Solar Grammatomantic Calendar

So, based on that last post where I discussed possibilities of forming a divinatory cycle of days based on the grammatomantic meanings of the Greek letters, I came up with my first draft of a kind of grammatomantic calendar, based on a simple cycle of the letters.  In many ways, this functions much like the tzolk’in calendar of the Maya, but with a little bit of their haab’ thrown in, too.  Essentially, I’ve created a cyclical calendar capable of dating many years into the future or, with some modifications, to the past.  For simplicity, I use the Greek alphabet itself as the core cycle used for this calendar, which is tied to the spring equinox every year.  In effect, I’ve developed a solar grammatomantic calendar, or SGC.  While an interesting little system of noting dates and times in a really obscure fashion, it is at heart a divinatory tool expanding on the methods of grammatomancy applied to a general flow of time, noting how a particular person or event might be affected by the forces at work in the cosmos at that particular time.

So, let’s set some rules and definitions to calculate dates and times in the SGC:

• Letter-day: Duration of time starting at a particular sunrise and the next sunrise. The first value in a cycle of 24 letter-days is Α, then cycles around as expected
• Letter-month: 24 consecutive letter-days. The first value in a cycle of 15 letter-months dependent on letter-year, and cycle around as expected:
  • Α if letter-year is Α, Ι, or  Ρ
  • Π if letter-year is Β, Κ, or Σ
  • Η if letter-year is Γ, Λ, or Τ
  • Χ if letter-year is Δ, Μ, or Υ
  • Ν if letter-year is Ε, Ν, or Φ
  • Δ if letter-year is Ζ, Ξ, or Χ
  • Τ if letter-year is Η, Ο, or Ψ
  • Κ if letter-year is Θ, Π, or Ω
• Letter-year: 15 consecutive letter-months, or 360 consecutive letter-days plus some number of intercalary days. The first value in a cycle of 24 letter-years is Α, then cycles around as expected. Begins from the first sunrise after or coinciding with the spring equinox
• Intercalary day: Days used to align the cycle of 15 letter-months with the solar year. Not associated with any particular letter, nor are they considered letter-days or belonging to a letter-month. Placed at the end of the letter-year, after the last day of the 15th month of the current year but before the first day of the 1st month of the next year. There are as many intercalary days as needed to fill the gap between the number of letter-days and the number of days in the solar year.
• Letter-age: 24 letter-years, 360 letter-months, or 8640 letter-days plus some number of intercalary days. The first value in a cycle of 24 letter-great-years is Α, then cycles around as expected
• Letter-era: 24 letter-ages, 576 letter-years, 8640 letter-months, or 207360 letter-days plus some number of intercalary days. The first value in a cycle of 24 letter-ages is Α, then cycles around as expected.  At most 13824 years can denoted using only 24 values for the letter-era.

A table for converting one of the larger units of letter-dating into smaller ones shows the relationships between the units.  Note that asterisks in the letter-day column indicate that intercalary days will cause this number to increase as the number of letter-years increases.

Of course, even though I’ve listed only five place values for a SGC date, we’d end up with a weird kind of Y2K-esque problem once we finish the ultimate letter-era Ω completely, approximately 13824 years after the first possible date.  Although it’s unlikely to be needed, further spans of time may be indicated by adding larger units, such as a letter-eon which is equivalent to 24 letter-eras; 24 letter-eons would be equivalent to 576 letter-eras, 13824 letter-ages, or 7962624 letter-years.  This easily reaches up into geological or cosmological timeframes, but could be useful for indicating distant, mythological, or astronomical/astrological phenomena.

As noted above, all the cycles have 24 values, each lettered according to the Greek alphabet starting at Α and ending with Ω, with the exception of the letter-months.  Instead, the cycle of letter-months within a letter-year is dependent on the value of the letter-year itself.  Though this seems arbitrary, this is to preserve the cycle caused by there being 15 letter-months within a letter-year.  For instance, the first letter-month of the overall cycle of letter-months is Α, the first letter in the Greek alphabet; the last letter-month of the same year is Ο, the 15th letter in the Greek alphabet.  The second letter-year continues the pattern of assigning letters to the letter-months: since Ο was the previous letter used, Π is the letter assigned to the first letter-month of the second letter-year.  Continuing this cycle, the first letter-month of the third letter-year is assigned with Η, the first letter-month of the fourth letter-year is assigned with Χ, and so on until the last letter-month of the last letter-year is given to Ω, after which the cycle begins anew with Α.  This produces a cycle of eight letter-years; since there are 24 letter-years in a letter-age, this cycle repeats three times.  By taking the remainder of dividing the letter-year ordinal value by eight (substituting 8 for a result of 0), the table below shows the letters associated with the letter-months for a given letter-year in the cycle.

As for the epoch, or the reference date from which the letter-calendar is calculated, I’ve settled on April 3, 1322 BC as the first date in this letter-calender system.  My readers will likely be utterly confused as to why I chose such a distant year and date.  Since I’m a fan of ancient Greek history and civilization, I decided to look back as far as I reliably could, and recalled dimly somewhere in my memory that archaeoastronomers had calculated a date in the Trojan War based on mentions of eclipses in book 17 of the Iliad as well as Hittite and other archaeological records.  As it turns out, such an eclipse happened on November 6, 1312 BC at around 12:35 p.m.  Since the Trojan War took about ten years according to the myths, I wanted to set the epoch date to the day after the spring equinox ten years before the year in which this eclipse occurred.  Looking at an ephemeris for the year 1322 BC, we know that the spring equinox (Sun ingress Aries) occurred sometime on April 2, 1322 BC, making the following dawn of April 3, 1322 BC the start of the first official day of the SGC.  Negative dates, or dates that come before April 3, 1322 BC would not be possible in this system, making the first day “day zero” and anything before prehistory or mythical.  If reverse calculations were desired, the rules to convert dates could be adapted for this, with some kind of inversion applied to the notation (writing it upside down, for instance).

To mark a given date using the SGC, let’s use the notation A.B.C.D.E, where A indicates the letter-era, B indicates the letter-age, C indicates the letter-year, D indicates the letter-month, and E indicates the letter-day.  Each of these could be represented equally well in Greek letters (Α.Ρ.Ψ.Χ.Ε) as they could in Arabic numerals (1.17.23.22.5), so long as one uses the ordinal placement of the letters in the Greek alphabet in mind as well as the funky letter-month 8-year cycle given above.  For intercalary days which don’t belong to any letter-month, a dash, dot, or zero is used for the letter-month position and a Greek letter to indicate the intercalary day.  So, for the fourth intercalary day on the letter-era Α, letter-age Ρ, and letter-year Ψ, we might use the notation Α.Ρ.Ψ.–.Δ with the dash, Α.Ρ.Ψ.•.Δ with the dot, or Α.Ρ.Ψ.0.Δ with the zero.  Arabic numeral representations of the intercalary “month” should use the numeral zero.

Now that we have the units defined, the cycles understood, the epoch proclaimed, and the notation set up, it’s time to begin our rules for converting dates from this letter-calendar to Gregorian dates and back.  Let’s use E, A, Y, M, and D to indicate the ordinal values of the letter-era, letter-age, letter-year, letter-month, and letter-day in these conversions; in other words, these variables represent the Arabic numerals associated with the place values, bearing in mind the funky ordinal values associated with the Greek letters for the letter-month.

To convert a Gregorian calendar date to a letter-calendar date:

1. Find the number of years elapsed (J) between the Gregorian calendar year (GY) and the epoch year (EY).  If the Gregorian calendar date falls on or after the first sunrise after or coinciding with the spring equinox in its year, J = GY − EY.  If the Gregorian calendar date falls before the first sunrise after or coinciding with the spring equinox in its year, J = GY − EY − 1.
2. Divide J by 576 and take the whole part to find the number of letter-eras that have passed (JW), and take the fractional part to find how much other time has passed (JF).
3. Calculate the letter-era: E = JW + 1.  E should be a whole number between 1 and 24.  Assign E the Greek letter according to its ordinal value.
4. Multiply JF by 24 and take the whole part to find the number of letter-ages that have passed (AW), and take the fractional part to find how much other time has passed (AF).
5. Calculate the letter-age: A = AW + 1.  A should be a whole number between 1 and 24.  Assign A the Greek letter according to its ordinal value.
6. Multiply AF by 24 and take the whole part to find the number of letter-years that have passed (YW), and take the fractional part to find how much other time has passed (YF).
7. Calculate the letter-year: Y = YW + 1.  Y should be a whole number between 1 and 24.  Assign Y the Greek letter according to its ordinal value.
8. Find the number of days that have elapsed (T) between the Gregorian calendar date (GD) and the most recent spring equinox date (ED).
9. If T is greater than 360, this is an intercalary day.  Set the letter-month M = 0 or missing.  Calculate the intercalary day D = T −  D.
10. Otherwise, if T is less than or equal to 360, this is a letter-day.
    1. Divide T by 24 and take the whole part to find the number of letter-months that have elapsed (TM), and the fractional part to find the number of days that have elapsed (TD).
    2. Calculate the letter-month:  M = TM.  M should be a whole number between 1 and 15.    Assign M the Greek letter according to its ordinal value according to the eight-year cycle above based on Y.
    3. Calculate the letter-day: D = TD  × 24.  D should be a whole number between 1 and 24.    Assign D the Greek letter according to its ordinal value.

To convert a letter-calendar date to a Gregorian calendar date:

1. Sum together the year-based units multiplied by their coefficients to get the number of years elapsed since the epoch: S = (576 × E) + (24 × A) + Y
2. If the date refers to an intercalary period, sum the total number of letter-days plus the intercalary days: Z = 360 + D
3. If the date refers to a non-intercalary period, sum the count of letter-days plus the number of letter-months multiplied by the number of letter-days in each month: Z = D + (24 × M)
4. Add the number of elapsed years S to the epoch year to find the year of the Gregorian calendar date.
5. Add the number of elapsed days Z to the date of the first dawn after or coinciding with the spring equinox of the Gregorian calendar year to find the month and day of the Gregorian calendar date.

Since we’ve already done this much work to clarify letter-days, we can focus our attention on dividing up individual days into smaller units.  I don’t think it’ll be necessary to get into the magnitude (or lack thereof) of seconds, but having letter-hours might not be a bad idea.  Since there 24 letters, we can create 24 letter-hours for each day.  The process for this would be nearly the same as calculating planetary hours.  Let’s define a letter-hour to equal either 1/12 of the time between sunrise and sunset of the current letter-day or 1/12 of the time between sunset of the current letter-day and sunrise of the following letter-day, whichever period the letter-hour is found within.  Each letter-hour is assigned to one of the 24 letters in the Greek alphabet, in the order of the Greek alphabet starting with Α.  We might augment our notation of date to also include time using the notation A.B.C.D.E:F, where F indicates the letter-hour.

To convert a modern time to a letter-hour or vice versa for a given date and location:

1. Find the time of sunrise and sunset for the given date and location, and the time of sunrise for the day following the given date and location.
2. Divide the total length of time between sunrise and sunset by 12 to find the length of the diurnal hour (DH).
3. Establish the divisions of the diurnal hours starting at sunrise according to DH, assigning them the letter values Α through Μ or number values 1 through 12.
4. Establish the divisions of the nocturnal hours starting at sunset according to NH, assigning them the letter values Ν through Ω or number values 13 through 24.
5. Locate the time given among the letter-hours to convert the modern time to a letter hour, or establish the time limits on the given letter-hour to find an approximate modern time.

So, examples!  Let’s take September 1, 2013 at 10:35 a.m. for Washington, DC, USA and convert it into SGC date:time notation.

• Letter-day and letter-month: on this year, the spring equinox occurred on March 20, 2013 after dawn; thus, the first day of this year began on March 21, 2013.  There are 166 days between these two dates.  166 ÷ 24 = 6.91666…, indicating that the letter-month is 6 and the letter-day is 0.91666… × 24 = 22, or Χ.
• Letter-era, letter-age, and letter-year: between 2013 AD and 1322 BC, there are 3334 years.  3334 ÷ 576 = 5.78819444…, indicating that the letter-era is 6 (5 + 1).  0.78819444… × 24 = 18.91666…, indicating that the letter-age is 19 (18 + 1).  0.91666… × 24 = 22, indicating that the letter-year is 23 (22 + 1).
• Letter-hour: on this day, sunrise was at 6:37 a.m. and sunset at 7:38 p.m., with the next sunrise at 6:38 a.m.  The length of a diurnal hour in this day was about 65 minutes long, and a nocturnal hour was about 55 minutes long.  10:35 a.m. falls during unequal hour 4.
• Notation: the full Arabic numeral notation for this date is 6.19.23.6.22:4.  The full Greek letter notation for this date is Ζ.Τ.Ψ.Ω.Χ:Δ.  The letter-month is Ω, not Ζ as might be expected for the ordinal value of 6, due to the letter-year being Ψ (see the chart above).

In the opposite way, let’s convert the SGC date Η.Ρ.Λ.Ο.Υ:Α for Washington, DC, USA to Gregorian notation.

• Conversion to Arabic numerals: The date Η.Ρ.Λ.Ο.Υ:Α resolves to 7.17.11.9.20:1, using the table above to resolve the letter-year.letter-month combination Λ.Ο to 11.9.  Since the letter-month is not blank or missing, this is not an intercalary date.
• Sum the years: There have been (576 × 7) + (24 × 17) + 11 = 4451 years since the epoch date.
• Find the year and spring equinox: 4451 years elapsed from the epoch year 1322 BC refers to the year 3130 AD.  The spring equinox occurred at night after March 20 that year, so the first day of the SGC year would be on March 21.
• Sum the days: There have been (9 × 24) + 20 = 236 days since the year’s first dawn after or coinciding with the spring equinox.
• Find the day: 236 days after March 21, 3130 AD leads to November 12, 3130 AD.
• Find the time: The letter-hour Α indicates the first unequal hour of the day, sometime just after dawn.  Sunrise for this day in Washington, DC, USA occurs at 6:47 a.m., and sunset at 4:56 p.m.; an unequal diurnal hour here would be about 49 minutes long, so the letter-hour Α indicates a time between 6:47 a.m. and 7:38 a.m.

Well, this was all well and good, and despite the complexity only took a day to hash out all the major parts of forming a new calendar system from scratch.  However, while this was a fun exercise in computus of a sort, this doesn’t actually say much about why it was made to begin with: divination using the flow of time itself!  Since I’ve ranted on long enough about the minutiae of date conversions, let’s leave that for next time when we start putting the SGC in practice and making use of its mechanisms for divination, as well as seeing how it lines up with other solar or theophanic phenomena.