This is a slightly edited copy of a note, that I sent to CALNDR-L on 1 November 2001. I've updated it on 5 November 2003 and on 9 December 2005.
Go to Martyrological Wheel
The Ogam Wheel is a rotary calculating device that calculates an approximate moon phase for a date in a 13-month Celtic Tree Calendar.
It consists 3 concentric wheels that can rotate relative to each other. The outer wheel is divided into 30 sectors and is marked with years of the 19-year Metonic cycle and some dates from the year of Celtic Tree calendar. The next smaller wheel also has 30 sectors. These sectors correspond to phases of the moon and are marked with runes from a 16-rune alphabet forwards for the dark moon to full moon inclusive and backwards for the full moon to dark moon inclusive. The inner wheel acts as a pointer to a sector in the other two wheels.
The outer two wheels are set for a given year by placing the FULL MOON sector of the moon phase wheel by the sector of the year on the outer wheel.
Normally the inner wheel is turned one sector clockwise for each day passed.
Because the mean lunar month is about 29.53 days rather than 30 days a moon phase rune occasionally needs to be skipped. This is known as the sacrifice. The sacrificed rune is always one of the two uruz runes adjacent to the dark moon rune. One sacrifice occurs in each of a particular six tree calendar months. I'll refer to the days of these 6 tree months as the sacrifice periods. An additional uruz rune is sacrificed once every 19 years, to form the 19-year Metonic cycle.
Usually but not always, there is a choice of two uruz runes, one of which must be sacrificed. Charles chooses one so that the dark moon rune occurs (always?) on the dark moon rune day.
I show you the years and dates on the Outer Wheel of the Ogam Wheel. The years are for the current 19-year cycle 1988 to 2006 (Golden #1 to #19) and the dates that are the equivalents of the first and last day of each tree months. More precisely these dates mark the start and end of the tree months, inclusive of any sacrifice. The extra day (Dec 23) is also shown. The number at the start of each row is the position number referred to in other notes.
1: 2000 Jan 20 Dec 22 2: 1989 Jan 21 Dec 23 3: Dec 24 4: 1997 6: 2005 7: 1994 9: 2002 10: 1991 12: 1999 13: 1988 Nov 24 14: Nov 25 15: 1996 Oct 27 16: Oct 28 17: 2004 Sep 29 18: 1993 Sep 30 Sept 1 19: Sept 2 20: 2001 Aug 4 21: 1990 Aug 5 July 7 22: July 8 23: 1998 June 9 24: Jun 10 May 12 25: 2006 May 13 26: 1995 Apr 14 27: Apr 15 Mar 17 28: 2003 Mar 18 29: 1992 Feb 17 30: Feb 18
In a leap year of the tree calendar, the wheel must be turned exactly as many times as in a common year. This can be done by cancelling one of the six sacrifices. The tree calendar leap day then occurs at or close to this cancelled sacrifice. Alternatively, it can be done by simply not turning the Ogam Wheel on a leap day.
Charles Moyer's original notes about the Ogam wheel and pictures are at ogindex.html to which I have added a caveat about leap days and the 19-year cycle.
Also there is
The Martyrological Wheel
The outer wheel of the Martyrological wheel has its 30 sectors corresponding to epacts numbered in anti-clockwise order. Each sector is also given the corresponding martyrological letter. The moon phase wheel has sectors numbered 1 to 30 clockwise. 1 represents the new moon, 14 the full moon and 29 (presumably) the dark moon. These numbers define the age of the moon.
The outer two wheels are set for a given year by placing the NEW MOON sector (value 1)of the moon phase wheel by the sector of the epact/Martyrological letter of the year on the outer wheel. For January 1, the pointer on the inner wheel is pointed to position #0 on the outer wheel.
As with the Ogam wheel there are 6 sacrifices in each year plus an extra sacrifice once every Metonic cycle (at the end/start).
The sacrifice occurs by skipping moon age 30, whenever it would otherwise occur within each of the 6 sacrifice periods. These sacrifice periods are
Feb 5 - Mar 5 Apr 5 - May 3 Jun 3 - Jul 1 Aug 1 - Aug 29 Sep 29 - Oct 27 Nov 27 - Dec 25
when the golden number of the year is no greater than 11, else the sacrifice periods are one day earlier than shown above. This difference only matters in years with epact 25. Note that since each sacrifice period has exactly 29 non-leap days, there is always exactly one occurrence of 30 that is sacrificed.
The position of each date on the outer wheel the same as its epact, except for a date within a sacrifice period before the sacrifice. Such days are one place anti-clockwise/up from the epact position.
Whereas, the Ogam wheel has its sacrifice periods beginning at different positions on the outer wheel, the martyrological wheel has its sacrifice periods beginning at the same position on the outer wheel within each year. This is position 25 for years with golden number no more than 11 and position 26 for other years. Below, I show some years and dates on the outer wheel.
00: P 2006 Jan 1 29: N 1995 Feb 1 Apr 1 28: M 27: H 2003 Jun 1 26: G start of sacrifice period (Golden > 11) 25: F 2011 start of sacrifice period (Golden < 12) 24: E 2000 Jul 3 23: D Sep 1 22: C 2008 21: B Nov 1 20: A 19: u 2005 Dec 31 18: t 17: s 2013 16: r 2002 15: q 14: p 2010 13: n 1999 12: m 11: l 2007 10: k 1996 Mar 21 09: i 08: h 2004 07: g 06: f 2012 05: e 2001 04: d 03: c 2009 02: b 1998 01: a Sep 23NB: 2011 has Golden number 17 so, its sacrifice periods begin early at position #26.
Now for some examples:
Was such a wheel ever used?