Editing Roman calendar (section)

===Republican calendar===
The attested calendar of the [[Roman Republic]] was quite different. It had twelve months, already including [[Ianuarius|January]] and [[Februarius|February]] during the winter.

According to Livy, it was Numa Pompilius, the second king of Rome {{nowrap|(715–673 BC),}} who divided the year into twelve lunar months (History of Rome, I.19). Fifty days, says Censorinus, were added to the calendar and a day taken from each month of thirty days to provide for the two winter months: Januarius (January) and Februarius (February), both of which had 28 days (The Natal Day, XX). This was a lunar year of 354 days but, because of the Roman superstition about even numbers, an additional day was added to January to make the calendar 355 days long. Auspiciously, each month now had an odd number of days: Martius (March), Maius (May), Quinctilis (July), and October continued to have 31; the other months, 29, except for February, which had 28 days. Considered unlucky, it was devoted to rites of purification (februa) and expiation appropriate to the last month of the year. (Although these legendary beginnings attest to the venerability of the lunar calendar of the Roman Republic, its historical origin probably was the publication of a revised calendar by the Decemviri in {{nowrap|450 BC}} as part of the [[Twelve Tables]], Rome's first code of law.)
{{sfnp|Grout|2023}}

The inequality between the lunar year of 355 days and the [[tropical year]] of 365.25 days led to a shortfall over four years of (10.25 × 4) = 41 days.<ref name=mommy/> Theoretically, 22 days were interpolated into the calendar in the second year of the four-year cycle and 23 days in the fourth.<ref name=mommy/> This produced an excess of four days over the four years in line with the normal one day excess over one year. The method of correction was to truncate February by five days and follow it with the intercalary month which thus commenced (normally) on the day after February 23 and had either 27 or 28 days. February 23 was the [[Terminalia (festival)|Terminalia]] and in a normal year it was ''{{lang|la|a.d. VII Kal. Mart.}}'' Thus the dates of the festivals of the last five days of February were preserved<ref name=rupkenuma1>{{harvp|Rüpke|2011|p=[https://books.google.com/books?id=pThna2LDwDsC&pg=PA40 40]}}</ref> on account of them being actually named and counted inclusively in days before the [[kalends]] of March; they were traditionally part of the celebration for the new year. There was occasionally a delay of one day (a {{lang|la|dies intercalaris}} being inserted between February 23 and the start of the {{lang|la|mensis intercalaris}}) for the purpose of avoiding a clash between a particular festival and a particular day of the week (see {{slink|Hebrew calendar|Rosh Hashanah postponement rules}} for another example).  The Roman superstitions concerning the numbering and order of the months seem to have arisen from [[Pythagoreans|Pythagorean]] superstitions concerning the luckiness of [[odd number]]s.<ref name=momma>{{harvp|Mommsen & al.|1864|p=[https://archive.org/stream/historyrome00dickgoog#page/n244/mode/2up 219]}}.</ref>

These Pythagorean-based changes to the Roman calendar were generally credited by the Romans to [[Numa Pompilius]],{{sfnp|Grout|2023}} [[Romulus]]'s successor and the second of [[kings of Rome|Rome's seven kings]], as were the two new months of the calendar.{{sfn|Macrobius|loc=Book I, Ch. 12, §34}}{{sfnp|Kaster|2011|p=153}}{{efn|[[Plutarch]] reports this tradition while claiming that the months had more probably predated or originated with Romulus.<ref name=gossipgirl/><ref name=worchestershire/>}} Most sources thought he had established intercalation with the rest of his calendar.{{citation needed|date=March 2017}} Although [[Livy]]'s Numa instituted a lunar calendar, the author claimed the king had instituted a 19-year system of intercalation equivalent to the [[Metonic cycle]]{{sfnp|Livy|loc=Book I, Ch. 19, §6}} centuries before its development by [[Babylonian astronomers|Babylonian]] and [[Ancient Greek astronomy|Greek astronomers]].{{efn|This equivalence was first described by [[Temple Stanyan|Stanyan]] in his history of ancient Greece.{{sfnp|Stanyan|1707|p=[https://archive.org/stream/grecianhistoryf00stangoog#page/n373/mode/2up 330]}}}} [[Plutarch]]'s account claims he ended the former chaos of the calendar by employing 12{{spaces}}months totalling 354{{spaces}}days—the length of the [[synodic month|lunar]] and [[ancient Greek calendars|Greek years]]—and a biennial intercalary month of 22{{spaces}}days called [[Mercedonius]].<ref name=gossipgirl/><ref name=worchestershire/>

According to Livy's [[Periochae]], the beginning of the consular year changed from March to 1{{spaces}}January in 153{{spaces}}BC to respond to a rebellion in Hispania.<ref>Livy, ''Periochae'', [https://www.livius.org/sources/content/livy/livy-periochae-46-50/#47.1 47.13 and 47.14]: "[47.13] In the five hundred and ninety-eighth year after the founding of the city, the consuls began to enter upon their office on 1{{spaces}}January. [47.14] The cause of this change in the date of the elections was a rebellion in Hispania."</ref> Plutarch believed Numa was responsible for placing January and February first in the calendar;<ref name=gossipgirl/><ref name=worchestershire/> [[Ovid]] states January began as the first month and February the last, with its present order owing to the [[Decemvirs]].{{sfnp|Ovid|loc=Book II}}{{sfnp|Kline|2004|loc=[https://www.poetryintranslation.com/PITBR/Latin/OvidFastiBkTwo.php#anchor_Toc69367683 Book II, Introduction]}} [[W. Warde Fowler]] believed the [[Ancient Roman religion|Roman priests]] continued to treat January and February as the last months of the calendar throughout the Republican period.{{sfnp|Fowler|1899|p=5}}

{|class="wikitable" style="margin:.5em auto;line-height:1.4"
|+ Roman Republican calendar ({{circa|700 BC}} or {{circa|450 BC}} – 46 BC)
|-
!scope="col" colspan="3" rowspan="2"| English
!scope="col" colspan="3" rowspan="2"| Latin
!scope="col" colspan="2" rowspan="2"| Meaning
!scope="col" colspan="4"| Length in days{{sfn|Macrobius}}{{sfnp|Kaster|2011}}<ref name=gossipgirl>{{harvp|Plutarch|loc=''Life of Numa'' section XVIII}}.</ref><ref name=worchestershire>{{harvp|Perrin|1914|pp=[https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Lives/Numa*.html#Romulan_year 368 ff]}}.</ref>
|-
!scope="col" style="line-height:1.25"| 1st<br /> year<br /> <small>([[Common year|cmn.]])</small>
!scope="col" style="line-height:1.25"| 2nd<br /> year<br /> <small>([[Leap year|leap]])</small>
!scope="col" style="line-height:1.25"| 3rd<br /> year<br /> <small>(cmn.)</small>
!scope="col" style="line-height:1.25"| 4th<br /> year<br /> <small>(leap)</small>
|-style="background:#CFC"
|style="text-align:right"| 1. ||colspan="2"| January
|style="text-align:right"| I. ||colspan="2"| [[Mensis Ianuarius]]
|colspan="2"| Month of [[Janus]]
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|-style="background:#CFC"
|rowspan="2" style="text-align:right"| 2. ||colspan="2"| February
|rowspan="2" style="text-align:right"| II. ||colspan="2"| [[Mensis Februarius]]
|colspan="2"| Month of the [[Lupercalia|Februa]]
|style="text-align:center"| 28
|style="text-align:center"| 23
|style="text-align:center"| 28
|style="text-align:center"| 23
|-style="background:#CFC"
|style="border-top:hidden;border-bottom:hidden;width:1em"| &nbsp; || Intercalary Month
|style="border-top:hidden;border-bottom:hidden;width:1em"| &nbsp; || Intercalaris Mensis ([[Mercedonius]])
|style="border-top:hidden;border-bottom:hidden;width:1em"| &nbsp; || Month of Wages
|style="border-top:hidden;text-align:center"| &nbsp;
|style="text-align:center"|'''27'''
|style="border-top:hidden;text-align:center"| &nbsp;
|style="text-align:center"|'''28'''
|-
|style="text-align:right"| 3. ||colspan="2"| March
|style="text-align:right"| III. ||colspan="2"| [[Martius (month)|Mensis Martius]]
|colspan="2"| Month of [[Mars (mythology)|Mars]]
|style="text-align:center"| 31
|style="text-align:center"| 31
|style="text-align:center"| 31
|style="text-align:center"| 31
|-
|style="text-align:right"| 4. ||colspan="2"| April
|style="text-align:right"| IV. ||colspan="2"| [[Mensis Aprilis]]
|colspan="2"| Month of [[Aphrodite]] – from which the [[Etruscan language|Etruscan]] Apru might have been derived
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|-
|style="text-align:right"| 5. ||colspan="2"| May
|style="text-align:right"| V. ||colspan="2"| [[Mensis Maius]]
|colspan="2"| Month of [[Maia]]
|style="text-align:center"| 31
|style="text-align:center"| 31
|style="text-align:center"| 31
|style="text-align:center"| 31
|-
|style="text-align:right"| 6. ||colspan="2"| June
|style="text-align:right"| VI. ||colspan="2"| [[Iunius (month)|Mensis Iunius]]
|colspan="2"| Month of [[Juno (mythology)|Juno]]
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|-
|style="text-align:right"| 7. ||colspan="2"| July
|style="text-align:right"| VII. ||colspan="2"| [[Mensis Quintilis]]
|colspan="2"| Fifth Month (from the earlier calendar starting in March)
|style="text-align:center"| 31
|style="text-align:center"| 31
|style="text-align:center"| 31
|style="text-align:center"| 31
|-
|style="text-align:right"| 8. ||colspan="2"| August
|style="text-align:right"| VIII. ||colspan="2"| [[Mensis Sextilis]]
|colspan="2"| Sixth Month
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|-
|style="text-align:right"| 9. ||colspan="2"| September
|style="text-align:right"| IX. ||colspan="2"| [[September (Roman month)|Mensis September]]
|colspan="2"| Seventh Month
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|-
|style="text-align:right"| 10. ||colspan="2"| October
|style="text-align:right"| X. ||colspan="2"| [[October (Roman month)|Mensis October]]
|colspan="2"| Eighth Month
|style="text-align:center"| 31
|style="text-align:center"| 31
|style="text-align:center"| 31
|style="text-align:center"| 31
|-
|style="text-align:right"| 11. ||colspan="2"| November
|style="text-align:right"| XI. ||colspan="2"| [[November (Roman month)|Mensis November]]
|colspan="2"| Ninth Month
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|-
|style="text-align:right"| 12. ||colspan="2"| December
|style="text-align:right"| XII. ||colspan="2"| [[December (Roman month)|Mensis December]]
|colspan="2"| Tenth Month
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|style="text-align:center"| 29
|-
!scope="row" colspan="8" style="text-align:right"| Whole year:
|style="text-align:center"| 355
|style="text-align:center"| 377
|style="text-align:center"| 355
|style="text-align:center"| 378
|}

According to the later writers Censorinus and Macrobius, to correct the mismatch of the correspondence between months and seasons due to the excess of one day of the Roman average year over the tropical year, the insertion of the intercalary month was modified according to the scheme: common year (355 days), leap year with 23-day February followed by 27-day Mercedonius (377 days), common year, leap year with 23-day February followed by 28-day Mercedonius (378 days), and so on for the first 16 years of a 24-year cycle. In the last 8 years, the intercalation took place with the month of Mercedonius only 27 days, except the last intercalation which did not happen. Hence, there would be a typical common year followed by a leap year of 377 days for the next 6 years and the remaining 2 years would sequentially be common years. The result of this twenty-four-year pattern was of great precision for the time: 365.25 days, as shown by the following calculation:

<math>\frac{355\times 13+377\times 7+378\times 4}{24}=\frac{8,766}{24}=365\tfrac{1}{4}</math>

The consuls' terms of office were not always a modern calendar year, but ordinary consuls were elected or appointed annually. The traditional [[list of Roman consuls]] used by the Romans to date their years began in 509 BC.<ref name=matlock>{{harvp|Mathieson|2003|p=[https://books.google.com/books?id=krcp3GU2MssC&pg=PA14 14]}}.</ref>

{{anchor|Gnaeus Flavius}}