Lunisolar Grammatomantic Calendar

In my first post on grammatomantic calendars and day cycles, I hypothesized that it would be possible to a kinds of calendar suitable for assigning a Greek letter (and, by extension, the rest of its oracular and divinatory meaning) to a whole day without an explicit divination being done, similar to the Mayan tzolk’in calendar cycle.  I did this creating a solar calendar of 15 months of 24 days each, each day assigned to a different letter of the Greek alphabet in a cycle, and also extended it to months, years, and longer spans of time; its use could be for mere cyclical divination or for more complex astrological notes.  At its heart, however, it is essentially a repeating cycle of 24 days, plus a few correctional days every so often to keep the calendar year in line with the solar year.  Because of this, it is essentially a solar calendar, keeping time with the seasons according to the passage of the sun.

Awesome as all this was, it’s also completely innovative as far as I know; the Greeks didn’t note time like this in any recorded text we have, and it takes no small amount of inspiration from the Mesoamerican Long Count calendar system.  Wanting a more traditional flavor of noting time, I also hypothesized that it might be interesting to apply a grammatomantic cycle of days to an already-known calendar system used in ancient Greece, the Attic festival calendar.  In this case, the calendar system already exists with its own set of months and days; it’s just a matter of applying the letters to the days in this case.  No epoch nor long count notation is necessary for this, since it’s dependent on a lunar month a certain number of months away from the summer solstice (the starting point for the Attic festival calendar).  The primary issues with this, however, is that the Attic festival calendar is lunisolar following the synodic period of the Moon, so it has months roughly of 29 or 30 days, depending on the Moon.  This is more than 24, the number of letters used in Greek letter divination, and 27, the number of Greek letters including the obsolete digamma, qoppa, and sampi.  With there being only 12(ish) months in this calendar system, this is going to have some interesting features.  To pair this calendar with the Solar Grammatomantic Calendar (SGC), let’s call this the Lunisolar Grammatomantic Calendar (LGC).

So, to review the Attic festival calendar, this is a lunisolar calendar, a calendar that more-or-less follows the passage of the Sun through the seasons using the Moon as a helpful marker along the way to determine the months.  Many variations of lunisolar calendars have been created across cultures and eras, since the changing form of the Moon has always been helpful to determine the passage of time.  With the Greeks, and the Attics (think Athenians, about whom we know the most), they used the fairly commonplace system of 12 months as determined by the first sighting of the new Moon.  As mentioned, the start date for the Attic festival calendar was officially the first new Moon sighted after the summer solstice, so the year could start as early as late June or as late as late July depending on the lunar cycle in effect, making mapping to the Gregorian calendar difficult.  The names of the 12 months along with their general times and sacredness to the gods are:

1. Hekatombaion (Ἑκατομϐαιών), first month of summer, sacred to Apollo
2. Metageitnion (Μεταγειτνιών), second month of summer, sacred to Apollo
3. Boedromion (Βοηδρομιών), third month of summer, sacred to Apollo
4. Pyanepsion (Πυανεψιών), first month of autumn, sacred to Apollo
5. Maimakterion (Μαιμακτηριών), second month of autumn, sacred to Zeus
6. Poseideon (Ποσειδεών), third month of autumn, sacred to Poseidon
7. Gamelion (Γαμηλιών), first month of winter, sacred to Zeus and Hera
8. Anthesterion (Ἀνθεστηριών), second month of winter, sacred to Dionysus
9. Elaphebolion (Ἑλαφηϐολιών), third month of winter, sacred to Artemis
10. Mounikhion (Μουνιχιών), first month of spring, sacred to Artemis
11. Thergelion (Θαργηλιών), second month of spring, sacred to Artemis and Apollo
12. Skirophorion (Σκιροφοριών), third month of spring, sacred to Athena

Each month had approximately 30 days (more on that “approximately” part in a bit), divided into three periods of ten days each (which we’ll call “decades”):

The first day of the month was officially called the New Moon, or in Greek, the νουμηνια, the date when the Moon would officially be sighted on its own just after syzygy.  The last day of the month was called the Old and New, or ενη και νεα, which was the actual date of the syzygy between the Earth, Moon, and Sun.  The last day of the second decade and the first of the third decade were both called “the 10th”, with the earlier 10th being the first day and the later 10th being the second.  Days in the months would be referred to as something like “the third day of Thargelion waning”, or Thargelion 28.  Only days 2 through 10 were referred to as “rising”, and days 21 through 29 were referred to as “waning”; the middle block of days from 11 to 19 were unambiguous.  When a month was “hollow”, or had only 29 days instead of 30, the 2nd waning day was omitted, leading to the 3rd waning day becoming the penultimate day of the month instead of the 2nd waning day.  Since this was all based on observation, there was no hard and fast rule to determine which month was hollow or full without the use of an almanac or ephemeris.

At this point, we have enough information to start applying the Greek alphabet to the days.  As mentioned before, there are fewer letters in the Greek alphabet than there are days, so there are some days that are simply going to remain letterless; like the intercalary days of the solar calendar, these might be considered highly unfortunate or “between” times, good for little except when you have a sincere need for that bizarre state of day.  A naive approach might be to allot the 24 letters of the Greek alphabet to the first 24 days of the lunar month, then leave the last six or seven days unallocated, but I have a better idea.  If we include the otherwise useless obsolete letters digamma (Ϝ), qoppa (Ϙ), and sampi (Ϡ), we end up with 27 days, which is 9 × 3.  In using the Greek letters as numerals (e.g. isopsephy), letters Α through Θ represent 1 through 9, Ι through Ϙ represent 10 through 90, and Ρ through Ϡ represent 100 through 900.  In other words,

In this system of numerics, it’s easy to group the letters into three groups of nine based on their magnitude.  This matches up more or less well with the three decades used in a lunar month, so I propose giving the first nine letters to days 1 through 9 (Α through Θ) and skipping the 10th rising day, the second nine letters (Ι through Ϙ) to days 11 through 19 and skipping the earlier 10th day, and the third nine letters (Ρ through Ϡ to days 21 through 29, and leaving the Old and New day unassigned.  If the month is hollow and there is no 2nd waning day for Ϡ, then the Old and New day (last day of the month) is assigned Ϡ.  Letterless days might repeat the preceding letter; thus, the 10th day of the month (or the 10th rising day) might be called “second Θ”, but still be considered effectively letterless.

With the usual Attic festivals celebrated monthly (they treated the birthdays of the gods as monthly occurrences), the lunar month with all its information would look like the following:

That’s it, really.  All in all, it’s a pretty simple system, if we just take the lunar months as they are, and is a lot easier than the complicated mess that was the SGC.  Then again, that’s no fun, so let’s add more to it.  After all, the fact that the months themselves are 12 and the Greek letters are 24 in number is quite appealing, wouldn’t you say?  And we did add letters to the months in the SGC, after all, so why not here?  We can also associate the months themselves with the Greek letters for grammatomantic purposes; if we assign Α to the first month of the year, we can easily get a two-year cycle, where each of the months alternates between one of two values.  For example, if in one year Hekatombaion (first month of the year) is given to Α, then by following the pattern Skirophorion (last month of the year) is given to Μ; Hekatombaion in the next year is given to Ν to continue the cycle, as is Skirophorion in the next year given to Ω.  The next Hekatombaion is given to Α again, and the cycle continues.  Note that the obsolete Greek letters digamma, qoppa, and sampi would not be used here; I only used them in the lunar month to keep the days regular and aligned properly with the decades.

The thing about this is that the lunar months don’t match up with the solar year very well.  Twelve lunar months add up to about 354 days, and given that a solar year is about 365 days, the year is going to keep drifting back unless we add in an extra intercalary (or, more properly here, “embolismic”) month every so often to keep the calendar from drifting too far.  Much as in the SGC with the intercalary days, we might simply leave the embolismic month unlettered in order to keep the cycle regular.  Days within this month would be lettered and celebrated as normal, but the month itself would be otherwise uncelebrated.  For the LGC, we would add the embolismic month at the end of the year, after Skirophorion, so that the next Hekatombaion could occur after the summer solstice as it should.  I depart from the Athenian practice here a bit, where other months would simply be repeated (usually Poseideon).

Of course, figuring out which years need the embolismic month is another problem.  To keep the cycle regular, we’d need to add in an embolismic month one year out of every two or three.  Although there’s no evidence that the Athenians used it, I propose we make use of the Metonic cycle, a period of 19 years in which 12 of the years are “short” (consisting of only 12 months) and 7 are “long” or leap years (consisting of 13, or 12 months plus an embolismic month).  This cycle has been in use for quite some time now in other calendrical systems, so let’s borrow their tradition of having years 3, 6, 8, 11, 14, 17, and 19 be long years, and the other years being short.  Just as with the months, the 12 short years might be assigned letters of their own, while the long years would be unlettered due to their oddness (in multiple senses of the word).  Since the Metonic cycle has an odd count of years, two of these cycles (or 38 years) would repeat both a cycle of letter-years as well as letter-months in the LGC.  Since the use of an epoch for the LGC isn’t as necessary as in the SGC, figuring out where we are in the current Metonic cycle can be determined by looking at another calendar that uses it; I propose the Hebrew calendar, which does this very thing.  In this case, the most recent Metonic cycle began in 1998, with the long years being 2000, 2003, 2005, 2008, 2011, 2014, and 2016; the next Metonic cycle begins in 2017.  The two Metonic cycles, which we might call a LGC age or era,  starting in 1998 and ending in 2035, are below, and the same cycle is repeated forward and backward in time for every 38 years.

A few others of these cycle-epochs include the following years, covering the 20th and 21st centuries, each one 38 years apart from the previous or next one:

• 1884
• 1922
• 1960
• 1998
• 2036
• 2074
• 2112

Creating an epoch to measure years from, although generally useful, isn’t particularly needed for this calendar.  After all, the Attic calendar upon which the LGC is based was used to determine yearly and monthly festivals, and years were noted by saying something like “the Nth year when so-and-so was archon”.  Similarly, we might refer to 2013 as “the 16th year of the 1998-age” or 2033 as “the 35th year after 1998″.  In practice, we might do something similar such as “the sixth year when Clinton was president” or “the tenth year after Hurricane Sandy”; measuring years in this method would still be able to use the system of letter-years in the LGC, simply by shifting the start of the epoch to that year and starting with letter-year Α.  The Metonic cycle would continue from that epoch cyclically until a new significant event was chosen, such as the election of a new president, the proclamation of a peace between nations, and so forth.

Associating the letters with the years and months here is less for notation and more for divination, since the LGC is an augmentation of the Attic festival calendar (with some innovations), and not a wholly new system which needs its own notation.  That said, we can still use the letters to note the years and the months; for instance, the 16th year of the cycle given above might be called the “year Λ in the 1998-age”, while the 17th year (which has no letter associated with it) might be called just “the 17th year” or, more in line with actual Attic practice, “the second Λ year”, assuming that (for notational purposes) a letterless year repeats the previous year’s letter.  Likewise, for embolismic months, we might say that the 12th month of a year is either “the Μ month” or “the Ω month”, and the 13th month of a year (if any) could be said as “the 13th month”, “the empty month”, or ”the second Μ/Ω month” (depending on whether the preceding month was given to Μ or Ω).

Converting a date between a Gregorian calendar date and a LGC date or vice versa is much easier than the SGC conversion, but mostly because it involves looking things up.  To convert between a Gregorian calendar date and a LGC date:

1. Find the year in the cycle of the LGC ages to find out whether the year is a long or short year.
2. Count how many new moons have occurred since the most recent summer solstice.
3. Find the date of the current moon phase.

For instance, consider the recent date September 1, 2013.  This is the 16th year in the LGC age cycle, which has only 12 months and is associated with the letter Λ.  The summer solstice occurred on June 21 this year, and the next new moon was July 8, marking the first month of the LGC year.  September 1 occurs in the second month of Metageitnion, associated with the letter Ξ this year which starting on the new moon of August 7, on the 26th day of the lunar month, or the 5th waning day, associated with the letter Χ.  All told, we would say that this is the “fifth day of Metageitnion waning in the year Λ of the cycle starting in 1998″; the letters for this day are Λ (year), Ξ (month), and Χ (day).

Now that your brain is probably fried from all the tables and quasi-neo-Hellenic computus, we’ll leave the actual uses of the LGC for the next post.  Although the uses of the SGC and LGC are similar in some respects, the LGC has interesting properties that make it especially suited for magical work beyond the daily divination given by the letter-days.  Stay tuned!