Dear Calendar People Via the home page of calendar reform http://myweb.ecu.edu/mccartyr/calendarreform.html I found a calendar, which is effectively a minimum displacement leap week calendar at http://twentytwentythree.wixsite.com/thecommoncalendar
It is called the Common Calendar by Catsanos. I reckon the displacements of years 2009 to 2019 are 2009: 3.000000 2010: 1.757801 2011: 0.515602 2012: +0.726597 2013: +1.968796 2014: +3.210995 leap week 2015: 2.546806 2016: 1.304607 2017: 0.062408 2018: +1.179791 2019: +2.421990 Karl 16(10(11 
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Karl Palmen [[hidden email]]
Sent: Monday, June 05, 2017 11:29
Via the home page of calendar reform
http://myweb.ecu.edu/mccartyr/calendarreform.html I found a calendar, which is effectively a minimum displacement leap week calendar at http://twentytwentythree.wixsite.com/thecommoncalendar It is called the Common Calendar by Catsanos. I started to look into this to consider adding it to my solar calendar jitter charts. It is a minimum jitter calendar, in the same way as a smoothly spread fixed arithmetic leap cycle is, but my collection already includes such examples. Catsanos misguidedly chose a particular estimate of the Mean Tropical Year (MTY) as his target mean year, and he is apparently obvious to his mistake (confusing mean solar days with the atomic time units of the MTY), no equinox and/or solstice observations can verify the accuracy of his calendar. Month lengths 31+29+31 days per quarter is very strange. Why? For symmetry! (explained in his FAQ #4) He is insisting on the last month of each quarter having 31 days so that 25 December and January 1 can both land on Sundays, although I can't imagine what is so special about those particular dates... The way that he explains the arithmetic, one can procedurally go sequentially through years, but there is no way to jump across arbitrary intervals to determine the calendar for any desired year number or to perform calendrical calculations. Thus calendrical date functions can't be implemented along the lines that he describes. He never mentions using MODULO arithmetic to determine his intercalation, but he says that the displacement can range from 3.5 (inclusive) to +3.5 (exclusive). This could be implemented using MODULO arithmetic but note that many computer systems and programming languages don't handle negative and/or floating point operands properly when performing MODULO arithmetic. This issue is explained and solved in "Calendrical Calculations" by Dershowitz & Reingold. He has no idea how many years are in his leap cycle  apparently he doesn't care. Since he is adding 0.242199 as a displacement for each year, and this can't be represented as a fraction simpler than 242199/1000000, it would seem that his leap cycle is absurdly long. Hey, in his "Concessions" section point #2 he concedes that he should use my 293year leap rule rather than his minimum displacement rule! (And he cites my name, web page, and the Sym454 and Sym010 calendars.) So if he has conceded this then why hasn't he revised his "Basic Information" page accordingly? Even with the 293year leap rule, his calendrical calculation functions remain undefined.  Irv Bromberg, University of Toronto, Canada http://www.sym454.org/ 
Dear Irv and Calendar People Thank you Irv for your reply. I reply below. From: East Carolina University Calendar discussion List [mailto:[hidden email]]
On Behalf Of Irv Bromberg From: East Carolina University Calendar discussion List [[hidden email]]
on behalf of Karl Palmen [[hidden email]] Sent: Monday, June 05, 2017 11:29 Via the home page of calendar reform
http://myweb.ecu.edu/mccartyr/calendarreform.html I found a calendar, which is effectively a
minimum displacement leap week calendar at http://twentytwentythree.wixsite.com/thecommoncalendar
It is called the Common Calendar by Catsanos.
KARL REPLIES: Yes there is no point in adding any more minimum jitter calendars to your examples.
KARL REPLIES: I regard the precision as excessive. He’s defined the precision to less than one tenth of a second and I think it would take around one decade for the mean tropical
year measured in real days do go down by that amount. Why not use 365.2422 days instead when it is so close? I think the answer could be that 365.242199 days is exactly equal to 52.177457 weeks.
KARL REPLIES: He expects birthdays and holidays to be celebrated on the same date rather than what the date of birth etc. would have been had the calendar been in use then. This would
also explain why he did not choose months that all begin on the same day of week like in the Symmetry454 calendar. FAQ #11 is very important. It shows how the displacement, which he refers to as the base can be used to reckon the season accurately, despite the jitter caused by the leap weeks.
His method implicitly defines a minimum displacement leapday calendar whose displacement is equal to the amount subtracted from the leapweek displacement to round it to the nearest integer.
KARL REPLIES: That is a shame, because of course one can jump across arbitrary intervals to determine the calendar for any desired year or perform calendrical calculations. It explains
why he chose 2009 to have displacement of 3 days rather than something like year 1 having displacement 0. May be he could not calculate that year 2009 would then have displacement +2.335592 days and so have a leap week (as it did in ISO week dates and Symmetry454).
KARL REPLIES: It is 1.242199 he adds, because it is a leap week calendar. , and this can't be represented as a fraction simpler than 242199/1000000, it would seem that his leap cycle is absurdly long. KARL REPLIES: The appropriate fraction (for leap weeks) is 177,457/1,000,000. Such a calendar does not need to be run for a whole cycle. I do agree that the precision is excessive.
Four or even three decimal places would be sufficient. The year before the year of minimum (most negative) displacement would serve as year 0 in D&G’s calculations, even if it’s well outside the range of years for which the calendar is accurate. Instead of 365.242199 days = 52.177457 weeks, one could choose 365.242 days, 52.1775 weeks (365.2425 days) or perhaps 52.1774 or 52.17745 weeks. Hey, in his "Concessions" section point #2 he concedes that he should use my 293year leap rule rather than his minimum displacement
rule! (And he cites my name, web page, and the Sym454 and Sym010 calendars.) So if he has conceded this then why hasn't he revised his "Basic Information" page accordingly? Even with the 293year leap rule, his calendrical calculation functions remain undefined. KARL REPLIES: I expect Catsanos didn’t figure out how to calculate the displacements. The displacement for a year is equal to the accumulator of the previous year minus 146 then multiplied
by 7/293 days. The accumulator of year Y is ( 52*Y + 146) mod 293. Rather than subtract the 146, I just forget to add it when calculating the accumulator and then if the result is greater than 146, subtract 293 (so it’s in range 146 to +146). I’ve calculated the accumulator minus 146 of 2008 to be 108, and so the displacement of year 2009 to be +(2 & 170/293) days = +2.580205… days.
Year 2016 has an accumulator minus 146 of 231293 = 62 and so the displacement of 2017 is = (1 & 141/293) days = 1.481229… days.
Karl 16(10(12 
In reply to this post by Irv Bromberg
Dear Irv and Calendar People I’ve also noticed that the leap week is inserted between June and July rather than at the end of the year to ensure December 25 is always one week before January 1. When would Christmas be celebrated in the Symmetry454 calendar? Karl 16(10(12 From: East Carolina University Calendar discussion List [mailto:[hidden email]]
On Behalf Of Irv Bromberg From: East Carolina University Calendar discussion List [[hidden email]]
on behalf of Karl Palmen [[hidden email]] Sent: Monday, June 05, 2017 11:29 Via the home page of calendar reform
http://myweb.ecu.edu/mccartyr/calendarreform.html I found a calendar, which is effectively a
minimum displacement leap week calendar at http://twentytwentythree.wixsite.com/thecommoncalendar
It is called the Common Calendar by Catsanos.

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