 1 JD 2407522.5, 657435 days, ave year = 365.24167, per Meeus @ year 0 = 365.241726, var = 0.0000059 1 Asvina 1, JD 1790179.5 to 1801 Asvina 1, JD 2407615.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242496, var = 0.000274 1 Pausa 1, JD 1750269.5 to 1801 Pausa 1, JD 2407705.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242883, var = 0.000661 1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24222, per Meeus @ 2000 = 365.242374, var = 0.000152 1801 Asadha 1, JD407522.5 to 3601 Asadha 1, JD 3064957.5, 657435 days, ave year = 365.24167, per Meeus @ 2000= 365.241626, var = 0.000047 1801 Asvina 1, JD 2407615.5 to 3601 Asvina 1, JD 3605050.5, 657435 days, ave year = 365.24167, per Meeus @ 2000 = 365.242018, var = 0.000351 1801 Pausa 1, JD 2407705.5 to 3601 Pausa 1, JD 3605141.5, 657436 days, ave year = 365.24222, per Meeus @ 2000= 365.242740, var = 0.000518 What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all cases given here, the seasons in each period with the shorter average year length, will correspond to to shorter seasonal tropical years as determined by Meeus and Savoie Walter Ziobro Original Message
From: Karl Palmen <[hidden email]> To: CALNDRL <[hidden email]> Sent: Tue, Jan 31, 2017 11:21 am Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Walter, Amos and Calendar People
In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do
one of my own
Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would
be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE.
Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error.
Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for
the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days
and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox.
Karl
16(06(04
From: East Carolina University Calendar discussion List [[hidden email]]
On Behalf Of Walter J Ziobro
Sent: 31 January 2017 05:10 To: CALNDR[hidden email] Subject: REFORMED INDIAN SOLAR CALENDAR REFORMED INDIAN SOLAR CALENDAR
The socalled Indian National Calendar is a solar calendar adopted for use in India in 1957. It is a solar calendar in which the month lengths are distributed in such a manner as to cause the beginnings of each season to fall on or near the first of four months. The months, beginning with the first month Chaitra, which begins at, or near, the northward equinox, follow the sequence of monthlengths of 30 (31 in leap years)  3131313131303030303030 days. It is described in detail here: https://en.wikipedia.org/wiki/Indian_national_calendar This interesting {to me, anyway} calendar has some good points, and a couple of flaws. The major good point, IMO, is that it attempts to reflect the actual, relative lengths of the seasons in a rule based calendar. It uses a leap day rule that is identical to the 400 year rule of the Gregorian Calendar, with which it is in sync, by design. However, the Gregorian leap day rule is somewhat jittery, with the start dates of each season moving over a range of several days, and the calendar has no rule to adjust for the precession of the equinoxes relative to the apsides (perihelion and aphelion). My proposal attempts to remedy these two problems. The first reform would be to adopt a truncated 900 year, 33year leap day rule. What that means is that the leap year would follow the leap day rule of the Dee calendar, with a leap day every fourth year of a 33 year cycle (with a gap of 5 years from the 32nd year of one cycle until the 4th year of the following) , which would continue for 27 cycles of 891 years. This would be followed by a short period of 9 years, with leap days falling in the 4th and 8th years, after which a new cycle of 900 years would begin. . The total period of 900 years would thus have (((32 x 365.25) + 365) x 27) + ((8 x 365.25) +365) = (12,053 x 27) +3,287 = 328,718 days, which would give an average year length of 365.24222.., which is the exact average year length of the Reformed Julian calendar, and very close to the length of the mean tropical year at this time. Over a period of 3,600 years, it would be exactly one day shorter than the Gregorian Calendar. The use of the 33 year rule would also reduce the jitteriness of the start dates of each quarter relative to the seasonal points. The second reform would be to shift the month lengths by one month every 1800 years (once every 2900 year cycles), to reflect the gradual precession of the equinoxes relative to the apsides. Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 328,718 days later on JD 3064866.5, or 21 March 3679 AD/CE. The months in the 1st 1800 year period of the Saka Era of this proleptic calendar would have the lengths of: 313131313130303030303030/31 days each, which, in the current period would have shifted to: 30/313131313131303030303030 days each, which in the next Saka period commencing in 3601 (3679 AD/CE), will shift to: 3030/3131313131313030303030 days. Walter Ziobro 
Dear Walter and Calendar People Walter said What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all cases given here, the seasons
in each period with the shorter average year length, will correspond to shorter seasonal tropical years as determined by Meeus and Savoie If Walter worked through most of a precession cycle (reckoned to be 21,600 years), he’d find three 36.24222, 365.24167 and 365.24278 days of which the first
and one of the other two occur at any one 1800year period. The 7^{th} month Ashwin would deviate from the mean calendar year the most, but not for the current 1800year period, which is why I chose the 6^{th} month Bhaadra for my demonstration.
The comparisons of average year with Meeus tropical year gives significant more negative than positive ‘var’ values, so suggesting that the mean year is too
low. For other mean calendar years, the other two average year lengths would differ from it by 1/1800 day. If the mean calendar year were raised by 0.0002 day to 365.24242 days we’d get 1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24242, per Meeus @ 2000 = 365.242374, var = 0.000048 Which has more balanced ‘var’ values. In the long term, the leap year rule would need changing several times over a precession cycle and for this it is not sufficient to compare average years, one
needs to compare the month starts with their corresponding solar ecliptic longitudes, which are equal to the Chinese calendar principal terms or equivalently the times when the sun enters a sign of the Western zodiac. Karl 16(06(05 From: East Carolina University Calendar discussion List [mailto:[hidden email]]
On Behalf Of Walter J Ziobro Dear Karl and Calendar List:
Original Message Dear Walter, Amos and Calendar People In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do
one of my own Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the
first 1800 year period would be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE. Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error. Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for
the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days
and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox. Karl 16(06(04 From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro REFORMED INDIAN SOLAR CALENDAR 
Dear Karl and Calendar People:
I thank you for that information. Even though there are problems with my proposal, I believe that I have made my essential point that a calendar with regularly shifting month lengths can produce reasonable values for the lengths of each of the seasonal tropical years. I note that the bias toward the negative variances in the periods that I have chosen may be due to the presence of only two average year values in those periods, 365.24222 days and 365.24167 days. Might not periods with the average year length values of 365.24222 days and 365.24278 days.produce a bias toward positive variances? Also, might there not be lengths of tropical years determined from other start points in the periods selected by me with 365.24278 days that would smooth out the variances within a period? Also, I acknowledge that there would have to be other adjustments over longer periods. I didn't bring them up in my proposal because I thought just getting people to see the operation of the concepts over a 3600 year period would be sufficient for a new idea that is nowhere in use now. All calendars have long term problems over several millennia. For instance, it is well known and often mentioned in this group that the length of the tropical year, measured from whatever reference point,is slowly decreasing over the millennia. A leap day rule with fewer days will have to devised for any calendar used in the distant future. Also, as Dr Irv often reminds us, the eccentricity of the Earth's orbit varies over time, and the relative lengths of the months in a seasonal calendar like the Indian National Calendar will have to be adjusted. (We could try and minimize the variance in the Earth's orbital eccentricity by blowing up Venus, but that would probably mean no more ice ages, which we may need someday to cool us down. ;/ ) For example, if the Earth's orbital eccentricity were reduced to 0, then a calendar with month lengths such as 30/313031303130313031303130 would be used. Also, again as Dr Irv likes to remind us, the precession of the equinoxes relative to the apsides would be much quicker then, meaning that any month length shifts would have to be more frequent than every 1800 years. On the other hand, when the point is reached at some distant time in the future that the Earth's orbital eccentricity is greater than now, then the month lengths will have to be further compressed, such as with 30/31313132313130303029303030 days in each month. But this is way too far into the future to worry about now. Walter Ziobro Original Message
From: Karl Palmen <[hidden email]> To: CALNDRL <[hidden email]> Sent: Wed, Feb 1, 2017 8:05 am Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Walter and Calendar People
Walter said
What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all cases given here, the seasons
in each period with the shorter average year length, will correspond to shorter seasonal tropical years as determined by Meeus and Savoie
If Walter worked through most of a precession cycle (reckoned to be 21,600 years), he’d find three 36.24222, 365.24167 and 365.24278 days of which the first
and one of the other two occur at any one 1800year period. The 7^{th} month Ashwin would deviate from the mean calendar year the most, but not for the current 1800year period, which is why I chose the 6^{th} month Bhaadra for my demonstration.
The comparisons of average year with Meeus tropical year gives significant more negative than positive ‘var’ values, so suggesting that the mean year is too
low.
For other mean calendar years, the other two average year lengths would differ from it by 1/1800 day.
If the mean calendar year were raised by 0.0002 day to 365.24242 days we’d get
1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24242, per Meeus @ 2000 = 365.242374, var = 0.000048
1801 Asadha 1, JD407522.5 to 3601 Asadha 1, JD 3064957.5, 657435 days, ave year = 365.24187, per Meeus @ 2000= 365.241626, var = 0.000247 1801 Asvina 1, JD 2407615.5 to 3601 Asvina 1, JD 3605050.5, 657435 days, ave year = 365.24187, per Meeus @ 2000 = 365.242018, var = 0.000151 1801 Pausa 1, JD 2407705.5 to 3601 Pausa 1, JD 3605141.5, 657436 days, ave year = 365.24242, per Meeus @ 2000= 365.242740, var = 0.000318 Which has more balanced ‘var’ values.
In the long term, the leap year rule would need changing several times over a precession cycle and for this it is not sufficient to compare average years, one
needs to compare the month starts with their corresponding solar ecliptic longitudes, which are equal to the Chinese calendar principal terms or equivalently the times when the sun enters a sign of the Western zodiac.
Karl
16(06(05
From: East Carolina University Calendar discussion List [[hidden email]]
On Behalf Of Walter J Ziobro
Sent: 01 February 2017 05:48 To: CALNDR[hidden email] Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Karl and Calendar List:
In order to see how the seasonal tropical year lengths determined by my Reformed Indian Solar Calendar compare to known seasonal year lengths, I have computed the seasonal year lengths at the beginning of the months of Caithra, Asadha, Asvina, and Pausa (months 1,4,7,and 10, which correspond respectively to the equinox and solstices, for 2  1800 year periods of the calendar, Saka 11800 (AD/CE 791878), and Saka 18013600 (AD/CE 18793678), and compared them to calculations given by Meeus and Savoie, for year 0, and year 2000, per Wikipedia: 1 Caithra 1, JD 174994.5 to 1801 Caithra 1, JD 2407430.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242137, var = 0.0000852 1 Asadha 1, JD 1750087.5 to 1801 Caithra 1 JD 2407522.5, 657435 days, ave year = 365.24167, per Meeus @ year 0 = 365.241726, var = 0.0000059 1 Asvina 1, JD 1790179.5 to 1801 Asvina 1, JD 2407615.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242496, var = 0.000274 1 Pausa 1, JD 1750269.5 to 1801 Pausa 1, JD 2407705.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242883, var = 0.000661 1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24222, per Meeus @ 2000 = 365.242374, var = 0.000152 1801 Asadha 1, JD407522.5 to 3601 Asadha 1, JD 3064957.5, 657435 days, ave year = 365.24167, per Meeus @ 2000= 365.241626, var = 0.000047 1801 Asvina 1, JD 2407615.5 to 3601 Asvina 1, JD 3605050.5, 657435 days, ave year = 365.24167, per Meeus @ 2000 = 365.242018, var = 0.000351 1801 Pausa 1, JD 2407705.5 to 3601 Pausa 1, JD 3605141.5, 657436 days, ave year = 365.24222, per Meeus @ 2000= 365.242740, var = 0.000518 What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all cases given here, the seasons in each period with the shorter average year length, will correspond to to shorter seasonal tropical years as determined by Meeus and Savoie Walter Ziobro Original Message
From: Karl Palmen <[hidden email][hidden email]> To: CALNDRL <[hidden email][hidden email]> Sent: Tue, Jan 31, 2017 11:21 am Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Walter, Amos and Calendar People
In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do
one of my own
Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the
first 1800 year period would be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE.
Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error.
Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for
the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days
and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox.
Karl
16(06(04
From: East Carolina University Calendar discussion
List [[hidden email][hidden email]]
On Behalf Of Walter J Ziobro
Sent: 31 January 2017 05:10 To: CALNDR[hidden email][hidden email] Subject: REFORMED INDIAN SOLAR CALENDAR REFORMED INDIAN SOLAR CALENDAR
The socalled Indian National Calendar is a solar calendar adopted for use in India in 1957. It is a solar calendar in which the month lengths are distributed in such a manner as to cause the beginnings of each season to fall on or near the first of four months. The months, beginning with the first month Chaitra, which begins at, or near, the northward equinox, follow the sequence of monthlengths of 30 (31 in leap years)  3131313131303030303030 days. It is described in detail here: https://en.wikipedia.org/wiki/Indian_national_calendar This interesting {to me, anyway} calendar has some good points, and a couple of flaws. The major good point, IMO, is that it attempts to reflect the actual, relative lengths of the seasons in a rule based calendar. It uses a leap day rule that is identical to the 400 year rule of the Gregorian Calendar, with which it is in sync, by design. However, the Gregorian leap day rule is somewhat jittery, with the start dates of each season moving over a range of several days, and the calendar has no rule to adjust for the precession of the equinoxes relative to the apsides (perihelion and aphelion). My proposal attempts to remedy these two problems. The first reform would be to adopt a truncated 900 year, 33year leap day rule. What that means is that the leap year would follow the leap day rule of the Dee calendar, with a leap day every fourth year of a 33 year cycle (with a gap of 5 years from the 32nd year of one cycle until the 4th year of the following) , which would continue for 27 cycles of 891 years. This would be followed by a short period of 9 years, with leap days falling in the 4th and 8th years, after which a new cycle of 900 years would begin. . The total period of 900 years would thus have (((32 x 365.25) + 365) x 27) + ((8 x 365.25) +365) = (12,053 x 27) +3,287 = 328,718 days, which would give an average year length of 365.24222.., which is the exact average year length of the Reformed Julian calendar, and very close to the length of the mean tropical year at this time. Over a period of 3,600 years, it would be exactly one day shorter than the Gregorian Calendar. The use of the 33 year rule would also reduce the jitteriness of the start dates of each quarter relative to the seasonal points. The second reform would be to shift the month lengths by one month every 1800 years (once every 2900 year cycles), to reflect the gradual precession of the equinoxes relative to the apsides. Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 328,718 days later on JD 3064866.5, or 21 March 3679 AD/CE. The months in the 1st 1800 year period of the Saka Era of this proleptic calendar would have the lengths of: 313131313130303030303030/31 days each, which, in the current period would have shifted to: 30/313131313131303030303030 days each, which in the next Saka period commencing in 3601 (3679 AD/CE), will shift to: 3030/3131313131313030303030 days. Walter Ziobro 
Dear Walter and Calendar People From: East Carolina University Calendar discussion List [mailto:[hidden email]]
On Behalf Of Walter J Ziobro Dear Karl and Calendar People: KARL REPLIES: It is the idea that the leap year rule should create a mean year near the mean tropical year that is wrong and I believe it is the cause of the
bias observed. It should be the tropical year that starts when the calendar year starts, which in this case is the March Equinox tropical year, when I moved the mean calendar year towards this, the bias disappeared.
KARL REPLIES: Future adjustments of the calendar would have to take account of this and the changing rate of precession, which would affect the timing of the
monthlength shifts. If as expected the June solstice tropical year length becomes stable, then one could use a leap year rule based on the June solstice tropical year, provided one makes each monthlength shift take effect on the 4^{th} month of the
year. Karl 16(06(06
Original Message Dear Walter and Calendar People Walter said What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all
cases given here, the seasons in each period with the shorter average year length, will correspond to shorter seasonal tropical years as determined by Meeus and Savoie If Walter worked through most of a precession cycle (reckoned to be 21,600 years), he’d find three 36.24222, 365.24167 and 365.24278 days of which the first
and one of the other two occur at any one 1800year period. The 7^{th} month Ashwin would deviate from the mean calendar year the most, but not for the current 1800year period, which is why I chose the 6^{th} month Bhaadra for my demonstration.
The comparisons of average year with Meeus tropical year gives significant more negative than positive ‘var’ values, so suggesting that the mean year is too
low. For other mean calendar years, the other two average year lengths would differ from it by 1/1800 day. If the mean calendar year were raised by 0.0002 day to 365.24242 days we’d get 1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24242, per Meeus @ 2000 = 365.242374, var = 0.000048 Which has more balanced ‘var’ values. In the long term, the leap year rule would need changing several times over a precession cycle and for this it is not sufficient to compare average years, one
needs to compare the month starts with their corresponding solar ecliptic longitudes, which are equal to the Chinese calendar principal terms or equivalently the times when the sun enters a sign of the Western zodiac. Karl 16(06(05 From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro Dear Karl and Calendar List:
Original Message Dear Walter, Amos and Calendar People In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do
one of my own Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would
be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE. Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error. Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for
the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days
and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox. Karl 16(06(04 From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro REFORMED INDIAN SOLAR CALENDAR 
Dear Karl and Calendar List:
I have given this matter a bit more consideration. I have noticed that there are three ways that a 33 year cycle can be truncated to produce years of varying average lengths: The shortest is 100 years (ie 3 33 year cycles + 1 common year) which has 36,524 days, with an average year of 365.24 days The next is the 900 year cycle, which I have been using (ie 27 33 year cycles + 2 olympiads + 1 common year) which has 328,718 days, with an average year of 365.242222 days (same as Reformed Julian Calendar) The next is the untruncated 33 year cycle itself, which has 365.242424... days (same as the Dee and Dee Cecil Calendars) The final is 400 years (ie 12 33 year cycles + 1 olympiad) which has 146,097 days, with as average year of 365.2425 days (same as the current Gregorian Calendar) So, if I understand your criticism of my proposed Reformed Indian Solar Calendar, the best leap year rule for the current era would be the untruncated 33 year cycle. After some period of time, this could be switched to the 900 year cycle, and finally to the 100 year cycle. At some distant point in the future, the 33 year leap day rule would not work well. Walter Ziobro Original Message
From: Karl Palmen <[hidden email]> To: CALNDRL <[hidden email]> Sent: Thu, Feb 2, 2017 8:04 am Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Walter and Calendar People
From: East Carolina University Calendar discussion List [[hidden email]]
On Behalf Of Walter J Ziobro
Sent: 02 February 2017 05:02 To: CALNDR[hidden email] Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Karl and Calendar People:
I thank you for that information. Even though there are problems with my proposal, I believe that I have made my essential point that a calendar with regularly shifting month lengths can produce reasonable values for the lengths of each of the seasonal tropical years. I note that the bias toward the negative variances in the periods that I have chosen may be due to the presence of only two average year values in those periods, 365.24222 days and 365.24167 days. Might not periods with the average year length values of 365.24222 days and 365.24278 days.produce a bias toward positive variances? Also, might there not be lengths of tropical years determined from other start points in the periods selected by me with 365.24278 days that would smooth out the variances within a period? KARL REPLIES: It is the idea that the leap year rule should create a mean year near the mean tropical year that is wrong and I believe it is the cause of the
bias observed. It should be the tropical year that starts when the calendar year starts, which in this case is the March Equinox tropical year, when I moved the mean calendar year towards this, the bias disappeared.
Also, I acknowledge that there would have to be other adjustments over longer periods. I didn't bring them up in my proposal because I thought just getting people to see the operation of the concepts over a 3600 year period would be sufficient for a new idea that is nowhere in use now. All calendars have long term problems over several millennia. For instance, it is well known and often mentioned in this group that the length of the tropical year, measured from whatever reference point,is slowly decreasing over the millennia. A leap day rule with fewer days will have to devised for any calendar used in the distant future. Also, as Dr Irv often reminds us, the eccentricity of the Earth's orbit varies over time, and the relative lengths of the months in a seasonal calendar like the Indian National Calendar will have to be adjusted. (We could try and minimize the variance in the Earth's orbital eccentricity by blowing up Venus, but that would probably mean no more ice ages, which we may need someday to cool us down. ;/ ) For example, if the Earth's orbital eccentricity were reduced to 0, then a calendar with month lengths such as 30/313031303130313031303130 would be used. Also, again as Dr Irv likes to remind us, the precession of the equinoxes relative to the apsides would be much quicker then, meaning that any month length shifts would have to be more frequent than every 1800 years. On the other hand, when the point is reached at some distant time in the future that the Earth's orbital eccentricity is greater than now, then the month lengths will have to be further compressed, such as with 30/31313132313130303029303030 days in each month. But this is way too far into the future to worry about now. KARL REPLIES: Future adjustments of the calendar would have to take account of this and the changing rate of precession, which would affect the timing of the
monthlength shifts. If as expected the June solstice tropical year length becomes stable, then one could use a leap year rule based on the June solstice tropical year, provided one makes each monthlength shift take effect on the 4^{th} month of the
year.
Karl
16(06(06
Walter Ziobro Original Message
From: Karl Palmen <[hidden email]> To: CALNDRL <[hidden email]> Sent: Wed, Feb 1, 2017 8:05 am Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Walter and Calendar People
Walter said
What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all
cases given here, the seasons in each period with the shorter average year length, will correspond to shorter seasonal tropical years as determined by Meeus and Savoie
If Walter worked through most of a precession cycle (reckoned to be 21,600 years), he’d find three 36.24222, 365.24167 and 365.24278 days of which the first
and one of the other two occur at any one 1800year period. The 7^{th} month Ashwin would deviate from the mean calendar year the most, but not for the current 1800year period, which is why I chose the 6^{th} month Bhaadra for my demonstration.
The comparisons of average year with Meeus tropical year gives significant more negative than positive ‘var’ values, so suggesting that the mean year is too
low.
For other mean calendar years, the other two average year lengths would differ from it by 1/1800 day.
If the mean calendar year were raised by 0.0002 day to 365.24242 days we’d get
1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24242, per Meeus @ 2000 = 365.242374, var = 0.000048
1801 Asadha 1, JD407522.5 to 3601 Asadha 1, JD 3064957.5, 657435 days, ave year = 365.24187, per Meeus @ 2000= 365.241626, var = 0.000247 1801 Asvina 1, JD 2407615.5 to 3601 Asvina 1, JD 3605050.5, 657435 days, ave year = 365.24187, per Meeus @ 2000 = 365.242018, var = 0.000151 1801 Pausa 1, JD 2407705.5 to 3601 Pausa 1, JD 3605141.5, 657436 days, ave year = 365.24242, per Meeus @ 2000= 365.242740, var = 0.000318 Which has more balanced ‘var’ values.
In the long term, the leap year rule would need changing several times over a precession cycle and for this it is not sufficient to compare average years, one
needs to compare the month starts with their corresponding solar ecliptic longitudes, which are equal to the Chinese calendar principal terms or equivalently the times when the sun enters a sign of the Western zodiac.
Karl
16(06(05
From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro
Sent: 01 February 2017 05:48 To: CALNDR[hidden email] Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Karl and Calendar List:
In order to see how the seasonal tropical year lengths determined by my Reformed Indian Solar Calendar compare to known seasonal year lengths, I have computed the seasonal year lengths at the beginning of the months of Caithra, Asadha, Asvina, and Pausa (months 1,4,7,and 10, which correspond respectively to the equinox and solstices, for 2  1800 year periods of the calendar, Saka 11800 (AD/CE 791878), and Saka 18013600 (AD/CE 18793678), and compared them to calculations given by Meeus and Savoie, for year 0, and year 2000, per Wikipedia: 1 Caithra 1, JD 174994.5 to 1801 Caithra 1, JD 2407430.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242137, var = 0.0000852 1 Asadha 1, JD 1750087.5 to 1801 Caithra 1 JD 2407522.5, 657435 days, ave year = 365.24167, per Meeus @ year 0 = 365.241726, var = 0.0000059 1 Asvina 1, JD 1790179.5 to 1801 Asvina 1, JD 2407615.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242496, var = 0.000274 1 Pausa 1, JD 1750269.5 to 1801 Pausa 1, JD 2407705.5, 657436 days, ave year = 365.24222, per Meeus @ year 0 = 365.242883, var = 0.000661 1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24222, per Meeus @ 2000 = 365.242374, var = 0.000152 1801 Asadha 1, JD407522.5 to 3601 Asadha 1, JD 3064957.5, 657435 days, ave year = 365.24167, per Meeus @ 2000= 365.241626, var = 0.000047 1801 Asvina 1, JD 2407615.5 to 3601 Asvina 1, JD 3605050.5, 657435 days, ave year = 365.24167, per Meeus @ 2000 = 365.242018, var = 0.000351 1801 Pausa 1, JD 2407705.5 to 3601 Pausa 1, JD 3605141.5, 657436 days, ave year = 365.24222, per Meeus @ 2000= 365.242740, var = 0.000518 What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all cases given here, the seasons in each period with the shorter average year length, will correspond to to shorter seasonal tropical years as determined by Meeus and Savoie Walter Ziobro Original Message
From: Karl Palmen <[hidden email]> To: CALNDRL <[hidden email][hidden email]> Sent: Tue, Jan 31, 2017 11:21 am Subject: Re: REFORMED INDIAN SOLAR CALENDAR Dear Walter, Amos and Calendar People
In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do
one of my own
Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would
be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE.
Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error.
Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for
the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days
and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox.
Karl
16(06(04
From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro
Sent: 31 January 2017 05:10 To: CALNDR[hidden email] Subject: REFORMED INDIAN SOLAR CALENDAR REFORMED INDIAN SOLAR CALENDAR
The socalled Indian National Calendar is a solar calendar adopted for use in India in 1957. It is a solar calendar in which the month lengths are distributed in such a manner as to cause the beginnings of each season to fall on or near the first of four months. The months, beginning with the first month Chaitra, which begins at, or near, the northward equinox, follow the sequence of monthlengths of 30 (31 in leap years)  3131313131303030303030 days. It is described in detail here: https://en.wikipedia.org/wiki/Indian_national_calendar This interesting {to me, anyway} calendar has some good points, and a couple of flaws. The major good point, IMO, is that it attempts to reflect the actual, relative lengths of the seasons in a rule based calendar. It uses a leap day rule that is identical to the 400 year rule of the Gregorian Calendar, with which it is in sync, by design. However, the Gregorian leap day rule is somewhat jittery, with the start dates of each season moving over a range of several days, and the calendar has no rule to adjust for the precession of the equinoxes relative to the apsides (perihelion and aphelion). My proposal attempts to remedy these two problems. The first reform would be to adopt a truncated 900 year, 33year leap day rule. What that means is that the leap year would follow the leap day rule of the Dee calendar, with a leap day every fourth year of a 33 year cycle (with a gap of 5 years from the 32nd year of one cycle until the 4th year of the following) , which would continue for 27 cycles of 891 years. This would be followed by a short period of 9 years, with leap days falling in the 4th and 8th years, after which a new cycle of 900 years would begin. . The total period of 900 years would thus have (((32 x 365.25) + 365) x 27) + ((8 x 365.25) +365) = (12,053 x 27) +3,287 = 328,718 days, which would give an average year length of 365.24222.., which is the exact average year length of the Reformed Julian calendar, and very close to the length of the mean tropical year at this time. Over a period of 3,600 years, it would be exactly one day shorter than the Gregorian Calendar. The use of the 33 year rule would also reduce the jitteriness of the start dates of each quarter relative to the seasonal points. The second reform would be to shift the month lengths by one month every 1800 years (once every 2900 year cycles), to reflect the gradual precession of the equinoxes relative to the apsides. Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 328,718 days later on JD 3064866.5, or 21 March 3679 AD/CE. The months in the 1st 1800 year period of the Saka Era of this proleptic calendar would have the lengths of: 313131313130303030303030/31 days each, which, in the current period would have shifted to: 30/313131313131303030303030 days each, which in the next Saka period commencing in 3601 (3679 AD/CE), will shift to: 3030/3131313131313030303030 days. Walter Ziobro 
In reply to this post by Amos Shapir2
Amos
On Tue, Jan 31, 2017 at 3:44 AM, Amos Shapir <[hidden email]> wrote:
That would be news to all of those who say that, currently, a MTY is 365.24219 atomic days, and 365.24217 current mean solar days.
Yes, and those various tropical yearlengths have a mean. So isn't the MTY the mean of those tropical yearlengths, all around the eclliptic? I haven't been able to find an actual definition of the MTY on the Internet, but if "mean tropical year" means anything, then it must mean what I suggested in the paragraph before this one. Here's a possible operational definition that I suggested in a recent post: Solve two successive Earth orbits, with planetary perturbations. Record the solar ecliptic longitudes at many times during those orbits. From that information, determine the length of the tropical year at each of those many points of the eclliptic. Numerically integrate tropicalyearlength, with respect to solar ecliptic longitude. Divide the result by 2 pi radians. That will give the mean of those many tropical year lengths all around the ecliptic. That's surely how the length of the mean tropical year is determined. Michael Ossipoff .

I said: "From that information, determine the length of the tropical year at each of those many points of the eclliptic." Of course the reason why I said to solve two successive orbits is that's necessary to find the time between two occurrences of the same solar ecliptic longitude. Michael Ossipoff On Sat, Feb 4, 2017 at 1:10 PM, Michael Ossipoff <[hidden email]> wrote:

In reply to this post by Karl Palmen
Karl said: This calendar has well defined ‘desired dates’ of 12 ecliptic longitudes each at the start of a month and so my definition of yearround accuracy can be applied and this calendar would have a much better yearround accuracy than any calendar than any calendar Michael Ossipoff has proposed It would certainly be more accurate than any leapweek calendar that I, or anyone else, has proposed. ...as measured as I've suggested, by the greatest calendardisplacement (with respect to the completionpercentage of the MTY) from one displacementextreme to the next. ...by the D1 or D2 measure of calendardisplacment. ...I suggest D1. But the correspondence of weather & date isn't close enough to justify a need for that greater accuracy. So it isn't meaningful or fair to compare the accuracy of a leapweek calendar to that of a leapday calendar. Karl continues: , but would be more complicated. Michael’s definition of yearround accuracy would be grossly misleading. Yes, especially since I haven't proposed a definition of yearround accuracy for a calendar. :^) As I've repeated many, many times, I used the term "yearround accuracy" to refer to the allaroundtheecliptic accuracy of a Y value...by which I meant the overall closeness of a Y value, to the tropical year lengths defined with respect to the various solar ecliptic longitudes, all around the ecliptic. "Year round accuracy" was an unfortunate wording. But I've 1) quit using it; and 2) clarified what I mean by it, (as I said) many, many times. I used that term only with reference to a standard for choosing the Y value for the MinimumDisplacement Calendar. I did not use, suggest or offer "year round accuracy" as a way of comparing the accuracy of two calendars with eachother. I've said that many times, but Karl still insists on saying othwerwise. Michael Ossipoff On Tue, Jan 31, 2017 at 8:24 AM, Karl Palmen <[hidden email]> wrote:

In reply to this post by Walter J Ziobro
Walter You said:"The major good point, IMO, is that it attempts to reflect the actual, relative lengths of the seasons in a rule based calendar." On Tue, Jan 31, 2017 at 12:10 AM, Walter J Ziobro <[hidden email]> wrote: REFORMED INDIAN SOLAR CALENDAR 
In reply to this post by Walter J Ziobro
Dear Walter and Calendar People Walter said So, if I understand your criticism of my proposed Reformed Indian Solar Calendar, the best leap year rule for the current era would be the untruncated 33 year cycle.
After some period of time, this could be switched to the 900 year cycle, and finally to the 100 year cycle. At some distant point in the future, the 33 year leap day rule would not work well. And I agree, except about how the 33year cycle would be changed later on. The most general truncation of the 33year cycle is the removal of an Olympiad to create 29 year cycle of 7 leap years etc.. The revised leap year rule can
then provide a mixture of 33year and 29year cycles. One example is three 33year cycles and
one 29year cycle, which creates the often mentioned 128year cycle. Another is
eleven 33year cycles and three 29year cycles, which make 450year cycle equal to half a 900year cycle. Also these 33year and 29year cycles can be arranged to produce minimum jitter. Also a minimumdisplacement leap year rule would automatically create a mixture of 33year and 29year cycles with minimum jitter, if the calendar mean year
(Y) is in the appropriate range. A very long time in the future, a 29year cycle will then suffice and then become too long, then subtract another Olympiad to get a 25year cycle and so on.
A minimum displacement leap year rule would do this automatically. Karl 16(06(14 From: East Carolina University Calendar discussion List [mailto:[hidden email]]
On Behalf Of Walter J Ziobro Dear Karl and Calendar List: Original Message Dear Walter and Calendar People From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro Dear Karl and Calendar People: KARL REPLIES: It is the idea that the leap year rule should create a mean year near the mean tropical year that is wrong and I believe it is the cause of the
bias observed. It should be the tropical year that starts when the calendar year starts, which in this case is the March Equinox tropical year, when I moved the mean calendar year towards this, the bias disappeared.
KARL REPLIES: Future adjustments of the calendar would have to take account of this and the changing rate of precession, which would affect the timing of the
monthlength shifts. If as expected the June solstice tropical year length becomes stable, then one could use a leap year rule based on the June solstice tropical year, provided one makes each monthlength shift take effect on the 4^{th} month of the
year. Karl 16(06(06
Original Message Dear Walter and Calendar People Walter said What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all cases given here, the seasons
in each period with the shorter average year length, will correspond to shorter seasonal tropical years as determined by Meeus and Savoie If Walter worked through most of a precession cycle (reckoned to be 21,600 years), he’d find three 36.24222, 365.24167 and 365.24278 days of which the first
and one of the other two occur at any one 1800year period. The 7^{th} month Ashwin would deviate from the mean calendar year the most, but not for the current 1800year period, which is why I chose the 6^{th} month Bhaadra for my demonstration.
The comparisons of average year with Meeus tropical year gives significant more negative than positive ‘var’ values, so suggesting that the mean year is too
low. For other mean calendar years, the other two average year lengths would differ from it by 1/1800 day. If the mean calendar year were raised by 0.0002 day to 365.24242 days we’d get 1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24242, per Meeus @ 2000 = 365.242374, var = 0.000048 Which has more balanced ‘var’ values. In the long term, the leap year rule would need changing several times over a precession cycle and for this it is not sufficient to compare average years, one
needs to compare the month starts with their corresponding solar ecliptic longitudes, which are equal to the Chinese calendar principal terms or equivalently the times when the sun enters a sign of the Western zodiac. Karl 16(06(05 From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro Dear Karl and Calendar List:
Original Message Dear Walter, Amos and Calendar People In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do
one of my own Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would
be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE. Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error. Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for
the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days
and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox. Karl 16(06(04 From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro REFORMED INDIAN SOLAR CALENDAR 
Dear Karl and Calendar List I thank you for your observations Your comment about combining 29 and 33 year cycles reminded me of a leap year algorithm created by Ahmad Birashk for the Iranian Calendar Perhaps his algorithm could be usefully applied to the Indian National Calendar Walter Ziobro Sent from AOL Mobile Mail On Friday, February 10, 2017 Karl Palmen <[hidden email]> wrote: Dear Walter and Calendar People
Walter said So, if I understand your criticism of my proposed Reformed Indian Solar Calendar, the best leap year rule for the current era would be the untruncated 33 year cycle.
After some period of time, this could be switched to the 900 year cycle, and finally to the 100 year cycle. At some distant point in the future, the 33 year leap day rule would not work well. And I agree, except about how the 33year cycle would be changed later on.
The most general truncation of the 33year cycle is the removal of an Olympiad to create 29 year cycle of 7 leap years etc.. The revised leap year rule can then provide a mixture of 33year and 29year cycles. One example is three 33year cycles and one 29year cycle, which creates the often mentioned 128year cycle. Another is eleven 33year cycles and three 29year cycles, which make 450year cycle equal to half a 900year cycle. Also these 33year and 29year cycles can be arranged to produce minimum jitter.
Also a minimumdisplacement leap year rule would automatically create a mixture of 33year and 29year cycles with minimum jitter, if the calendar mean year (Y) is in the appropriate range.
A very long time in the future, a 29year cycle will then suffice and then become too long, then subtract another Olympiad to get a 25year cycle and so on. A minimum displacement leap year rule would do this automatically.
Karl
16(06(14
From: East Carolina University Calendar discussion List [mailto:CALNDRL@...] On Behalf Of Walter J Ziobro Sent: 03 February 2017 15:20 To: CALNDRL@... Subject: Re: REFORMED INDIAN SOLAR CALENDAR
Dear Karl and Calendar List:
Original Message Dear Walter and Calendar People
From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro
Dear Karl and Calendar People:
KARL REPLIES: It is the idea that the leap year rule should create a mean year near the mean tropical year that is wrong and I believe it is the cause of the bias observed. It should be the tropical year that starts when the calendar year starts, which in this case is the March Equinox tropical year, when I moved the mean calendar year towards this, the bias disappeared.
KARL REPLIES: Future adjustments of the calendar would have to take account of this and the changing rate of precession, which would affect the timing of the monthlength shifts. If as expected the June solstice tropical year length becomes stable, then one could use a leap year rule based on the June solstice tropical year, provided one makes each monthlength shift take effect on the 4^{th} month of the year.
Karl
16(06(06
Original Message Dear Walter and Calendar People
Walter said What is noticeable is that my Reformed calendar will only produce two average year lengths, 365.24222 and 365.24167, but that in all cases given here, the seasons in each period with the shorter average year length, will correspond to shorter seasonal tropical years as determined by Meeus and Savoie If Walter worked through most of a precession cycle (reckoned to be 21,600 years), he’d find three 36.24222, 365.24167 and 365.24278 days of which the first and one of the other two occur at any one 1800year period. The 7^{th} month Ashwin would deviate from the mean calendar year the most, but not for the current 1800year period, which is why I chose the 6^{th} month Bhaadra for my demonstration.
The comparisons of average year with Meeus tropical year gives significant more negative than positive ‘var’ values, so suggesting that the mean year is too low.
For other mean calendar years, the other two average year lengths would differ from it by 1/1800 day.
If the mean calendar year were raised by 0.0002 day to 365.24242 days we’d get
1801 Caithra 1, JD 2407430.5 to 3601 Caithra 1, JD 3064866.5. 657436 days, ave year = 365.24242, per Meeus @ 2000 = 365.242374, var = 0.000048
Which has more balanced ‘var’ values.
In the long term, the leap year rule would need changing several times over a precession cycle and for this it is not sufficient to compare average years, one needs to compare the month starts with their corresponding solar ecliptic longitudes, which are equal to the Chinese calendar principal terms or equivalently the times when the sun enters a sign of the Western zodiac.
Karl
16(06(05
From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro
Dear Karl and Calendar List:
Original Message Dear Walter, Amos and Calendar People
In case, Walter is not convinced about the folly of using the mean tropical year as a mean year for such a calendar, I show one of his calculations then do one of my own
Thus, if we consider the epact of the Indian calendar to be 1 Chaitra 1 (JD 1749994.5, 22 March 79 AD/CE, proleptic Gregorian), the first 1800 year period would be completed on JD 2407430.5, or 22 March 1879 AD/CE. The following, or current period would likewise end 657,436 days later on JD 3064866.5, or 21 March 3679 AD/CE. Firstly, I corrected the number of days in 1800 years, which is TWO 900year cycles so has 657,436 days instead of 328,718 days. The JDs do not have this error.
Now let’s work out how many days there is in 1800 years beginning with the 6^{th} month (Bhaadra) instead of the 1^{st} month (Chaitra) for the current period (18793679). In 1879, the first five months all have 31 days and so we subtract 155 days from the 657,436 days. In 3679, the first month has 30 days, and the next four have 31 days, so we add 154 days back, giving a total of 657,435 days and so a mean year of 365.24166666666… days instead of 365.242222222… days. The resulting mean year is near the June solstice tropical year, but the 6^{th} month is just before the September equinox.
Karl
16(06(04
From: East Carolina University Calendar discussion
List [[hidden email]]
On Behalf Of Walter J Ziobro
REFORMED INDIAN SOLAR CALENDAR 
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