# Computus

The computus is the method of determining the date of Easter and thus the moveable feasts of the liturgical year. Since the date of Easter is nominally related to the Jewish calendar, and the Jewish calendar is a lunar calendar, it is necessary to perform a series of calculations to determine the date according to the solar calendar used by the Church. Fundamental to these are a series of cycles, the longest of which is 532 years, and from these cycles a number of constants:

• ʿāmata qamar (ዓመተ፡ ቀመር፡), the position within the cycle of 532 years
• manbar (መንበር፡), the position within a shorter cycle of 19 years
• ʾabaqte (አበቅቴ፡) and maṭqǝʿ (መጥቅዕ፡), which recur in 19-year cycles and always add up to 30 (in light of this, only one is strictly necessary)
• ṭǝntyon (ጥንትዮን፡), the day of the week of the first day of the year, where 1 = Wednesday, 2 = Thursday, etc.

# Method of Calculation

(See below for an explanation of the mathematical notation used here.)

The position within the 532-year cycle (ʿāmata qamar) is most easily determined using the year according to the ʿāmata ʿālam (ዓመተ፡ ዓለም፡, 'era of the world'), the system of counting years since the theoretical beginning of Creation, fixed at 5493 B.C. As an example, let us use the year 7000 ʿāmata ʿālam, corresponding to 1507/1508 A.D.:

7000 mod 532 = 84

From here we can determine the manbar, the position within the 19-year cycle:

84 mod 19 = 8

Using the manbar, we can determine the ʾabaqte and maṭqǝʿ, of which we only really need one. In this case, we can use the maṭqǝʿ, which represents the theoretical date of the Jewish New Year.

(8 - 1) × 19 mod 30 = 13

The date of the theoretical Jewish New Year is always either at the end of the month of Maskaram or the beginning of Ṭǝqǝmt. The rule in this case is that if the number is greater than 14 then it is the date in Maskaram; if it is less than 14, then it is the date in Ṭǝqǝmt.

From 13 Ṭǝqǝmt, we add 190 days to determine the theoretical Jewish Passover, and then Easter is the first Sunday after this. This is why ṭǝntyon is important, as it helps us to determine on which day of the week the theoretical Passover occurs. To find ṭǝntyon, we can apply the formula (again using ʿāmata ʿālam):

7000 + ⌊7000 ÷ 4⌋ - 1 mod 7 = 6

A ṭǝntyon of 6 indicates that the first day of the year (1 Maskaram) was Monday. 13 Ṭǝqǝmt is, of course, 42 days after 1 Maskaram, and so the theoretical Passover will be 232 days after 1 Maskaram. Since we know the weekday of 1 Maskaram (i.e. ṭǝntyon), mathematically we can determine the weekday of the day 232 days later in this way:

6 + (232 mod 7) mod 7 = 0 (equivalent to 7)

According to the rules for ṭǝntyon, where 1 = Wednesday, 2 = Thursday, etc., 7 is Tuesday, meaning we must add a further 5 days to get to Sunday. Since the months of the Ethiopian calendar are all 30 days long, the 237th day after 1 Maskaram is:

⌊237 ÷ 30⌋ = 7 months and

237 mod 30 = 27 days after 1 Maskaram

This leaves us, finally, with 28 Miyazya as the date of Easter in the year 7000.

# Moveable Feasts

While the computus is most importantly used in determining the date of Easter, there are a number of liturgical commemorations and fasting periods which are influenced by the date of Easter. These are:

• Fast of Nineveh: begins 69 days before Easter
• Great Fast (Lent): begins 55 days before Easter
• Feast of the Mount of Olives (Dabra Zayt): 28 days before Easter
• Palm Sunday (Hosāʿnā): 7 days before Easter
• Good Friday (Səqlat): 2 days before Easter
• (Rəkba Kāhənāt): 24 days after Easter
• Feast of the Ascension (ʿƎrgat): 39 days after Easter
• Pentecost (Ṗarāqliṭos): 49 days after Easter
• Apostles' Fast: 50 days after Easter
• Salvation Fast (i.e. resumption of weekly fasting Wednesdays and Fridays): 52 days after Easter

# Computus Tables

Since the date of Easter follows a 532-year cycle, it is enough to prepare a table containing the data for each year in the cycle and it will be reusable in future cycles.

# Mathematical Notation

• x mod y — the remainder when x is divided by y, e.g., 20 mod 15 = 5
• ⌊x⌋ — the integer part of x, e.g., ⌊10.75⌋ = 10

Augustine Dickinson