Here I compare the short term accuracy of an experimental lunar calendar, which uses the full moon cycle (fumocy) to obtain a better short term accuracy than is possible with the Yerm lunar calendar. I do the comparison over a 98-month period corresponding to the first 6 yerms.
This experimental fumocy calendar is as follows:
Fumocy Types (L = 30 day month, s = 29 day month): 15: LLsLsLssLsLsLLs (3,5,7,8,10,12,15 short) 13: LLsLsLssLsLsL (3,5,7,8,10,12 short) 12: LLsLssLssLLs (3,5,6,8,9,12 short) Sequence beginning 52(13(01 [Fumocy 0] 0 1 2 3 4 5 6 7 15:15:13:15:12:15:13:15I started with my Yerm Calendar Table . Then ....
ye(mo begins noon (h) (d) Fumocy Date (hf) 03(02 1999-09-11 +38 +1 02-11-02 +14 04(02 2000-11-27 +37 +1 03-13-02 +13 02(06 1998-08-23 +34 +1 01-13-02 +10 02(04 1998-06-25 +32 +1 01-11-02 +08 03(04 1999-11-09 +32 +1 02-13-02 +08 01(08 1997-06-06 +29 +1 00-13-02 +05 04(14 2001-11-16 +29 +1 04-10-02 +05 01(10 1997-08-04 +28 +1 00-15-01 04(01 2000-10-28 +28 +1 03-12-01 05(10 2002-12-05 +28 +1 05-11-02 +04 06(08 2004-02-21 +27 +1 06-11-02 +03 02(08 1998-10-21 +26 +1 01-15-01 03(14 2000-08-30 +26 +1 03-10-01 04(12 2001-09-18 +26 +1 04-08-01 06(06 2003-12-24 +26 +1 06-09-02 +02 01(06 1997-04-08 +25 +1 00-11-02 +01 05(08 2002-10-07 +25 +1 05-09-02 +01 03(01 1999-08-12 +25 +1 02-10-01 05(12 2003-02-02 +25 +1 05-13-02 +01 02(02 1998-04-27 +24 +1 01-09-02 00 03(03 1999-10-10 +24 +1 02-12-01 04(04 2001-01-25 +23 0 03-15-01 04(16 2002-01-14 +23 0 04-12-01 06(04 2003-10-26 +23 0 06-07-01 06(10 2004-04-20 +23 0 06-13-02 -01 02(05 1998-07-24 +22 0 01-12-01 01(04 1997-02-08 +21 0 00-09-02 -03 01(02 1996-12-11 +19 0 00-07-01 01(12 1997-10-02 +19 0 01-02-01 02(07 1998-09-21 +19 0 01-14-01 04(03 2000-12-26 +19 0 03-14-01 06(02 2003-08-28 +19 0 06-05-01 03(06 2000-01-07 +18 0 03-02-01 01(09 1997-07-05 +17 0 00-14-01 02(16 1999-06-14 +17 0 02-08-01 03(12 2000-07-02 +17 0 03-08-01 05(02 2002-04-13 +17 0 05-03-01 05(06 2002-08-09 +17 0 05-07-01 05(14 2003-04-02 +17 0 05-15-01 02(03 1998-05-26 +16 0 01-10-01 04(10 2001-07-21 +16 0 04-06-01 03(15 2000-09-28 +16 0 03-11-01 04(13 2001-10-17 +16 0 04-09-01 05(11 2003-01-03 +16 0 05-12-01 06(12 2004-06-18 +16 0 07-02-01 01(07 1997-05-07 +15 0 00-12-01 04(15 2001-12-15 +15 0 04-11-01 05(09 2002-11-05 +15 0 05-10-01 06(07 2004-01-22 +15 0 06-10-01 02(10 1998-12-19 +13 0 02-02-01 03(05 1999-12-08 +13 0 03-01-01 06(05 2003-11-24 +13 0 06-08-01 06(09 2004-03-21 +13 0 06-12-01 01(11 1997-09-02 +12 0 01-01-01 05(04 2002-06-11 +12 0 05-05-01 01(05 1997-03-09 +11 0 00-10-01 04(06 2001-03-25 +11 0 04-02-01 06(14 2004-08-16 +11 0 07-04-01 01(14 1997-11-30 +10 0 01-04-01 02(17 1999-07-13 +10 0 02-09-01 03(13 2000-07-31 +10 0 03-09-01 05(01 2002-03-14 +10 0 05-02-01 02(01 1998-03-28 +09 0 01-08-01 04(08 2001-05-23 +09 0 04-04-01 04(11 2001-08-19 +09 0 04-07-01 05(07 2002-09-07 +09 0 05-08-01 05(13 2003-03-03 +09 0 05-14-01 06(03 2003-09-26 +09 0 06-06-01 01(01 1996-11-11 +08 0 00-06-01 01(03 1997-01-09 +08 0 00-08-01 02(09 1998-11-19 +08 0 02-01-01 02(14 1999-04-16 +08 0 02-06-01 03(10 2000-05-04 +08 0 03-06-01 05(16 2003-05-31 +08 0 06-02-01 03(08 2000-03-06 +07 0 03-04-01 06(11 2004-05-19 +07 0 07-01-01 01(16 1998-01-28 +06 0 01-06-01 02(12 1999-02-16 +05 0 02-04-01 06(01 2003-07-29 +05 0 06-04-01 04(05 2001-02-23 +04 0 04-01-01 04(17 2002-02-12 +04 0 05-01-01 01(13 1997-10-31 +02 0 01-02-30 +26 05(03 2002-05-12 +01 0 05-04-01 05(05 2002-07-10 +01 0 05-06-01 06(13 2004-07-17 +01 0 07-02-30 +25 02(15 1999-05-15 +00 0 02-06-30 +24 04(09 2001-06-21 +00 0 04-04-30 +24 03(11 2000-06-02 -00 -1 03-06-30 +24 05(15 2003-05-01 -00 -1 06-01-01 03(07 2000-02-05 -01 -1 03-02-30 +23 06(15 2004-09-14 -02 -1 07-04-30 +22 04(07 2001-04-23 -03 -1 04-02-30 +21 02(11 1999-01-17 -04 -1 02-02-30 +20 01(15 1997-12-29 -05 -1 01-04-30 +19 01(17 1998-02-26 -05 -1 01-06-30 +19 03(09 2000-04-04 -06 -1 03-04-30 +18 02(13 1999-03-17 -07 -1 02-04-30 +17 05(17 2003-06-29 -07 -1 06-02-30 +17
From this it becomes obvious that the Yerm Calendar variation of +38 to -07 (45 hours) is improved to +28 to -03 (31 hours). This shows that it worthwhile going on to find a long term sequencing rule for the three fumocy types, like what I have suggested in earlier notes.
Also of interest is the correlation between (h) and the month of fumocy.
Karl Palmen, 30 October 2002