heniautos 1.2.0

Ancient Athenian calendar generator

Heniautos

Naive ancient Attic calendar generator and calendar equation explorer.

Installation

pip install heniautos

On an M1 Macintosh

Heniautos uses a package named Skyfield for astronomical calculations which, in turn, requires NumPy. NumPy cannot yet be installed the normal way on a Macintosh with an M1 processor. These steps should work to install Heniautos on an M1 Mac:

pip install cython
pip install --no-binary :all: --no-use-pep517 numpy
pip install heniautos

(See this StackOverflow comment)

Usage

Command Line

Generate a calendar for 416 BCE:

heniautos 416

Solve the calendar equation Metageitniṓn 9 = Prytany I 39:

calendar_equation -e Met 9 I 39

In a Program

Generate a calendar for 416 BCE

import heniautos as ha
ha.init_data()
ha.festival_calendar(ha.bce_as_negative(416))

Solve the calendar equation Metageitniṓn 9 = Prytany I 39:

ha.equations((ha.Months.MET, 9), (ha.Prytanies.I, 39), ha.Prytany.ALIGNED_10)

Note: Heniautos will automatically download an ephemeris file rom jpl.nasa.gov the first time you use it (or anytime it cannot find the file). This is normal.

The Basics

Heniautos (Greek for "the span of a year") generates examples of possible Athenian calendars for any given year, ancient or modern, and provides has features for exploring the calendar and working with calendar equations. It is hopefully useful for:

• Learning about and teaching the ancient Athenian Calendar
• Following along with often complex discussions of dating of events in ancient Greek history
• Just having fun with questions like "When would the City Dionysia be this year, if it was still being held."

Heniautos comes with two command-line programs--heniautos for generating calendars, and calendar-equation for exploring information provided mostly by ancient inscriptions--and a Python library for writing your own programs. See the Guide for details.

What A. W. Gomme wrote in 1970 (Gomme, 1945-1981,) 4.264) is still true today—"It does not seem easy at the present time to make any statement about the Athenian calendar which is both significant and undisputed." Still, there are a few certain principals by which the Athenian calendar functioned:

• It was lunisolar, depending partly on the sun, partly on the moon.
• There were twelve months. Each began on the new moon and had 30 days (called a "full" month) or 29 (called a "hollow" month)
• The year began on the first new moon following the summer solstice
• Twelve lunar months are 11 days shorter than one solar year, so about every third year a thirteenth month had to be added ("intercalated") to fill out the time until the next solstice.

The same principals were followed throughout the ancient Greek world, although different cities used different names for the months and began the year at different times. For instance, in Sparta the year began after the fall equinox.

Beyond this there are many questions. Did the months alternate regularly between full and hollow? If not, what determined whether a month was full or hollow? Was there a fixed schedule of intercalations (as the Julian and Gregorian calendars have a fixed rule for leap years)? If not how was this determined? Did the Athenians fix the new moon by observation, by calculation, or even by guessing?

Heniautos generates "naive" calendars, aligning ancient Greek dates with Julian calendar dates, according to astronomical data (provided by the Skyfield library) using a few simple rules:

1. Each month begins, by default, on an "observed" new moon two days after the astronomical conjunction (though you can choose other values).
2. The year begins on the first observed new moon (by rule #1) on or after the day of the summer solstice.
3. Intercalations are made when astronomically necessary. Essentially, if one year ends close enough to the summer solstice that twelve lunar months will not be enough to reach the next solstice, then the next year will be intercalary.

For example, Heniautos' calendar for 416/415 BCE:

#	Month	Julian Date	# days
1	Hekatombaiṓn	BCE 0416-Jul-20	29
2	Metageitniṓn	BCE 0416-Aug-18	30
3	Boēdromiṓn	BCE 0416-Sep-17	29
4	Puanopsiṓn	BCE 0416-Oct-16	30
5	Maimaktēriṓn	BCE 0416-Nov-15	30
6	Posideiṓn	BCE 0416-Dec-15	29
7	Gamēliṓn	BCE 0415-Jan-13	30
8	Anthestēriṓn	BCE 0415-Feb-12	30
9	Elaphēboliṓn	BCE 0415-Mar-14	29
10	Mounuchiṓn	BCE 0415-Apr-12	30
11	Thargēliṓn	BCE 0415-May-12	29
12	Skirophoriṓn	BCE 0415-Jun-10	30

Notice that the hollow and full months do not alternate regularly (unless you observed enough over a long enough period of time to see the actual, natural cycles of the moon). 19-year cycles of intercalation recognized by the ancients (Metonic cycles, 7 intercalations every 19 years) do appear in Heniautos, but by orbital calculations, rather than by prescription.

417/416 BCE is an example of an intercalary year:

#	Month	Julian Date	# days
1	Hekatombaiṓn	BCE 0417-Jul-01	29
2	Metageitniṓn	BCE 0417-Jul-30	30
3	Boēdromiṓn	BCE 0417-Aug-29	29
4	Puanopsiṓn	BCE 0417-Sep-27	30
5	Maimaktēriṓn	BCE 0417-Oct-27	30
6	Posideiṓn	BCE 0417-Nov-26	30
7	Posideiṓn hústeros	BCE 0417-Dec-26	29
8	Gamēliṓn	BCE 0416-Jan-24	30
9	Anthestēriṓn	BCE 0416-Feb-23	30
10	Elaphēboliṓn	BCE 0416-Mar-25	29
11	Mounuchiṓn	BCE 0416-Apr-23	30
12	Thargēliṓn	BCE 0416-May-23	29
13	Skirophoriṓn	BCE 0416-Jun-21	29

Posideiṓn hústeros ("later Posideiṓn") is the intercalated month. Without this extra month, the 12th month would end on June 20, before the solstice (June 28 on the Julian calendar at this time). Athenians intercalated by repeating one of the months, usually Posideiṓn as shown here, which Heniautos intercalates by default (you can choose other months).

Example

We can find a "modern" date for the the peace treaty between Athens and Sparta which, according to Thucydides (5.19.1) was signed on this "the sixth day of the waning moon of Elaphēboliṓn":

ἄρχει δὲ τῶν σπονδῶν <ἐν μὲν Λακεδαίμονι> ἔφορος Πλειστόλας Ἀρτεμισίου μηνὸς τετάρτῃ φθίνοντος, ἐν δὲ Ἀθήναις ἄρχων Ἀλκαῖος Ἐλαφηβολιῶνος μηνὸς ἕκτῃ φθίνοντος. ὤμνυον δὲ οἵδε καὶ ἐσπένδοντο.

The treaty begins in Lakedaimōn in the ephorate of Pleistolas on the fourth day of the waning moon of Artemisios, in Athens in the arkhonship of Alkaios on the sixth day of the waning moon of Elaphēboliṓn.

Alkaios was arkhon in 422/421 so to find the "sixth day of the waning moon" we can start with the calendar for Elaphēboliṓn that year:

> heniautos 422 --month Ela
     Year     |        Month          | Day |      Start      | DOY
--------------|-----------------------|-----|-----------------|----
BCE 422/421   | Elaphēboliṓn          |   1 | BCE 0421-Mar-19 | 237
BCE 422/421   | Elaphēboliṓn          |   2 | BCE 0421-Mar-20 | 238
BCE 422/421   | Elaphēboliṓn          |   3 | BCE 0421-Mar-21 | 239
BCE 422/421   | Elaphēboliṓn          |   4 | BCE 0421-Mar-22 | 240
BCE 422/421   | Elaphēboliṓn          |   5 | BCE 0421-Mar-23 | 241
BCE 422/421   | Elaphēboliṓn          |   6 | BCE 0421-Mar-24 | 242
BCE 422/421   | Elaphēboliṓn          |   7 | BCE 0421-Mar-25 | 243
BCE 422/421   | Elaphēboliṓn          |   8 | BCE 0421-Mar-26 | 244
BCE 422/421   | Elaphēboliṓn          |   9 | BCE 0421-Mar-27 | 245
BCE 422/421   | Elaphēboliṓn          |  10 | BCE 0421-Mar-28 | 246
BCE 422/421   | Elaphēboliṓn          |  11 | BCE 0421-Mar-29 | 247
BCE 422/421   | Elaphēboliṓn          |  12 | BCE 0421-Mar-30 | 248
BCE 422/421   | Elaphēboliṓn          |  13 | BCE 0421-Mar-31 | 249
BCE 422/421   | Elaphēboliṓn          |  14 | BCE 0421-Apr-01 | 250
BCE 422/421   | Elaphēboliṓn          |  15 | BCE 0421-Apr-02 | 251
BCE 422/421   | Elaphēboliṓn          |  16 | BCE 0421-Apr-03 | 252
BCE 422/421   | Elaphēboliṓn          |  17 | BCE 0421-Apr-04 | 253
BCE 422/421   | Elaphēboliṓn          |  18 | BCE 0421-Apr-05 | 254
BCE 422/421   | Elaphēboliṓn          |  19 | BCE 0421-Apr-06 | 255
BCE 422/421   | Elaphēboliṓn          |  20 | BCE 0421-Apr-07 | 256
BCE 422/421   | Elaphēboliṓn          |  21 | BCE 0421-Apr-08 | 257
BCE 422/421   | Elaphēboliṓn          |  22 | BCE 0421-Apr-09 | 258
BCE 422/421   | Elaphēboliṓn          |  23 | BCE 0421-Apr-10 | 259
BCE 422/421   | Elaphēboliṓn          |  24 | BCE 0421-Apr-11 | 260
BCE 422/421   | Elaphēboliṓn          |  25 | BCE 0421-Apr-12 | 261
BCE 422/421   | Elaphēboliṓn          |  26 | BCE 0421-Apr-13 | 262
BCE 422/421   | Elaphēboliṓn          |  27 | BCE 0421-Apr-14 | 263
BCE 422/421   | Elaphēboliṓn          |  28 | BCE 0421-Apr-15 | 264
BCE 422/421   | Elaphēboliṓn          |  29 | BCE 0421-Apr-16 | 265

heniautos 422 --month Ela means "show me the calendar for the month Elaphēboliṓn in 422/421 BCE (see heniautos Command in the guide for more details). Now, "the sixth day of the waning moon" sounds very poetic, but it was simply the way of naming days in the last ten days of the month. There is disagreement over exactly how to interpret a date like ἕκτῃ φθίνοντος in a hollow month (which this month is since it has 29 days, see The Backwards Count in the guide) so this might mean either the 24th or the 25th. These correspond to either April 11 or April 12, 421 BCE.

This is simply a starting point. If you want to state something more concretely you will need to apply other evidence or hypotheses. Meritt (1928, 109) first made it April 9 while Dinsmoor (1931, 334-335) said April 10. Meritt then citicized Dinsmoor at some length (1932, 146-151) to conclude (1932, 178) that it should be April 11--Heniautos arrives at this date but by a different path than Meritt. Gomme concludes that it should be "about March 12" (1945-1981, 4.711-713) because he has a different view about the intercalations. Most recently, Planeux calculates April 11 again (forthcoming, 187).

That said, the date given by Heniautos is close to all calculations, (though least close to Gomme's because of the intercalation). "About April 11" is good enough for most purposes. That is not bad over a span of 2,442 years or more than 890,000 days. This margin of error should hold for any ancient date. The cited discussions are complex, and Heniautos can hopefully help anyone less steeped in ancient Athenian calendar equations follow along and check their calculations.

Learn More

Please read the Guide for more about the Athenian calendar and what calendar equations are and how they're used, as well as for details about the usage of heniautos command, the calendar-equation command, and the Python library.

Works Cited

• Dinsmoor, William Bell. 1931. The Archons of Athens in the Hellenistic Age. Cambridge: Harvard University Press.
• Gomme, A. W., A. Andrewes, and K. J. Dover. 1945-1981. A Historical Commentary on Thucydides. 5 vols. Oxford: Oxford University Press.
• Meritt, Benjamin D. 1928. The Athenian Calendar in the Fifth Century. Cambridge: Harvard University Press.
• ----------. 1932. Athenian Financial Documents of the Fifth Century. Ann Arbor: University of Michigan Press.
• Planeux, Christopher. Forthcoming. The Athenian Year Primer.