# Callippian cycle

The Callippic Cycle is called

## General

### Bound lunar calendar: linked to the solar year

At the time of Callippus, bound lunar calendars ( lunisolar calendars ) were in use. The lunar month was approximated to the mean astronomical lunar month ( synodic month ), the length of which was known relatively precisely. The link to the solar year was made with the help of an occasional leap month , which was based on the equation already known to the Babylonians and believed to be correct

• 235 months = 19 years or 940 months = 76 years

could be regulated.

This period, which has already been measured twice, must still be specified in days - the smallest calendar unit. The merit of Callippus (possibly a whole school around him) was to assume a quarter of a day less than usual for 19 years, so that the average calendar year coincided better with the solar year:

• Solar year: 365.2422 days / year
• Meton calendar year: 6940 days ÷ 19 years = 365.2632 days / year; Difference = 0.021 days / year (about 1 day / 48 years)
• Calendar year of Callippus: 27,759 days ÷ 76 years = 365.25 days / year; Difference = 0.0078 days / year (about 1 day / 128 years)

The calendar year of Callippus (from the 4th century BC) was as long as the later Julian calendar year (from the 1st century BC). With the Gregorian reform of the Julian calendar, the remaining difference has been practically eliminated, as one (leap) day is canceled every 133 years on average ( solar equation ).

### The calendar month

In a lunisolar calendar, the calendar month is the primary unit and is aligned with the synodic month. The individual calendar year is a summary of twelve or 13 calendar months, so it has at least two different lengths. When summarizing and choosing empty (29 days each) and full (30 days each) calendar months, it is important to ensure that the Callipean equation

• 940 calendar months = 27,759 days

is fulfilled. One possible solution was to alternate six hollow and six full months. This is initially 76 normal years with a total of 912 months. In 28 years of this a leap month was added, which was 13 times 30 days and 15 times 31 days.

With his measure, Kallippos also achieved that the average calendar month coincides better with the astronomical lunar month than with Meton:

• astronomical lunar month: 29.53059 days,
• Calendar month of the Meton: 6940 days ÷ 235 months = 29.53192 days / month; Difference = 0.001325 days / month (about 1 day / 755 months, about 1 day / 61 years)
• Calendar month of Callippus: 27,759 days ÷ 940 months = 29.53085 days / month; Difference = 0.00026 days / month (about 1 day / 3830 months, about 1 day / 310 years).

The Gregorian reform of the Julian calendar practically eliminates the remaining difference in its lunar application for the Easter calculation by reducing a lunar month in the calendar by one day every 312.5 years ( lunar equation ).

### The Callipean Period in Easter

In the case of the Easter bill, the 76-year Kallippos period is superficially not applied because the addition of a leap day is outsourced from the bill every four years. The 19-year Meton period, which is shortened to 6935 days and consists of 19 calendar years of 365 days each and 115 hollow and 120 full lunar months, becomes visible. The leap day added every four years makes the affected year and the affected lunar month one day longer. In 19 years, an average of 4.75 days are added (five days in three periods, four days in the fourth period), the balance for the Meton period “improved” by Kallippus leads to an average of 6939.75 days. This is followed by three periods with actually 6940 days each and one period with actually 6939 days in length. But every 76-year period consists of the same number, namely 27,759 days.

The length of the Easter cycle with 532 years is the least common multiple (in this case the product) of the leap year period (four years), the weekday period (seven years) and the 19-year period (19 years). Leap year and weekday periods are usually first combined to form the so-called solar circle (28 years). Then this is multiplied by the 19-year period. You can also formally combine the leap year and 19-year period in a first step to form the 76-year Callippic period and offset this against the weekday period. In this way, the Callipean period would remain in the foreground, the length of which, in contrast to the Meton period, consists of a whole number of days.

## history

### Written sources

Written records made by Kallippos himself have not been preserved.

That Kallippos adjusted the calendar year better to the solar year with the help of his 76-year cycle is mentioned in the oldest representation of ancient Greek astronomy made by Geminos of Rhodes . Geminus reported that the calculations of Euktemon (a contemporary of Meton) were inconsistent with the assumed length of 365.25 days for the solar year at his (Geminous') time, and concluded that the “erroneous excess ... of Astronomers from the school of Callippus through an improved ... cycle was corrected. "

In Athens - Meton's hometown - a bound lunar calendar ( Attic calendar ) was already in use, but it was in constant confusion, which is why it is assumed that Meton had already developed his own calendar for reproducible dating of astronomical observations, which Callippus improved and continued used. A modern historian criticizes this already old approach by stating that the Egyptian 365-day solar calendar was also used in Greek astronomy at this time. A calendar from Meton or Callippus had no influence on civil use, because the insertion of a leap month was still made arbitrarily.

The Jewish and Julian calendars are important later calendars with the Callipean length of the middle calendar year of 365.25 days . The cycle was also known in the calendar of ancient China ( Chinese  默 冬 章 Zhang cycle , approx. 2nd century BC).

Whether such a system existed and was used in detail by Kallippos himself has not yet been proven with certainty. The following representations are backward-looking considerations based on reliable knowledge in later times.

### Beginning of the first Callipean calendar period

In the Attic calendar , the first Callipean period began in 330 BC. On the evening of June 28th jul. / 23. June greg. , the day of the solstice . The new light on the first day of the month of Hekatombaion fell in the Attic calendar at dusk on June 29th July. / 24. June greg. .

### Leap years

In 28 of the 76 calendar years (see above) a leap month is added to create a rough link to the solar year. The following diagram shows a possible procedure.

Cycle interval Cycle year Cycle year Cycle year Cycle year Cycle year Cycle year Cycle year Callippian cycle: Fixed leap years in the Callippian calendar system (76 years) 1 (1st to 19th year) 1 3 6th 9 11 14th 17th 2 (20th to 38th year) 20th 22nd 25th 28 30th 33 36 3 (39th to 57th year) 39 41 44 47 49 52 55 4 (58th to 76th year) 58 60 63 66 68 71 74

### Astronomical events

Copies of the astronomical events observed in Athens were available in Alexandria . The scribes from Greece noted in Alexandria the corresponding date of correspondence of the ancient Egyptian calendar .

cycle Cycle year year Attic date Ancient Egyptian date Julian calendar 1. Achet I (July calendar) Callippi cycle: astronomical events in correspondence with the ancient Egyptian calendar 1 36 (leap year) 295 BC Chr. 25. Poseideon (6th month) 16. Achet II 20th of December November 5th (295 BC) 1 36 (leap year) 294 BC Chr. 15. Elaphebolion (9th month) 5. Peret I 9th March November 5th (295 BC) 1 47 (leap year) 283 BC Chr. 8. Anthesterion (8th month) 29. Achet III January 29th November 2nd (284 BC) 1 48 (normal year) 283 BC Chr. 6th pyanopsion (4th month) 7. Achet I November 8th November 2nd (283 BC)

## literature

• L. Bartel van der Waerden: Greek astronomical calendars. II. Callippos and his calendar. In: Archive for History of Exact Sciences . 29, 2, 1984, , pp. 115-124.
• James Evans: The History & Practice of Ancient Astronomy . Oxford University Press, New York et al. 1998, ISBN 0-19-509539-1 , pp. 186-187.
• Alexander Jones: Calendrica I. New Callippic Dates . In: Journal of Papyrology and Epigraphy . 129, 2000, , pp. 141-158.
• Alexander Jones (Ed.): Astronomical Papyri from Oxyrhynchus . (P. Oxy. 4133-4300a). Vol. I-II. American Philosophical Society, Philadelphia PA 1999, ISBN 0-8716-9233-3 ( Memoirs of the American Philosophical Society 233).
• Otto Neugebauer , Richard Anthony Parker , Karl-Theodor Zauzich: A demotic lunar Eclipse Text of the first Century BC In: Proceedings of American Philosophical Society . 125, No. 4, 1981, , pp. 312-327.

## Remarks

1. In the historical sciences, the strict scientific distinction between a cycle and the duration ( period ) between cyclical events is generally not usual.
2. Otto Neugebauer: The Metonic Cycle and the Callippic . P. 622 f.
3. Heinz Zemanek “Calendar and Chronology” Oldenbourg 1990, p. 43: The moon circle was already known to Babylonian astronomers from about 747 BC. Known.
4. In the early days of the Julian calendar, the leap day had no date of its own, it left no trace in the calendar. February 24th was counted twice: ante diem to sextum calendas martias
5. Heiner Lichtenberg only mentions the Callippian period in his formula, which extends Gaussian Easter formula . [1]
6. ^ J. Evans and JL Berggren: Geminus, Introduction to the Phenomena , Princeton University Press, 2006, VIII 58 and 59, pages 184 and 185
7. a b Hans Kaletsch, day and year, the history of our calendar. Artemis, 1970, page 53, 2nd and 3rd paragraph
8. ^ Otto Neugebauer : A History of Ancient Mathematical Astronomy , Springer 1975, p. 617
9. ^ Bernhard Peter: Calendar and time calculation: The lunisolar calendar in the Chinese calendar . Web document  - kultur-in-asien.de
10. The day change in the Attic calendar with the sunset. The June 28th of the Attic calendar therefore began only at dusk on the Julian June 28th.
11. The solstice took place on June 28, 330 BC. (Julian calendar) around 12:51 pm. In the Attic calendar, the solstice fell on the previous day, which only ended with sunset on the Julian June 28th.
12. The sunset in Athens took place on June 29th around 7.45pm; the crescent moon was visible from around 8:15 p.m. before the moon set around 8:45 p.m.
13. Alexander Jones: Calendrica I: New Callippic Dates . P. 145.
14. Alexander Jones: Calendrica I: New Callippic Dates . P. 142.
15. a b The 1st Hekatombaion probably fell on July 1st, 295 BC. Chr. (Julian calendar), the new light certainly on July 2nd.
16. ^ 1 Poseidon fell on November 26, 295 BC. (Julian calendar), the new light on November 27th.
17. The 1st Elaphebolion fell on February 23, 294 BC. (Julian calendar), the new light on February 24th.
18. The 1st Hekatombaion probably fell on June 29, 284 BC. (Julian calendar), the new light certainly on June 30th. The leap month probably began on June 19, 283 BC. BC, since the new light on June 20, 283 BC. BC fell.
19. The 1st Anthesterion fell on January 22nd, 283 BC. (Julian calendar), the new light on January 23rd.
20. The 1st pyanepsion fell on November 3rd, 283 BC. (Julian calendar), the new light on November 14th.