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by Peter Meyer to the CALNDR-L mailing list.
February 24, 2010
A new calendar has been born. It is called the 'Archetypes Calendar'. It is a lunar calendar with years of 12 or 13 months, each with 29 or 30 days. The rules for when a year has 13 months and when a month has 30 days are fairly simple and not hard to remember.
The mean month is 29.530583 days and the mean year is 365.24237 days.
The months track lunations fairly closely. On average, midnight at the start of a calendar month occurs within one hour of the corresponding dark moon, and in 95% of cases the dark moon occurs either on the 1st day of the month or on the last day of the preceding month.
The years accord more or less with the seasonal years. New Years Day in the Archetypes Calendar occurs anywhere from December 13 to January 13 in the CE Calendar [but see below]. The month and day numbers of the CE dates of New Years Days in the Archetypes Calendar which are exactly 19 years apart are usually the same, or if not then they differ by one day. This is an expression of the 19-year Metonic Cycle.
Each month in this calendar consists either of three 10-day weeks or of two 10-day weeks followed by a 9-day week.
February 25, 2010
The combined Meeus/Stephenson&Houlden calculations of the vernal equinox year (as given by Simon Cassidy at http://www.hermetic.ch/cal_stud/cassidy/err_trop.htm range from 365.242350 days (c. 1820 CE) through 365.242353 (c. 2050 CE) to 365.242453 (c. 3180 CE). To six decimal places, the mean year of the Archetypes Calendar is 365.242374, and it seems that the VE year will coincide with the mean ARC year sometime between now and 2600 CE.
Pluto is one of the ten planetary archetypes which are the subject of Richard Tarnas's book Cosmos and Psyche, and its status as an archetype is unaffected by some astronomers' recent downgrading of Pluto to the status of "minor planet", since (when it comes to planets) those astronomers can only judge importance by physical size.
The names of the first seven months are the same as the names of the deities associated in the Roman [or Greek] tradition with the seven celestial bodies known to the ancients. The names of the last five are those of deities which can plausibly be associated with Uranus, Neptune or Pluto (in particular, according to Richard Tarnas, Prometheus-Uranus).
The order of the months (not weeks [rather, weekdays]) is heliocentric (Sun to Pluto). The order of the days preserves the order of days in the current 7-day week if Monday is considered the first day of the weeek: Monday-Moon, Tuesday-Mars, Wednesday-Mercury, Thursday-Jupiter, Friday-Venus, Saturday-Saturn, Sunday-Sun. (See http://www.hermetic.ch/cal_stud/hlwc/why_seven.htm ). Then the last three days of the 10-day week are simply those of Uranus, Neptune and Pluto.
Just as we now have a 5-day business week (Monday to Friday) with two days following, so with the Archetypes Calendar we could have a 5-day business week (Moon Day to Venus Day) with 5 days following, or a 7-day business week (Moon Day to Sun Day) with 3 days following (or 6 and 4, or 8 and 2).
Irv Bromberg said: "There are a 'whole number' of weeks in any number of months or years of his [Peter's] cycle because of his definition of variable week lengths."
Which makes it possible to develop schedules which (unlike with the Common Era Calendar) don't need to be changed from year to year to keep events (such as university lectures) on the same day of the week every year.
I have decided to change the target range for new year's days from December/January to January 20 to February 20, so that on average the ARC new year's day is approximately halfway between the winter solstice and the vernal equinox. In my opinion the winter solstice is too early for new year's day because we still have two months of winter ahead of us, and the vernal equinox is too late since spring is a'blooming considerably a few weeks before the equinox. I think the Chinese situated their new year's day quite well, not too early and not too late.
March 8, 2010
Fortunately in the end (after extensive revision of work done) a successful result has been achieved (or rather, saved), namely, that a certain unique JDN for day 1-1-1 ARC produces a calendar with (i) all the properties of the original version of the Archetypes Calendar (except for the positions in the seasons of new year's days), (ii) a Helios cycle of years and (iii) rather interesting connections to the Chinese Calendar.
March 10, 2010
After a rather intensive programming effort during the last few days I've completed the revision to the Archetypes Calendar, whose description is now to be seen at http://www.hermetic.ch/cal_stud/arch_cal/arch_cal.htm
The major changes were: (a) revision of rules for long years and leap years in accord with Karl's suggestion for obtaining a 1803-year Helios cycle and (b) retargeting the range of new year's days to coincide with that of the Chinese Calendar. I also take a somewhat different approach to the definition of the calendar.
The average (mean) difference between dark moons and month starts is -0.0213 days, that is, about 31 minutes prior to the midnight. For the 1001 consecutive dark moons studied, the largest positive difference is 1.4288 (about 1 day 10.5 hours) and the largest negative difference is -1.4693 (about 1 day 11.25 hours). The time of the dark moon differs from the start of the month by more than 24 hours in only 44 cases (4.4%).
New year's days always occur from January 21 through February 21, which is the same as for the Chinese Calendar. [Actually it is January 20 through February 21; see below.] What was unexpected was the degree of the correlation between new year's days in both calendars. For the 500 years studied (1900 CE through 2399 CE), close to 2/3rds of new year's days in the Archetypes Calendar occur on the same CE date as Chinese new year's days, close to 1/3rd occur one day earlier or later, and only 0.04% occur one month earlier or later. There are just two such cases; they occur in 1996 CE and 2167 CE. [This is corrected below.]
For the 500 years that I studied, it is in fact almost always true that a year in the Archetypes Calendar is a long year if and only if the corresponding Chinese year has 13 months. For these 500 years it was true for all but two years (99.6%).
But this depends on a judicious choice for a Julian Day number by which to tie the calendar to the sequence of days. There are lots of choices which can be made which give mean dark moons close to midnight but which don't result in a close correlation between 13-month Chinese years and long ARC years.
This result of the selection of the JDN that was made, namely, the Archetypes Calendar in its present form, is interesting because the Chinese Calendar is based on the determination of the exact times of dark moons and solar terms (as described at http://www.hermetic.ch/cal_stud/chinese_cal.htm) by means of complicated astronomical calculations, whereas the Archetypes Calendar is based on fairly simple rules.
March 12, 2010
The exact degree of proximity of the mean dark moon to midnight at the start of the month is not especially important, as long as it's within an hour, since the mean dark moon is not actually experienced
When the Archetypes Calendar and the Chinese Calendar differ in regard to long years the Chinese years possess certain properties concerning the minor solar terms. I have yet to examine this more closely. The pattern of long years in the Chinese Calendar is due to its rules regarding solar terms, and these rules occasionally produce cases which could be regarded as anomalous.
BTW I have changed the names of the first two months from "Sol" and "Luna" to "Apollo" and "Diana" (the Greek and Roman deities associated with the Sun and the Moon respectively). I find it curious that the Americans chose the name of a Sun deity rather than the name of a Moon deity as the name for their 1960s Moon missions.
March 15, 2010
Karl Palmen said: "The Chinese calendar is subject to short term variations in the synodic month. The effects of this are aggravated by making the month 11 rather than lunation 11 have the southern solstice, so bringing time-zone dependence into the leap month rule."
I see that to make the Chinese Calendar timezone-independent in the way Karl suggests we have to introduce the concept of lunation-associated-with-month (but see below). The definitional problem is to introduce this concept into the process whereby lunar months (in the Chinese Calendar) are divided into suis and nians while retaining the present Chinese definitions of those two kinds of years.
What follows is an explanation of how the Chinese lunar calendar is structured (this explanation is also available at my "The Structure of the Chinese Calendar" at http://www.hermetic.ch/cal_stud/chinese_cal.htm).
A lunar month is the period consisting of the day (i.e., the nychthemeron, Beijing time) containing a dark moon up to but not including the day containing the next dark moon. We thus obtain a sequence of consecutive lunar months. A 'sui' is any group of consecutive months beginning with a month containing a northern winter solstice (NWS) up to but not including the month containing the next NWS. We now number the months in the suis (and thus all months) as follows: Any month containing a NWS is numbered '11'. Consider a particular '11'-month. There are either eleven or twelve months between (but not including) it and the next '11'-month. If there are eleven then we simply number them '12', '1', '2', ..., '10'. If there are twelve then we must consider the locations of the major solar terms (MST) in the sui. (For an explanation of 'major solar term' see my article cited above). There are exactly twelve MSTs, so one of the thirteen months in the sui lacks a MST (it cannot be the '11'-month because by definition that contains one of the MSTs, namely, the northern winter solstice). Following the '11'-month we number the months containing a MST as '12', '1', '2', ..., '10', skipping the month which does not. That leaves one month unnumbered, and this is the intercalary month, which is given the number of the month preceding it, distinguished by an asterisk, as in '6*'. A year (called 'nian') in the lunar calendar is then simply a group of consecutive months beginning with a month numbered '1' up to but not including the next month numbered '1'. Q.E.D.
The problem now is how to modify this process of numbering the months so as to incorporate Karl's suggestion that 'lunation 11' be substituted for 'month 11' (thus eliminating timezone-dependence) without doing violence to the traditional and current concepts of 'sui' and 'nian'.
Lunar months start close to, but not exactly at the same time as, lunations. A month may begin up to almost 24 hours before a lunation begins. But months and lunations are closely correlated, so we may speak of the lunation associated with any given month. We can then change the description of the above process as follows:
Replace: "Any month containing a NWS is numbered '11'."
with: "Any month whose associated lunation contains a NWS is numbered '11'."
But this leads to a problem: The above description says: "There are exactly twelve MSTs, so one of the thirteen months in the sui lacks a MST (it cannot be the '11'-month because by definition that contains one of the MSTs, namely, the northern winter solstice)."
Under the redefinition of '11'-month the parenthetic comment is no longer true. Consider the case where a dark moon occurs at 23:30 (local time, Beijing, Hanoi or whatever), preceded by the NWS at 22:30. On this day (nychthemeron) a lunar month begins (since it contains the dark moon). Call this month 'B', preceded by month 'A'. Under the original definition of an '11'-month, month 'B' is an '11'-month, since it contains the NWS. But under the modified definition, month 'A' is the '11'-month because the lunation associated with 'A' (namely, the lunation which ends at 23:30 on the first day of month 'B') contains a NWS. So 'A' is an '11'-month but does not itself contain a NWS (since the NWS in this example occurs on the first day of month 'B'). Further, month 'A' may or may not contain a MST. So in this hypothetical case the process described above for structuring the months is disrupted. Thus the replacement mentioned above will not work, so timezone-independence (if possible at all without doing violence to the current method of structuring the months of the Chinese Calendar) must be obtained in some other way.
March 17, 2010
I discovered an error in one of the programs I used for this ARC-Chinese comparison of new year's days, and I have to report revised figures. Fortunately they are better than what I reported earlier (the range of 500 years is the same):
- In 71.8% of years the CE dates of new year's day in the two calendars are the same.
- In 10.2% of years the ARC new year's day is a day later than the Chinese.
- In 17.4% of years it is a day earlier.
- In 0.4% of years (two cases) it is 30 days earlier.
- In 0.2% of years (one case) it is 29 days later.
Three years, instead of two as reported before, have a difference of 29 or 30 days. Previously I said that the two years were 1966 and 2167 CE. The revised comparison shows that the three years are 2186 (when the ARC NYD is 29 days later than the Chinese NYD) and 1985 and 2319 (when the ARC NYD is 30 days earlier).
In these 500 years the ARC year is long if and only if the Chinese year has 13 months except for six years, as follows:
1984 Chinese year long, ARC year short
1985 Chinese year short, ARC year long
2185 Chinese year short, ARC year long
2186 Chinese year long, ARC year short
2318 Chinese year long, ARC year short
2319 Chinese year short, ARC year long
For 1965-67 we have:
1965 Chinese year short, ARC year short
1966 Chinese year long, ARC year long
1967 Chinese year short, ARC year short
Thus for the next 174 years the ARC year will be long if and only if the Chinese year is.
A closer examination of the years 1984-85 (made possible by the Chinese Calendrics software, http://www.hermetic.ch/chcal/chcal.htm ) reveals that in the month which began the sui at the end of 1984 the northern winter solstice (NWS) occurred at 1984-12-22 CE 00:23 CCT (= Beijing time) and the dark moon occurred about 19 hours later at 1984-12-22 CE 19:47 CCT. As we know, the dark moon times are irregular, due to the irregular Earth-Moon dynamics. So had the dark moon occurred five hours later, at 1984-12-23 CE 00:47 CCT, the NWS would have occurred in the previous month. In that case the previous month would have been the start of the sui, and so in 1984 the Chinese year would have had only 12 months, like the ARC year.
Note also that this is an instance of the hypothetical case that I mentioned in my message of March 15 ("Re: Lunations vs months in the Chinese Calendar") since the the dark moon occurs at 19:47 CCT, preceded by the NWS at 00:23 CCT, both on the first day of the month.
When we examine the case of 2185-86 we find it is a little more complex. The NWS occurred at 2185-12-21 CE 19:11 CCT, followed about 12 hours later by the dark moon at 2185-12-22 CE 05:26 CCT. Had the dark moon occurred six hours earlier then it would have occurred on the same day as the NWS (2185-12-21). In that case the month beginning 2185-12-21 would contain the NWS and so would be the start of the sui, in which case the preceding month would have been the final month of the preceding sui (and would lack a major solar term, so would be the intercalary month '10*'), which would then have 13 months and not 12. The month containing the NWS would, of course, be month '11', and the following month would be month '12'. The result is that in 2185 the Chinese year would have had 13 months, like the ARC year.
The 2318-19 case is similar to the 1984-85 case. The NWS occurred at 2318-12-23 CE 01:54 CCT and the dark moon occurred about 21 hours later at 2318-12-23 CE 23:12 CCT. Had the dark moon occurred just one hour later then the NWS would have occurred in the previous month, and so in 2318 the Chinese year would have had only 12 months, like the ARC year.
2319 CE is one of the rare years when Chinese NYD occurs on February 21.
All Chinese NYDs occur from January 20 through February 21. The extreme cases are rare. Here are some instances during 0-2400 CE (there may be others), with comparison to ARC NYDs (first number is the year CE, followed by the date of the ARC NYD):
Chinese NYD on February 21:
1108 Feb. 21 (same)
2319 Jan. 22 (one month earlier)
Chinese NYD on January 20:
30 Feb. 20 (one month later)
49 Feb. 19 (one month later)
421 Feb. 19 (one month later)
497 Jan. 20 (same)
869 Jan. 20 (same)
Thus, considering only the extreme dates in the range of Chinese NYDs, it seems that prior to 500 CE the ARC NYD is one month later, from 500-2300 it is the same, and after 2300 it is one month earlier. This suggests some regularity, but the data is too scanty to be sure.
I would like to publish these and related results in some scientific journal, but due to the lack of academic recognition of calendrics as a branch of science, what journal would have even a slight interest?
March 19, 2010
Karl Palmen said: "Peter could modify his Chinese calendar software to accommodate ... changing the time zone."
If by "time zone" Karl means the local midnight implied by the longitude used for the prime meridian then the 'Chinese Calendrics' software already accommodates this. See "Times" at http://www.hermetic.ch/chcal/gmt.htm where it says: "'Chinese Calendrics' allows you to specify a prime meridian, any value from 100 degrees East to 145 degrees East ..." This allows the software to be used to display results for both the Vietnamese lunar calendar and the Japanese lunar calendar. I suppose this is news to almost everyone.
I said earlier: "I don't see how replacing 'months' with 'lunations' could be worked into an explanation of how the years and months of the Chinese Calendar are formed."
Karl said: "It cannot be worked into an explanation of the existing Chinese calendar, but can form a possible variation of the Chinese calendar."
One approach to this is to replace 'lunar month' in my description of the construction of the Chinese Calendar given in my message of March 15:
"A lunar month is the period consisting of the day (i.e., the nychthemeron, Beijing time) containing a dark moon up to but not including the day containing the next dark moon. We thus obtain a sequence of consecutive lunar months. ..."
with 'lunation', and at the end of the construction, after numbering the lunations as described in the construction, simply transfer the numbers of the lunations to the lunar months associated with the lunations. This would produce a Chinese-like calendar which was timezone-independent, but it would not have the same structure as the Chinese calendar. It might, however, be sufficiently similar that when the time comes for the Chinese Calendar to be used as a global calendar (after the demise of the present Western hegemony and along with it the demise of the Gregorian Calendar) it would be acceptable to the Chinese as a replacement for their traditional timezone-dependent calendar.
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