On Timing Daily Prayers to the Degrees of the Decans

I’ve had this idea in my head for prayer practice that revolves around the notion of cycles.  For instance, as part of my daily prayer practice, I’ve written a set of seven prayers, one for each of the seven days of the week, which I recite on an ongoing cycle.  They’re not necessarily planetary prayers, like you might find in the Hygromanteia or Heptameron, but they do have some planetary allusions and hints thrown into them.  The seven-day week, which is fundamentally a Mesopotamian invention, makes for a simple cycle of prayers, but I’ve been thinking about ways I could incorporate more cycles into my prayers.  For instance, a simple and short invocation for each of the days of a lunar month—with my Grammatēmerologion, my oracular Greek letter lunisolar calendar—based around the powers and potencies of each of the letters of the Greek alphabet, along with their spirits or gods, could be something fun to toy around with.  There’s lots of opportunities for this sort of practice:

  • the four turns of the Sun each day, a la Liber Resh (sunrise, noon, sunset, midnight)
  • the seven days of the week
  • the 24 planetary hours of a given day
  • the four (or eight) phases of the Moon (new, crescent, first quarter, gibbous, full, disseminating, third quarter, balsamic)
  • the 29/30 days of a synodic lunar month
  • the 28 days of a sidereal lunar month (a la the 28 lunar mansions)
  • the 30/31 days of a solar month (a la the 12 signs of the Zodiac)
  • the four seasons (solstices and equinoxes), perhaps also with the four cross-quarter days (midpoints between the solstices and equinoxes)
  • the 10 days of a decan
  • when a planet stations retrograde or direct
  • when eclipses occur
  • when a planet or star is seen at its heliacal rising or setting

There are lots of opportunities to engage in prayers linked to or with the natural cycles of the cosmos, many of which are fundamentally astrological in nature.  The idea of coming up with a large-scale overarching prayer practice that engages in such cycles, to me, would be a fantastic way to recognize these natural cycles, bring oneself into alignment with them, and tap ever more greatly into the power of these cycles, especially when certain cycles interact or sync up with each other.  By aligning ourselves with these cycles, we can not just make use of χρονος khronos “time” generally, but also καιρος kairos “the moment”, the fleeting opening of opportunity itself that allows us to do the best thing possible.  There’s this Hermetic notion—it’s hard to find the note I was referencing for it, but I’m pretty sure it’s in Copenhaver’s Hermetica or Litwa’s Hermetica II—that we rely on kairos in order to fully carry out the process of rebirth in the Hermetic mystical sense, and that would be determined by the processes of Providence, Necessity, and Fate along with the very will of God.

Along these lines, I wanted to come up with a new cycle of prayers for myself, one specifically for the decans.  Some might know these as faces, the 36 10° segments of the ecliptic, three to a sign of the Zodiac.  The decans are old, as in ancient Egyptian old, and play a part in the astrological prognosticatory and magical literature of the Egyptians, Arabs, Brahmins, and Hermeticists the world over.  We see them referenced in magical-medical texts going back to the classical period, and they also appear in such texts as the Picatrix as well as Cornelius Agrippa (book II, chapter 37).  Though they come up time and time again, they also take so many wildly different forms between traditions and texts, which is fascinating on its own merits.  We even see Hermēs Trismegistus himself talk about the decans and their importance in the Sixth Stobaean Fragment.  In that part of the Hermetic cannon, Hermēs explains to Tat that the decans belong to a celestial sphere between the eighth sphere of the fixed stars and the higher sphere of the All, being a backdrop to the very stars themselves, and thus higher than the constellations and signs of the Zodiac.  These decans exert “the greatest energy” on us and the world, and they drive “all general events on the earth: overthrows of kings, uprisings in cities, famines, plagues, tsunamis, and earthquakes”.  In other Hermetic texts, like the Sacred Book of Hermēs to Asclepius, the decans also rule over specific parts of the body and the injuries and illnesses that afflict them (which is a very Egyptian concept indeed that we see in purer forms of Egyptian religion and spiritual practice).

You can probably guess where I’m going with this: more prayers and a ritual practice dedicated to the decans.  This would consist of two parts:

  • An invocation of the powers of the decan itself, according to its specific form and name and virtues, to be done when the Sun enters that decan.
  • One prayer per each day the Sun is in a given decan, a set of ten prayers to be recited over a ten day decanal “week”.  Since the Sun spends about one day per degree, this means that each degree of a decan can be considered a separate day, and each day with its own prayer.

After some thinking, I was able to come up with a relatively straightforward set of prayers for the decans themselves at the moment (or the first sunrise following) the Sun’s ingress into them, but it’s the latter part I’m still struggling with.  I have ideas about what to base them on—the ten Hermetic virtues from the Corpus Hermeticum, the Pythagorean symbolism of the first ten numbers, and so forth—but coming up with those prayers is a slow process, indeed.

In the meantime, I’ve been working on a bit of a programming project, something to plan ahead and help me figure out what such a prayer practice would look like scheduled out.  This is basically what I was doing with my Grammatēmerologion project, coding up a variety of astronomical functions to calculate the various positions and attributes of celestial bodies for any given moment, and courtesy of SUBLUNAR.SPACE (whose online customizable almanac is an invaluable and deeply treasured tool for any magician nowadays), I was tipped off to a much easier and faster way to develop such astronomical programs: the Swiss Ephemeris codebase, of which I found a Python extension for even more flexibility.

And that’s when the problems started.  (Beyond the usual mishaps that come along with any nontrivial programming project.)

See, as it turns out, there are more days in a year than there are degrees in a circle—which means that while the Sun moves roughly one degree per day, it actually moves slightly less than one degree per day.  This is why we have 365 days (or 366 days, in leap years) in a year.  To the ancient Egyptians, they considered the civil solar year to only have 12 months of 30 days each, each month consisting of three decans, with a leftover set of five days at the end of the year, considered to be the birthdays of the gods Osiris, Horus, Set, Isis, and Nephthys.  These intercalary (or epagomenal) days were considered a spiritually dangerous and liminal time, but once those days were over, the calendar was brought back into sync with its proper cycle.  However, what I wanted to do is to come up with a 10-day cycle linked to the degrees of the Sun, which means I would have to deal with these epagomenal days throughout the year instead of bundled up all at the end.  My logic was simple:

  • Start counting decan day assignments (decan day-numbers) starting from the first sunrise after the March equinox (which is when the Sun enters 0° Aries as well as the first decan).
  • Judge the degree of the ecliptical position of the Sun based on sunrise of any given day.
  • Take the whole degree of the Sun (e.g. if 9.459°, then 9), divide by 10, take the remainder, and that’s your day in the cycle.  Thus, if o°, then this is our first day; if 1°, the second day; if 2°, the third day;…if 9°, the tenth day.  Thus, when we hit the next o° day, we start the cycle over.
  • If the whole degree of the Sun is the same as the previous day (e.g. 7.998° for today and 7.014° for yesterday), then this is an epagomenal day, and we say either no prayer at all or an eleventh special prayer not otherwise used except for epagomenal days.

A relatively simple method, all told.  Or so I thought.  When I actually ran the program, I noticed that there were not five epagomenal days (e.g. 1-2-3-4-5-X-6-7-8-9-10, where X is the epagomenal day) in the final count, but seven, which was…weird.  This would mean that there were 367 days, which would be wrong, except that there were 365 outputs.  It turns out that there were two skipped days (e.g. 1-2-3-4-5-6-7-9-10, but no 8), one in early December and one in mid-February.  On top of that, although I expected the epagomenal days to be spaced out more-or-less equally throughout the year, they were all between early April and mid-September.  After looking into this, and making sure my code was correct (it was), what’s going on is this:

  • I made the mistake of assuming that the Sun moves at a constant speed each and every day of the year.  It doesn’t, for a variety of astronomical factors.
  • The Sun spends more time in the northern celestial hemisphere (about 185 days) than in the southern celestial hemisphere (about 180 days).
  • The Sun moves slower in winter around perihelion than in the summer around aphelion.
  • From winter through summer, the sunrise gets earlier and earlier, pushing the judgment-time of each day earlier and earlier, while in summer through winter, the reverse happens.

Talk about vexation: I had here what I thought was a perfectly reasonable method—and to a large extent, it is—yet which results in the cycle just skipping days, which I intensely dislike, since it breaks the cycle.  Without doubling up prayers on the skipped days, which I’d really rather like to avoid, it means that I couldn’t use this otherwise simple method to figure out a decanal 10-prayer schedule that would be in sync with the Sun.

After thinking about it some, I considered five different ways to associate the days to the degrees of the decans:

  1. The “Egyptian” method.  This is the most old-school and traditional, and mimics the behavior of the actual ancient Egyptian calendar: starting from the New Year, assign an unbroken cycle of days from day one to day ten 36 times.  This gradually becomes more and more unsynced as time goes on, but we throw in five or six epagomenal days at the very end to catch up all at once before the next New Year.  Simple, traditional, clean, but it’s really the worst of the bunch with the accumulating degree differences that get resolved all at once at the end of the year instead of periodically throughout the year.
  2. The “plan-ahead” method. Like the Egyptian”method, this is a pretty artificial way to allocate the days, but elegant in its own way, and spreads out the epagomenal days across the year more-or-less regularly.  We know that, at least for the foreseeable future, we’re going to deal with either normal years of 365 days or leap years of 366 days.  For normal years, we need to have five epagomenal days, so we insert an epagomenal day after the 8th, 15th, 22nd, 29th, and 36th decans (or, in other words, every seventh decan not including the first).  For leap years, we need six epagomenal days, which we insert after the 6th, 12th, 18th, 24th, 30th, and 36th decan (i.e. every sixth decan).  Note that we judge a year to be a normal year or a leap year based on the Gregorian calendar year prior to a given March equinox; thus, for this method, we start assigning days from the March 2020 equinxo using the normal method because the prior calendar year, 2019, was not a leap year; we use the leap year method starting from the March 2021 equinox because the prior calendar year, 2020, was a leap year.
  3. The “true degree” method.  This is the method mentioned before: starting with the New Year at the March equinox, when the true degree of the Sun is exactly 0° and using sunrise at one’s location as the reference time, take the degree of the Sun and compare it to the degree at the previous day’s reference time.  If the degree is in the next whole number (e.g. 23.005° and 22.025°), the day proceeds to the next whole number; if the degree is in the same whole number (e.g. 23.985° and 23.005°), then it’s an epagomenal days.  The problem, as stated earlier, is that due to the varying speed of the Sun as the Earth travels between perihelion and aphelion (which also has the effect of the Sun spending more time in the northern celestial hemisphere than in the southern celestial hemisphere), we end up with more epagomenal days than expected around aphelion, and with days that are outright skipped around perihelion.  While the exact match of day to degree is appealing, it’s the skipped days that breaks cycles and which ruins the whole prayer system I was trying to devise.
  4. The “average degree” method.  This is a variation on the true degree method, only instead of using the Sun’s true position at the reference time on each day, we take a theoretical position of the Sun based on its average daily motion of 360.0°/365.2421897 days = 0.98564735989°/day.  Starting with the New Year at the March equinox, when both the true degree and average degree of the Sun is exactly 0°, using sunrise at one’s location as the reference time, take the theoretical average degree of the Sun (advancing it by the Sun’s average daily motion day by day at the reference time) and compare it to the degree at the previous day’s reference time, with the same epagomenal rule as before.  The benefit to this method is that it gets us the expected number of epagomenal days which are evenly distributed throughout the year without skipping any other days; the downside is that, as we get closer to the September equinox, the theoretical average position of the Sun drifts further away from the true position by as much as 3.780°, putting us three or four days out of sync with the true position.
  5. The “rebalanced true degree” method.  This is an extension of the true degree method above.  We start with the assignments of days to degrees as before, extra epagomenal days and skipped days and all, but we “rebalance” the days by removing some epagomenal days and reinserting them where we were earlier skipping days.  For every skipped day, we alternate between choosing the first and last of the epagomenal days.  So, if we have seven epagomenal days on year days 24, 59, 83, 105, 127, 151, and 182, and we have two skipped days on days 274 and 333, then we first remove the first epagomenal day from day 24 and reinsert it on day 274, and then the last epagomenal day from day 181 (was 182 before we removed the other one) and insert it on day 333.

So, five different methods of assigning days a decan day-number, one of which (the Egyptian method) being the most regular and artificial with the worst drift, one of which (the true degree method) being the most accurate and realistic yet which skips days entirely, and three other methods (plan-ahead, average degree, rebalanced true degree) that vary in terms of computational complexity and accuracy.  We know that the true degree method is the most accurate, so we can plot the various other methods against it to visually see how bad the drift is between it and the other methods.  In the following graphs, the true degree method is given in red, with the other method being compared to it in blue.  Epagomenal days are marked as having a decan day-count number of -1, hence the severe dips at times.  Where the blue and red lines are more in sync, the method is better; where the lines depart, the method gets worse.  The true degree method gives an epagomenal day in decans 3, 6, 8, 11, 13, 15, and 18, and if you look close enough, you can see the skip in the days towards the end of decans 27 and 33.

Just visually looking at these methods, we can see that all four methods start off the same for a little more than the first two decans, but after that, most of them begin to diverge.  The Egyptian method is worse in how often and by how much it diverges, with that nasty flatline of epagomenal days at the end, and the plan-ahead method doesn’t fare much better, either; note also how both of these methods end with epagomenal days for at least the final day of the year.  The average degree method doesn’t look too bad, though it does get worse around the September-October area of the year before it gets better again, eventually getting back in sync for the final three decans of the year.  By far the most pleasing and in-sync graph we see is with the rebalanced true degree method, which does vary a little bit but by no means as bad or as irregularly as the other methods; we have about five decans where they’re in sync, 22 where they’re one day off, and nine when they’re off by two days.

But, besides just looking at them with my eyeballs, how should I best compare the accuracy of all these methods?  What I settled on was a ratio between the day’s decan day-number according to a particular method and the true degree expected for the Sun for that day:

  1. If a given day is an epagomenal day, throw out the value entirely, and don’t factor it into calculations.
  2. For a given day reckoned at the reference time (sunrise on the March equinox for a given location), find the Sun’s true ecliptic position.
  3. Take the whole degree of the Sun (e.g. if 9.227°, 9).
  4. Divide the number from the previous step by 10 and take the remainder.
  5. Add one to the previous step.
  6. Divide a given day’s decan day-number by the previous step.

The shortcut to this method would basically be to divide the method’s decan day-number for a given day against the true degree method’s decan day-number, but I wanted to be sure I was getting the Sun’s true position here for mathematical rigor.  This ratio indicates the general percentage difference we expect; if the ratio is 1, then the given method’s decan day-number is what we’d expect; if more than 1, it’s ahead of what we expect; if less than 1, behind what we expect.

Doing some simple math on these ratios for these given methods gets us the following statistics (omitting the epagomenal days entirely), judged against the year from the March 2020 equinox through the March 2021 equinox (considered a normal year).  I calculated these results based on a prototype decanal calendar starting on March 20, 2020 at 11:12 UTC (the first sunrise after the spring equinox for my town’s given longitude) for 365 days.

Method Mean Median Min Max STD Variance
Egyptian 1.71222574 1 0.1 8 1.856253825 3.445678262
Plan-ahead 1.467144864 1.333333333 0.1 6 1.09989769 1.209774928
True degree 1 1 1 1 0 0
Average degree 1.351345416 1.166666667 0.1 5 0.9200161032 0.8464296301
Rebalanced true degree 1.211630551 1.2 0.1 3 0.5348857385 0.2861027532

In the 2020/2021 year, we can see that it’s the rebalanced true degree method that has the lowest standard deviation and variance, with the mean closest to 1.  This means that the rebalanced true degree method gets us the closest decan day-numbers to what the Sun’s actual position is on the whole, being at worst three days ahead (compared to the potential of being five, six, or eight days ahead with the other non-true degree methods).

For another look, we can also consider the leap year (according to our rule above) for the March 2021 equinox through the March 2022 equinox.  I calculated these results based on a prototype decanal calendar starting on March 20, 2021 at 11:13 UTC for 366 days.

Method Mean Median Min Max STD Variance
Egyptian 1.704857316 0.85 0.1 8 1.89868141 3.604991096
Plan-ahead 1.432609127 1.333333333 0.1 6 1.044951208 1.091923027
True degree 1 1 1 1 0 0
Average degree 1.338694885 1.2 0.1 5 0.8991436886 0.8084593728
Rebalanced true degree 1.142828483 1.142857143 1 2 0.3982472329 0.1586008585

We get even better results during leap years, it’d seem, at least based on this example alone; we’re only a max of two days ahead of the Sun’s true position, and we have even less variance and deviation than before.

If I were to go with any system of assigning a 10-day repeating cycle of prayers to the days to keep more-or-less in sync with the position of the Sun as it goes through the decans, I’d go with the rebalanced true degree method.  Still, even if it’s the most in sync, it’s not truly in sync, as there really isn’t such a system possible without skipping days due to the inconvenient misalignment of physical phenomena with discrete human systems of calendrics.  As SUBLUNAR.SPACE commiserated with me about on Facebook, as he found out when he was coding his own almanac program, the decans “do not like to be pushed into human patterns”, and that we really have to choose degrees or days, because we can’t have both.  In his almanac, he settled with marking things by the actual ingress, which was the common practice in the decan calendars of Ptolemaic times.  On top of that, as far as calculation goes, it’s among the more complicated, requiring manual rebalancing after figuring out the true degree day equivalences first for the whole year until the next March equinox; easy enough to do by a computer program, but tedious or outright difficult to do by hand.

For now, I’m going to content myself with marking the Sun’s ingress into the decans, and leave it at that.  For one, though I’d like to engage in a 10-day cycle of prayers aligned with the decans, and even though I have some sort of system in place to explore that, I still don’t have those damn ten (or eleven) prayers written up for them.  But, at least knowing what the schedule looks like is a start.

Correspondence of Spirits to the Greek Alphabet

Judging from my recent blog post history, you’d be forgiven if you thought that this whole damn blog, and my whole damn practice, was just about geomancy.  Technically, that’d be wrong, but I do, indeed, talk about geomancy a lot.  There’s just a lot to talk about when it comes to that topic.  One of the things I still keep up with, albeit not as much as I’d like or as much as I’d otherwise have time for, is my old Mathēsis practice, that whole system of Greek letter mystiticsm, a kind of neo-Pythagorean quasi-Hermetic system of theurgy and meditation that works closely with the Greek gods.  I’ve made some good innovations when it comes to developing this practice, from coming up with a Tetractys-based “map” of the cosmos, as well as various other meditative and purificatory practices that, even when I’m not working in a mathētic framework, still help out one way or another.  This whole thing came about through my interest and development of grammatomancy, the Greek alphabet oracle, which I’ve found to be an excellent system of divination that I also specialize in along with geomancy.  One of my finest innovations, I think, is the Grammatēmerologion, a lunisolar calendar that maps the days, months, and years themselves to different letters of the Greek alphabet for tracking feasts, holidays, rituals, and meditations, whether according to the days purely or overlaps between the letters of the days along with astrological and astronomical phenomena.  I’ve found it incredibly helpful, and I hope that others can, as well.

One of the things I find it especially useful for is arranging the days of the lunar month, from New Moon to New Moon, to the different gods of the Hellenic pantheon and other aspects of ancient Greek and Mediterranean mythos.  However, in a naïve or simple way, the Greek letters don’t really have very many associations to the various deities, divinities, and spirits, but I wanted to see how far I could take things.  For instance, it makes sense to honor Asklēpios along with Apollōn, his father, and by extension the goddesses of health like Panakeia or Hygieia or Iasō.  But what about the more obscure divinities, like Triptolemos or Amphitritē or Themis?  I began to expand the associations I was working with to associate the Greek letters to the gods, and I ended up with…well, quite a large set, especially because I wanted to be pretty darn complete or at least reasonably so.  Yanno, just in case.

That ended up in making a table so big even I wasn’t comfortable with it, so I ended up making four tables of correspondences of the various deities and spirits of a Hellenic, Pythagorean, or generally Greek pagan practice to the letters of the Greek alphabet.  I tried to make the associations as reasonably as I could, and despite the overwhelming number of entities present in Greek myth, I tried to focus on those that tended to receive cult in classical times.  Below are those tables, as reasonably complete as I could make them.  When gaps exist in the tables, that indicates that I couldn’t find anything to fit there, but that doesn’t mean that there can’t be; perhaps this table could be expanded upon over time, and I’d look forward to it.  Heck, even for the cells that are populated, I’m sure there can be additions or changes made.

What’s also nice is that these tables can also play well with the use of the Kyranides, a famous proto-grimoire “index” of the various minerals, animals, and plants of the world according to their initial letter by their Greek names; connections between those sorts of associations according to the Greek alphabet and how they might play well with the associations given by other authors and sources would be a great thing for me to (eventually) research.

Before we begin, let me share a few resources that were helpful, instrumental, or otherwise important in helping me devise these tables of divine correspondences to the Greek alphabet:

Table I: The Table of the Whole.  This table gives the high-level associations of the letters of the Greek alphabet, both the 24 letters in use from ancient times to modern times as well as the three obsolete letters Digamma, Qoppa, and Sampi, to their various associations: those of the various forces of the cosmos of the elements, planets, and signs of the Zodiac based on Cornelius Agrippa’s associations (book I, chapter 74); the singlemost important deity for that letter of the alphabet based on its corresponding force; a sacred word of power taken from PGM CI.1-53, a holy angel for each letter taken from the Coptic magical manuscript Berlin 11346, and a general part of the body commonly associated with the letters of the Greek alphabet apart from other zodiacal associations.  Note that the three obsolete letters Digamma, Qoppa, and Sampi lack most associations, and are instead given to three classes of spirits of the dead: Digamma has Ancestors of Kin (one’s own blood- and name-related family), Qoppa has Ancestors of Work (ancestors, founders, and forebears of one’s mundane and spiritual professions and lineages), and Sampi has Ancestors of the Great (culture heroes, legendary founders of cities and civilizations, as well as forgotten and wandering dead).  Other oddities, such as the presence of Eōsphoros and Hesperos for Ēta or Zeus Euēnemos for Phi are discussed below in tables for that specific class of letters.

Letter Force Deity Word Angel Body


Taurus Aphroditē ΓΕΝΙΟΜΟΥΘΙΓ
Gemini Apollōn ΔΗΜΟΓΕΝΗΔ
Mercury Stilbōn ΕΝΚΥΚΛΙΕ
of Kin
Cancer Hermēs ΖΗΝΟΒΙΩΘΙΖ
Venus Eōsphoros and
Earth Hēra Geēros ΘΩΘΟΥΘΩΘ
Sun Hēlios ΙΑΕΟΥΩΙ
Virgo Dēmētēr ΛΟΥΛΟΕΝΗΛ
Libra Hēphaistos ΜΟΡΟΘΟΗΠΝΑΜ




Water Persephonē ΞΟΝΟΦΟΗΝΑΞ
Mars Pyroeis ΟΡΝΕΟΦΑΟ
Sagittarius Artemis ΠΥΡΟΒΑΡΥΠ
Ancestors of
Capricorn Hestia ΡΕΡΟΥΤΟΗΡ
Pisces Poseidōn ΤΑΥΡΟΠΟΛΙΤ
Jupiter Phaethōn ΥΠΕΦΕΝΟΥΡΥ
Air Zeus
Spirit Dionysos ΨΥΧΟΜΠΟΛΑΨ
Saturn Phainōn ΩΡΙΩΝ
Ancestors of
the Great

Table II: the Table of the Seven Vowels.  This table expands on the seven vowels of the Greek alphabet, which are given most strongly to the seven traditional planets.  Each planet has its own specific astral titan associated with it, such as Selēnē for the Moon or Hēlios for the Sun, but note that Venus has two astral titans for it, Eōsphoros and Hesperos, because historically this planet was reckoned as two separate entities, Eōsphoros as the Morning Star when Venus rose before the Sun and visible in the dawn hours before sunrise, and Hesperos as the Western Star when Venus set after the Sun and visible in the dusk hours after sunset.  Based on the directions associated with these letters as given in the Heptagram Rite of PGM XIII.734—1077, each of these planets may also be given to the four Elder Titans along with their mother Gaia and their father Ouranos.  Other deities may also be assigned to the planets, such as Artemis for the Moon, along with clusters of lesser deities and other spirits associated with those deities.

Letter Planet Star Titan Deities Cluster
Α Moon Selēnē Hyperiōn Hekatē,
Ε Mercury Stilbōn Koios Hermēs Dioskouroi
Η Venus Eōsphoros,
Iapetos Aphroditē Hesperides
Ι Sun Hēlios Kriōs Apollōn, Dionysos,
Eōs, Theia
Ο Mars Pyroeis Gaia Arēs, Hēphaistos,
Υ Jupiter Phaethōn Kronos Zeus,
Ω Saturn Phainōn Ouranos Kronos, Adrasteia,

Table III: the Table of the Five Complex Consonants. This table expands on the five complex or double consonants of the Greek alphabet, which are given to the four elements plus the quintessence, the meta-element of Spirit.  Each of these is presided over by one of five gods, with the four classical elements associated with Zeus, Hēra, Hadēs, and Persephonē according to the Greek philosopher Empedocles.  To distinguish this specific Zeus and Hēra from their other forms, the titles “Zeus Euēnomos” (Zeus of the Good Winds) and “Hēra Geēros” (Hera of the Earth) are given specifically to them.  Along with these major divinities, other minor divinities who often received cult and are associated with these elements are given, along with important clusters of (often-named individual) spirits and lesser gods as well as general classes of various spirits.

Letter Element Major
Cluster Spirits
Θ Earth Hēra Geēros Gaia, Rhea, Kybelē,
Mēter Theōn
Ξ Water Persephonē Aphroditē, Ōkeanos,
Tēthys, Hekatē
Seirenēs Naiades,
Φ Air Zeus Euēnemos Aiolos,
Χ Fire Hadēs Hēphaistos, Hestia,
Ψ Spirit Dionysos Promētheus, Iakkhos,

Table IV: the Table of the Twelve Simple Consonants.  This table expands on the twelve simple or single consonants of the Greek alphabet, which are given to the twelve signs of the Zodiac.  Each of these zodiac signs are assigned to one of the twelve Olympian gods according to the Orphic Scale of Twelve as given by Cornelius Agrippa (book II, chapter 14) as their prime divinity, along with lesser or alternate divinities who are closely associated with the functions, roles, and ideals of those gods.  Along with these, other sacred figures are given according to the specific body of the zodiac sign, such as the divine twins Dioskouroi to the sign of the twins of Gemini, as well as important clusters of (often-named individual) spirits and lesser gods as well as general classes of various spirits that are also associated with the major divinities of these letters.

Letter Zodiac
Cluster Spirits
Β Aries Athēna Nikē, Mētis, Pronoia,
Hēphaistos, Erikhthonios
Γ Taurus Aphroditē Erōs, Adonis, Harmonia,
Peithō, Parēgoros
Δ Gemini Apollōn Aristaios, Lētō,
Hymenaios, Asklēpios,
Hygeia, Panakeia, Iasō
Dioskouroi Mousai
Ζ Cancer Hermēs Pan, Morpheus,
Maia, Hērakles
Pleiades Panes, Oneiroi,
Κ Leo Zeus Tykhē, Nemesis, Themis,
Ganymēdēs, Hēraklēs,
Bia, Nikē, Kratos, Zēlos
Λ Virgo Dēmētēr Persephonē, Triptolemos,
Hekatē, Ploutos, Iakkhos
Asteria Hōrai
Μ Libra Hēphaistos Athēna, Kēladiōn Dikē Kyklōpes,
Ν Scorpio Arēs Phobos, Deimos,
Eris, Enyō
Π Sagittarius Artemis Lētō, Hekatē Kheirōn Nymphai,
Ρ Capricorn Hestia Pan
Σ Aquarius Hēra Hēbē, Eileithyia, Iris Ganymēdēs Hesperides,
Τ Pisces Poseidōn Prōteus, Amphitritē,
Tritōn, Nēreus,
Palaimon, Leukotheua

One of the fascinating things I find about this Table IV is that there’s a subtle logic in how the major divinities are assigned to the signs of the Zodiac based on the opposing sign.  Consider that Pan is the god most commonly associated with the actual form of the sign Capricorn, but Pan is also often associated with Hermēs in mythos, sometimes even being Hermēs’ own son; there’s an interesting dichotomy here between these two signs, with Hestia essentially being the goddess of what happens inside the home while Hermēs is the god of what happens outside the home.  Likewise, note how the famous centaur Kheiron (or Chiron in modern spelling) is the god of the form of the sign Sagittarius, the opposite sign of Gemini, which itself is associated with Apollōn, his adoptive father and also the father of Asklēpios, whom Kheiron later teaches as his pupil.  Ganymēdēs, too, was the famous cup-bearer taken up by Zeus and placed into the sky as the sign Aquarius, yet this sign itself is given to Hēra, who disapproved of Ganymēdēs, while the sign opposite of both Hēra and Ganymēdēs is none other than Leo, given to Zeus himself.  It’s kinda fascinating to see the logic and polarities going on with how the gods are given to the signs and how they play off each other in a coherent whole of reinforcing-oppositions.

And there you have it!  My system of correspondences I use to categorize and organize the various gods, demigods, daimones, and spirits of the classical and mythic Hellenic world according to the letters of the Greek alphabets.  I’ve personally gotten good mileage out of it, and I hope others can, too, inasmuch as a letter-based system of mysticism might be helpful, but also to just pick out associations and links between the different entities of Hellenic mythos.

On Ritual Days in the Grammatēmerologion

Lately I’ve been going over my Grammatēmerologion text again—you know, that gigantic calendar ebook I put out that goes from March 2015 to March 2053.  It’s essentially my exploration into a lunisolar calendar that maps the letters of the Greek alphabet to the days of the lunar month as well as to the months of the lunar (really, lunisolar) year.  It’s up on my Books page for free download, if you’re interested.  It’s a beast of a PDF, and it’s roughly broken down into three parts: a description of how the Grammatēmerologion is constructed as well as how it can be used, an “almanac” that lists certain types of days as they occur in the 2015—2053 period, and the actual calendar of months.  A preview of October 2018 can be seen below giving you an idea of what it looks like:

Well, I’ve been taking another look at it.  Since printing out a copy for my own temple use, I’ve noticed that there are a few typos in it, a few things that need correcting, and just general improvements to formatting that can be made.  The content is largely the same, but I’ve been mulling lately how to better ply the Grammatēmerologion for calendar-specific ways to organize and arrange my rituals.  As I see it, there are three ways the Grammatēmerologion can be used for this specific purpose:

  1. Use the correspondences of the letters to the Greek, Hellenic, and other gods according to the letter-days.  For instance, given Agrippa’s Orphic Scale of Twelve (book II, chapter 14), we know that the zodiac sign of Cancer is associated with Hermēs.  Because the letter for the sign of Cancer is Zēta (book I, chapter 74), we can give the letter Zēta to Hermēs.  Thus, the fifth day of the lunar month, given to Zēta, can be used for worship and ritual of Hermēs.
  2. Use the interlocking cycles of letter-days and letter-months.  Because most (not every) month is also given a letter of the Greek alphabet, every lettered month will have one lettered day where the letters of the day and month match up; these are termed the Megalēmerai, the Great Days of the Grammatēmerologion.  Thus, the Gregorian calendar month of October 2018, which starts in the grammatēmerologic month of Sigma, October 1 has the letter of Sigma associated with it.  Thus, October 1, 2018 is the Megalēmera of Sigma, because it’s the day of Sigma in the month of Sigma.  Sigma is associated with Aquarius, and further to Hēra.
  3. Use the interlocking cycles of letter-days, letter-months, and letter-years.  Just as the days and months are associated with letters, so are most of the years of a single 38-year grammatēmerologic cycle (composed of two modified 19-year Metonic cycles).  Just as Megalēmerai are days when the letters of the day and month line up, there are also days when the letters of the day, month, and year line up as well; these are the Megistēmerai, or the Greatest Days of the Grammatēmerologion.  Unlike Megalēmerai, which occur for every letter and which happen for all but maybe one month a year, Megistēmerai are significantly rarer; only twelve Megistēmerai are possible across an entire 38-year cycle, and those only for the letters of Γ, Δ, Η, Θ, Ι, Μ, Ο, Π, Τ, Υ, Φ, and Ω.  Megistēmerai are essentially superpowered Megalēmerai, though I’m investigating to see if there’s any reasonable pattern or thread that can be used to connect those letters given above to see if something special can be done with them above and beyond their usual significations.

These days can be plied so that you could do monthly rituals of a god that’s important to you—for instance, celebrating Hermēs every month on the day of Zēta—or you could tone it back to just monthly ceremonies for the gods, one each on their own proper Megalēmera across a two-year period.  Megistēmerai would be big festivals, as I’m thinking of them, since they’re so uncommon, and any given Megistēmera would be a once- or twice-in-a-lifetime event.  For the record, the Megistēmerai of the current cycle according to the Grammatēmerologion are:

  1. Gamma: June 6, 2019
  2. Deltla: July 13, 2021
  3. Ēta: September 30, 2025
  4. Thēta: November 9, 2027
  5. Iōta: December 17, 2029
  6. Mu: March 4, 2034
  7. Omikron: June 20, 2038
  8. Pi: July 27, 2040
  9. Tau: October 15, 2044
  10. Upsilon: November 24, 2046
  11. Phi: December 31, 2048 (happy New Years, indeed!)
  12. Ōmega: March 18, 2053

The next one after that, another Megistēmera of Gamma, would occur in June 2057.  Never let it be said that I don’t enjoy long-term planning.

These are all useful ways to consider ritual according to the Grammatēmerologion, but there are other ways to ply special dates out of it, too, based on the interaction of the seven-day week.  Even though I don’t make use of such a cycle as part of the Grammatēmerologion proper, as there’s no way to get a seven-day week to fit neatly with any of the cycles already in place, I still make use of it in tandem with the Grammatēmerologion, and based on the intermeshing of these two cycles, there are other nifty days we can recognize.  I go over this in the ebook about it, but to summarize:

  • Planētēmerai or “Days of the Planets” are days when a day with a letter associated with a planet falls on the weekday ruled by that same planet.  For instance, if Alpha is associated with the planet of the Moon, then the Planētēmera of the Moon occurs when the day of Alpha falls on a Monday, which is also ruled by the Moon.
  • Astrēmerai or “Days of the Stars” are days when a day with a letter associated with a zodiac sign falls on the weekday ruled by the planet of that sign’s domicile.  Thus, if Mu is associated with the zodiac sign of Libra, and if Venus has its domicile in Libra, then the day of Mu falling on a Friday would be an Astrēmera.  Because Venus also has domicile in Taurus, itself associated with the Greek letter Gamma, then the day of Gamma falling on a Friday would also be an Astrēmera; any planet that rules two zodiac signs would also have two Astrēmerai.
  • Doksēmerai or “Days of Glory” are days when a day with a letter associated with a zodiac sign falls on the weekday ruled by the planet of that sign’s exaltation.  Thus, if Mu is associated with the zodiac sign of Libra, and if Saturn has its exaltation in Libra, then the day of Mu falling on a Saturday would be a Doksēmera.
  • Phthorēmerai or “Days of Ruin” are days when a day with a letter associated with a zodiac sign falls on the weekday ruled by the planet of that sign’s fall.  Thus, if Mu is associated with the zodiac sign of Libra, and if the Sun has its fall in Libra, then the day of Mu falling on a Sunday would be a Phthorēmera.
  • Phugēmerai or “Days of Flight” are days when a day with a letter associated with a zodiac sign falls on the weekday ruled by the planet of that sign’s exile.  Thus, if Mu is associated with the zodiac sign of Libra, and if Mars has its exile in Libra, then the day of Mu falling on a Tuesday would be a Phugēmera.  As with the Astrēmerai, planets with two domiciles also have two exiles, so the Phūgemera of Mars would also occur when the day of Gamma, associated with Mars’ other exile Taurus, falls on a Tuesday.

As I reckon it, the strictly Grammatēmerologion letter-based days above (the monthly rituals for the gods, the Megalēmerai, and the Megistēmerai) are good mostly for days of worship for the gods, though the Megalēmerai and Megistēmerai can be used for astrological and stellar rituals as well.  However, these five types of days that work with both the Grammatēmerologion and the seven-day week are excellent for planetary rituals, and can offer some insight into how strong a given day might be based on how the Grammatēmerologic lunar day of the month plays with the seven-day week and planetary rulerships—or, conversely, how strong or weak a given planet’s influence can be on its day of the week based on where it falls in a lunar month according to the Grammatēmerologion.

Of course, all of these are divested from any properly astrological phenomena, save for the phase of the Moon itself; this is an alternate system of reckoning fortuitous or appropriate days for ritual instead of using electional astrology, which (of course) is an entirely different field, and I don’t mean to supplant electional astrology nor claim that the Grammatēmerologion system used for this type of thing is as powerful or as good as it.  It’s just another alternative system for those who don’t bother or don’t know about it, and for that purpose, is fine for most non-astrologically-minded magicians.  Still, of these five latter types of days can be useful if you want to, for instance, plan a particular ritual of Venus and want its domicile quality of being in Libra or Taurus instead of its exaltation quality of being in Pisces.  That said, in all honesty, I’d probably just use the Planētēmerai before any of the other such days given here, because it’s such a strong connection that overlaps these two cycles.

Still, I feel like the Grammatēmerologion can be used for more that just playing with cycles of letters or how those cycles play with the seven-day week.  It’s this that I’m trying to expand on most now for the Grammatēmerologion ebook, but also for my own practice.  How can I better ply “days of power” out of this system?  Consider my Mathēsis system that uses a Great Tetractys with its Gnosis Schema, a set of twelve paths that traverse the ten sphairai on the Tetractys, paths which I liken to the twelve signs of the Zodiac as the Sun travels in its course through the ecliptic every year:

One of the reasons why I want to develop the Grammatēmerologion is to develop ways to time certain rituals, such as my Ingress Rituals (which I still need to work on fleshing out more).  So, let’s say I wanted to perform a Path Ritual of Aries, which connects the sphaira of Mercury to the sphaira of Jupiter (or of Air).  Aries is associated with the letter Bēta, so I’d want to pick a time associated with Bēta.  But, here’s the thing: how?  Do I want to use any old day of Bēta?  I could, but why not a Megalēmera of Bēta?  This makes sense, to use a Bēta-day in a Bēta-month, but the month of Bēta occurs only once every two years, which would be unfortunate if I miss it.  More than that, though, performing a ritual of Aries seems odd if there’s no connection going on with Aries, so why not a time when the Sun is actually, yanno, in Aries, especially if the whole idea of traversing the Gnosis Schema is to mimic the passage of the Sun through the signs of the Zodiac.  So, the obvious solution would be to pick a day of Bēta—essentially the day of Aries—when the Sun is in Aries.

This idea led me to a new kind of ritual day, the Kōmastēmerai or “Days of Revel”.  The term comes from Greek κωμαστηριον, literally “processional way” originally referring to a meeting-place of Bacchic celebrants, but which is used in the Greek Magical Papyri to refer to the Sun’s or other stellar passages through heaven along the ecliptic or other celestial routes.  Thus, “Days of Revel” could also be called “Processional Days”, days with a letter associated with a zodiac sign that fall while the Sun is in that same sign.  In this way, every month of the year, regardless whether any given month has a letter at all or what it might be, has at least one Kōmastēmera, and every sign of the Zodiac can be celebrated every year as opposed to once every two years using the Megalēmera-based method.  Interestingly, some signs have two Komastēmerai, if the letter-day falls on the day of or just after the ingress of the Sun into that sign, which means that some calendar years can have as many as 16 Komastēmerai, though most years just have one per month.

As an example, consider October 2018 again.  In October 2018 (as in every other October every year), the Sun is first in Libra (associated with the Greek letter Mu), then it passes to Scorpio (which is associated with the letter Nu).  The Sun passes into Scorpio at 11:22 UTC on Wednesday, October 23, 2018, which happens to be a day of Mu.  Where I live, the Sun enters into Scorpio just before sunrise, and because days in the Grammatēmerologion are reckoned from sunrise, this means that by the time the day of Mu starts at sunrise, the Sun will already be in Scorpio.  This means that the next day, October 24, which happens to be a day of Nu which is associated with Scorpio, is the Kōmastēmera of Scorpio.  This makes Thursday, October 24, 2018 an excellent day to perform a Mathētic Ritual of the Sun’s Ingress into Scorpio.

Like how there can be weekday-influenced days of power and days of weakness, as with the Astrēmerai and Phugēmerai or the Doksēmerai and Phthorēmerai, why not make similar corollaries to the Kōmastēmerai?  If these days occur when the letter-day of the month lines up with the sign the Sun is currently in, why not make days when the letter-day of the month lines up with the sign opposite the Sun?  Thus, we can also envision Kruphēmerai, “Days of Hiding”, days with a letter associated with a zodiac sign that fall while the Sun is in its opposing sign.  Recall that the next Kōmastēmera is that of Scorpio, falling on the day of Nu on October 24; the opposite sign of Scorpio is Taurus, which is associated with the letter Gamma, so the corresponding Kruphēmera of Scorpio would be the day of Gamma, which happens to fall on November 10, 2018.  While the purpose of the Kōmastēmerai seem pretty obvious to me, it’s not clear what purpose Kruphēmerai would serve.  What comes to mind are days of danger, harm, or otherwise ill omen due to the mismatch of ebbs and flows of power between the zodiac signs of the current time of the lunar month versus those in power of the Sun.  Again, something to be experimented with.

One could expand this system a bit more, too, by not just recognizing the solar Kōmastēmerai and Kruphēmerai but also their lunar equivalents of Epainēmerai, “Days of Praise”, and Aiskhēmerai“Days of Shame”, which would be the same idea but for the Moon.  Interestingly, because of how the Grammatēmerologion works, I don’t think there can reasonably be a day that is both Kōmastēmera and Epainēmera at the same time; this would require the Sun and Moon to be in the same sign or conjunct and on a day given to a letter associated with a sign of the Zodiac.  A day when the Sun and Moon are so close only happens around the New Moon, but the last few days of a Grammatēmerologic month aren’t associated with signs of the Zodiac, and the first day of the lunar month is given to Alpha, which is associated with the Moon.  I haven’t done the calculations, but this means that such a day probably couldn’t occur, except extraordinarily rarely and then only for the sign of Aries (the second day of the lunar month).  I’d need to check to see whether this is a thing.  Even then, though, I don’t think such days could be that common anyway, given how the synodic lunar months don’t really match up well with the Zodiac, given the variable start date from month to month.  For instance, consider that the Kōmastēmera of Scorpio on October 24, the day of Nu, falls on the Full Moon, which means the Moon is in Taurus opposite the Sun in Scorpio, and the next time the day of Nu comes about, the Moon will again be approaching fullness in late Taurus.  I’d need to do the calculations on this, but I don’t think Epainēmerai are really that common, or if they are, whether they can equally happen for all of the zodiac signs.  Thinking about it more, though, if you end up with one Epainēmera, then you might end up with two in a row, if the Moon changes sign at some point between those two days, though that might be even rarer.  All that above is ditto for Aiskhēmerai.  Still, given the solar focus of so much of Mathēsis ritual work and timing, I’m not sure Epainēmerai and Aiskhēmerai would have much of a place, especially given how rare or odd they might be.

What if we were to bring the seven-day week into this mix?  Now we’re getting into some really unusual or rare alignments of conditions, and I’m really not sure how many of these there might be.  Some ideas of possible things to recognize would be:

  • Sigēmerai, or “Days of Silence”, days when a day with a letter associated with a planet falls on the weekday ruled by that same planet but only while that planet is retrograde.  For instance, if Epsilon is associated with the planet of Mercury, then the Sigēmerai of the Mercury occurs when the day of Epsilon falls on a Wednesday while Mercury is retrograde.  In other words, Sigēmerai can only occur on their corresponding Planētēmerai while that given planet is retrograde.  Sigēmerai cannot occur for the Sun and the Moon, because they cannot be retrograde.  A real example of this is the Sigēmera of Jupiter coming up on June 27, 2019; this is a day of Upsilon on a Thursday, and so would normally be a Planētēmera of Jupiter if it weren’t for the fact that Jupiter is retrograde from April 10 to August 11 in 2019.
  • Khrusēmerai, or “Days of Gold”, days when a day with a letter associated with a planet falls during the sign in which the Sun is currently to be found and which that planet has domicile.  For instance, if the Sun is in Scorpio, then the planetary ruler of Scorpio is Mars, which is associated with the letter Omikron.  So, the day of Omikron while the Sun is in Scorpio (or in Aries!) becomes a Khrusēmera.  Just such a day is coming up on Friday, October 26, 2018, the day of Omikron (Mars) while the Sun is in Scorpio.
  • Argurēmerai, or “Days of Silver”.  Given the whole parallel structure I’ve previously set up with the Sun and the Moon, this could be used to refer to days when a day with a letter associated with a planet fall during the sign in which the Moon is currently to be found and which that planet has domicile.  However, given how rare and unlikely this seems, I’d rather give this instead to days when a day with a letter associated with a planet falls during the sign in which the Sun is currently to be found and which that planet has exaltation.  Thus, consider September 14, 2018; this was a day of Epsilon, and thus associated with Mercury, that occurred while the Sun was in Virgo, the exaltation of Mercury.  (Also note that this would also be a Khrusēmera, too, because Mercury has both exaltation and domicile in Virgo.)
  • Rupēmerai and Aukhmēmerai, “Days of Filth” and “Days of Tarnish”, respectively, which are basically like Khrusēmerai and Argurēmerai except, instead of relating to the current Sun sign’s domicile and exaltation, the current Sun sign’s exile (Rupēmerai) or fall (Aukhmēmerai).  So, if the Sun is currently in Libra, the corresponding Rupēmera would be the day of Omikron (associated with Mars, which has exile in Libra) and the day of Iōta (associated with the Sun, which has fall in Libra).
  • What if a Khrusēmera, Argurēmera, etc. happens while the planet in question is retrograde?  In this case, if the planet is the current Sun sign’s exaltation or fall or exile (but not domicile), then they cancel out and the day becomes just another ordinary day, but if it’s the current Sun sign’s domicile planet, then it becomes Arrhētēmera, or “Unspeakable Day”.
  • What if a Khrusēmera, Argurēmera, etc. happens on the proper weekday of that planet itself?  In other words, what happens if a Khrusēmera is also a Planētēmera?  At this point, why not just recognize them separately?  No special term needed for this; the day of Alpha (of the Moon) while the Sun is in Cancer falling on a Monday can be a Khrusēmera and Planētēmera, though the terms can be combined: Khrusoplanētēmera, or “Golden Day of the Planet”.  Likewise, we could have a Arguroplanētēmera or Rupoplanētēmera or Aukhmoplanētēmera, depending on what the type of day is, though if the planet is retrograde, it would simply be Sigēmera or Arrhētēmera, as above.
  • The prefixes Mega- and Megist- can be applied to any of the above terms if they also happen to be a Megalēmera or Megistēmera, respectively.  For example, April 7, 2020 is a Tuesday, and is also the day of Nu in the month of Nu.  Because the day and the month share the same letter, this is a Megalēmera; because the letter Nu is associated with Scorpio and this day falls on a Tuesday, which is ruled by Mars as the domicile-ruler of Scorpio, this is also an Astrēmera.  Thus, because this day is both Megalēmera and Astrēmera, it can be called a Megalastrēmera.  Similarly, March 4, 2034, is the day of Mu in the month of Mu in the year of Mu (Megistēmera), which also happens to fall on a Saturday (day of Libra on the day of Saturn, the exaltation of Libra).  Thus, this would be a Megistodoksēmera.  (And a Full Moon, no less, so plan early and mark your calendars!)

I’m sure I could come up with other terms to mix the weekday cycle, the Grammatēmerologic cycle, and the actual astrological phenomena of the skies, but I’m not sure all such possible combinations of interactions would need terms.  Heck, in this post alone, I’ve introduced over twenty types of “special days”, and I’m starting to feel like a bad fantasy author who’s badly trying to incorporate some kind of elvish or alien conlang.  Even if I were to come up with names, that doesn’t mean that they’re all equally valuable.  Honestly, I think the most important regularly (or semi-regularly) occurring special days to keep track of are:

  • Noumēniai, the celebration of a new month just after the New Moon
  • Megalēmerai and their rarer version Megistēmerai, the celebration of matching cycles of days
  • Planētēmerai and their retrograde version Sigēmerai to mark especially potent days (if the former) or days to be utterly avoided (if the latter) for planetary works
  • Kōmastēmerai to mark the passage of the Sun through the signs of the Zodiac
  • Khrusēmerai and their retrograde version Arrhētēmerai to mark the ruling planetary power of the current Sun sign, whether direct (if the former) or retrograde (if the latter) and how to approach that planet’s power

It’s good that we’re developing a technical vocabulary for specific workings, but let’s be honest, not all of these need to be known or marked, especially given how obscure or rare some of them might be.  When it comes to writing and developing (and redeveloping and refining) this Grammatēmerologion ebook, it also becomes a question of what really needs to get accounted for in the calendar and almanac itself, and how easy it is to calculate certain things.  Megalēmerai and Megistēmerai are near trivial to calculate, and figuring out the weekday special days (Planētēmerai, Astrēmerai, etc.) are easy enough as well.  It’s when we get into the astrological bits that I start having to bust out the algorithms and programming, and I haven’t yet gotten around to coding the relevant parts of Jean Meeus’ Astronomical Algorithms to determine whether any given planet on any given day is retrograde is not.

Even then, with this small selection of eight (really five if you don’t count the variations) special days, we’re coming up with a regular and notable ritual schedule that arises from the use of the Grammatēmerologion apart from simply using it to order rituals of worship and sacrifice to the gods, and a sort of regular theurgic and spiritual practice begins to take form.  This is precisely just what the Grammatēmerologion is designed to help with: a temporal tool and aide to structure and organize rituals in a lunisolar calendar based on the letters of the Greek alphabet.  The current Grammatēmerologion ebook suffices for this, but I am working on getting a better version out that incorporates some of these other special days in.

Another Look at the Circle of Petosiris

Again with the same damn text as before, I suppose.  Lately I’ve been polishing up some of my own notes and personal texts that I don’t publicly share, one of which is my personal binder of divination texts I use for the Greek stuff I do, namely grammatomancy, astragalomancy, and some references to the Delphic Maxims that I like.  In the section I have on grammatomancy—much pared down from my De Grammatomanteia ebook, but refined to have more information and correspondences that I personally find useful—I’ve been trying to reorganize some of the information in a better way that reduces my reliance on external resources.  Of course, it’s mostly a “just in case” thing, and some of the stuff I don’t really use…but it doesn’t hurt to have.

One of the things I’ve been wrestling with is how much numerology stuff I want to include.  After all, numerology was considered pretty useful in classical times, and if nothing else, it’s informative and instructive to consider.  I’ve written about it before, specifically onomatomancy, literally “divination by names” (previously I called it “onomancy”, which isn’t wrong but isn’t as correct a term as I should be using).  I wrote three posts about it: one that overlaps numerology with stoicheia, one about using pythmēnes to determine winners, and one that uses particular numerological devices to determine the outcomes of events.  I’ve been debating whether to include summaries of these methods and their charts or rules in my divination binder for my temple, and it’s not a bad idea to, I suppose, though I’m unconvinced I really need to.  Still, it wouldn’t be bad to have, and having the stoicheia-based rules thrown in could be useful, so I’m leaning towards doing it anyway.  That’s what got me looking, once again, at the Circle of Petosiris, a particularly fun numerological tool to determine whether one will recover and live or succumb and die to an illness based on the numerological interactions between a person’s name and the lunar date on which they fall ill.

Get a drink and buckle up, dear reader.  This post got a bit longer than I had anticipated.

For some background on my resources for this, the first reference I found that discussed this particular device was Hugo Magnus’ Superstition in Medicine (1905).  Magnus touches on the topic briefly giving an outline of the topic, but he refers to two other texts: Marcellin Berthelot’s Introduction a l’étude de la chimie des anciens et du moyen age (1889) and a truly wondrous work, Auguste Bouché-Leclerq’s L’astrologie grecque (1899).  Indeed, it’s from Bouché-Leclercq that I ultimately got my images for the Circle of Petosiris, which he’s modified slightly to fix what he believes is an error in the original diagram.  Both of these Circles, however, ultimately come from MS Grec 2419 from the Bibliothèque nationale de France, which is a beast of a 15th century Greek manuscript that contains all sorts of magical, astrological, Solomonic, and other divinatory texts in Greek that I wish someone would translate at some point into English.

With that, let’s look at Bouché-Leclercq’s versions of the two Circles of Petosiris from MS Grec 2419.  Both of these Circles are found in MS Grec 2419, though I could only find them after looking hard; the way the BnF digitized the damn thing screwed up all the folio numbers.  All the same, let’s go with Bouché-Leclercq’s nicely-redone versions of the Circles, because the originals are rather messier and harder to read:

For comparison, take a look at what the Circles look like from the original text.  The two tables on either side of the Circle are, according to Bouché-Leclercq, computations of the days of the lunar month, though I’m not really sure what that means.  In either case, Bouché-Leclercq omits the tables, while Berthelot includes them in his own (faithfully reproduced) image.


If you take a closer look at both of these Circles (at least in Bouché-Leclercq’s versions), they have the same basic structure: a circle divided into four quadrants each filled with numbers, with a central middle column divided into an upper half and lower half also filled with numbers.  Thus, each circle contains six zones, and each of them are labeled with a particular outcome based on numbers; going clockwise from the 9 o’ clock position, these are Great Life (upper left), Average Life (upper central), Small Life (upper right), Small Death (lower right), Average Death (lower central), and Great Death (lower left).  Interestingly, the middle sections of the fancier Circle of Petosiris on the right aren’t labeled, but given the similarities and positioning between the Great and Small outcomes on either side, it can be inferred that the middle refers to Average.  In either case, the upper zones reflect outcomes of Life, and the lower zones the outcomes of Death.

Just to make sure the Circles are fully understood, let’s take a closer look at the Greek script in each.  On the left, simple Circle, the central line says Πετοσίρου κύκλος, literally “circle of Petosiros” (spelling intentional on this one).  Around the edge, starting at the 9 o’ clock position and going clockwise, we get the

  1. ἡ μεγάλη ζωή (“the great life”)
  2. μέση ζωή (“middle life”)
  3. ἡ μικρά ζωή (“the small life”)
  4. μικρός θάνατος (“small death”)
  5. μέσος θάνατος (“middle death”)
  6. ὁ μέγας θάνατος (“the great death”)

The fancier Circle has a lot more going on inside it. Above the diagram, there’s the phrase κύκλος Πετοσίρεως, or “circle of Petosiris”.  On the horizontal, we have ὅροι ζωῆς καὶ θανάτου, literally “the borders of life and death”, a pleasant label for such a device, I suppose.  The “lobes” around the edge of the fancier Circle, starting at the 9 o’ clock position and going clockwise, indicate both the course of the Sun around the Earth in a single day as well as the four elements:

  1. ἀρκτικός μεσόγειος (“Arctic [star] over the earth”, i.e. midnight)
  2. πῦρ (“fire”)
  3. ἀνατολή ὑπέργειος (“rising above the earth”, i.e. sunrise)
  4. ἀήρ (“air”)
  5. μεσημβρία μεσόγειος (“midday over the earth”, i.e. noon)
  6. ὕδωρ (“water”)
  7. δύσις ὑπόγειος (“setting under the earth”, i.e. sunset)
  8. γῆ (“earth”)

In other words, if the fancier Circle of Petosiris were to be considered as a compass, north would be to the left, east at the top, south to the right, and west to the bottom.  The use of the elements here is interesting, as it might be thought to allocate certain elemental qualities to certain times of the day.  Continuing on, going around the outermost circle quadrant by quadrant, there are the following four messages:

  1. οὗτοι ταχέως σώζουσιν (“these save from death quickly”)
  2. οὗτοι ἐντός ἑπτά ἡμερῶν σώζουσιν  (“these save from death within seven days”, i.e. slowly)
  3. οὗτοι ἐντός ἑπτά ἡμερῶν ἀναιροῦσιν (“these kill within seven days”, i.e. slowly)
  4. οὗτοι ταχέως ἀναιροῦσιν (“these kill quickly”)

These line up with the text outside the circle and past the lobes, respectively μεγάλη ζωή (“great life”), μικρά ζωή (“small life”), μικρός θάνατος (“small death”), and μέγας θάνατος (“great death”).  It might be inferred, then, that the Average Life and Average Death zones would take effect in a span of three days or less, to use the same week-based timeframe for the Small Life and Small Death, while the Great Life and Great Death zones would take effect within a day.  It’s an odd timing system to use, I suppose, but it does offer a relative sense of scale.

Each quadrant also has a longer message in the innermost circle, though it’s repeated twice within each quadrant, once within each eighth-part of the circle:

  1. ἀρκτικά ὑπέργεια του βοῥῥᾶ (“Arctic [stars] above the earth [in the region] of Boreas [i.e. the north]”)
  2. μεσημβρία ὑπέργειος του βοῥῥᾶ (“midday [stars] above the earth [in the region] of Boreas [i.e. the north]”)
  3. μεσημβρία ὑπόγειος του νότου (“midday [stars] under the earth [in the region] of Notos [i.e. the south]”)
  4. ἀρκτικά ὑπόγεια του νότου (“Arctic [stars] under the earth of the [in the region] of Notos [i.e. the south]”)

These latter messages are probably supposed to represent the four parts of the day—viz. late night between midnight and sunrise, early day between sunrise and noon, late day between noon and sunset, early night between sunset and midnight—but these are given using kind of unusual astronomical phrases that I’m not fully certain I have right.  However, Berthelot doesn’t describe why these additions of times of day, positions of stars, or elements to the fancier Circle of Petosiris might be here, and they don’t seem to actually be used for numerological or onomatomantic divination; Bouché-Leclercq brings this up, and says that their inclusion is a “strange whim” and unknown how it might have been used.  However, based on some of the text (great life, small death, three zones of numbers per hemisphere, etc.), we have an almost identical setup of the basic arrangement of numbers, though Bouché-Leclercq says that the order is mysterious, i.e. it’s unknown why or how the numbers are arranged the way that they are.

The only real difference in how these two Circles of Petosiris are used is by what number one divides by to obtain a remainder; when using the simple Circle, one divides by 29, while with the fancy Circle, one divides by 30.  This matches how the simple Circle only contains numbers from 1 to 29 (αʹ to κθʹ) while the fancier Circle goes from 1 to 30 (αʹ to λʹ).  We know that lunar months have either 29 days (a hollow month) or 30 days (a full month), so it struck me that the simple Circle should be used when one falls ill during a hollow month, and the fancier Circle during a full month; neither Berthelot nor Bouché-Leclercq suggest this, but this makes so much more sense, in that these two Circles can be used alongside each other, just not at the same time!  After all, both of these Circles appear in the same overall text (though perhaps not by the same actual author), so using one for one kind month and the other for the other kind of month makes some sense so that nothing is missed.  Using this idea, the simple Circle can be called the Hollow Circle of Petosiris for use with hollow months of 29 days, and the fancier one the Full Circle of Petosiris for use with full months of 29 days.

In this light, we can compare how the outcomes match between the two Circles:

Quality Outcome Hollow Month
(29 days)
Full Month
(30 days)
Bright Great Life 2, 3, 7, 9, 11 2, 3, 7, 9, 10, 11
Average Life 13, 14, 16, 17, 19, 20 13, 14, 16, 17, 19, 20
Small Life 22, 23, 26, 28 22, 23, 26, 28
Dark Small Death 1, 25, 27, 29 1, 25, 27, 30
Average Death 4, 10, 15, 18, 21, 24 4, 15, 18, 21, 24, 29
Great Death 5, 6, 8, 12 5, 6, 8, 12

Perhaps unsurprisingly, the outcomes of the hollow Circle and the full Circle are almost exactly the same!  There are only three differences between how the days are arranged between the two circles:

  • Day 30 (which doesn’t exist in hollow months) is given to Small Death in full months
  • Day 29 is given to Average Death in full months and to Small Death in hollow months
  • Day 10 is given to Great Life in full months and to Average Death in hollow months

This further reinforces the notion that one circle really is meant for hollow months and the other for full months, and that the two Circles really belong to the same overall system, using one or the other based on the specific month of the illness.  In that sense, we can rearrange this table slightly to show how similar both systems really are:

Quality Outcome Hollow Month
(29 Days)
Common Full Month
(30 Days)
Bright Great Life 2, 3, 7, 9, 11 10
Average Life 13, 14, 16, 17, 19, 20
Small Life 22, 23, 26, 28
Dark Small Death 29 1, 25, 27 30
Average Death 10 4, 15, 18, 21, 24 29
Great Death 5, 6, 8, 12

Note that the regions above the horizon in the full Circle, marked as above the Earth according to the time of day, are labeled in the table above as “Bright”, while the lower regions marked as below the earth are labeled as “Dark”.  This gives an interesting binary quality to each day of the month, which can also help predict how things overall turn out in addition to simple illnesses:

  1. Take the name of the person, find the isopsephic value of the name, divide by the total number of days in the month, and find out whether the remainder is Bright or Dark according to the proper Circle of Petosiris for the type of month.
  2. Find whether the given day of the lunar month on which one initiates a new project, task, or journey is Bright or Dark, according to the proper Circle of Petosiris for the type of month.
  3. If both numbers are Bright, the whole of the project, task, or journey will be fortunate and good.
  4. If both numbers are Dark, the whole of the project, task, or journey will be unfortunate and bad.
  5. If the number of the person is Bright and the number of the day is Dark, the person will be in danger, but they will escape the danger.  More generally, fortune will occur under the appearance of misfortune.
  6. If the number of the person is Dark and the number of the day is Bright, misfortunes will occur under the appearance of fortune, and although things appear to go well, hidden dangers and traps lie about.

In either case, it should be noted that there are slightly more Bright days than there are Dark days; there are always 14 Dark days every month, with 15 Bright days in hollow months and 16 Bright days in full months.  At least there’s a greater chance of success or survival than not, I suppose.

Yet another way that the Circles can be used is to determine which of two parties in a contest, fight, or battle will win.  Take the isopsehic values of each of their names, divide by 30, and find the remainder using the Full Circle of Petosiris to compare their respective results; the value with the better quality will determine the winner.  For instance, in the ever-popular onomatomantic example, Achilles (Αχιλλευς) has the isopsephic value of 1267, which gives a remainder of 7, landing in “Great Life”, while Hector (Εκτωρ) has a value of 1225, which gives a remainder of 25, landing in “Small Death”.  Though not as much is said about this method, several other

  • Bright outcomes automatically become victorious over Dark outcomes.
  • Especially in fatal conflicts, Dark outcomes indicate actual death, whether immediately or after a long-sustained injury or infection.
  • If both parties end up in Dark outcomes, the one with the least bad result will survive the longest but both will lose.
  • If both parties end up in Bright outcomes, the contest may be brought about to an amicable end, with the party with the better outcome having the upper hand.
  • If both parties end up in the same outcome, the contest may be conceived of as equal and coming to a truce or stalemate, or we can resort to other numerological and onomatomantic methods instead (such as the pythmēnes method), though we could also use a simpler rule of just looking at the outcome numbers themselves and comparing directly with them, unless those two numbers are also the same.

In general, it seems like the Circle of Petosiris is actually a multipurpose numerological and onomatomantic tool of divination that can be used to not just determine the outcome of illnesses but of any general event, battle, or project.  What’s interests me and which can be another useful diagnostic tool, however, is the attribution of Brightness or Darkness to particular days.  After all, I already have a lunar calendar (well, really, lunisolar calendar), the Grammatēmerologion, which gives individual days of the lunar months to the letters of the Greek alphabet for prognostication and ritual planning.  If Bright and Dark days can be thought of as naturally tending to fortune or misfortune, respectively, especially for particular people based on their names, then it wouldn’t be hard to conceive of this as further enhancing the Grammatēmerologion system:

Hollow Month
(29 days)
Full Month
(30 days)
1 Α Dark
2 Β Bright
3 Γ Bright
4 Δ Dark
5 Ε Dark
6 Ϝ Dark
7 Ζ Bright
8 Η Dark
9 Θ Bright
10 Dark Bright
11 Ι Bright
12 Κ Dark
13 Λ Bright
14 Μ Bright
15 Ν Dark
16 Ξ Bright
17 Ο Bright
18 Π Dark
19 Ϙ Bright
20 Bright
21 Ρ Dark
22 Σ Bright
23 Τ Bright
24 Υ Dark
25 Φ Dark
26 Χ Bright
27 Ψ Dark
28 Ω Bright
29 ϡ Dark
30 Dark

This is kind of weird, though, when you look at it.  Some days that are given to really beneficial or naturally “bright” letters (like Alpha, “the god says that you will do everything well”, or Ēta, “the bright Sun who watches all watches you”) are given to be Dark, and vice versa (like Ōmega, given to Saturn, also has the comparatively awful oracle “you will have a worthless harvest, not a useful one”).  Additionally, the days that are given to obsolete letters (6, 19, and 29) or to unlettered days (10, 20, and 30) don’t really have much of a pattern as to which are Bright or Dark, even though it’s considered in the base Grammatēmerologion system that unlettered days are naturally considered unlucky or ill-favored for ritual or work.  I mean, I’m not really that surprised, considering how the Circle of Petosiris and the Grammatēmerologion system have no connection or shared logic behind them besides both relying on the use of a lunar month, and the fact that the Greek manuscript dates to the 1400s CE, but still.  Perhaps there is a logic behind how the Circle of Petosiris arranges days as Bright or Dark, or amongst the Great/Average/Small Life and Death categories, and I just don’t see it yet. At least I’m in good company of earlier scholars, I suppose.

It’s trying to figure out that order that reminded me of one of the first reasons why I ever learned about the Circle of Petosiris, namely the Sphere of Dēmokritos from PGM XII.351—364, something I mentioned in the original post about this stuff.  It’s a much simpler system, but the underlying method is the same: take the value of the person who has fallen ill, add to it the number of the day of the lunar month, divide by thirty, and take the remainder.

Unlike the more complex Circle of Petosiris with its threefold division of either life or death, the Sphere of Dēmokritos gives only two outcomes: if the result falls in the upper part of the table from PGM XII.351—364, the person will live, and if in the lower section, they will die.

  • Live: 1, 2, 3, 4, 7, 9, 10, 11, 13, 14, 16, 17, 19, 20, 23, 25, 26, 27
  • Die: 5, 6, 8, 12, 15, 18, 21, 24, 22, 28, 29, 30

On a whim, if we redefine “live” as Bright and “die” as Dark, I decided to compare how the Sphere of Dēmokritos matches up with our Circle of Petosiris scheme:

Day Letter Hollow
Sphere of
1 Α Dark Dark Bright
2 Β Bright
3 Γ Bright
4 Δ Dark Dark Bright
5 Ε Dark
6 Ϝ Dark
7 Ζ Bright
8 Η Dark
9 Θ Bright
10 Dark Bright Bright
11 Ι Bright
12 Κ Dark
13 Λ Bright
14 Μ Bright
15 Ν Dark
16 Ξ Bright
17 Ο Bright
18 Π Dark
19 Ϙ Bright
20 Bright
21 Ρ Dark
22 Σ Bright Dark Dark
23 Τ Bright
24 Υ Dark
25 Φ Dark Dark Bright
26 Χ Bright
27 Ψ Dark Dark Bright
28 Ω Bright Dark Dark
29 ϡ Dark
30 Dark Dark

The overlap here is, frankly, astounding; in general, of the thirty days of the Sphere of Dēmokritos, eight are different from either the Hollow or Full Circles of Petosiris (days 1, 4, 10, 22, 25, 27, 28, and 30), and if we just limit ourselves to the Full Circle of Petosiris, the overlap is even greater where only four days are different (days 1, 4, 25, and 27).  For one text that dates back to the fourth century and another that’s dated to the fifteenth, that’s incredible.  The striking similarities between these systems shows that either they were developed independently using a similar method that happened upon similar results, or (perhaps and hopefully) more likely, that the Sphere of Dēmokritos is an earlier form of the Circle of Petosiris, or closely-related to one of the Circle’s forebears, with only a few changes/copyist errors slipping in along the way and the Circle developing a finer gradation of results from a simple “live” or “die” outcome.

In fact, if you think about it, consider how the numbers are arranged in the Sphere of Dēmokritos: an upper and a lower half, with the upper half indicating life and a lower half indicating death, with three groups of numbers in each half: one on the left, one on the right, and one in the middle.  Consider where the overlaps apply even in how these numbers are arranged: in the Great Life section in the upper left of the Circle of Petosiris, you have 2, 3, 7, 9, and 11; in the Sphere of Dēmokritos, the upper left column has 1, 2, 3, 4, 7, and 9, with 1 and 4 being known as flipped in brightness and with 11 being found in the middle column of the Sphere.  If you plot not only what the overlaps are but where they occur, you have essentially same system, just represented in a more rectangular format!

It’s at this point that I’m getting really hooked now, because now I want to know what the logic is behind why the numbers of the lunar month are arranged the way they are on the Circle of Petosiris.  After a bit, it seems like one of the few (maybe the only?) text that discusses this topic is Otto Neugebauer and George Saliba’s 1989 paper On Greek Numerology (Centaurus, vol. 31, pp. 189—206).  Neugebauer and Saliba document a number of instances of the Circle of Petosiris that are extant in a variety of texts, including the Sphere of Dēmokritos, and even claim that the list of lucky and unlucky days of the Egyptian calendar given in PGM VII.272—283 is a highly corrupted version of this same system.  Neugebauer and Saliba go over about a dozen manuscripts, but they don’t go into depth on how significantly different the Circles of Petosiris of each might differ.  My idea of using one such Circle for hollow months and another for full months makes sense (though I could just as easily use the Hollow Circle for both and just add on day 30 where we’d expect in the Full Circle and make no other changes), but who’s to say whether such a combined approach might ever have been used, especially if there were so many other variations available?  That Bouché-Leclerq inter alia share two such Circles, one based on the number 29 and another based on the number 30, might just be a coincidence of fate and philology.

What’s interesting from Neugebauer and Salida’s paper is something that I glossed over as unimportant at the beginning of this post.  Recall those tables by the Hollow Circle of Petosiris from MS Grec 2419?  Bouché-Leclercq says that those are “computations of the days of the lunar month”.  Neugebauer and Saliba, based on a hint from some of Paul Tannery’s chapter on fragments of similar numerological devices in from Notices et extraits des manuscrits de la Bibliothèque nationale et autres bibliothèques (1886, vol. 31, part 2, pp.231—260), figured out that the large numbers are the numerological equivalents of the actual names of the dates of the lunar month plus an extra word or phrase.  For instance, in the first row of the left table, there’s the number ͵αφπθ = 1589.  Neugebauer and Salida reckon this to be the equivalent of the words ΠΡΩΤΗ (1288) and ΣΕΛΗΝΗ (301), which together add to be 1589.  Indeed, they find that the numerical values of each row are equivalent to the spelled-out name of the date plus the word for Moon in Greek, as the text itself indicates: “reckon also the name of the Moon if it falls from conjunction to full-moon”.  Likewise, the values in the right table all have the number 138 added as a constant, which is explained as “the number of the waning-moon”, literally the word “hollow” (ΚΟΙΛΗ).   Thus, the top row of the right table, day 16, we would expect then to be “sixteen hollow” or ΕΞ ΚΑΙ ΔΕΚΑΤΗ and ΚΟΙΛΗ: 5 + 60 + 20 + 1 + 10 + 4 + 5 + 20 + 1 + 300 + 5 = 431, then 431 + 138 = 569.  Indeed, we find the number φμθʹ, which is 569.

If we were to develop a complete reproduction of this kind of table, then we’d end up with the following.  Where there is more than one set of values for a given day, this shows that there were different ways to write out the name of the day based on the given source of the specific Circle method, e.g. day 16 could be written as ΔΕΚΑΤΗ ΕΚΤΗ or it could be written as ΕΞ ΚΑΙ ΔΕΚΑΤΗ.  I know some of these aren’t necessarily what’s used in modern Greek, but they are attested in the literature Neugebauer and Saliba reference as well as other classical sources.

Day Name Modifier Sum
Word Value Word Value
1 ΠΡΩΤΗ 1288 ΣΕΛΗΝΗ 301 1589
2 ΔΕΥΤΕΡΗ 822 ΣΕΛΗΝΗ 301 1123
3 ΤΡΙΤΗ 718 ΣΕΛΗΝΗ 301 1019
4 ΤΕΤΑΡΤΗ 1014 ΣΕΛΗΝΗ 301 1315
5 ΠΕΜΠΤΗ 513 ΣΕΛΗΝΗ 301 814
6 ΕΚΤΗ 333 ΣΕΛΗΝΗ 301 634
7 ΕΒΔΟΜΗ 129 ΣΕΛΗΝΗ 301 430
8 ΟΓΔΟΗ 155 ΣΕΛΗΝΗ 301 456
9 ΕΝΑΤΗ 364 ΣΕΛΗΝΗ 301 665
ΕΝΝΑΤΗ 414 715
10 ΔΕΚΑΤΗ 338 ΣΕΛΗΝΗ 301 639
11 ΕΝΔΕΚΑΤΗ 393 ΣΕΛΗΝΗ 301 694
12 ΔΩΔΕΚΑΤΗ 1142 ΣΕΛΗΝΗ 301 1443
13 ΔΕΚΑΤΗ ΤΡΙΤΗ 1056 ΣΕΛΗΝΗ 301 1357
14 ΔΕΚΑΤΗ ΤΕΤΑΡΤΗ 1352 ΣΕΛΗΝΗ 301 1653
15 ΔΕΚΑΤΗ ΠΕΜΠΤΗ 851 ΣΕΛΗΝΗ 301 1152
16 ΔΕΚΑΤΗ ΕΚΤΗ 671 ΚΟΙΛΗ 138 809
17 ΔΕΚΑΤΗ ΕΒΔΟΜΗ 447 ΚΟΙΛΗ 138 585
18 ΔΕΚΑΤΗ ΟΓΔΟΗ 453 ΚΟΙΛΗ 138 591
19 ΔΕΚΑΤΗ ΕΝΑΤΗ 702 ΚΟΙΛΗ 138 840
20 ΕΙΚΟΣΤΗ 613 ΚΟΙΛΗ 138 751
21 ΕΙΚΟΣΤΗ ΠΡΩΤΗ 1901 ΚΟΙΛΗ 138 2039
22 ΕΙΚΟΣΤΗ ΔΕΥΤΕΡΗ 1435 ΚΟΙΛΗ 138 1573
23 ΕΙΚΟΣΤΗ ΤΡΙΤΗ 1331 ΚΟΙΛΗ 138 1469
24 ΕΙΚΟΣΤΗ ΤΕΤΑΡΤΗ 1627 ΚΟΙΛΗ 138 1765
25 ΕΙΚΟΣΤΗ ΠΕΜΠΤΗ 1126 ΚΟΙΛΗ 138 1264
26 ΕΙΚΟΣΤΗ ΕΚΤΗ 946 ΚΟΙΛΗ 138 1084
28 ΕΙΚΟΣΤΗ ΟΓΔΟΗ 768 ΚΟΙΛΗ 138 906
29 ΕΙΚΟΣΤΗ ΕΝΑΤΗ 977 ΚΟΙΛΗ 138 1115
30 ΤΡΙΑΚΟΣΤΗ 1009 ΚΟΙΛΗ 138 1147

The reason why these tables are given in MS Grec 2419 and other texts is due to a particular way of using the Circle of Petosiris that I wasn’t taking into account earlier.  The method I thought would be used—perhaps biased by my first encounter with this sort of technique from the Sphere of Dēmokritos from PGM XII.351—364—would be to take the value of the person’s name and the actual number of the lunar date, sum them together, divide by the number of days in the lunar month, and use the remainder.  Rather, it seems that instead of using the raw number (perhaps as a later development, or as an alternative technique?) one would use the value of the actual name of the lunar date instead, and in most cases (there’s at least one manuscript that doesn’t do this) modified by whether the date was during the waxing or waning moon.  The benefit to using the numbers in the table above, whether of the name itself or the name plus a modifier, has the benefit of making more erratic the results of dividing and taking the remainder in a discontinuous, semi-unpredictable way (1589, 1123, 1019, 1315, …), as compared to the sequential order of the actual numbers of the days of the lunar month (1, 2, 3, 4, …).

That means we have several methods to use now for the Circle of Petosiris, although several of them can be ignored because they confuse adding pure numbers with names of numbers.  In any case, we’d take the same approach: come up with a sum, divide by the number of days in the lunar month, and find the remainder among the zones of the proper Circle of Petosiris:

  1. Add the value of the name of the person to the number of the lunar day.
  2. Add the value of the name of the person to the number of the lunar day plus the number of the day of the week.
  3. Add the value of the name of the person to the number of the lunar day plus the value of the name of the day of the week.
  4. Add the value of the name of the person to the value of the name of the lunar day.
  5. Add the value of the name of the person to the value of the name of the lunar day plus the number of the day of the week.
  6. Add the value of the name of the person to the value of the name of the lunar day plus the value of the name of the day of the week.
  7. Add the value of the name of the person to the value of the name of the lunar day plus a modifier.
  8. Add the value of the name of the person to the value of the name of the lunar day plus a modifier and the number of the day of the week.
  9. Add the value of the name of the person to the value of the name of the lunar day plus a modifier and the value of the name of the day of the week.

The same could likewise be done by comparing the value of the name of the person against the number of the lunar date or the value of the name of the date, after dividing and taking the remainder of each by the number of days in the lunar month, and seeing where each remainder falls to compare them.

This is all well and good, and Neugebauer and Saliba have done some pretty intense work to correlate and investigate all the variations in these weird sums and modifiers found where there are such tables with Circles of Petosiris.  However, in an incredibly disappointing conclusion, they finish their paper by saying that “obviously one should now explain how these numbers were classified into strong, medium, and weak ones…our attempts in this direction did not lead to any convincing result.”  As the mathematician and historian Joel Kalvesmaki says on this specific point, they “solved many important problems but left many more outstanding”.  What we’re likely relying on is a fundamentally old tradition of lucky and unlucky numbers within the context of lunar dates, and it doesn’t seem to be clear to anyone why the Circle of Petosiris or the Sphere of Dēmokritos or other such techniques arrange the numbers the way they do.  Neugebauer and Saliba suggest that “since these numbers represent lunar dates, it is plausible to search for astrological motivations”, although Kalvesmaki makes a good point that such a kind of system of days can have any number of mutually-nonexclusive origins: making observations from experience and experiment, informative myths, zodiacal considerations, and the like.

It seems that, unfortunately, I’m at a dead end with this sort of investigation.  Unless I get access to a wide number of manuscripts dating back some two millennia and somehow pick up classical and medieval Greek, I doubt I can get much further along this line of thinking.  I suppose the only thing left is to experimentation.  One easy way would be to use the comparison method: take the value of my name and compare it to any of the combinations above: the number of the lunar day as reckoned from the Noumēnia in my Grammatēmerologion with or without the number of the day of the week added, or the value of the name of the day according to the table with or without the modifier value with or without the value of the name of the number of the day of the week.  I suppose it wouldn’t be hard to write a simple program to do just that, then keep a running log of how good or bad a given day is.  It’s not as satisfying as discovering some long-lost ancient logic or system, but picking out patterns can be just as sweet once you sift through the salt.