Footnotes to
"The Liberalia Triday Calendar"

1. The origins of the 7-day week are obscure, but probably lie in Sumerian/Babylonian culture. According to S. Langdon (see his book Babylonian Menologies and the Semitic Calendars, 1933) in the early Mesopotamian calendars there were numerous special days of the month, e.g., the 1st, 3rd, 7th, 12th, etc., which were often associated with certain gods or goddesses and on which certain things could be done or should or should not be done. Some of these fell into disuse, but by the 7th C. BCE among the Assyrians the following were days when it was not good to do anything: the 7th, the 14th, the 19th, the 21st and the 28th. (No reason is known, according to Langdon, for the presence of the 19th in this series, although it is known that the 19th was the day of Gula, goddess of health and childbearing.)

We may speculate that the Assyrian distinction of the 7th, 14th, 21st and 28th days was an attempt to divide the lunar month into four parts (with the 19th being the day of the goddess associated with medicine, and thus perhaps considered too important not to receive official recognition). This division of the month, however, does not constitute a system of fixed 7-day weeks, because following the 28th day there were always one or two days before the next dark moon and the beginning of the first "week" of the next month.

It is not known for sure when the system of fixed 7-day weeks, with no relation to the lunar cycle, came into use, but it may well have been due to the Jewish custom of the sabbath. The Jews were commanded to observe "the seventh day" as one on which no work was to be performed (in contrast to the other days when work was done). If this is understood as every seventh day (rather than the seventh day of some period such as the month) then a sequence of fixed 7-day weeks emerges.

The fixed 7-day week had probably been in use for a millennium or more by the time of Jesus, and since Christianity was a development from Judaism it was continued by the early Christians.

Constantius I was a Roman general active in Britain. There he married Helena, who later converted to Christianity. Constantius I became Emperor and on his death their son, Constantine the Great, became Emperor. Under the influence of his mother Constantine recognized Christianity as an official religion and encouraged the adoption of Christian institutions, including the 7-day week. The widespread use of the fixed 7-day week in the modern world can thus be traced back firstly to a commandment to the Jews and secondly to the official adoption of the week by a semi-Christianized Roman Emperor in the 4th Century CE.

2. "It seems that we also owe him [Saturninus, a follower of Simon Magus] the idea that the evil demiurges, the ignoble Aeons responsible for the world — and he named them the Archons — are none other than the seven planets." — Jacques Lacarrière, The Gnostics.

3. In an earlier version of this calendar lunar year numbers were unbounded, like solar year numbers. Karl Palmen pointed out that there is no need for two such year counts, and lunar years could form a cycle. I adopted this suggestion and added the cycle number (as in the Meyer-Palmen Solilunar Calendar). This renders the lunar years cyclic but preserves the ability to identify any day by means of a lunar date as well as by means of a solar date.

4. In the earliest version of this calendar Abrasax normally had 32 tridays, and two tridays were dropped from Abrasax every 792 years (in addition to the triday dropped because of the divisible-by-4 part of the rule). Karl Palmen pointed out that, instead, one triday could be dropped every 396 years without changing the average length of the year, and that this would reduce the amplitude of the variation of the vernal equinox.

Later I realized that the rule for the length of the 4th quarter could be simplified by dropping one triday from Abrasax once every 198 years rather than two tridays once every 396 years, with the result that Abrasax would always have either 30 or 31 tridays (instead of 30, 31 or 32).

5. The thought might arise to some to divide the quarters into three to give twelve "months" in a solar year, each of 10 or 11 tridays. The reasons against this are as follows:

A solar year usually is about 4 tridays (12 days) longer than than a lunar year. So if we were to have solar "months" they would usually begin 3 or 4 tridays later than the lunar months each year, so the set of solar "months" would progress (in an irregular manner) about one month in three years against the set of lunar months.

Also a "month" should correspond more or less to a lunation. But dividing quarters into three to get "solar months" would not give "months" which kept in sync with the Moon, so really shouldn't be called "months" — despite the fact that we are so used to non-lunar "months" from the use of Gregorian calendar "months" that we usually don't notice that the term "month" is a misnomer in that case.

The point of having both a lunar calendar component and a solar calendar component in the Liberalia Triday Calendar is that we get both true quarters (more or less the seasons) and true months (more or less lunations).

6. The existence of this relationship was first pointed out by Karl Palmen in a message to the CALNDR-L mailing list of 1999-11-18.

7. An integer x is equivalent modulo 10 to an integer y if the difference, y - x, is exactly divisible by 10.

8. This formulation was first published in one of my messages to the CALNDR-L mailing list of 1999-11-18. Karl Palmen put forward an alternative formulation in his message to that list of 1999-11-19.

9. Historically, lunar calendars have months which begin with some observable phase of the Moon. Almost always this is the new crescent moon, though in some cases it is the full moon. Richard A. Parker mentions two East African tribes which begin the lunar month with the first invisibility of the old crescent moon (The Calendars of Ancient Egypt, p.9), and argues that the Egyptians also began their lunar month in this way.

The Lunar Liberalia Triday Calendar differs from these older lunar calendars in that it attempts to synchronize the start of the lunar month with the dark moon, i.e. the time of conjunction of the Moon and the Sun. This phase of the Moon is not directly observable but can be calculated on the basis of modern astronomical knowledge.

10. Feeling the need to return home he rode his bicycle through the streets of Basel under the influence, hence the name of the day.

11. For permission to reprint this article by other means, or to translate it into other languages, please contact the author.

Footnotes last modified: Norasday, 6 Loios 98, 22 Samlo 95 (a.k.a. 1999-11-23 CE)

The Liberalia Triday Calendar