Sunday letter

The Sunday letter SB (also Dominical letter or littera dominicalis ) of a calendar year is the day letter of its Sundays .

origin

The system of seven letters of the day and the identification of a calendar year with the Sunday letter emerged from the system of eight nouns (A to H) and the identification of a calendar year with the market day letter of the Etruscans and initially also the Romans . With them, instead of the seven-day week used much earlier in other cultures, the eight-day week Nundinum ( market week ) beginning with the market day was used.

Scheme

The days of a calendar year are marked with the seven day letters A to G: January 1st has the day letter A, January 7th the day letter G. These seven day letters repeat from January 8th and every seventh day thereafter.

For example, the Sunday letter is the day letter on the first Sunday of the year:

first Sunday of the year is on	1.	2.	3.	4th	5.	6th	7th	January
Sunday letter of the year is	A.	B.	C.	D.	E.	F.	G

Exception in leap years

The scheme of the day letters applies to the 365 days of a common year . In order to be able to use a calendar that used to be laboriously handwritten with the assignment between the calendar data and the day letters, the day inserted in leap years was assigned the same day letter D as March 1st. However, since the days of the week and thus the Sundays are shifted to a later calendar day, the Sunday letter changes by one place after the leap day in these years. As a result, leap years have two Sunday letters: one until the leap day and the second for the time thereafter until the end of the year, such as the years 2008 and 2012 in the following list:

year	...	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	...
Sunday letter (s)	...	B.	A.	G	FE	D.	C.	B.	AG	F.	E.	D.	...

Specification in the calendar

It was only possible to enter the Sunday letters in the calendar when a new calendar could be published every year after the introduction of book printing. In addition to the weekday Sunday , the corresponding calendar days were also given the Sunday letters that were valid for the year in question, capitalized and printed in red.

In the Middle Ages, the usual, elaborately handwritten "perpetual" calendars were used to get a better overview of the week sequence, with the day letter "A" capitalized and red, the other day letters "b, c, d, e, f and g" black and were written in lower case.

Day letters

Allocation between calendar date and day letter
Date of month	Jan.	February	March	April	May	June	July	Aug	Sept	Oct	Nov	Dec
1, 08, 15, 22	A.	D.	D.	G	B.	E.	G	C.	F.	A.	D.	F.
2, 09, 16, 23	B.	E.	E.	A.	C.	F.	A.	D.	G	B.	E.	G
3, 10, 17, 24	C.	F.	F.	B.	D.	G	B.	E.	A.	C.	F.	A.
4, 11, 18, 25	D.	G	G	C.	E.	A.	C.	F.	B.	D.	G	B.
5, 12, 19, 26	E.	A.	A.	D.	F.	B.	D.	G	C.	E.	A.	C.
6, 13, 20, 27	F.	B.	B.	E.	G	C.	E.	A.	D.	F.	B.	D.
7, 14, 21, 28	G	C.	C.	F.	A.	D.	F.	B.	E.	G	C.	E.
29	A.	D.	D.	G	B.	E.	G	C.	F.	A.	D.	F.
30th	B.	-	E.	A.	C.	F.	A.	D.	G	B.	E.	G
31	C.	-	F.	-	D.	-	B.	E.	-	C.	-	A.

Sunday letters in the Julian and Gregorian calendars

In the Julian calendar , the sequence of Sunday letters is repeated every 28 years. This cycle is called the solar circle . Each of these 28 years j is assigned a number SZ, also called a solar circle, in the following scheme :

SZ = (j + 9) mod 28; Result: SZ = 0 *), 1,…, 26 or 27.
*) Instead of the previously unknown zero, the divisor, here 28, is written.

The constant Julian assignment between sun circle SZ and Sunday letter SB is shown in the following table:


SZ	0	1*	2	3	4th	5 *	6th	7th	8th	9 *	10	11	12	13 *
SB	A.	GF	E.	D.	C.	BA	G	F.	E.	DC	B.	A.	G	FE
SZ	14th	15th	16	17 *	18th	19th	20th	21 *	22nd	23	24	25 *	26th	27
SB	D.	C.	B.	AG	F.	E.	D.	CB	A.	G	F.	ED	C.	B.

*) Every 4 years the Sunday letter SB is shifted by 2 letters in the alphabet
(second shift after the leap day). The first Sunday letter applies in January and February (February 29 is assigned the same letter of the day as March 1), the second from March.

In the Gregorian calendar , the assignment of the Sunday letters to the solar circle is no longer constant. It always changes when the leap day is canceled in the full centuries that cannot be divided by 400. Each time all Sunday letters move one position forward in the alphabet.

The Gregorian assignment between the sun circle SZ and the Sunday letter SB for the years 1900 to 2099 (no loss of the leap day in 2000) is shown in the following table :


SZ	0	1*	2	3	4th	5 *	6th	7th	8th	9 *	10	11	12	13 *
SB	G	E.	D.	C.	B.	G	F.	E.	D.	B.	A.	G	F.	D.
SZ	14th	15th	16	17 *	18th	19th	20th	21 *	22nd	23	24	25 *	26th	27
SB	C.	B.	A.	F.	E.	D.	C.	A.	G	F.	E.	C.	B.	A.

For both the Julian and the Gregorian calendar, the Sunday letters can also be read from the W. Bogatyrjow calendar (in leap years only the second, valid after the leap day).

Table of Sunday letters for the years 5 - 2899

This table according to Grotefend takes into account both the Sunday letters according to the Gregorian and the Julian calendar. For the years that are not listed there, one uses the fact that the Sunday letters in the Gregorian calendar repeat exactly every 400 years (the years 2100, 2200 and 2300 are not leap years). In the Julian calendar, the Sunday letters are repeated every 28 years, 25 times as much for the simple use of the table: The repetition every 700 years.

year	1300 1700 2100 2500	-	1400 1800 2200 2600	-	1500 1900 2300 2700	1600 2000 2400 2800	-
year	Century in the Gregorian calendar							Only one in four centuries is a leap year in the Gregorian calendar.
00	C.	-	E.	-	G	BA	-
01 29 57 85	B.	C.	D.	E.	F.	G	A.
02 30 57 86	A.	B.	C.	D.	E.	F.	G
03 31 59 87	G	A.	B.	C.	D.	E.	F.
04 32 60 88	FE	GF	AG	BA	CB	DC	ED
05 33 61 89	D.	E.	F.	G	A.	B.	C.
06 34 62 90	C.	D.	E.	F.	G	A.	B.
07 35 63 91	B.	C.	D.	E.	F.	G	A.
08 36 64 92	AG	BA	CB	DC	ED	FE	GF
09 37 65 93	F.	G	A.	B.	C.	D.	E.
10 38 66 94	E.	F.	G	A.	B.	C.	D.
11 39 67 95	D.	E.	F.	G	A.	B.	C.
12 40 68 96	CB	DC	ED	FE	GF	AG	BA
13 41 69 97	A.	B.	C.	D.	E.	F.	G
14 42 70 98	G	A.	B.	C.	D.	E.	F.
15 43 71 99	F.	G	A.	B.	C.	D.	E.
16 44 72	ED	FE	GF	AG	BA	CB	DC
17 45 73	C.	D.	E.	F.	G	A.	B.
18 46 74	B.	C.	D.	E.	F.	G	A.
19 47 75	A.	B.	C.	D.	E.	F.	G
20 48 76	GF	AG	BA	CB	DC	ED	FE
21 49 77	E.	F.	G	A.	B.	C.	D.
22 50 78	D.	E.	F.	G	A.	B.	C.
23 51 79	C.	D.	E.	F.	G	A.	B.
24 52 80	BA	CB	DC	ED	FE	GF	AG
25 53 81	G	A.	B.	C.	D.	E.	F.
26 54 82	F.	G	A.	B.	C.	D.	E.
27 55 83	E.	F.	G	A.	B.	C.	D.
28 56 84	DC	ED	FE	GF	AG	BA	CB
00	DC	ED	FE	GF	AG	BA	CB	All centuries are leap years in the Julian calendar.
year	0 700 1400 2100	100 800 1500 2200	200 900 1600 2300	300 1000 1700 2400	400 1100 1800 2500	500 1200 1900 2600	600 1300 2000 2700
year	Century in the Julian calendar
Italic characters apply to the Julian calendar only.

Individual evidence

^ Hermann Grotefend: Time calculation of the German Middle Ages and the modern times. 2 volumes, Hahnesche Hofbuchhandlung, Hanover 1891–1898, panel II "Sunday letters"

[1] Hermann Grotefend: Time calculation of the German Middle Ages and the modern times. 2 volumes, Hahnesche Hofbuchhandlung, Hanover 1891–1898, panel II "Sunday letters"