Golden number (time)

Last updated

Month of January from Calendarium Parisiense (fourth quarter of the 14th c.). The golden numbers, in the leftmost column, indicate the date of the new moon for each year in the 19-year cycle Calendarium Parisiense enh.jpg
Month of January from Calendarium Parisiense (fourth quarter of the 14th c.). The golden numbers, in the leftmost column, indicate the date of the new moon for each year in the 19-year cycle

A golden number (sometimes capitalized) is a number assigned to each year in sequence which is used to indicate the dates of all the calendric new moons for each year in a 19-year Metonic cycle. They are used in computus (the calculation of the date of Easter) and also in Runic calendars. The golden number of any Julian or Gregorian calendar year can be calculated by dividing the year by 19, taking the remainder, and adding 1. (In mathematics this can be expressed as (year number modulo 19) + 1.)

Contents

For example, 2024 divided by 19 gives 106, remainder 10. Adding 1 to the remainder gives a golden number of 11.

The golden number, as it was later called, first appears in a calendar composed by Abbo of Fleury around the year 1000. Around 1162 a certain Master William referred to this number as the golden number "because it is more precious than the other numbers." [1] The name refers to the practice of printing golden numbers in gold. [2] The term became widely known and used, in part through the computistic poem Massa Compoti written by Alexander de Villa Dei around 1200. [3]

See also

Related Research Articles

<span class="mw-page-title-main">Hebrew calendar</span> Lunisolar calendar used for Jewish religious observances

The Hebrew calendar, also called the Jewish calendar, is a lunisolar calendar used today for Jewish religious observance and as an official calendar of Israel. It determines the dates of Jewish holidays and other rituals, such as yahrzeits and the schedule of public Torah readings. In Israel, it is used for religious purposes, provides a time frame for agriculture, and is an official calendar for civil holidays alongside the Gregorian calendar.

<span class="mw-page-title-main">Lunisolar calendar</span> Calendar with lunar month, solar year

A lunisolar calendar is a calendar in many cultures, incorporating lunar calendars and solar calendars. The date of lunisolar calendars therefore indicates both the Moon phase and the time of the solar year, that is the position of the Sun in the Earth's sky. If the sidereal year is used instead of the solar year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In some cases ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.

<span class="mw-page-title-main">Metonic cycle</span> 19-year pattern in lunisolar calendars

The Metonic cycle or enneadecaeteris is a period of almost exactly 19 years after which the lunar phases recur at the same time of the year. The recurrence is not perfect, and by precise observation the Metonic cycle defined as 235 synodic months is just 2 hours, 4 minutes and 58 seconds longer than 19 tropical years. Meton of Athens, in the 5th century BC, judged the cycle to be a whole number of days, 6,940. Using these whole numbers facilitates the construction of a lunisolar calendar.

<span class="mw-page-title-main">New moon</span> First lunar phase, the definition varies

In astronomy, the new moon is the first lunar phase, when the Moon and Sun have the same ecliptic longitude. At this phase, the lunar disk is not visible to the naked eye, except when it is silhouetted against the Sun during a solar eclipse.

The Julian day is the continuous count of days since the beginning of the Julian period, and is used primarily by astronomers, and in software for easily calculating elapsed days between two events.

<span class="mw-page-title-main">Dionysius Exiguus</span> Byzantine saint (c. 470 – c. 544)

Dionysius Exiguus was a 6th-century Eastern Roman monk born in Scythia Minor. He was a member of a community of Scythian monks concentrated in Tomis, the major city of Scythia Minor. Dionysius is best known as the inventor of Anno Domini (AD) dating, which is used to number the years of both the Gregorian calendar and the (Christianised) Julian calendar. Almost all churches adopted his computus for the dates of Easter.

The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.

<span class="mw-page-title-main">Date of Easter</span>

As a moveable feast, the date of Easter is determined in each year through a calculation known as computus. Easter is celebrated on the first Sunday after the Paschal full moon. Determining this date in advance requires a correlation between the lunar months and the solar year, while also accounting for the month, date, and weekday of the Julian or Gregorian calendar. The complexity of the algorithm arises because of the desire to associate the date of Easter with the date of the Jewish feast of Passover which, Christians believe, is when Jesus was crucified.

The epact used to be described by medieval computists as the age of a phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, the epact is reckoned as the age of the ecclesiastical moon on 1 January. Its principal use is in determining the date of Easter by computistical methods. It varies from year to year, because of the difference between the solar year of 365–366 days and the lunar year of 354–355 days.

Dominical letters or Sunday letters are a method used to determine the day of the week for particular dates. When using this method, each year is assigned a letter depending on which day of the week the year starts. The Dominical letter for the current year 2024 is GF.

A blue moon is defined by the Oxford English Dictionary (OED) as (1) A moon that appears blue; (2) a long or indefinite length of time; a rarely recurring period or event ; (3) a second full moon in a calendar month, or formerly the third full moon in a season containing four full moons.

<span class="mw-page-title-main">Mesoamerican calendars</span>

The calendrical systems devised and used by the pre-Columbian cultures of Mesoamerica, primarily a 260-day year, were used in religious observances and social rituals, such as divination.

Annianus of Alexandria was a monk and writer who flourished in Alexandria during the pontificate of Theophilus I around the beginning of the 5th century.

The Buddhist calendar is a set of lunisolar calendars primarily used in Tibet, Cambodia, Laos, Myanmar, Bangladesh, India, Sri Lanka, Thailand and Vietnam as well as in Malaysia and Singapore and by Chinese populations for religious or official occasions. While the calendars share a common lineage, they also have minor but important variations such as intercalation schedules, month names and numbering, use of cycles, etc. In Thailand, the name Buddhist Era is a year numbering system shared by the traditional Thai lunar calendar and by the Thai solar calendar.

<span class="mw-page-title-main">Runic calendar</span> Perpetual calendar based on the 19-year-long Metonic cycle of the Moon

A Runic calendar is a perpetual calendar, variants of which were used in Northern Europe until the 19th century. A typical runic calendar consisted of several horizontal lines of symbols, one above the other. Special days like solstices, equinoxes, and celebrations were marked with additional lines of symbols.

Anatolius of Laodicea, also known as Anatolius of Alexandria, was a Syro-Egyptian saint and Bishop of Laodicea on the Mediterranean coast of Roman Syria in AD 268. He was not only one of the foremost scholars of his day in the physical sciences, as well as in Aristotelian and Platonic philosophies, but also a renowned computist and teacher of the Neoplatonic philosopher Iamblichus.

The Burmese calendar is a lunisolar calendar in which the months are based on lunar months and years are based on sidereal years. The calendar is largely based on an older version of the Hindu calendar, though unlike the Indian systems, it employs a version of the Metonic cycle. The calendar therefore has to reconcile the sidereal years of the Hindu calendar with the Metonic cycle's near tropical years by adding intercalary months and days at irregular intervals.

An ecclesiastical full moon is formally the 14th day of the ecclesiastical lunar month in an ecclesiastical lunar calendar. The ecclesiastical lunar calendar spans the year with lunar months of 30 and 29 days which are intended to approximate the observed phases of the Moon. Since a true synodic month has a length that can vary from about 29.27 to 29.83 days, the moment of astronomical opposition tends to be roughly 14.75 days after the previous conjunction of the Sun and Moon. The ecclesiastical full moons of the Gregorian lunar calendar tend to agree with the dates of astronomical opposition, referred to a day beginning at midnight at 0 degrees longitude, to within a day or so. However, the astronomical opposition happens at a single moment for the entire Earth: The hour and day at which the opposition is measured as having taken place will vary with longitude. In the ecclesiastical calendar, the 14th day of the lunar month, reckoned in local time, is considered the day of the full moon at each longitude.

The Gregorian calendar is the calendar used in most parts of the world. It went into effect in October 1582 following the papal bull Inter gravissimas issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years differently so as to make the average calendar year 365.2425 days long, more closely approximating the 365.2422-day 'tropical' or 'solar' year that is determined by the Earth's revolution around the Sun.

<span class="mw-page-title-main">Computus clock</span>

A computus clock is a clock equipped with a mechanism that automatically calculates and displays, or helps determine, the date of Easter. A computus watch carries out the same function.

References

  1. Nothaft, C. Philipp E. (2018). Scandalous Error: Calendar Reform and Calendrical Astronomy in Medieval Europe. Oxford: Oxford University Press. pp. 57–58. ISBN   978-0-19-879955-9. Archived from the original on 2021-06-17. Retrieved 2022-01-11.
  2. Pears cyclopaedia 2017-2018 : a book of reference and background information for all the family. Chris Cook (126th ed.). London, England. 2017. ISBN   978-0-14-198554-1. OCLC   990110486.{{cite book}}: CS1 maint: location missing publisher (link) CS1 maint: others (link)
  3. van Wijk, Walter Emile (1936). Le Nombre d'Or: Étude de chronologie technique suivie du texte de la Massa Compoti d'Alexandre de Villedieu [The Golden Number: A Study of the technique of chronology following the text of Massa Compoti by Alexandre de Villedieu] (in French). The Hague: Martinus Nijhoff. Archived from the original on 2020-10-19. Retrieved 2022-01-11.