| The Goddess Lunar Calendar |
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| by Peter Meyer |
It is possible to devise a lunar calendar which is simple to use (only elementary arithmetic is required for its use — a computer is not needed) and which may be expected to stay in sync with the lunar phases over a period of several millennia. This article presents such a calendar, more specifically, a rule-based solar-count lunar calendar. (For an explanation of types of calendars, with a brief discussion of lunar calendars in general, see Types of Calendars.) In this calendar, years have 12 or 13 months, which are named after goddesses from various cultures, and so this calendar is called the Goddess Lunar Calendar.
I shall now define this calendar, then I shall discuss the accuracy of it with respect to the lunar and solar cycles. Then I shall relate the Goddess Calendar to the Common Era Calendar (which is the same as the Gregorian Calendar except that instead of the A.D./B.C. year-numbering system the astronomical year-numbering sytem is used), and finally I shall provide software to allow conversion between dates in these two calendars.
The Goddess Lunar Calendar Defined
According to the Goddess Calendar, time, although not strictly cyclic, is measured in cycles — cycles of 1689 calendar years. For the purpose of viewing time as linear, and assigning each day a unique date, each 1689-year cycle is associated with an integer -2, -1, 0, 1, 2, ... Years within each cycle are numbered 1 through 1689.Years usually have twelve months, but sometimes thirteen (such years are known as 'long years'). A year has a 13th month if and only if the number of that year is divisible by 3 or if the digits of the year sum to 2, 22 or 23.
Months are numbered from 1 through 13. Odd-numbered months have 29 days and even-numbered months have 30 days.
The months are named after thirteen goddesses, as follows:
| Month number | Month name | Number of days |
| 1 | Astarte | 29 usually |
| 2 | Bast | 30 |
| 3 | Cybele | 29 |
| 4 | Diana | 30 |
| 5 | Eris | 29 |
| 6 | Freya | 30 |
| 7 | Gaia | 29 |
| 8 | Hathor | 30 |
| 9 | Isis | 29 |
| 10 | Juno | 30 |
| 11 | Kali | 29 |
| 12 | Lakshmi | 30 |
| 13 | Maat | 29 always |
The names of the months begin with the letters A, B, ... M, making it easier to remember their order.
The thirteen goddess names are taken from eight different cultures. There are four Egyptian goddesses, two Greek, two Roman, two Hindu and one goddess from each of the, Canaanite, Phrygian and Norse cultures. This is thus a multi-cultural calendar.
As stated above, the 1689-year cycles are numbered -2, -1, 0, 1, 2, 3 ...., the months are numbered 1 through 13 and the days are numbered 1 through 31 (in various months). Thus a date in the Goddess Calendar has the form "cycle-year-month-day", for example, "3-0825-02-27".
We will see later how dates in Goddess Calendar correspond to dates in the Common Era Calendar.
A year is a "long" year if it contains a thirteenth month. The rule for when a year is a long year was given above, and here more formally:
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A year is a long year (and so has a 13th month) if and only if 1.1 The year is divisible by 3 or 1.2 The digits of the year sum to 2, 22 or 23. |
1.1 and 1.2 are mutually exclusive possibilities (that is, a year is a long year by virtue of 1.1 or 1.2 but not both).
Examples:
- The year 0-567 in the Goddess Calendar is a long year because 567 is divisible by 3.
- The year 1-779 is a long year because the digits of the year sum to 23 (= 7 + 7 + 9).
- The year 2-1003 is not a long year because the digits of the year sum to 4 (= 1 + 0 + 0 + 3) and 1003 is not divisible by 3.
In any year (whether or not long) odd-numbered months (1, 3, ..., 13) have 29 days and even-numbered months (2, 4, ..., 12) have 30 days, except that in a long year the length of the first month is determined by the following rule:
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2.1 If the digits of the year sum to 2 then the first month has 28 days. 2.2 If the digits of the year sum to 22 then the first month has 29 days. 2.3 If the digits of the year sum to 23 then the first month has 30 days. 2.4 If the year is divisible by 9 then the first month has 30 days. 2.5 If the year is divisible by 3 but not by 9 then the first month has 31 days. |
These are mutually exclusive possibilities, so in a long year only one of 2.1 - 2.5 can be used to determine the number of days in the first month.
The regular structure of the Goddess Calendar (twelve months of alternating lengths 29 and 30 days, with an occasional 13th month of 29 days, and a variable length for the first month in long years), and the rule for when a year is a long year, are sufficiently simple to be remembered easily, and the rule for the length of the first month is not particularly difficult to remember.
To reckon time according to this calendar it is necessary only to know the Goddess date for a particular day and to be able to calculate the date which follows any given date. This requires only the ability to remember the rules of the calendar and to add four single-digit numbers and to divide a four-digit number by 3 and by 9, all of which can be done mentally.
For example, is the year 1686 (in any cycle) a long year? And if so, how many days are in the first month? Well, 1686 divided by 3 is 562 exactly, and divided by 9 is 187 with 3 over, so by rule 1.1 the year 1686 is a long year, and by rule 2.5 Astarte's month has 31 days (in this year).
Accuracy as a Lunar Calendar
We now turn to the question of how accurate the Goddess Calendar is with regard to the lunar cycle (the question of accuracy with respect to the solar cycle will be considered in the next section).As stated above, the synodic month is the mean (that is, average) interval between exact conjunctions of the Moon and the Sun. A lunar calendar, though it may not accord perfectly with the phases of the Moon, should keep in sync with them, on the average, over a long period. To ensure this the calendar must be designed so that the average length of a calendar month is as close as possible to the synodic month (at least during the period in which the calendar is expected to be usable, preferably for a few thousand years at least).
The apparent motion of the Moon around the Earth is regular but is not exactly uniform. The actual time from one new moon to the next varies by up to a day depending on the particular dynamical relationship of the Earth, the Moon and the Sun. Despite this variation, astronomers have calculated the synodic month to a high level of precision (relative to a given point in astronomical time). The value of the synodic month, during the 4500-year period 500 C.E. to 4000 C.E, is 29.53059 days (rounded to five decimal places). It is increasing at the rate of about one-fifth of a second (0.0000023 days) per millennium and so will retain this value for several millennia yet.
From considerations given in The Accuracy of the Goddess Calendar as a Lunar Calendar we may refine this estimate of the synodic month as follows:
| Year C.E. |
Synodic month in fixed-length days |
Year C.E. |
Synodic month in fixed-length days |
| 500 | 29.530586 | 2500 | 29.530590 |
| 1000 | 29.530587 | 3000 | 29.530591 |
| 1500 | 29.530588 | 3500 | 29.530592 |
| 2000 | 29.530589 | 4000 | 29.530593 |
Since 1689 = 3*563 there are 563 long years under rule 1.1. (Thus in this calendar every 563rd year is an occasion for celebration, as marking one-third of a 1689-year cycle.) To determine how many additional long years there are, under rule 1.2, it is sufficient to calculate this with the help of a computer program, namely LC3.C. The output of this program is given in LC3.OUT, including:
1:4 2:9 3:0 4:25 5:36 6:0 7:64 8:80 9:0 10:112 11:123 12:0 13:133 14:132 15:0 16:117 17:104 18:0 19:72 20:56 21:0 22:30 23:20 24:0 25:6 26:3 27:0 n0=187, n1=376, n0+n1=563 n2=9, n3=30, n4=20, n2+n3+n4=59 n0+n1+n2+n3+n4=622 |
The top part gives, for all years not divisible by 3, for all possible values resulting from summing the digits of those years, the frequency with which those values occur. We see that 2 occurs 9 times, 22 occurs 30 times and 23 occurs 20 times, thus the number of long years by virture of rule 1.2 is 9 + 30 + 20 = 59.
The bottom part says: There are 187 long years divisible by 9 , and 376 long years divisible by 3 but not by 9 (187 + 376 = 563). The next line summarizes the data for years which are long years by virtue of rules 2.1 - 2.3. Thus there are nine years whose digits sum to 2, 30 years with sum 22 and 20 years with sum 23, a total of 59 years. Thus the total number of long years implied by rules 1.1 and 1.2 is 563 + 59 = 622.
From this we may infer that the number of calendar months in the 1689-year cycle is 12*1689 + 622 = 20,890.
To find what we are looking for, namely, the average length of a Goddess Calendar month (and the average length of a Goddess Calendar year), we now need to find the number of days in a 1689-year cycle. Fortunately the LC3 program has counted the days while counting the months, and it reports:
In a 1689-year cycle there are 20890 calendar months and 616894 days. Thus the average length of a calendar month is 29.5305888 days
It is interesting to compare the value (a more precise calculation gives 29.5305887984 days) with the current value of the synodic month, which is 29.5305888531 days, so the length of the average Goddess Calendar month differs from this by about 0.000000055 days. Thus if the length of the synodic month were fixed (which it is not) it would require about 1/0.000000055, or approximately eighteen million, calendar months (about 1.47 million calendar years) for the Goddess Calendar to get out of sync (on average) with the lunar cycle by about a day.
Since the average length of the month in the Goddess Calendar is the same as the value of the current synodic month, to seven decimal places, it is reasonable to expect that the Goddess Calendar will stay in sync with the Moon over a period of at least several millennia. However, the rigorous examination of this question leads into some astronomical technicalities, and this matter is dealt with in a separate article (The Accuracy of the Goddess Calendar as a Lunar Calendar).
The probability of a month having a certain length can be calculated from the output of the LC3 program. These probabilities are:
| Month length |
Occurrences in 1689-year cycle |
Probability | ||
| 28 | 9 | 0.043% | ||
| 29 | 1689*6+30 = 10164 | 48.655% | ||
| 30 | 1689*6+187+20 = 10341 | 49.502% | ||
| 31 | 376 | 1.800% |
Accuracy as a Solar Calendar
The tropical year has been defined as "the time it takes the Sun to appear to travel around the sky from a given point of the tropical zodiac back to that same point in the tropical zodiac." As Simon Cassidy has pointed out (Error in Statement of Tropical Year) this value depends on where in the Earth's orbit one begins the measurement of one revolution about the Sun. If the point used is the point of the vernal equinox then the value is 365.24237 tropical days (so this is the value of the "vernal-equinox year"). If one wishes an average value that is the mean of the values obtained by using different orbital starting points, then a value of 365.24219 days emerges.As the output of the LC3 program shows, in a 1689-year cycle there are 616,894 days. Thus the average length of a year in the Goddess Calendar is 616894/1689 = 365.2421551 days, or 365.24216 days when rounded to five decimal places. This differs from the astronomers' tropical year (365.2421897 days) by 0.0000346 days, so we would expect that about 1/0.0000346, or about 29,000, years would be required for the Goddess Calendar to drift out of sync (on average) with the tropical year. If we consider the vernal equinox year (the mean interval between vernal equinoxes) of 365.24237 days then the Goddess Calendar year differs from this by 0.00021 days, leading to a discrepancy with respect to the seasons of one day in about 4762 years.
Although astronomers cannot actually predict very far ahead (see Comment On Future Accuracy), we can at least say that, on average, the years of the Goddess Calendar can be expected to accord with the seasons for several millennia yet.
In the Common Era Calendar (which is a solar calendar, but not a lunisolar calendar) the vernal equinox always falls on or close to March 21 of each year. The Goddess Calendar is not a solar calendar since the solstices and the equinoxes do not occur at (or close to) fixed dates in the Goddess Calendar year. It is a solar-count lunar calendar in that if we count Common Era years and Goddess Calendar years, the two counts will generally be the same (subject to a slight discrepancy at some calendar dates during the year resulting from the variable length of the Goddess Calendar year compared to the less variable length of the Common Era year).
The number of days in a 1689-year cycle is 616,894 which is twice a prime number, 308,447. Thus no reasonable length of a week (and not a 5-day or 7-day week) will divide evenly the number of days in a cycle. Thus dates in the Goddess Calendar will not occur on fixed weekdays in different cycles, regardless of the number of days in a week.
Correlation with the Common Era Calendar
In order to relate the Goddess Calendar to the Common Era Calendar we have to identify a date in the former and a date in the latter calendar which are dates for the same day. This then allows us to calculate the date in one calendar corresponding to any given date in the other calendar. The question may be reduced to: Which Julian day number corresponds to the "first" day in the Goddess Calendar, 0-0001-01-01? This number is termed "the Goddess Calendar base Julian day number", or "base number" for short.It seems desirable to use a base number far enough into the negative so that most dates in the Goddess Calendar for past events of interest will have a cycle number and a year number which are positive. For this and other reasons I chose the base number -829,029, which corresponds to the Common Era date -6982-02-04 (or 4th February 6983 B.C. in the Gregorian Calendar). (For an explanation of negative years see Astronomical Year Numbering.)
Using this base number we obtain the following correspondences between dates in the Goddess Calendar and dates in the Common Era Calendar:
Common Era -------- Goddess Calendar date -------- Julian day no.
-6982-01-31 -1-1689-13-26 Saturday, Maat 26, 1689 -829,033
-6982-02-01 -1-1689-13-27 Sunday, Maat 27, 1689 -829,032
-6982-02-02 -1-1689-13-28 Monday, Maat 28, 1689 -829,031
-6982-02-03 -1-1689-13-29 Tuesday, Maat 29, 1689 -829,030
-6982-02-04 0-0001-01-01 Wednesday, Astarte 1, 1 -829,029
-6982-02-05 0-0001-01-02 Thursday, Astarte 2, 1 -829,028
-6982-02-06 0-0001-01-03 Friday, Astarte 3, 1 -829,027
-6982-02-07 0-0001-01-04 Saturday, Astarte 4, 1 -829,026
-6982-02-08 0-0001-01-05 Sunday, Astarte 5, 1 -829,025
-6982-02-09 0-0001-01-06 Monday, Astarte 6, 1 -829,024
Common Era -------- Goddess Calendar date -------- Julian day no.
-4713-11-24 1-0582-12-20 Monday, Lakshmi 20, 582 0
-4713-11-25 1-0582-12-21 Tuesday, Lakshmi 21, 582 1
-4713-11-26 1-0582-12-22 Wednesday, Lakshmi 22, 582 2
-4713-11-27 1-0582-12-23 Thursday, Lakshmi 23, 582 3
-4713-11-28 1-0582-12-24 Friday, Lakshmi 24, 582 4
-4713-11-29 1-0582-12-25 Saturday, Lakshmi 25, 582 5
-4713-11-30 1-0582-12-26 Sunday, Lakshmi 26, 582 6
-4713-12-01 1-0582-12-27 Monday, Lakshmi 27, 582 7
-4713-12-02 1-0582-12-28 Tuesday, Lakshmi 28, 582 8
-4713-12-03 1-0582-12-29 Wednesday, Lakshmi 29, 582 9
-4713-12-04 1-0582-12-30 Thursday, Lakshmi 30, 582 10
-4713-12-05 1-0582-13-01 Friday, Maat 1, 582 11
-4713-12-06 1-0582-13-02 Saturday, Maat 2, 582 12
-4713-12-07 1-0582-13-03 Sunday, Maat 3, 582 13
Common Era -------- Goddess Calendar date -------- Julian day no.
1-06-01 4-0228-07-26 Friday, Gaia 26, 228 1,721,577
1-06-02 4-0228-07-27 Saturday, Gaia 27, 228 1,721,578
1-06-03 4-0228-07-28 Sunday, Gaia 28, 228 1,721,579
1-06-04 4-0228-07-29 Monday, Gaia 29, 228 1,721,580
1-06-05 4-0228-08-01 Tuesday, Hathor 1, 228 1,721,581
1-06-06 4-0228-08-02 Wednesday, Hathor 2, 228 1,721,582
1-06-07 4-0228-08-03 Thursday, Hathor 3, 228 1,721,583
1-06-08 4-0228-08-04 Friday, Hathor 4, 228 1,721,584
Common Era -------- Goddess Calendar date -------- Julian day no.
1961-06-28 5-0500-04-17 Wednesday, Diana 17, 500 2,437,479
1961-06-29 5-0500-04-18 Thursday, Diana 18, 500 2,437,480
1961-06-30 5-0500-04-19 Friday, Diana 19, 500 2,437,481
1961-07-01 5-0500-04-20 Saturday, Diana 20, 500 2,437,482
1961-07-02 5-0500-04-21 Sunday, Diana 21, 500 2,437,483
1961-07-03 5-0500-04-22 Monday, Diana 22, 500 2,437,484
1961-07-04 5-0500-04-23 Tuesday, Diana 23, 500 2,437,485
Common Era -------- Goddess Calendar date -------- Julian day no.
2006-01-24 5-0544-12-26 Tuesday, Lakshmi 26, 544 2,453,760
2006-01-25 5-0544-12-27 Wednesday, Lakshmi 27, 544 2,453,761
2006-01-26 5-0544-12-28 Thursday, Lakshmi 28, 544 2,453,762
2006-01-27 5-0544-12-29 Friday, Lakshmi 29, 544 2,453,763
2006-01-28 5-0544-12-30 Saturday, Lakshmi 30, 544 2,453,764
2006-01-29 5-0545-01-01 Sunday, Astarte 1, 545 2,453,765
2006-01-30 5-0545-01-02 Monday, Astarte 2, 545 2,453,766
2006-01-31 5-0545-01-03 Tuesday, Astarte 3, 545 2,453,767
2006-02-01 5-0545-01-04 Wednesday, Astarte 4, 545 2,453,768
2006-02-02 5-0545-01-05 Thursday, Astarte 5, 545 2,453,769
Common Era -------- Goddess Calendar date -------- Julian day no.
3152-01-27 5-1689-13-25 Sunday, Maat 25, 1689 2,872,330
3152-01-28 5-1689-13-26 Monday, Maat 26, 1689 2,872,331
3152-01-29 5-1689-13-27 Tuesday, Maat 27, 1689 2,872,332
3152-01-30 5-1689-13-28 Wednesday, Maat 28, 1689 2,872,333
3152-01-31 5-1689-13-29 Thursday, Maat 29, 1689 2,872,334
3152-02-01 6-0001-01-01 Friday, Astarte 1, 1 2,872,335
3152-02-02 6-0001-01-02 Saturday, Astarte 2, 1 2,872,336
3152-02-03 6-0001-01-03 Sunday, Astarte 3, 1 2,872,337
3152-02-04 6-0001-01-04 Monday, Astarte 4, 1 2,872,338
3152-02-05 6-0001-01-05 Tuesday, Astarte 5, 1 2,872,339 |
If we count Goddess Calendar cycles from the year 0-001 then the first cycle began on 0-0001-01-01, 1st of Astarte in the year 0-0001 (the Common Era date 4 February -6982), and the second calendar cycle began on 1-0001-01-01 (the Common Era date 4 February -5293). The fifth cycle in the Goddess Calendar began on 5-0001-01-01 (1 February 1463 CE), and (as shown above) will end on 5-1689-13-29, 29th of Maat in the year 5-1689 (31 January 3152 CE).
Accord with Eclipse Dates
Although the synodic month in any century can be determined accurately there is considerable local, or cyclical, variation from month to month and from year to year. There are periods of about seven months when the Moon is "fast" or "slow". The length of any particular lunar month can vary significantly from the average value. (According to astronomers, lunations may range from 29.272 to 29.833 days in length.) This is due to the fact that the Earth and the Moon revolve about a point in space which is their common center of gravity, which itself moves along an elliptical orbit around the Sun.As shown above, the Goddess Calendar will stay in accord with the lunar phases (on average) over a period of thousands of years. However due to these local variations, occasionally a new moon will occur on the second day (and rarely on the third) of the calendar month, or the last day or the penultimate day of the preceding month.
The Goddess Calendar was designed with the help of a set of dates of 163 solar eclipses during the period 1619 - 3009 C.E. Solar eclipse dates are, of course, new moon dates. 71% of new moons in this set occur either on the first of the month in the Goddess Calendar or on the last day of the preceding month, and that all but three (98%) occur from the penultimate day of the preceding month through the second day of the month.
Since a full moon occurs about 29.53/2 days after a new moon, most full moons will occur on the 15th or the 16th of the calendar month. Thus a full-moon party which occurs on the same day each calendar month is best scheduled for the evening of the 14th or the 15th.
Due to the irregular motion of the Moon, mentioned above, a simple rule-based calendar, such as the Goddess Calendar, cannot be such that the new moon always falls on the first day of the calendar month — or even on either the first day or the last day of the preceding month. A lunar calendar which has this property must either be based on more complicated rules (and it is doubtful that any rule-based calendar with this property is possible) or it must incorporate astronomical observation to provide empirical corrections.
Seasonal Variation of New Year's Day
In nine of the twelve Common Era years 1995 through 2006 new year's day occurs on the same day in both the Goddess Calendar and in the Chinese Calendar, and in the other three years the Chinese New Year occurs on the day following the Goddess New Year. But this coincidence of new year's days in these two calendars will not endure for many decades, since new year's day in the Goddess Calendar varies slowly but significantly with respect to the seasons.The Common Era date of the Goddess Calendar new year's day varies in an irregular cycle whose average value for Cycle 5 (that is, for the years in the range 5-001 through 5-1689) is October 10th. The Goddess Calendar new year's day can differ from this date by up to one Common Era year, and the range of variation is 1.856 Common Era years. The following graphs show the actual variation over the 1689 Goddess Calendar years of Cycle 5:
Here the range of 1689 Goddess Calendar years is divided into three consecutive parts of 563 years each. Each yellow dot shows the position in the Common Era year (and thus in the seasons) for a Goddess Calendar new year's day in this 1689-year range. The average CE date for the Goddess Calendar new year's day is October 10th, and the vertical axis shows a range of two CE years. The CE date of 5-001-01-01 is February 1st, 1463. After increasing for awhile, there is a 600-year period in which the CE date of the Goddess Calendar new year's day regresses (on average) with respect to the seasons (currently we are at a position toward the end of this regression), eventually reaching a date in early December. Then follows a progression (on average) over about 400 years, with new year's day progressing through nearly two years during this period, finally reaching a date in early October. Then follows a 550-year regression and a return to the occurrence of new year's day in January-February.
The greatest average rate of change of the Goddess Calendar new year's day with respect to the seasons is a six-month progression over a 40-year period (at about halfway through the 1689-year cycle). People born in summer at the beginning of this period would celebrate their 40th birthday in winter. This is, however, exceptional, and the usual rate of change is a three-month regression over a 100-year period, implying that in a typical human lifetime the position of the Goddess Calendar new year's day usually will vary by less than three months. During such a typical period people born in summer would celebrate their 100th birthday (should they live that long) in spring.
Date Conversion Software
There is Windows software for converting between dates in the Common Era Calendar and dates in the Goddess Calendar (and a variety of other dates). For further details please see Lunar Calendars and Eclipse Finder Program.
| Goddess Calendar Date Conversion Software | ||
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