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.
************************************************************************* THE WEEK OF WEEKS OF NIGHTS OF FULL-MOON, SIMON CASSIDY, 1997. ************************************************************************* 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 4am*************************************************************************
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.