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Dates are Gregorian (YYYY.MM.DD) unless stated otherwise.

2013.05.19
Why Divide Hours into 1080 Parts? In the complete traditional molad cycle of 25920 months there are 793 more full months than one half cycle, exactly corresponding to the 793 parts excess over 29.5 days of the traditional molad interval. Added the duration of a "part" for the 1144-, 1095-, 850-, and 801-month lunar cycles, to illustrate that the traditional choice of 1080 parts per hour or 25920 parts per day has nothing to do with divisors nor with time resolution precision. Corrected a minor grammar error.
2013.03.31
Symmetry454 and Symmetry010 calendars: Posted a regenerated basic arithmetic PDF file. The old version was generated with a glitch that causes the symbols for CEILING to get lopped off, so that they looked like absolute value bars instead. No actual changes to the document, but the file size more than doubled as a consequence of the different generation method.
2013.01.21
Lengths of the Seasons: Expanded discussion of astronomical seasons and the lag between them and surface weather seasons.
2013.01.17
Torah Portions and Special Sabbaths: Added an analysis of Shabbat Rosh Chodesh frequencies.
2012.12.30
Torah Portions and Special Sabbaths: Added tables showing the 14 unique Hebrew calendar year types with their exact frequencies, and the number of combined portions for each year type in Israel and in the diaspora.
2012.11.27
Installing Kalendis under WINE or CrossOverMac: Minor revisions, most significantly that the display glitches of CrossOverMac are gone since the release of version 11.
2012.05.17
Torah Portions and Special Sabbaths: Mentioned that Shabbat Shekalim and Shabbat HaChodesh can coincide with Rosh Chodesh. Also mentioned Shabbat Channukah, and mentioned that it can occasionally occur on the both the first and last day of Channukah.
Why March 21st? : Added equinox jitter paragraphs to the Gregorian and Revised Julian calendar cycle comments.
Solar Calendar Leap Rules: Added comment explaining excess equinox jitter for the ISO leap cycle.
2012.02.29
Bahá'í Calendar: Added a list of alternate translations for the Arabic word Badí.
2012.02.27
Why Divide Hours into 1080 Parts? In the discussion of exact calculation, corrected a recurring error which inadvertently omitted 12 hours from the arithmetic expressions. (Thanks to Friedrich Reincke for bringing this error to my attention.) Also, in the discussion on that page about the progressively shorter mean synodic month, added links from there to where I show the differences between the molad interval and the mean synodic month.
2012.01.15
Mediant Fractions, Farey Pairs, and Ford Circles:
Released a newer version of the Ford Circles of Leap Cycles spreadsheet with VBA macro. Changed "Selected LS Cycles" and "Computus" cycles to use Excel formula expressions for decimal values. Computus feature is now prevented from running if the solar list is already lunisolar. Now including default lunar cycle list so that computus feature has a list to work with. Cycle Patterns: Fixed a problem that prevented some cells from getting the intended borders all around in Excel 2010.
2012.01.18
Mediant Fractions, Farey Pairs, and Ford Circles:
Updated the discussion of the Ford Circles of Leap Cycles spreadsheet to cover the new features (computus, cycle patterns, exact expressions for decimal columns), as well as a workaround for the case of leap day cycles with mixers 1/4 and 0/1.
2012.01.15
Mediant Fractions, Farey Pairs, and Ford Circles:
Released a newer version of the Ford Circles of Leap Cycles spreadsheet with VBA macro. Changed "Selected LS Cycles" and "Computus" cycles to use Excel formula expressions for decimal values. Computus feature is now prevented from running if the solar list is already lunisolar. Now including default lunar cycle list so that computus feature has a list to work with. Cycle Patterns: Fixed a problem that prevented some cells from getting the intended borders all around in Excel 2010.
Later updated the same spreadsheet yet again to further improve the pattern borders in Excel 2010, and reduced download file size from 2.8 MB to 1.1 MB.
2012.01.13
Mediant Fractions, Farey Pairs, and Ford Circles:
Released a new version of the Ford Circles of Leap Cycles spreadsheet with VBA macro. Changes:
2012.01.10
The Lengths of the Seasons: Added a new section near the top concerning Chinese Major Solar Terms.
2012.01.08
Symmetry454 and Symmetry010 calendars: Added a new section at the top, Credo: What We Believe.
2012.01.07
Symmetry454 and Symmetry010 calendars: Revised the Events PDF to repair a broken link to the WCC web site concerning a Common Date for Easter, and added quotations from that document, and to repair broken links to the Vatican web site concerning a papal ruling on calendar reform.
2012.01.04
Symmetry454 and Symmetry010 calendars: Revised the FAQs PDF and the Basic Arithmetic PDF. Both now discuss the on-going 4-week cycle that can be used for regular payments such as payroll or rental. The FAQs has a new topic heading discussing the impact of the leap week on the duration of contracts.
Why March 21st?: In the table at the end of the page, revised the discussion of the Gregorian calendar, and added a row to depict the March equinox on the Dee calendar.
2012.01.03
Why March 21st?: Added a new paragraph ("Religious sources...") explaining the novel insight that arranging the Gregorian calendar so that the spring equinox lands on March 21st ensures that the entire month of March falls within the spring weather season in Rome.
2012.01.01
Released new version of Kalendis: To learn what is changed, see the Release Notes.
2011.12.24
Seasonal Drift of the Traditional Hebrew Calendar: Added a new paragraph ("A major difficulty...") explaining why our traditional criteria actually imply that the entire month of Nisan must be within the spring weather season.
Symmetry454 and Symmetry010 calendar pages: Added Click here to see the detailed 293-year leap cycle pattern PDF icon 29 KB.
2011.12.14
Using Kalendis under Linux using WINE: This page was previously based on correspondence with other people who used Kalendis under WINE, but now that I actually have WINE running under Ubuntu the text is revised to provide specific instructions and tips.
2011.12.12
Exact Hebrew Calendar Full Cycle Weekday Frequencies: Further revision of the introductory text, using simpler direct arithmetic to calculate the full cycle length in years. Added "the month before the month before Nisan [Shevat or Adar Rishon], which is also calculated by checking only 4 years.
Repaired or removed broken external links throughout this site.
2011.12.04
Exact Hebrew Calendar Full Cycle Weekday Frequencies: Added some helpful shading to the first table, and revised the introductory text. In particular note that the exact weekday frequencies of all dates from the month before Nisan through to the 29th of Cheshvan can be calculated by checking only 4 years.
2011.11.12
Lengths of the Seasons and Seasonal Drift of the Traditional Hebrew Calendar and Request for Rain and Rambam and the Seasons: Improved the discussion of sunrise and sunset direction in relation to the astronomical equinoxes.
Irvember: Corrected the last paragraph, because the stand-alone leap week at the end of the year was restored as the Symmetry010 calendar default in Kalendis.
2011.07.20
Solar Calendar Leap Rules: Added sub-cycle information to all of the listed fixed arithmetic leap cycles. Every almost symmetrical cycle (even number of years per cycle with odd number of leap years per cycle) is identical to some combination of perfectly symmetrical sub-cycles.
2011.06.27
Lunar Cycle Variations: Major new section to demonstrate that periodic variations of the lunar cycle are least at lunar conjunctions and greatest at the first quarter.
2011.06.21
Solar, Lunar, Indiction cycle arithmetic: revised to incorporate corrections from Jean Meeus (solar, lunar, and indiction cycles all count from one, not zero), also now it warns when the user enters an invalid solar, lunar, or indiction number, and the warning shows the valid range for each field.
2011.06.13
Tekufat Nisan of Rav Adda: Added a final paragraph explaining how to use this equinox reckoning to reproduce traditional Hebrew calendar dates.
2011.05.16
Basic Leap Cycle Calculations: Added two example calculations to the new subsection detailing exact mean year calculations for lunisolar calendars. In the course of doing so, discovered a formula error which is now corrected, and also made the formula easier to understand.
2011.05.10
Mediant Fractions, Farey Pairs, and Ford Circles: Added a PDF list of lunar eclipse cycles. Posted new version of Ford Circles spreadsheet (minor bug fix: wasn't clearing mean month info on Ford chart if lunar cycles were drawn after lunisolar cycles).
2011.05.09
Seasonal Drift of the Traditional Hebrew Calendar: Added a paragraph the end section "Proposed More Accurate Leap Rule for the Hebrew Calendar" to explain that truncating a 19-year cycle to only 8 years (instead of 11 years) would have the opposite effect, making the equinox drift worse.
Why 1080 Parts?: HTML syntax improvements to pass W3C validation. Added a menu of topics, and added two paragraphs explaining the implied lunar cycle of the traditional molad interval, and which shorter cycles can yield comparable accuracy both for the past and for the present era.
2011.05.06
Leap Rules for Aligning Calendars Relative to the North Solstice: Moved the 296-year lunisolar cycle to the description cell belonging to the 327-year leap week cycle, and added the 611-year lunisolar cycle to the description cell for the 389-year leap week cycle.
2011.05.03
Leap Rules for Sidereal Calendars (Zodiac): Added 160-year lunisidereal cycle. Also added a paragraph to the discussion of the Ford Circles spreadsheet explaining how to use it to generate a list of lunisidereal cycles.
2011.04.28
Mediant Fractions, Farey Pairs, and Ford Circles: New version of the Ford Circles spreadsheet, now including lunar eclipse cycles.
2011.04.27
Exact Hebrew Calendar Full Cycle Weekday Frequencies: Added to the year types table the exact number of weeks for each year type. Only perfect leap years contain a whole number of weeks = 55.
2011.04.22
Exact Hebrew Calendar Full Cycle Weekday Frequencies: Reworded comments below the year types table.
2011.04.17
Exact Hebrew Calendar Full Cycle Weekday Frequencies: Added totals by weekday and by year length to the year types table.
2011.04.15
Drift of Fixed Arithmetic Lunar Cycles: Revised spreadsheet to replace some unimportant cycles with the 49-yerm and 25-saros cycles, and added details to all cycle comments on the "Lunar_Cycles" worksheet.
On the web page also updated table of fixed arithmetic lunar cycles.
Later also updated the Solar Calendar Drift spreadsheet to include the interesting 100-saros cycle.
2011.04.11
Exact Hebrew Calendar Full Cycle Weekday Frequencies: Revised to include a printable version that has a page break before each table, so that the print-optimized version can fit each table on a single A4 or Legal page. The print-optimized and view-optimized versions are interlinked at the top of the report. The view-optimized version has links for all months ahead of each table, but these are omitted in the print-optimized version so as not to waste space on the printout. Also corrected a recurring empty table cell HTML syntax error.
2011.04.07
The Duration of Twilight: Added menu of topics, plus a new topic, offering a freeware Excel spreadsheet that calculates and plots twilight moments and zmanim for an entire year for any specified locale.
2011.04.05
Exact Hebrew Calendar Full Cycle Weekday Frequencies: Minor typographical corrections and rewording of the introductory text. Index of links to months now is two lines with separate links to each Adar table.
2011.04.02
Basic Leap Cycle Calculations: Inserted a new subsection detailing exact mean year calculations for lunisolar calendars.
2011.04.01
Mediant Fractions, Farey Pairs, and Ford Circles: Major rewrite of the Ford Circles spreadsheet to introduce exact mean months for exact lunisolar leap cycles, and posted revised PDF charts including 4 variants of lunisolar cycles.
2011.04.01
Solar, Lunar, Indiction cycle arithmetic: small Excel spreadsheet posted, accessed directly from home page, to show how to interconvert year numbers with the Solar, Lunar, Indiction cycles.

Older records deleted 2011.12.12