The Octaeteris – The Eight-Year Cycle and the Aun Rule

Eight solar years correspond almost exactly to 99 lunar months. That is the whole idea. Antiquity credited the cycle to Cleostratus of Tenedos, active around 520 BC.[10] From this single approximation came Europe's oldest equalising cycle, the beat of the great sacrificial feasts in the North, and a mnemonic still being written down in the early modern period.

Why the cycle exists at all

The reason is religious, not mathematical. The ancient astronomer Geminus, reported at length by the chronologist Friedrich Karl Ginzel, names as the starting point of Greek time-reckoning the striving of the ancients to offer the gods the same sacrifices in the same seasons. That is possible only if the solstices and equinoxes always fall in the same months, and if the days are reckoned by the Moon so that their names agree with its shapes of light.[1]

Two demands are folded into that. The feasts must land in the right season, so you need the Sun. The day of the month must match the Moon's visible shape, so you need the Moon. Wanting both leaves no choice: you have to build a lunisolar calendar. Ginzel states the consequence plainly. The time-reckoning of the Greeks, and of other peoples working from lunisolar relations, consists "in a chain of approximations and gradual improvements."[2] The octaeteris is the first usable link in that chain.

The same logic carries the Germanic lunar calendar. There too the blót dates hang on full moons, and there too a leap month has to keep midwinter in winter.

Eight years, 99 months, three leap months

The arithmetic is simple enough to hold without writing. Twelve lunar months make a year of about 354 days, eleven days short. After three years that shortfall has grown to roughly a full month. Insert a thirteenth month three times across eight years and you arrive at 8 × 12 + 3 = 99 lunar months.

How well it lands depends on the values used. Antiquity put the solar year at 365¼ days, so eight years came to 2,922. Divide that by 99 and you get an awkward month of 29 5/99 days, on which Ginzel is terse: the octaeteris of 2,922 days was inaccurate.[3] Discussing the Roman calendar he is more precise: 2,922 days do not hold exactly 99 lunar months but closer to 2,923.[4]

Modern figures confirm it. 99 synodic months run to 2,923.53 days, eight tropical years to 2,921.94.[5] After eight years about 1.6 days are missing, roughly five hours a year. That is accurate enough for a festival calendar already tied to the observed Moon, and too coarse for astronomy. Hence the Metonic cycle with its 19 years, off by only 0.09 days after a full pass.

The Aun rule: keeping the cycle in your head

A cycle is little use if you cannot remember it. For the octaeteris there was a mnemonic that does exactly that, preserved in a Swedish verse: "Tunglet skiuter tolf och tiog," the Moon jumps twelve and twenty.[6]

What it tracks is the year-to-year shift of full-moon dates. Five times the date moves back twelve days, three times forward twenty. Work it through and it cancels: five times minus twelve gives sixty back, three times plus twenty gives sixty forward. After eight steps the Moon stands where it began. The three twenty-day jumps are the leap years; wherever a thirteenth month goes in, the date jumps forward instead of back.

The rule carries the name of the legendary King Aun, to whom tradition assigns a 300-year life. Andreas Nordberg reads this as folk memory of a longer cycle of 304 years, derived as 16 times 19.[7] The same number 304 appears in Greek astronomy, where Hipparchus quadrupled the 76-year cycle. Both routes reach the same period, which proves no borrowing; 304 falls out of multiplying the 19-year cycle.

One qualification belongs here: the verse itself is late. Olaus Rudbeck recorded it in the 17th century, so it is early modern Swedish and not runic.[6] The eight-year rhythm connects to runes by another route, through the Blekinge runestones.

Uppsala, Lejre, and the counting problem

The eight-year beat is attested more than once, though in a form that puzzles at first: the sources speak of feasts "every nine years."

Adam of Bremen reports the great sacrificial feast at Old Uppsala around 1075, and Thietmar of Merseburg the Danish Lejre around 1015, there in January and with 99 people sacrificed along with as many horses.[8] Different places, different centuries, the same rhythm.

The contradiction dissolves in the counting. These sources count inclusively, taking in both the first and the last year. Wait eight years from one feast to the next and you have touched nine. The same logic sits behind the French quinze jours for a fortnight. An eight-year interval thus becomes a nine-year feast without anything changing in the calendar.

In the Germanic calendar these years carry an especially large midwinter feast lasting nine nights. The Ártala app marks them as Aun years.

What the octaeteris is not

Two confusions are common enough to name.

The 33-year cycle is no relation. It describes the drift of a lunar calendar that is precisely not bound to the Sun, and it is not a leap cycle at all. The octaeteris does the opposite.

Ginzel also describes an eight-year cycle in Turkish calendars, made of 2,835 days, filling exactly 405 weeks.[9] Despite the shared number this is not the octaeteris: that cycle binds the lunar calendar to the week, not to the Sun.

For how differently cultures resolved the same discrepancy, see the survey on the history of lunar calendars.