On the Structure and Operations of the Geomantic Figures

When I did my recent site redesign and added all those new pages on prayers, rituals, and whatnot, I also consolidated a few pages into ones that fit neatly together, and got rid of a few entirely that didn’t need to be on here anymore.  There weren’t many of those, to be fair, but the main casualties of that effort were my handful of pages on geomancy.  While it may seem odd that I, of all people, would take down pages on the art I love so much, it was partially because I’m continuing to prepare for my book and wanted to rewrite and incorporate the information of those pages in a better way than what was presented there, and partially because the idea for those pages has long since turned stale; I was going to have an entire online “book” of sorts, but I figure that I’ve written enough about geomancy on my blog that it’s probably easier to just browse through the geomancy category and read.  So, if you end up finding a broken link (which I do my utmost to keep from happening), chances are you’re seeing a relic of an earlier age on this blog that connected to those pages.  After all, even though I’d like to keep my blog in perfect running order, I’m also not gonna scroll through 600-odd posts and comb through each and every link.

One of the things that those lost geomancy pages discussed was the mathematical operations of the figures.  I’ve talked about the mathematics behind the Judge and the Shield Chart before, as well as the Parts of Fortune and Spirit, and I’ve discussed a sort of “rotary function” that rotates the elemental rows up and down through the figures before, but there are three big mathematical operations one can do on the figures themselves that reveal certain relationships between them.  I mention them on my De Geomanteia posts of the figures themselves, though now that the original page that describes them is down, I suppose a new post on what they are is in order, if only to keep the information active, especially since every now and then someone will come asking about them.  This is important, after all, because this information is definitely out there, but it’s also largely a result of my own categorization; I haven’t seen anyone in the Western literature, modern or ancient, online or offline, talk about the mathematical relationships or “operations” between the figures in the way I have, nor have I seen anyone talk about one of the operations entirely, so this post is to clear up those terms and what they signify.

First, let me talk about something tangentially related that will help with some of the operation discussion below.  As many students of geomancy are already aware, a common way to understand the figures is in terms of their motion, which is to say, whether a figure is stable or mobile.  Structurally speaking, stable figures are those that have more points in the Fire and Air rows than in the Water and Earth rows (e.g. Albus), and mobile figures are those that have more points in the Water and Earth rows than in the Fire and Air rows (e.g. Puer).  In the cases where the top two rows have the same number of points as the bottom two rows (e.g. Amissio or Populus), the figures are “assigned” a motion based on their general effects.

  • Stable figures: Populus, Carcer, Albus, Puella, Fortuna Maior, Acquisitio, Tristitia, Caput Draconis
  • Mobile figures: Via, Coniunctio, Rubeus, Puer, Fortuna Minor, Amissio, Laetitia, Cauda Draconis

Stable figures are generally seen as graphically looking like they’re “sitting upright” when viewed from the perspective of the reader, while mobile figures are considered “upside down” or “unbalanced” when read the same way.  In a similar sense, stable figures generally have effects that are slow to arise and long to last, while mobile figures are just the opposite, where they’re quick to happen and quick to dissipate.  Consider mobile Laetitia: a figure of optimism, elevation, hope, and bright-burning joy, but it’s easy to lose and hard to maintain.  This can be contrasted with, for instance, stable Tristitia: a figure of slow-moving depression, getting stuck in a rut, languishing, and losing hope.

The idea of motion, I believe, is a simplification of an older system of directionality, where instead of there being two categories of figures, there are three: entering, exiting, and liminal.  All entering figures are stable, all exiting figures are mobile, and the liminal figures are considered in-between:

  • Entering figures: Albus, Puella, Fortuna Maior, Acquisitio, Tristitia, Caput Draconis
  • Exiting figures: Rubeus, Puer, Fortuna Minor, Amissio, Laetitia, Cauda Draconis
  • Liminal figures: Populus, Via, Carcer, Coniunctio

In this system, entering figures are seen as “bringing things to” the reader or reading, and exiting figures “take things away from” the reader or reading, while liminal figures could go either way or do nothing at all, depending on the situation and context in which they appear.  For instance, consider Acquisitio, the quintessential entering figure, which brings things for the gain of the querent, while exiting Amissio is the opposite figure of loss, taking things away, and all the while liminal Populus is just…there, neither bringing nor taking, gaining nor losing.

The liminal figures also serve another purpose: they are also sometimes called “axial” figures, because by taking the upper or lower halves of two axial figures, you can form any other figure.  For instance, the upper half of Populus combined with the lower half of Via gets you Fortuna Maior, the upper half of Coniunctio with the lower half of Carcer gets you Acquisitio, and so forth.  This way of understanding the figures as being composed of half-figures is the fundamental organization of Arabic-style geomantic dice:

Entering figures, like stable figures, look like they’re “coming towards” the reader, while exiting figures look like they’re “going away” from the reader, much like mobile figures.  The reason why the liminal figures (“liminal” meaning “at the threshold”) are considered in-between is that they look the same from either direction, and are either going both ways at once or going in no direction at all.  Populus and Carcer went from liminal to stable due to their long-lasting effects of stagnation or being locked into something, while Via and Coniunctio went from liminal to mobile for their indications of change, movement, and freedom.

Alright!  With the basic structural talk out of the way, let’s talk about operations.  In essence, I claim that there are three primary operations one can do on a figure to obtain another figure, which may or may not be the same as the original figure.  These are:

  • Inversion: replace the odd points with even points, and even points with odd points.  For instance, inverting Puer gets you Albus.
  • Reversion: flip the figure vertically.  For instance, inverting Puer gets you Puella.
  • Conversion: invert then revert the figure, or revert and invert the figure.  For instance, converting Puer gets you Rubeus (Puer →Albus → Rubeus to go the invert-then-revert route, or Puer → Puella → Rubeus to go the revert-then-invert route).

In my De Geomanteia posts, I briefly described what the operations do:

  • Inversion: everything a figure is not on an external level
  • Reversion: the same qualities of a figure taken to its opposite, internal extreme
  • Conversion: the same qualities of a figure expressed in a similar manner

And in this post on a proposed new form of Shield Cart company based on these operations, I described these relationships in a slightly more expanded way:

  • Inversion: The two figures fulfill each other’s deficit of power or means, yet mesh together to form one complete and total force that will conquer and achieve everything that alone they could not.
  • Reversion: The two figures are approaching the same matter from different directions and have different results in mind, looking for their own ends, but find a common thing to strive for and will each benefit from the whole.
  • Conversion: The two figures are similar enough to act along the same lines of power and types of action, but express it in completely different ways from the outside.  Internally, the action and thoughts are the same, but externally, they are distinct.  Think bizarro-world reflections of each other.

These trite descriptions are a little unclear and, now that several years have passed, I realize that they’re probably badly phrased, so it’s worth it to review what these relationships are and how they tie into other conceptions of figure relationships.  After all, inversion and reversion both deal with the notion of something being a figure’s opposite, but we often end up with two separate “opposites”, which can be confusing; and, further, if you take the opposite of an opposite, you get something similar but not quite the same (inversion followed by reversion, or vice versa, gets you conversion).

To my mind, inversion is the most outstanding of the operations, not because it’s any more important than the others, but because it’s so radical and fundamental a change from one figure to the other.  To invert a figure, simply swap the points with their opposites: turn the odd points even and the even points odd.  You could say that you’re turning a figure into its negative, I suppose, like flipping the signs, levels of activity, or polarity of each individual element.  Most notably, the process of inversion is the only one that we can perform through simple geomantic addition of one figure with another; to invert a figure, simply add Via to it, and the result will be that figure’s inversion.  Because inversion is simply “just add Via”, this is probably the easiest to understand: inverting a figure results in a new figure that is everything the original figure isn’t.  We turn active elements passive and passive elements active, male into female and female into male, light into dark and dark into light.  What one has, the other lacks; what one forgets, the other remembers.

So much for inversion.  Reversion is as simple as inversion, but there’s no “just add this figure” to result in it; it’s a strictly structural transformation of one figure based on that figure’s rows.  To be specific and clear about it, to revert a figure, you swap the Fire and Earth lines, as well as the Air and Water lines; in effect, you’re turning the figure upside down, so that e.g. Albus becomes Rubeus or Caput Draconis becomes Cauda Draconis.  Note that unlike inversion where the invert of one figure is always going to be another distinct figure, there are some figures where the reversion is the same as the original figure; this is the case only for the liminal figures (Populus, Via, Carcer, Coniunctio), since rotating them around gets you the same figure.  By swapping the points in the lines of the elements that agree with each other in heat (dry Fire with dry Earth, and moist Air with moist Water), you get another type of opposite, but rather than it playing in terms of a strict swap of polarity like from positive to negative, you literally turn everything on its head.

Both inversion and reversion get you an “opposite” figure, but there are different axes or scales by which you can measure what an “opposite” is.  As an example, consider Puer.  If you invert Puer, you get Albus; this is an opposite in the sense that the youthful brash boy with all the energy in the world is the “opposite” of the wise old man without energy.  What Puer has (energy), Albus lacks; what Albus has (experience), Puer lacks.  On the other hand, if you revert Puer, you get Puella; this is another kind of opposite in the sense that the masculine is the opposite of the feminine.  What Puer is (masculine, active, emitting), Puella isn’t (feminine, passive, accepting).  This type of analysis, where inversion talks about “has or has not” and reversion talks about “is or is not” is the general rule by which I understand the figures, and holds up decently well for the odd figures.  It’s when you get to the even figures that this type of distinction between the operations by means of their descriptions collapses or falls apart:

  • For non-liminal even figures, the inversion of a figure is the same as its reversion.  Thus, “is” is the same thing as “has”.  For instance, Acquisitio is the total opposite of Amissio, since they are both reversions and inversions of each other; gain both is not loss and loss does not have gain.
  • For liminal even figures, the reversion of a figure is the same figure as itself.  Thus, “has” makes no sense, because the figure isn’t speaking to anything one “has” or “lacks” to begin with.  For instance, Carcer’s reversion is Carcer; Carcer is imprisonment and obligation, it doesn’t “have” a quality of its own apart from what it already is.  On the other hand, Carcer’s inversion, what Carcer is not, is Coniunctio, which is freedom and self-determination.  Again, Coniunctio describes a state of being rather than any quality one has or lacks.

Between inversion and reversion, we can begin to understand the pattern of how the babalawos of Ifá, the West African development and adaption of geomancy to Yoruba principles and cosmology, organize their sixteen figures, or odu:

Rank Latin Name Yoruba Name Relationship
1 Via Ogbe inversion
2 Populus Oyẹku
3 Coniunctio Iwori inversion
4 Carcer Odi
5 Fortuna Minor Irosun inversion-
reversion
6 Fortuna Maior Iwọnrin
7 Laetitia Ọbara reversion
8 Tristitia Ọkanran
9 Cauda Draconis Ogunda reversion
10 Caput Draconis Ọsa
11 Rubeus Ika reversion
12 Albus Oturupọn
13 Puella Otura reversion
14 Puer Irẹtẹ
15 Amissio Ọsẹ inversion-
reversion
16 Acquisitio Ofun

With the exception of the even liminal figures, which are grouped in inversion pairs at the beginning of the order, it can be seen that the other figures are arranged in reversion pairs, with the even non-liminal figures grouped in what is technically either inversion or reversion, but which are most likely considered to just be reversions of each other.  Note how the non-liminal even figure pairs are placed in the order: they separate the strict-inversion pairs from the strict-reversion pairs, one at the start of the strict-reversion pairs and one at the end.  While it’s difficult to draw specific conclusions from this alone (the corpus of knowledge of odu is truly vast and huge and requires years, if not decades of study), the placement of the figures in this arrangement cannot be but based on the structure of the figures in their inversion/reversion pairs.

In another system entirely, Stephen Skinner describes some of the relationships of figures in Arabic geomancy in his book “Geomancy in Theory and Practice”, at least as used in some places in northern Africa, where the relationships are described in familial terms and which are all seemingly based on inversion:

  • Man and wife
    • Tristitia and Cauda Draconis
    • Laetitia and Caput Draconis
    • Albus and Puer
    • Puella and Rubeus
    • Coniunctio and Carcer
  • Brothers
    • Fortuna Minor and Fortuna Maior
    • Acquisitio and Amissio
  • No relation
    • Via and Populus

Stephen Skinner doesn’t elaborate on what “man and wife” or “brothers” means for interpreting the figures, but if I were to guess and extrapolate on that small bit of information alone (which shouldn’t be trusted, especially if someone else knowledgeable in these forms of geomancy can correct me or offer better insight):

  • For figures in “man and wife” pairings, the first figure is the “husband” and the second figure is the “wife”.  Though I personally dislike such an arrangement, it could be said that the husband figure of the pair dominates the wife figure, and though they may share certain similarities that allow for them to be married in a more-or-less natural arrangement, the husband figure is more powerful, domineering, overcoming, or conquering than the wife figure.  The central idea here is that of domination and submission under a common theme.
  • For figures in “brothers” pairings, the figures are of equal power to each other, but are more opposed to each other than in harmony with each other, though they form a different kind of complete whole.  Thus, they’re like two brothers that fight with each other (in the sense of one brother against the other) as well as with each other (in the sense of both brothers fighting against a third enemy).  The central idea here is that of oppositions and polarity that form a complete whole.
  • For the two figures that have no relation to each other, Via and Populus, this could be said that they are so completely different that they operate in truly different worlds; they’re not just diametrically opposed to each other to form a whole, nor is one more dominant over or submissive to the other in the same theme, but they’re just so totally and completely different that there is no comparison and, thus, no relationship.

Of course, all that is strictly hypothetical; I have nothing else to go on besides these guesses, and as such, I don’t use these familial relationships in my own understanding of the figures.  However, these are all indicative ways of how to view “opposites”, and is enlightening on its own.  However, note the specific figures in each set of relationships.  With the exception of Coniunctio and Carcer, all the husband-wife pairs are odd figures, so the only possible relationship each figure could have in their pair is inversion.  For the brother pairs, however, these are the even non-liminal figures, where the figures could be seen as either inversions or reversions of each other.  This could well be a hint at a difference between the meanings of inversion and reversion in an African or Arabic system of understanding the figures.

Alright, so that all deals with inversion and reversion, which leaves us with one final operation.  Conversion, as you might have gathered by now, is just the act of performing inversion and reversion on a figure at the same time: you both swap the parity of each row, and rotate the order of the row upside down (or vice versa, it’s the same thing and doesn’t matter).  In a sense, you’re basically taking the opposite of an opposite, but you’re not necessarily going from point A to point B back to point A; that’d just be inverting an inversion or reverting a reversion.  Rather, by applying both operations, you end up in a totally new state that is at once familiar while still being different.  For instance, consider Puella.  Puella’s conversion is Albus, and at first blush, it doesn’t seem like there’s much in similarity between these two figures except, perhaps, their ruling element (Water, in this case).  But bear in mind that both Puella and Albus don’t like to act, emit, or disturb things; Puella is the kind, welcoming hostess who accepts and nurtures, while Albus is the kind, wizened old man who accepts and guides.  Neither of them are chaotic, violent, energetic, or brash like Puer or Rubeus, and while they don’t do things for the same reason or in the same way, they end up doing things that are highly similar, like the same leitmotif played in a different key.

However, this is a little weird for the liminal figures, because a liminal figure’s reversion is the same as itself; this means that a liminal figure’s conversion is the same as its inversion (because the reversion “cancels out”).  Thus, converting Populus gets you Via, and converting Carcer gets you Coniunctio.  While these are clearly opposites of each other, it speaks to the idea that there’s a sort of “yin in the yang, yang in the yin” quality to these figure pairs.  This is best shown by Populus, which is pure potential with all activity latent and waiting to be sprung, and Via, which is pure activity but taken as a whole which doesn’t, on the whole, change.  Likewise, you can consider Carcer to be restriction of boundaries, but freedom to act within those set parameters, and Coniunctio, which is freedom of choice, but being constrained by the choices you make and the paths you take.

It’s also a little weird for the non-liminal even figures, because the reversion of these figures is the same as its inversion, which means that the conversion of an non-liminal even figure gets you that same figure itself.  While the “opposite of an opposite” of odd figures takes you from point A to B to C to D, the nature of the non-liminal even figures takes you from point A to B right back to A.  This reflects the truly is-or-is-not nature of these figures where there’s only so many ways you can view or enact the energies of what they represent: either you win or you lose, either you gain or you lose.  You might not win using the same strategy as you expected to use, but winning is winning; you may not get exactly what you thought you were after, but you’re still getting something you needed.

With these three operations said, I suppose it’s appropriate to have a table illustrating the three results of these operations for each of the sixteen figures:

Figure Inversion Reversion Conversion
Populus Via Populus Via
Via Populus Via Populus
Albus Puer Rubeus Puella
Coniunctio Carcer Coniunctio Carcer
Puella Rubeus Puer Albus
Amissio Acquisitio Acquisitio Amissio
Fortuna Maior Fortuna Minor Fortuna Minor Fortuna Maior
Fortuna Minor Fortuna Maior Fortuna Maior Fortuna Minor
Puer Albus Puella Rubeus
Rubeus Puella Albus Puer
Acquisitio Amissio Amissio Acquisitio
Laetitia Caput Draconis Tristitia Cauda Draconis
Tristitia Cauda Draconis Laetitia Caput Draconis
Carcer Coniunctio Carcer Coniunctio
Caput Draconis Laetitia Cauda Draconis Tristitia
Cauda Draconis Tristitia Caput Draconis Laetitia

Looking at the table above, we can start to pick out certain patterns and “cycles” of operations that group certain figures together:

  • A figure maintains its parity no matter the operation applied to it.  Thus, an odd figure will always result in another odd figure through any of the operations, and an even figure will always yield another even figure.
  • A figure added to its inverse will always yield Via.
  • A figure added to its reverse will always yield one of the liminal figures.
  • A figure added to its converse will always yield another of the liminal figures, which will be the inverse of the sum of the original figure and its reverse.
  • If the figure is odd, then its inversion, reversion, and conversion will all be unique figures, but each figure can become any of the others within a group of four odd figures through another operation.
  • If the figure is even and liminal, then its reversion will be the same as the original figure, while its inversion and conversion will be the same figure and distinct from the original.
  • If the figure is even and not liminal, then its inversion and reversion will be the same figure and distinct from the original, while its conversion will be the same as the original figure.

The odd figures are perhaps most interesting to analyze in their operation groups.  Note that the four figures that result from the operations of a single odd figure (identity, inversion, reversion, and conversion) all, at some point, transform into each other in a neverending cycle, and never transform in any way into an odd figure of the other cycle.  More than that, we can break down the eight odd figures into two groups which have these operational cycles, or “squadrons”, one consisting of Puer-Albus-Puella-Rubeus and the other of Laetitia-Caput Draconis-Cauda Draconis-Tristitia:

Note that the Puer squadron has only figures of Air (Puer and Rubeus) and Water (Puella and Albus), while the Laetitia squadron has only Fire (Laetitia and Cauda Draconis) and Earth (Tristitia and Caput Draconis), and that the converse of one odd figure yields another odd figure of the same element.  Coincidentally, it was this element-preserving property of conversion that led me to the Laetitia-Fire/Rubeus-Air correspondence, matching with the elemental system of JMG and breaking with older literature in these two figures.  More numerologically, also note how each squadron has two figures with seven points and two figures with five points; this was marked as somewhat important in how I allotted the figures to planetary arrangements before, but it could also be viewed under an elemental light here, too.  If each squadron has two figures of the pure elements (Albus and Rubeus in the Puer squadron, Laetitia and Tristitia in the Laetitia squadron), then the converse of each would be the harmonic opposite of the pure element according to their subelemental ruler::

  • Laetitia (pure Fire) converts to/harmonizes with Cauda Draconis (primarily Fire, secondarily Earth)
  • Rubeus (pure Air) converts to/harmonizes with Puer (primarily Air, secondarily Fire)
  • Albus (pure Water) converts to/harmonizes with Puella (primarily Water, secondarily Fire)
  • Tristitia (pure Earth) converts to/harmonizes with Caput Draconis (primarily Earth, secondarily Air)

On the other hand, now consider the even figures.  Unlike the odd figures, where the same “squadron scheme” applies for two groups, there are actually two such schemes for even figures, each scheme having one pair of figures.  For the liminal even figures, a figure’s inverse is the same as its converse, and its reverse is the original figure.  On the other hand, for the even entering/exiting even figures, a figure’s inverse is the same as it’s reverse, and its converse is the original figure:

Due to how the squadrons “collapse” from groups of four into groups of two for the even figures, the same elemental analysis of harmonization can’t be done for the even figures as we did above for the odd figures.  However, it’s also important to note that each element has four figures assigned to it, two of which are odd (as noted above) and two of which are even:

  • Fire: Fortuna Minor (primarily Fire, secondarily Air), Amissio (primarily Fire, secondarily Water)
  • Air: Coniunctio (primarily Air, secondarily Water), Acquisitio (primarily Air, secondarily Earth)
  • Water: Via (primarily Water, secondarily Air), Populus (primarily Water, secondarily Earth)
  • Earth: Carcer (primarily Earth, secondarily Fire), Fortuna Maior (primarily Earth, secondarily Water)

By looking at the inverse relationships of the even figures (which is also converse for liminal figures and reverse for non-liminal figures), we can also inspect their elemental relationships:

  • Carcer (primarily Earth, secondarily Fire) inverts to Coniunctio (primarily Air, secondarily Water).  Both the primary and secondary elements of each figure are the opposite of the other, making these two figures a perfect dichotomy in every way.
  • Via (primarily Water, secondarily Air) inverts to Populus (primarily Water, secondarily Earth).  Though both these figures share the same primary element, the secondary elements oppose each other.  In a sense, this is a more bland kind of opposition that Carcer and Coniunctio show.
  • Acquisitio (primarily Air, secondarily Earth) inverts to Amissio (primarily Fire, secondarily Water).  Unlike Carcer and Coniunctio, and despite that these figures are reversions-inversions of each other, their elemental natures complement each other in both their primary and secondary rulers by heat, as Air and Fire (primary rulers) are both hot elements, and Earth and Water (secondary rulers) are both cold elements.
  • Fortuna Maior (primarily Earth, secondarily Water) inverts to Fortuna Minor (primarily Fire, secondarily Air).  Similar to Acquisitio and Amissio, these two figures are reversions-inversions of each other, but their elemental natures complement each other in moisture, as Earth and Fire (primary rulers) are both dry elements, and Water and Air (secondary elements) are both moist elements).

Note that Carcer and Coniunctio along with Via and Populus (the liminal figures) show a more rigid opposition between them based on their inversion pairs than do Acquisitio and Amissio along with Fortuna Maior and Fortuna Minor (the non-liminal even figures).  Liminality, in this case, shows a forceful dichotomy in inversion, while actually possessing motion suggests completion of each other in some small way.  In this post I wrote on how the natures of the elements complement or “agree” each other based on the element of figure and field in the Shield Chart, these could be understood to say something like the following:

  • Disagree (Carcer and Coniunctio, Via and Populus): Undoing and harm to the point of weakness and powerlessness, force and constriction from one into the other unwillingly.  This is more pronounced with Carcer and Coniunctio than it is Via and Populus, since Via and Populus still agree in the more important primary element, in which case this is more a complete undoing for strength rather than weakness, an expression of transformation into an unknown opposite rather than a forced march into a known but undesired state.
  • Agree in heat (Acquisitio and Amissio): Completion and aid to both, but transformation in the process for complete change in goals and intent.
  • Agree in moisture (Fortuna Maior and Fortuna Minor): Balance and stabilization that lead to stagnation and cessation of action, but with potential that must be unlocked or initiated.

Admittedly, this post took a lot longer to write than I anticipated, largely because although the mathematics behind the operations is pretty easy to understand, the actual meaning behind them is harder to nail down, and is largely a result of introspection and reflection on the figures involved in these operations.  For my own part, I don’t claim that my views are the be-all-end-all of these mathematical or structural relationships between the figures, and I would find this a topic positively begging for more research and meditation by the geomantic community as a whole, not just to flesh out more of the meanings and the relationships of the figures themselves, but also how they might be applied in divination as part of divinatory technique rather than just symbolism, like how I suggested using them for a mathematical/structural form of Shield Chart company.

So, what about you?  Do you think anything of these operation-based relationships of the figures?  Are there any insights you’d be willing to share regarding these operations and relationships?  Is there anything you can thread together from the observations I’ve made above that makes things flow better or fit together more nicely?  Feel free to share in the comments!

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”):

Moon waxing
Moon full
Moon waning
New Moon
11th
later 10th
2nd rising
12th
9th waning
3rd rising
13th
8th waning
4th rising
14th
7th waning
5th rising
15th
6th waning
6th rising
16th
5th waning
7th rising
17th
4th waning
8th rising
18th
3rd waning
9th rising
19th
2nd waning
10th rising
earlier 10th
Old and New

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,

Α/1
Β/2
Γ/3
Δ/4
Ε/5
Ϝ/6
Ζ/7
Η/8
Θ/9
Ι/10
Κ/20
Λ/30
Μ/40
Ν/50
Ξ/60
Ο/70
Π/80
Ϙ/90
Ρ/100
Σ/200
Τ/300
Υ/400
Φ/500
Χ/600
Ψ/700
Ω/800
Ϡ/900

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:

Day
Name
Letter
Festival
1
New Moon
Α
Noumenia
2
2nd rising
Β
Agathos Daimon
3
3rd rising
Γ
Athena
4
4th rising
Δ
Heracles, Hermes, Aphrodite, Eros
5
5th rising
Ε
6
6th rising
Ϝ
Artemis
7
7th rising
Ζ
Apollo
8
8th rising
Η
Poseidon, Theseus
9
9th rising
Θ
10
10th rising
11
11th
Ι
12
12th
Κ
13
13th
Λ
14
14th
Μ
15
15th
Ν
16
16th
Ξ
Full Moon
17
17th
Ο
18
18th
Π
19
19th
Ϙ
20
earlier 10th
21
later 10th
Ρ
22
9th waning
Σ
23
8th waning
Τ
24
7th waning
Υ
25
6th waning
Φ
26
5th waning
Χ
27
4th waning
Ψ
28
3rd waning
Ω
29
2nd waning
Ϡ
Omitted in hollow months
30
Old and New
— (Ϡ if hollow month)

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.

Year
Cycle
Length
Letter
1
2
3
4
5
6
7
8
9
10
11
12 (13)
1998
1
12
Α
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
1999
2
12
Β
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2000
3
13
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2001
4
12
Γ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2002
5
12
Δ
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2003
6
13
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2004
7
12
Ε
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2005
8
13
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2006
9
12
Ζ
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2007
10
12
Η
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2008
11
13
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2009
12
12
Θ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2010
13
12
Ι
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2011
14
13
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2012
15
12
Κ
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2013
16
12
Λ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2014
17
13
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2015
18
12
Μ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2016
19
13
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2017
1 (20)
12
Ν
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2018
2 (21)
12
Ξ
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2019
3 (22)
13
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2020
4 (23)
12
Ο
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2021
5 (24)
12
Π
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2022
6 (25)
13
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2023
7 (26)
12
Ρ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2024
8 (27)
13
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2025
9 (28)
12
Σ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2026
10 (29)
12
Τ
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2027
11 (30)
13
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2028
12 (31)
12
Υ
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2029
13 (32)
12
Φ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2030
14 (33)
13
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2031
15 (34)
12
Χ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2032
16 (35)
12
Ψ
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2033
17 (36)
13
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
2034
18 (37)
12
Ω
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
2035
19 (38)
13
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω

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!

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.

 
Letter-day
Letter-month
Letter-year
Letter-age
Letter-era
Letter-day
1
       
Letter-month
24
1
     
Letter-year
360*
15
1
   
Letter-age
8640*
360
24
1
 
Letter-era
207360*
8640
576
24
1

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.

Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
Α, Ι, Ρ
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
Ν
Ξ
Ο
2
Β, Κ, Σ
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
Α
Β
Γ
Δ
Ε
Ζ
3
Γ, Λ, Τ
Η
Θ
Ι
Κ
Λ
Μ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
4
Δ, Μ, Υ
Χ
Ψ
Ω
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
5
Ε, Ν, Φ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
Α
Β
Γ
6
Ζ, Ξ, Χ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
Ν
Ξ
Ο
Π
Ρ
Σ
7
Η, Ο, Ψ
Τ
Υ
Φ
Χ
Ψ
Ω
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
8
Θ, Π, Ω
Κ
Λ
Μ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω

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.