Date: Tue, 18 Mar 1997
Sender: East Carolina University Calendar discussion List
From: Simon Cassidy
Subject: The week of weeks, of nights of full-moon.

Dear friends,

This current discussion, of the 7-day-week cycle, and ways of fitting it to the official SOLAR calendar got me to thinking about its supposed, early LUNAR rationale. Seven days is (to the nearest whole day) one quarter of a synodic month (lunation or cycle of the moon's phases) and seven days is also just over one quarter of a sidereal month. One phase lunation is about 29.531 days (to the nearest thousandth of a day) while a sidereal month (the time it takes the moon to return to the same star) takes 27.322 days.

I have not been able to see any way that these approximations could be very useful for long-term calendrical extrapolation, but, at the risk of "sinning" once again, by "retreating to the moon", let me set out an idea that did come to me, and which I call "the week of weeks of nights of full-moon". This was also inspired by a desire for a lunar calendar with emphasis on the several days (nucthemera), each month, when the moon's light is available all night and also for a lunar calendar which might somehow separate lunar phase-months into two classes, depending on whether they are odd or even in sequence. This odd-even feature has to do with the alternating function of the ovaries and a supposed natural tendency of ovulation to synch up to the phases of the moon.

Here is a text-based version of the full-moon calendar I came up with. It is based on Pacific Time (Standard and Daylight) of the USA.

         EVEN STRAND                      ODD STRAND
1997                           SATUR DAY  2am   February 22          1997
1997     9pm   MARCH 23        SUN   DAY________________________     1997
1997     ______________________MON   DAY                             1997
1997                           TUES  DAY  1pm   APRIL 22             1997
1997     NIGHT OF MAY 21       WEDNESDAY________________________     1997
1997     _2am__________________THURS DAY                             1997
1997                           FRI   DAY  12pm  JUNE 20              1997
1997     8pm   JULY 19         SATUR DAY________________________     1997
1997     ______________________SUN   DAY  NIGHT OF AUGUST 17         1997
1997                           MON   DAY   4am                       1997
1997     12pm   SEPTEMBER 16   TUES  DAY________________________     1997
1997     ______________________WEDNESDAY  9pm   OCTOBER 15           1997
1997     NIGHT OF NOVEMBER 13  THURS DAY                             1997
1997      6am                  FRI   DAY________________________     1997
1997     ______________________SATUR DAY  7pm  DECEMBER 13           1997
1998     NIGHT OF JANUARY 11   SUN   DAY                             1997
1998      9am                  MON   DAY________________________     1997
1998                           TUES  DAY  NIGHT OF FEBRUARY 10       1998
1998     ______________________WEDNESDAY   2am                       1998
1998     9pm  MARCH 12         THURS DAY________________________     1998
1998                           FRI   DAY                             1998
1998     ______________________SATUR DAY  2pm   APRIL 11             1998
1998     NIGHT OF MAY 10       SUN   DAY________________________     1998
1998      8am                  MON   DAY                             1998
1998     ______________________TUES  DAY  9pm   JUNE 9               1998
1998     NIGHT OF JULY 8       WEDNESDAY________________________     1998
1998      9am                  THURS DAY                             1998
1998     ______________________FRI   DAY  7pm   AUGUST 7             1998
1998     NIGHT OF SEPTEMBER 5  SATUR DAY________________________     1998
1998      4am                  SUN   DAY                             1998
1998     ______________________MON   DAY  1pm   OCTOBER 5            1998
1998     9pm   NOVEMBER 3      TUES  DAY________________________     1998
1998                           WEDNESDAY  NIGHT OF DECEMBER 2        1998
1998     ______________________THURS DAY   7am                       1998
1999     7pm   JANUARY 1       FRI   DAY________________________     1998
1999                           SATUR DAY  NIGHT OF JANUARY 30        1999
1999     ______________________SUN   DAY   8am                       1999
1999     11pm   MARCH 1        MON   DAY________________________     1999
1999                           TUES  DAY                             1999
1999     ______________________WEDNESDAY  3pm  MARCH 31              1999
1999     NIGHT OF APRIL 29     THURS DAY                             1999
1999      7am                  FRI   DAY________________________     1999
1999     ______________________SATUR DAY  11pm  MAY 29               1999
1999                           SUN   DAY                             1999
1999     3pm   JUNE 28         MON   DAY________________________     1999
1999     ______________________TUES  DAY  NIGHT OF JULY 27           1999
1999                           WEDNESDAY   4am                       1999
1999     5pm  AUGUST 26        THURS DAY________________________     1999
1999     ______________________FRI   DAY  NIGHT OF SEPTEMBER 24      1999


The above is one cycle of a repeating pattern of 49 nights of full-moon for each of the two strands of full-moons (the sixteen-slot even strand and the sixteen-slot odd strand). I use the words "even strand" and "odd strand" because I originally visualized the scheme as a pair of necklaces with one pearl for each night of full-moon and coral cylinders to divide the pearls into slots (groups of three or four consecutive full-moon nights). Seven distinct grades or colors of pearl would represent the cycle of weekdays and I use the odd/even terminology without any bias towards either strand but only because I am used to using the lunation numbers given by Jean Meeus in his eclipse canons.

The text-based scheme, as set out above, also gives the MONTH-DATE (in UPPER CASE) of the night for which the moon will be fullest, and the time of actual opposition (to the nearest civil hour, Pacific Time) in lower case. The calendar months and dates don't repeat but the weekdays do, (on average). The decision, as to which evening is that of the night of the "fullest moon", was made by deciding which local midnight was closest to the time of solar and lunar opposition.

This cycle is based on the separation between the periods of full-moon for each strand. This interval is two lunations long and can usually be reckoned as 8 weeks and 3 full-moon days. By using a full-moon period of four days for each 32nd. lunar phase-month (one of the sixteen periods of full-moon on each strand), one can round out the number of days of full-moon to 49, or a "week of weeks", for each strand. This "week of weeks" strategy thus improves the approximation of the synodic month from 29,5 days to exactly 29.53125 days. This is too long by only about 0.00066 days per lunation.

For extrapolations longer than a century, this residual error (in the "week of weeks" scheme), of one day every 1500 lunations can be compensated for by moving the four-day full-moons (one on each strand of the scheme) forward one slot for each 3rd. repetition of the cycle. This is conveniently achieved in the linear text-based scheme above, by merely moving the dividing line at the bottom of each strand's four-day full-moon period, upwards to the next text-line. An almanac of 150 pages (each page, as above, showing a "week of weeks of full-moon nights" for each strand) would thus cover 4802 lunations in 141,806 calendar days (about 388.25 years). This gives a long-term average lunation of 29.53061 days, with an error of less than a nucthemeron (24 calendar-hour period or "day") in four thousand years.

-- Dee's Y'rs, Simon Cassidy, 1053 47th.St. Emeryville Ca.94608. ph.510-547-0684.

Copyright © 1997 by Simon Cassidy
Emeryville Ca. U.S.A.
All rights reserved.