# GLOSSARY OF COMPUTISTICAL TERMS

**argumentum:**
A computistical formula.

**bissextus:**
Leap year (*annus bissextilis*) or leap-year day. In the Julian calendar, the leap-year day was inserted on the 6th kalends of March (24 February). The intercalated day was thus the "second (*bissextus*) 6th (kalends)."

**common year:**
A year in which there are 12 lunar months (354 days), in contrast to an embolismic year of 13 lunar months (384 days).

**concurrent: **
In the context of the 19-year cycle used by Bede and his successors, the concurrent is the number of the weekday of 24 March, counted from Sunday. Since the tropical year of 365 days contains 52 weeks plus 1 day, the concurrent will advance by one each year. However, the insertion of leap-year day will advance the concurrent by two every fourth year. It therefore requires 28 years for the cycle of concurrents to be complete: 7 weekdays, times 4 for the leap years.

**cycle: **
see "luni-solar cycle", "Paschal cycle".

**decennovennal cycle:**
see "Paschal cycle".

**dominical letters:**
The sequence of letters A-G inscribed against the dates of a calendar. The dominical letter indicates the Sundays (*dies dominica*) for a given year in the solar cycle. For example, if the year in question is year 1 of the cycle, the dominical letter is F, and all days in the calendar marked F will be Sundays. There are two dominical letters in leap years: the second becomes valid after the intercalary day in inserted on 24 February.

**embolism:**
Because the Julian solar calendar is 365 days long, and 12 lunar months of 29½ days total 354 days, the age of the Moon on any given calendar date increases by 11 days each year. When the accumulation tops 30 days, the maximum length of a calculated lunar month, an additional 13th lunar month is deemed to be inserted within the calendar year. This additional intercalated lunation is called an "embolism" and a year with 13 lunations is "embolismic".

**embolismic year: **
A year in which there are 13 lunar months, due to the insertion of the embolism (q.v.). Contrasts with common year.

**epact: **
Generally, the age of the moon on any given day. Specifically, and in the context of Dionysius Exiguus' 19-year cycle, "epact" refers to the age of the Moon on 22 March. In 84-year cycles, and in the tables of Victorius, the epact is the age of the Moon on 1 January.

**"full" lunar month: **
A synodic lunar month or lunation is slightly more than 29 1/2 days. However, in order to harmonize solar and lunar cycles (see "luni-solar cycle" and "luni-solar calendar" below) a normalized lunar month expressed as a number of whole solar calendar days must be adopted. Medieval computists consequently adopted the fiction that lunations are alternately 29 and 30 days long. 29-day lunations are "hollow", and 30-day lunations "full". Full and hollow lunations alternate throughout the year, January's (that is, the lunation terminating within the month of January) being full, February's hollow, etc. All embolisms are full.

**Golden Numbers: **
Numbers from 1-19 inscribed against dates in the calendar, and indicating the years of the 19-year Paschal cycle in which the new moons will fall.

**hendecas:**
The final 11 years of the 19-year cycle, where the pattern of common and embolismic years (q.v.) is CCECCECCECE. See also ogdoas.

**"hollow" lunar month: **
see "full lunar month".

**indiction:** A Roman bureaucratic cycle of 15 years, instituted in the reign of Diocletian and Constantine for taxation purposes. From the time of Constantine the cycle began on 1 September, the beginning of the fiscal year. Under Justinian, indictions became part of the official dating style for government documents. They were included in the Alexandrian Paschal tables, and hence migrated via Dionysius Exiguus into the standard Paschal tables used in the medieval west. Western inexperience with indictions led to some confusion as to their start date: Bede (De temporum ratione 48) began them on 24 September, and most computists simply assumed they were coterminous with the calendar year.

**intervallum:** The number of weeks separating Christmas from the beginning of Lent.

**leap of the Moon:**
see "*saltus lunae*".

**lunar cycle: **
The lunar cycle, as it was understood by medieval computists, is a 19-year cycle beginning when the moon is new on 1 January. Its structure replicates the Alexandrian Paschal 19-year cycle, but year 1 of the lunar cycle corresponds to year 3 of the Paschal cycle. The origin and function of this cycle is obscure, but it was enshrined in the Paschal table of Cyril of Alexandria, and carried over into the Paschal tables of Dionysius Exiguus and Bede.

**lunation:**
The period between one new Moon and the next, now calculated as approximately 29.5306 days. Also known as "synodic lunar month." Computists consider a lunation to "belong" to the solar month in which it ends, *i.e.* the lunation of January is the lunation which ends within the calendar month of January.

**luni-solar calendar:**
A lunar calendar adjusted to maintain the relationship of lunar months to solar seasons, by the insertion of embolisms.

**luni-solar cycle: **
A whole number of solar years into which a whole number of lunar months can be divided, so that the lunar phases fall on the same solar calendar dates after the end of the cyclic period.

**Nisan: **
A month in the Jewish lunar calendar, corresponding to the first lunation of spring. Bede identifies Nisan with April. The Christian rules for determining "Nisan" diverged from the Jewish ones. The 14th day of the Christian "Nisan" is the Paschal *terminus*.

**ogdoas: **
The first 8 years of the 19-year cycle, where the pattern of common and embolismic years is CCECCECE. See also *hendecas*.

**Quartodecimans: **
Early Christian communities in Syria and Asia Minor who celebrated Easter on the fourteenth day of the first lunation of spring, *i.e. *at the same time as the Jewish Passover, regardless of weekday.

**Paschal cycle:**
A luni-solar cycle modified to permit repeated projection of the dates of Easter into the future, normally by the incorporation of a third cycle to accommodate the shifting date of Sunday in the Julian calendar (see "concurrent", "solar cycle"). The 19-year luni-solar Paschal cycle used in the West is based on the cycle of Meton of Athens, as modified by the computists of Alexandria in the Patristic period. When combined with the 28-year cycle of recurrent weekdays, a perpetual Great Paschal Cycle of 532 years results.

**Paschal table: **
A table projecting the dates of Easter for a number of years into the future. A Paschal table is normally based on a Paschal cycle, and is often the means for testing the validity of the cycle.

**Paschal terminus:**
The date of 14 Nisan (as calculated by Christians) in any given year, the first Sunday after which will be Easter.

**regular: **
Bede uses the term "regular" to denote a number of computistical figures, but the most important and commonly used are the solar and lunar regulars. The solar regular is a number assigned to each month, and which represents the interval between the weekday of 24 March (the concurrent) and the weekday of the first day of the month in question. Solar regular plus annual concurrent yields the weekday of the first day of the month in the year in question. The monthly lunar regular is the age of the Moon on the first day of the month in question in year 1 of the 19-year Paschal cycle. The lunar regular, when added to the annual epact, will yield the age of the Moon on the first of the month in that year.

**saltus lunae:**
All luni-solar cycles gradually accumulate an additional *calculated* lunar day, because the average lunation is slightly longer than the notional month of 29.5 days. To bring the count of lunar days back into phase with reality, the calculated age of the Moon must from time to time "jump over" a day -- in other words, a day is deducted from the lunar count. This is called the *saltus lunae*. In the 19-year Paschal cycle, there is one *saltus* in each cycle, and it occurs in the final year. Bede (*De temporum ratione *42) argued that the *saltus* should take place in the final lunation of year 19 to avoid the need for adjustments to the lunar count for preceding months, but the more usual locus was the lunation of July.

**siderial lunar month:**
The length of time required for the moon to complete a circuit of the zodiac. It is sometimes referred to by computists as the "lunar year."

**solar or weekday cycle: **
The solar year of 365 days fills 52 weeks plus one day. Therefore, if 1 January falls on a Monday this year, it will fall on Tuesday next year. In leap years, the intercalation of an extra day in February results in an increment of two days; in other words, if this is a leap year, 1 January will fall on a Wednesday next year. The pattern of weekday on which any calendar date will fall repeats over 28 years -- seven weekdays times the four leap years.

**synodic lunar month:**
see "lunation."

**year: **The tropical or solar year is the period of time required for the Earth to orbit the Sun, or in medieval terms, the time required for the Sun to complete its journey through the zodiac. The modern length of the tropical year is 365.2422 days. A lunar year is 12 or 13 lunations, depending on whether the year is common or embolismic.