(* Ogam wheel rules of operation.
* Version 2, Dr A.R (Tom) Peters, 20020721
* Interpretation of Charles Moyer's original rules,
* plus an independent long-period leap day scheme devised by TP.
*)
0. Modifications of the Ogam wheel to indicate special conditions:
A. Split "Birch" on the inner wheel over 2 positions: one on the currently open space between the 365th day marker and the current position of the Birch rune; and a second one at the current position of the Birch rune.
(* We can do away with this if we do the annual epact adjustment right after counting the 365th day at position 13; but I do not yet fully understand the consequences of this change as compared to Charles original rules *)
B. Mark that an Uruz already has been sacrificed this month by covering it on the middle wheel.
C. Count the years in a 334-year cycle, and keep count of Meton cycles in this period (17 complete and 1 incomplete Meton cycle).
I. Initialization.
Initialize the Ogam wheel, according to today's tree calendar month, day, Moon phase, and year number in the 19-year cycle. See Table 1 for Moon phase runes, and Table 2 for Tree months.
- The Full Moon rune Yr on the middle wheel must align with the current golden number (year number in 19-year cycle) on the outer wheel.
- The pointer must be stuck in the inner wheel at the rune position of the current tree month.
- This pointer must point to the current Moon phase rune on the middle wheel.
If the wheel is thus properly aligned, then:
- if you locate the current tree month rune to the right of the divisions on the outer wheel;
- from there, count the days passed of the current tree month clockwise on the middle wheel, skipping over any Uruz that may have been sacrificed this month;
then you will end at the position of the pointer on the inner wheel.
If you do not know all of these, use one of these methods:
a) Copy the configuration of today from someone else.
b) Set the configuration from a known configuration at a specific Gregorian calendar date, and andvance the wheel following the rules below, up to and including the present day.
c) Deduce the tree month date from the approximate correlation with the Gregorian calendar, and obtain the age of the Moon from an astronomical almanac.
(for Tree-Gregorian correlations see Table 2 below).
This method c) may be in error by a day, and should be avoided in the period 22 Dec. of one year through 1 March of the following year, and in Gregorian leap years.
d) The current 334-year period started with 1 Birch, a Thorn (1-day Moon), on 25 Dec. 1927 (JD 2425239.5).
II. Long-term corrections.
1) IF the pointer is at the first Birch month rune on the (modified) inner wheel, and points to the end of Birch at position 1 of the outer wheel, THEN:
a) Move the middle and inner wheel counterclockwise 11 positions with respect to the outer wheel: this moves the Yr rune of the Full Moon on the middle wheel, to re-align with the next higher Golden Number on the outer wheel, which is that of the current new year that started with the beginning of this Birch month;
IF this is the year following the 334th year of the long cycle (i.e. after year 11 of Meton cycle 18) THEN:
b) Move the middle wheel clockwise 1 or 2 positions such that the Yr rune aligns with the Golden Number on the outer wheel that is 8 higher (modulo 19) instead (i.e. from G.N. 12 at pos. 15 on the outer wheel, to G.N. 1 at pos. 17). By leaving the inner wheel in place, the Moon phase is effectively decreased by 1 or 2 days.
(* Note: By jumping 8 years ahead in the Meton cycle, the Moon phases fall about a day and a half later in the solar year: this compensates for the discrepancy that accumulated between the Sun and Moon during the 334 period, due to the imperfection of the Meton cycle *).
c) However in the year with Golden Number 4, move the middle wheel an additional position counterclockwise to the second segment labelled '4' at position 13 of the outer wheel. By leaving the inner wheel in place, the Moon phase is effectively increased by a day (a "Ger" is skipped). This is the "saltus lunae" that occurs once every 19 years.
(* Note: The above is an interpretation of Charles' rules 7 and 8, combined with a long-period correction. Making things less complicated, we may choose to do all this immediately after counting the 365th day at position 13, when starting the new year with 1 Birch, which would be at pos. 3 on the outer wheel *).
III. Daily advances.
==> Move the inner wheel 1 position clockwise. <==
2) IF the pointer now points to a new tree month rune at the right of a dividing line on the outer wheel, THEN:
a) Note todays Moon phase rune;
b) Stick the pointer on the inner wheel onto the position of the next tree month (or 365th day marker);
c) Rotate the inner wheel counterclockwise a bit so that the pointer again points at todays Moon phase rune;
d) Remove any marks indicating that an Uruz has been sacrificed the previous month.
3) IF:
- the Moon phase rune is an Uruz, and
- we are in a sacrifice month, and
- this is not a month assigned for an intercalary day (see Table 3), and
- no sacrifice has yet been made:
THEN decide if to sacrifice this Uruz, based on the following rules:
- this is an u- and we are in the last day or last day but one in the month (as counted to the position of the end-of-month rune on the outer wheel); or
- this is an u+ :
THEN a sacrifice must be made;
(* Note: unless we need to count this rune as an intercalary day *)
ELSE IF:
- this is an u- (and we are in a sacrifice month and no sacrifice has yet been made), and
- in the previous sacrifice month we also sacrificed an u- :
THEN sacrifice this Uruz.
(* Note: this is an heuristic that seems to create nice yerms *)
Sacrificing an Uruz means:
a) Advance the inner wheel clockwise one position with respect to the middle wheel, to point to the next (non-Uruz) rune;
b) Mark the Uruz rune we skipped over, in order to indicate a sacrifice has been made.
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Table 1
Moon phase runes
The 16 runes as used by Charles Moyer: 15 are from the Younger FUThARK, but "ar" has been replaced by the older *Jeran,ger.
Rune name Latinization Moon age
(Old Germanic,Anglo-Saxon,Norwegian|Icelandic)
+++ waxing Moon
*Fehu,feoh,fe f 0
*Uruz,ur,ur U - or 1
*Thurisaz,thorn,thurs D (Th) 1 or 2
*Ansuz,os,oss A 2 or 3
*Raidho,rad,reidh R 3 or 4
*Kaunaz,cen,kaun C 4 or 5
*Haglaz,haegl,hagall H 5 or 6
*Naudiz,nyd,naudh N 6 or 7
*Isaz,is,iss I 7 or 8
*Jeran,ger,- G 8 or 9
*Sowilo,sigel,sol S 9 or 10
*Tiwaz,tir,tyr T 10 or 11
*Berkanan,beorc,bjarkan B 11 or 12
*Mannaz,man,madhr M 12 or 13
*Laukaz,lagu,lo:gr L 13 or 14
yr Y 14 or 15
--- waning Moon
l 15 or 16
m 16 or 17
b 17 or 18
t 18 or 19
s 19 or 20
g 20 or 21
i 21 or 22
n 22 or 23
h 23 or 24
c 24 or 25
r 25 or 26
a 26 or 27
d 27 or 28
u 28 or 29 or -
( f 29 or 30)
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Table 2
Tree months
Celtic Rune Tree Letter Sacrif. Approximate period
in Gregorian calendar
Beith bjarkan Birch B + 24 Dec..20 Jan
Luis lo:gr Rowan L - 21 Jan..17 Feb
Nion naudh Ash N - 18 Feb..17 Mar
Fearn fe Alder F + 18 Mar..14 Apr
Saille sol Willow S - 15 Apr..12 May
Huath hagall Hawthorn H + 13 May.. 9 Jun
Duir thurs Oak D - 10 Jun.. 7 Jul
Tinne tyr Holly T + 8 Jul.. 4 Aug
Coll kaun Hazel C - 5 Aug.. 1 Sep
Muin madhr Vine M + 2 Sep..29 Sep
Gort *Jeran,ger Ivy G - 30 Sep..27 Oct
Ngetal ing Reed I - 28 Oct..24 Nov
Ruis reidh Elder R + 25 Nov..22 Dec
365th day X - 23 Dec
On the inner and outer wheel Charles Moyer does not use Ogam signs (of which there are 15 for consonants) to designate the tree months (of which there are 13), but instead 11 runes from the Younger FUThARC, 1 from the Elder FUThARC (Jeran,"gar" - which he also uses among the Moon phase runes), and one from the Anglo-Saxon version (ing - which is not a Moon phase rune).
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Table 3
Suspended sacrifice months in the 334-year cycle, and spared Uruzes as intercalary days.
(* Note: Intercalary days extend the length of the tree month from the normal 28, to 29 days. This is possible because for sacrifice tree months the marks for begin and end on the outer wheel are separated by 29 spaces: on of these is skipped at a sacrifice. By not making the sacrifice at the begin or end of a sacrifice tree month, an day is intercalated that can be counted as day 0 or 29 of that tree month. *)
Saved Uruzes are listed below by Golden Number (year in the Meton cycle), tree Month letter, day of tree month, and Moon Phase rune (U after Fehu (Dark Moon rune), or u before Fehu).
cycle GN;Mdd:Ph GN;Mdd:Ph GN;Mdd:Ph GN;Mdd:Ph GN;Mdd:Ph
1 2;T 0:U 7;F29:U 11;R29:U 15;F 0:U 19;B 0:U(a)
2 5;M28:u(b) 10;H29:U 15;F 0:U 18;H 0:U
3 2;T 0:U 7;F29:U 11;R29:U 16;M29:U 19;R 0:U
4 2;T 0:U 7;F29:U 11;R29:U 15;F 0:U 19;B 0:U(a)
5 5;M28:u(b) 10;H29:U 15;F 0:U 18;H 0:U
6 2;T 0:U 7;F29:U 11;R29:U 16;M29:U 19;R 0:U
7 2;T 0:U 7;F29:U 11;R29:U 15;F 0:U 19;B 0:U(a)
8 5;M28:u(b) 10;H29:U 15;F 0:U 18;H 0:U
9 2;T 0:U 7;F29:U 11;R29:U 16;M29:U 19;R 0:U
10 2;T 0:U 7;F29:U 11;R29:U 15;F 0:U 19;B 0:U(a)
11 5;M28:u(b) 10;H29:U 15;F 0:U 18;H 0:U
12 2;T 0:U 7;F29:U 11;R29:U 16;M29:U 19;R 0:U
13 2;T 0:U 7;F29:U 11;R29:U 15;F 0:U 19;B 0:U(a)
14 5;M28:u(b) 10;H29:U 15;F 0:U 18;H 0:U
15 2;T 0:U 7;F29:U 11;R29:U 16;M29:U 19;R 0:U
16 2;T 0:U 7;F29:U 11;R29:U 15;F 0:U 19;B 0:U(a)
17 5;M28:u(b) 10;H29:U 15;F 0:U 18;H 0:U
18 2;T 0:U 7;F29:U (c)
(a) This actually falls in the next year (G.N.1), but before the annual adjustment of the Golden Number after 18 Birch, so is listed with the previous year.
(b) The 29th day of this tree month is the Fehu that follows.
(c) The U after 11;R28:f is sacrificed, in preparation for the G.N. correction at the end of the cycle.