A proposal for an intercalation scheme for the Ogam Wheel lunar & tree calendar.
Dr A.R. (Tom) Peters, 20020716
Some Minor corrections were done to the text by Karl Palmen on 2003-11-04.
The Ogam Wheel combines lunations of 29 or 30 days, indicated by runes,
with a solar year of 13 tree months of 28 days and an extra (365th) day.
In 6 of 13 tree months ("sacrifice months") a lunation rune
(one of the Uruzes on either side of the Fehu that marks the day of Dark Moon)
is to be "sacrificed" (skipped), yielding a lunation of 29 instead of 30 days.
With an annual adjustment, the Ogam Wheel generates a Meton cycle of
235 lunations and 19 years: however, it lasts only 6935 days.
In order to extend the cycle to proper periods of 6939 or 6940 days,
4 or 5 intercalary days have to be inserted into each cycle.
One way of doing this (proposed by Karl Palmen) is to halt the wheel whenever
a leap day occurs in some external solar calendar (e.g. the Gregorian calendar).
Another way is to regularly spare any Uruzes in a sacrifice tree month;
this extends these months to count 29 days (and the lunation to 30 days).
This can be done consistently with the wheel itself, since the marks indicating
the begin and end of a sacrifice tree month are separated by 29 divisions on
the outer wheel of the device (normally one division is skipped when an Uruz on
the middle wheel is sacrificed).
I hereby propose an intercalation scheme (in the table at the end below),
which spans 18 Meton cycles of 19 years, for a total of
334 years = 4131 lunations = 121991 days.
Legenda
=======
Sacrifice tree months:
B: # 1 (Birch)
F: # 4 (Alder)
H: # 6 (Hawthorn)
T: # 8 (Holly)
M: #10 (Vine)
R: #13 (Elder)
Moon phase runes:
u: waning Uruz (Moon age 29)
f: Fehu (Moon age 0 or 30: Dark Moon)
U: waxing Uruz (Moon age 1)
Intercalary day types:
TreeMonthDate MoonPhaseRune
Type 1:
0 U
Type 2:
0 f
1 U
Type 3:
29 U
Type 4:
28 u
29 f
I count days with tree dates 0 or 29 as intercalary days,
which in case of types 2 and 4 is a Fehu that otherwise falls on
date 1 or 28 respectively;
the spared Uruzes for these two types fall on dates 1 and 28 respectively.
I do not use type 2 (unlike Charles Moyer and Karl Palmen).
Possible intercalary days:
No. GN Month Date Rune Type
#1 1 B 0 U 1
#2 2 T 0 U 1
#3 4 F 0 f 2
#4 5 M 29 f 4
#5 7 F 29 U 3
#6 7 H 0 f 2
#7 8 R 0 f 2
#8 9 B 0 f 2
#9 10 H 29 U 3
#10 10 T 0 f 2
#11 11 R 29 U 3
#12 13 M 0 f 2
#13 15 F 0 U 1
#14 16 M 29 U 3
#15 18 H 0 U 1
#16 19 R 0 U 1
Of these 16 possibilities, only 4 or 5 should be selected for each 19-year
Meton cycle. I do not use type 2, but do use the remaining 10 options.
Meton cycle types:
C = short Meton cycle: 6939 days;
A = After short cycle: 6940 days;
B = Before short cycle: 6940 days;
D = Defective cycle: 4017 days,
skip the intercalary day by sacrificing the U at year 11, R29;
resume with cycle 1, Golden Number 1
[Tree month][Tree date][Moon phase rune]
GN
Cy,MTy 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
1 B - T0U - - - - F29U - - - R29U - - - F0U - - - B0U
2 C - - - - M29f - - - - H29U - - - - F0U - - H0U -
3 A - T0U - - - - F29U - - - R29U - - - - M29U - - R0U
4 B - T0U - - - - F29U - - - R29U - - - F0U - - - B0U
5 C - - - - M29f - - - - H29U - - - - F0U - - H0U -
6 A - T0U - - - - F29U - - - R29U - - - - M29U - - R0U
7 B - T0U - - - - F29U - - - R29U - - - F0U - - - B0U
8 C - - - - M29f - - - - H29U - - - - F0U - - H0U -
9 A - T0U - - - - F29U - - - R29U - - - - M29U - - R0U
10 B - T0U - - - - F29U - - - R29U - - - F0U - - - B0U
11 C - - - - M29f - - - - H29U - - - - F0U - - H0U -
12 A - T0U - - - - F29U - - - R29U - - - - M29U - - R0U
13 B - T0U - - - - F29U - - - R29U - - - F0U - - - B0U
14 C - - - - M29f - - - - H29U - - - - F0U - - H0U -
15 A - T0U - - - - F29U - - - R29U - - - - M29U - - R0U
16 B - T0U - - - - F29U - - - R29U - - - F0U - - - B0U
17 C - - - - M29f - - - - H29U - - - - F0U - - H0U -
18 D - T0U - - - - F29U - - - -
Note:
The first intercalary day: B0:U;1 , occurs at the start of year 1 of
type C Meton cycles. But since according to the procedure of Charles Moyer,
the annual 11-day correction of the epact and the concurrent increment of the
Golden Number occurs only at the 18th day of Birch, the year count is still at GN 19,
and listed as such in the table above in the line of the previous Meton cycle (type B).
Therefore 5 intercalary days are listed for the short Meton cycle type C,
but only the first 4 actually occur within the period of that cycle.
Similarly for B0:f;2 , which occurs at the beginning of year 9 but would be
observed at the GN of the previous year; I do not use that type of day in my
intercalation scheme however.