metonic

Generation and manipulation of hypothetical Metonic cycles.

Installation

pip install metonic

Usage

In the ancient Greek calendars, the “standard” Metonic cycle of ordinary (12-month, 354-day) and intercalary (13-month, 384-day) lunisolar years conforms to a few rules:

• Nineteen years long
• Seven of the nineteen years are intercalary
• One intercalary year cannot follow another
• No more than two ordinary years may occur in succession

metonic generates Metonic cycles based on these descriptive rules (or based on changes to these rules) and provides methods for manipulating them.

Most of this is actually unnecessary. The trend over the last century of scholarship has been to see the Greek (mostly meaning the Athenian) calendar as very regular and conforming closely to astronomical phenomena. Still, there is a lot of literature, primarily by Benjamin D. Meritt, that views the calendar as very irregular. metonic might be useful for exploring and understanding these earlier reconstructions.

Cycles of Ordinary and Intercalary Years

metonic represents cycles as strings of ordinary (“0”) and intercalary (“1”) years. The standard Athenian Metonic cycle is available as a constant:

>>> import metonic
>>> metonic.ATHENS
'0100100101001001010'

This is a 19-year cycle of twelve ordinary and seven intercalary years. The first year of the first cycle is 432/431 BCE.

To get the year at any position of any cycle:

>>> metonic.from_metonic(1, 1)
-431
>>> metonic.from_metonic(5, 12)
-344

The values returned are astronomical years—years BCE are negative numbers and 1 BCE is 0. You can use another library (eparkhontos)[https://pypi.org/project/eparkhontos/] to make it easier to work with Greek and astronomical years

You can also get the Metonic cycle from the year:

>>> metonic.to_metonic(-431)
(1, 1)
>>> metonic.to_metonic(-344)
(5, 12)

Generating Cycles

cycle_set() will generate all the unique cycles that satisfy the given conditions: length of cycle (n), number of intercalary years (i_count), maximum number of intercalary years in a row (max_i), and maximum number of ordinary years in a row (max_o). The defaults are those listed above (19 years, 7 intercalary, no more than 1 intercalary and 2 ordinary in a row):

>>> for _ in metonic.cycle_set():
...     print(_)
...
0010010010010010101
0010010010010100101
0010010010100100101

The cycles will be output in the lowest possible “alphabetical” order (which is the same as numeric if these are treated as binary numbers). These default parameters output three cycles because there are three unique cycles that satisfy those rules. Only the third “exists in nature”. It might not look at first like this matches the Athenian Metonic cycle:

0010010010100100101
0100100101001001010 # metonic.ATHENS

But since this is a cycle, it repeats and the standard Athenian cycle is just a version of this cycle shifted to the right.

00100100101001001010010010010100100101 # × 2
 0100100101001001010                   # metonic.ATHENS
  |  |  | |  |  | |                    # intercalary years line up

When testing equivalency and uniqueness, metonic takes these repetitions into account.

If you want to allow two intercalary years in a row you will get a different set:

>>> for _ in metonic.cycle_set(max_i=2):
...     print(_)
...
0010010010010010011
0010010010010010101
0010010010010100101
0010010010100100101

As you will if you allow 8 intercalary years or 4 ordinary in a row:

>>> len(metonic.cycle_set(i_count=8))
7
>>> len(metonic.cycle_set(max_o=3))
38 

i_count can be an iterable allowing multiple values, such as 7 or 8 intercalary years:

>>> len(metonic.cycle_set(i_count=[7,8]))
10

Or you can make up any rules you want:

>>> metonic.cycle_set(n=5, i_count=2, max_o=3)
('00101',)

Segments

segments() finds all the unique segments of a cycle of any given length. For instance all the five year segments of the Athenian cycle:

>>> for _ in metonic.segments(metonic.ATHENS, 5):
...     print(_)
...
00100
00101
01001
01010
10010
10100

Segments wrap from end to beginning. All the segments of length 4 for the cycle "00001" are:

>>> metonic.segments("00001", 4)
('0000', '0001', '0010', '0100', '1000')

The last three show this wrapping, i.e. (wrapping point indicated by the bar (“|”):

00001|00001
0000
 0001
  001 0
   01 00
    1 000

Testing segments against cycles

in_cycle() will test whether a segment is in a cycle or group of cycles, wrapping when necessary:

>>> metonic.in_cycle("0100", "00001")
True

This true because "0100" matches a segment in "00001" treated as a ring:

0000100001
   0100

If you test against an iterable, the test will be repeated for each member of the iterable. The result will be a tuple of cycles for which there is a match, an empty tuple if there are no matches:

>>> metonic.in_cycle("0010101", metonic.cycle_set())
('0010010010010010101',)
>>> metonic.in_cycle("11", metonic.cycle_set())
()

All Combinations

cycle_set() begins with all possible combinations of ordinary and intercalary years before reducing them to unique cycles. The non-unique combinations can be gotten from combinations(). This takes the same parameters and defaults as cycle_set so, with no arguments, it returns a tuple of all combinations according to the standard Metonic criteria:

>>> len(metonic.combinations())
57

The 57 combinations are 19 “rotations” of 3 unique cycles (19 × 3 = 57). The difference between combinations() and cycle_set() is that combinations() returns all the rotations while cycle_set() only returns one example of each unique cycle (specifically the one that comes first in an alphabetical sort).

cycle_set() can also take an iterable of combinations. This:

>>> c = metonic.combinations()
>>> metonic.cycle_set(c)

is the same as calling cycle_set() by itself. Likewise for any combination of parameters:

>>> c = metonic.combinations(i_count=8)
>>> metonic.cycle_set(c)

is the same as:

>>> metonic.cycle_set(i_count=8)

Contributing

Bug reports and pull requests are welcome on GitHub at https://github.com/seanredmond/metonic