Metonic cycle
Metonic cycle (Greek Μέτωνος κύκλος ) or Metonic cycle (also Enneakaidekaeteris, Enneadekaeteris; Greek εννεαδεκαετηρίς: " nineteen " ) denotes
- A period that is both 19 solar years and 235 lunar periods long (both soft LAYOUT only about two hours from each other ),
- A suspected calendar system that the ancient Greek astronomer Meton Euctemon and in the fifth century BC lined up, in the 19 years contained 6940 days,
- And thus the possibility for a 19-year calendar cycle, which includes 12 years with exactly 12 months and 7 years 13 months.
The de facto equality of the two astronomical LAYOUT (19 x 365.25 days = 235 lunations ) and their length of about 6940 days was known since ancient times, and among the Babylonians the basis of their lunar calendar. Meton was next Euctemon the first Greek astronomer and probably the first Greeks, who learned of it. Why later Greek historians exclusively so brought his name to connect to is not known. A neutral term is Lunisolarzyklus.
- 2.1 19 calendar years
- 2.2 235 lunar months
- 3.1 19 calendar years
- 3.2 235 lunar months
History
Meton as a contemporary of Euctemon
Neither of Euctemon still of Meton are provided with written records. Both will only be disclosed isolated from a century after their work. The name Euktemons happens quite frequently. Meton is mentioned in connection with the observation of the summer solstice in the year 432 BC and the establishment of an astronomical and weather forecast calendar ( Parapegma ). The fact that both worked together, is not certain. The knowledge of Greek astronomy until the first century BC has Geminus of Rhodes summarized. He calls the name Metons not and leads the " nineteen -year cycle " in a calendar system to "Astronomers from the school of Euctemon, Philippos and Callippus " back. The latter two lived only a century after Euctemon and Meton.
The historical sources
In the fourth century BC, Eudoxus of Cnidus mentioned in Greek literature a " nineteen -year period of Euctemon ". A short time later Meton was first mentioned by Theophrastus in this context. A century later, calls Aratus of Soli the astronomer Callippus, the BC, the " nineteen -year Metonic calendar system " modified in the year 330. Philochorus reported that Meton, built a Heliotropion that the destination of the Summer Solstice served on the Pnyx. In Eudoxus Papyrus, which was written in Giza by 190 BC, and in the writings of Geminus of Rhodes, which emerged about 70 BC, Democritus, Eudoxus, Euctemon and Callippus are called, but not Meton.
Only the historian Diodorus mentions a Parapegma in conjunction of the summer solstice as " nineteen -year cycle ( έννεακαιδεκαετηρίδα ), the Meton, son of Pausanias introduced ". Vitruvius mentions among astronomers, who had developed a related weather forecasts Calendar ( Parapegma ), next Euctemon and Meton all aforementioned name. Claudius Ptolemy records in his astronomical records of the Almagest only once over a " nineteen -year period " with the background of an observed by Meton and Euctemon summer solstice.
From the ancient traditions is not clear who has designed the model of the " Metonic calendar system " and how it looked. Often a joint work of Meton and Euctemon is suspected. The modern critical assessment by Otto Neugebauer reduced calendar system to the undertaking given by his patron identification of 19 years with 6940 days. Meton would thus indirectly specified only the length of the solar year, created a pure solar calendar, so that the annual weather report contained in his Parapegma would receive eternal validity. Thus, it remains uncertain whether the Meton period of 19 solar years or 6940 days ever sat with moon periods equal to 235 and from herleitete an application.
The application of a period in the Easter calculation ( Computus ) that is both 19 solar years and 235 lunar periods long, yet is inextricably bound up with the name Metons, notwithstanding that the astronomical background of the Metonic cycle was already known before Meton and that the Meton period is equated not with 6940, but since Callippus with 6939.75 days.
Meton and the summer solstice in 432 BC
Diodorus writes that Meton in the same year, as Apseudes in Athens the office of archon eponymous held on the 13th day of the month Skirophorion laid the beginning of his calculated nineteen -year calendar system. This month was the last of the fourth year of the 86th Olympiad, which ranged 433-432 BC. Claudius Ptolemy noticed that Meton and Euctemon observed in this context, the summer solstice in the year 432 BC. In the same text he gives as a day for the 21 Phamenoth in the Egyptian calendar. This is in the Julian calendar June 27 (June 22 in the Gregorian calendar ), and also applies from today's perspective as a reliable date for the summer solstice in the year 432 BC. Neulicht This fell to 16 June in the Julian ( 11 June in the Gregorian ) calendar. Assuming that the terminology used in Athens months coincided with the phases of the moon, Meton had found too late the summer solstice day: 1 Skirophorion on June 16; 13 Skirophorion on June 28 ( Julian dates ).
Otto Neugebauer already draws from the entry of the 13th Skirophorion as the start date to conclude that Meton have not tried to create a new calendar year, but was only looking for a unique starting point in the solar year for the compilation of a Parapegmas. A calendar year, he would have had to begin on the day of a new lunar month ( Neulicht ). Such did not fall in 432 BC along with the Somme summer solstice. The nineteen -year calendar Metons, which the Greeks used according to Diodorus in his time, he considers this Parapegma.
Distribution of 235 lunar months in 6940 days
Calendar months always consist of an integral number of days. Months, the phases of the moon ( mean period: about 29.53 days ) to follow are, in annäherndem change 29 days ( hollow months) and 30 days ( full months ) long. The Metonic period of 6940 days can be uniquely composed only of 110 hollow months and 125 full months. Control calculation: 110.29 125.30 = 3190 3750 = 6940th Because the number of hollow and full months is not equal, a regular change is not an option in the order. Whether the astronomers of ancient Greece formed from six hollow and six full months, and occasionally leap years with an extra month after the Babylonian model normal years, is not known. Geminus has Euctemon to the following indirect method that leads to a favorable result from the full and half months: Allen 235 months are formally first 30 days. The sum is too large with 7050 days to 110 days. Therefore, every 64th day of 7050 days is skipped, so you get to 6940 days and being mostly a hollow follows a full month. Fifteen times follow each two full months. Would have been that this approach actually applicable, is supported by two works by Fotheringham (1924 ) and van der Waerden ( 1960).
But Geminus also reports that the calculations of the Euctemon not related to the assumed his ( Geminus ') time length of 365.25 days for the solar year in compliance, and noted in conclusion that the " erroneous excess of the later of astronomers from the school Callippus has been corrected by an improved nineteen -year cycle. "
Differences in a nineteen -year-old calendar system for 6940 days
Calculation with the present values of the solar year and the lunar period ( lunation ):
19 calendar years
19 calendar years are 0.3982 days too long. The calendar, after approximately 48 years compared to the solar year by one day.
235 lunar months
235 lunar months are 0.31135 days too long. The calendar goes to about 755 lunar months ( about 61 calendar years ) compared to the moon periods by one day.
A nineteen year old calendar system to 6939.75 days
A century after Meton corrected Callippus indirectly, the 19 -year period of 6939.75 days. The specified in whole days Kallippische cycle divides 76 years 27'759 days. The first known use of the length contained therein of 365.25 days for the single year happened in a in Egypt at the time of Ptolemy III. in the third century BC briefly used a solar calendar. Whether knowing the year length of 365.25 days was taken over by Callippus, is not known. The involvement of an additional day every four years, was later adopted by the Julian calendar, after Julius Caesar had personally experienced in Egypt it. At the time of Jesus Christ, a bound lunar calendar was used in Palestine. The memory of the Christians at Easter, the "Day of the Resurrection of Jesus Christ" is based on this calendar, which is within the Julian solar calendar ( and the improved Gregorian calendar ) continue to apply. Binding to the lunar months is embodied in the fact that the Easter Sunday to be followed by the first full moon of spring, so is on the first lunar month of the Jewish religious calendar. In determining the year in the Julian (now in the Gregorian ) calendar other Easter date, the 19 -year period plays an essential role.
Calculation with the present values of the solar year and the lunar period ( lunation ):
19 calendar years
19 calendar years are 0.1482 days too long. The calendar, after approximately 128 years compared to the solar year by one day.
This difference was in the Gregorian calendar reform virtually eliminated by the calendar on average every 133.3333 years a leap fails ( Sun equation).
235 lunar months
235 lunar months are 0.06135 days too long. The calendar, after approximately 3'830 lunar months ( about 310 calendar years ) compared to the moon periods by one day.
This difference was in the Gregorian calendar reform virtually eliminated by was also determined once a lunar month one day to be set shorter in the Easter calculation on average every 312.5 years ( lunar equation).
Difference between 19 solar years and 235 lunar periods
Calculation with the present values of the solar year and the lunar period ( lunation ):
Difference