instruments / chronology / derived/irish_521.txt Β· raw
THE IRISH ANNALS AGAINST THE 521-YEAR CYCLE (Armagh). Offsets tested: [-1042, -532, -521, 0, 521, 532, 1042]. 521 Julian years = 190,295 d = 6443.996 synodic = 6992.998 draconic = 6906.12 anomalistic months = 27185 weeks.
A. DAY-TEETH: for each offset, the nearest eclipse of that body to the stated day (Ξ days), visible at Armagh, magnitude at Armagh, and the stated hour / weekday / lunar age against the sky.
id offset Ξd vis mag hour(statedβsky) feria(statedβsky) luna(statedβsky) says
U664.1 -1042 1 . 0.0 9β2.1β darkness β
U664.1 -532 31 . 9β darkness
U664.1 -521 1 v 0.89 9β8.5β darkness β
U664.1 +0 0 v 1.0 9β9.7β darkness β
U664.1 +521 0 v 0.95 9β7.3β darkness β
U664.1 +532 -31 . 9β darkness
U664.1 +1042 0 v 0.68 9β3.7β darkness β
U692.5 -1042 137 . colour of blood
U692.5 -532 -158 . colour of blood
U692.5 -521 137 . colour of blood
U692.5 +0 136 . colour of blood
U692.5 +521 136 . colour of blood
U692.5 +532 105 . colour of blood
U692.5 +1042 136 . colour of blood
U734.2 -1042 3 .
U734.2 -532 33 .
U734.2 -521 2 .
U734.2 +0 2 .
U734.2 +521 2 .
U734.2 +532 -29 .
U734.2 +1042 2 .
T734.2 -1042 1 v 1.0
T734.2 -532 31 .
T734.2 -521 0 v 1.0
T734.2 +0 0 v 1.0
T734.2 +521 0 v 1.0
T734.2 +532 -31 .
T734.2 +1042 0 . 1.0
U865.1 -1042 1 . 0.0 moon same month β
U865.1 -532 31 .
U865.1 -521 1 v 0.81 moon same month β
U865.1 +0 0 v 1.0 moon same month β
U865.1 +521 0 v 0.93 moon same month β
U865.1 +532 -31 .
U865.1 +1042 0 . 0.0 moon same month β
U878.8 -1042 -1 v 0.68 4β3β 14β14.1β about the third watch
U878.8 -532 31 . 4β 14β about the third watch
U878.8 -521 -1 v 0.87 4β3β 14β14.5β about the third watch
U878.8 +0 0 v 1.0 4β4β 14β15.1β about the third watch
U878.8 +521 0 . 1.0 4β4β 14β15.5β about the third watch
U878.8 +532 -32 . 4β 14β about the third watch
U878.8 +1042 -1 . 1.0 4β4β 14β15.6β about the third watch
U921.9 -1042 0 . 0.91 1β7.3β 3β2β
U921.9 -532 30 . 1β 3β
U921.9 -521 -1 v 1.0 1β1.7β 3β2β
U921.9 +0 -1 v 1.0 1β1.9β 3β2β
U921.9 +521 -1 v 1.0 1β10.6β 3β2β
U921.9 +532 -32 . 1β 3β
U921.9 +1042 -1 . 1.0 1β3.8β 3β2β
U1023.1 -1042 -1 v 0.56 5β4β 14β14.0β solar a fortnight after β
U1023.1 -532 31 . 5β 14β
U1023.1 -521 -1 v 0.69 5β4β 14β14.2β solar a fortnight after β
U1023.1 +0 -1 v 0.91 5β4β 14β14.8β solar a fortnight after β
U1023.1 +521 0 v 1.0 5β5β 14β15.4β solar a fortnight after β
U1023.1 +532 -32 . 5β 14β
U1023.1 +1042 -1 v 1.0 5β5β 14β15.6β solar a fortnight after β
M664.4 -1042 -1 . 0.0
M664.4 -532 29 .
M664.4 -521 -1 v 0.89
M664.4 +0 -2 .
M664.4 +521 -2 .
M664.4 +532 -33 .
M664.4 +1042 -2 .
M1030.8 -1042 0 . 0.0
M1030.8 -532 31 .
M1030.8 -521 0 v 0.36
M1030.8 +0 0 v 0.72
M1030.8 +521 0 v 0.56
M1030.8 +532 -31 .
M1030.8 +1042 -1 v 0.19
B. YEAR-LEVEL AND DESCRIPTIVE ENTRIES: at each offset, is there an eclipse of that body visible at Armagh in the stated year, and does the description fit (max magnitude at Armagh that year; 'stars seen'/'darkness' need β₯0.95, 'colour of blood' needs a total lunar eclipse, 'morning'/'midday'/'ninth hour' need the hour).
year body says -1042 -532 -521 +0 +521 +532 +1042
496 sun visible β0.26 β0.70 . . β0.47 . .
512 sun β0.17 . β0.16 β0.18 β0.68 β0.79 β0.28
591 sun dark morning . v0.24 . β0.14 v0.08 . v0.24
689 sun part of the sun . . . . . . .
718 moon at its full . β0.22 . β0.14 β0.34 β0.26 β0.50
807 moon colour of blood β1.00 β1.00 β1.00 β1.00 v0.94 v0.88 v0.77
885 sun stars seen v0.93 . v0.89 β0.98 v0.84 . β0.97
674 sun T: heavenly arc, fourth . β0.27 β0.29 . . . .
692 moon T: bloody colour, St Mar . . . . . . .
734 moon T: 9 Kal Feb β1.00 β1.00 β1.00 β1.00 β1.00 β1.00 β1.00
1023 sun T: at midday + lunar sam . . v0.60 β0.98 v0.92 . v0.83
444 sun AI: ninth hour . . v0.66 . . β0.28 .
594 sun AI: morning β0.53 . β0.58 β1.00 . . .
626 sun AI . β0.28 β0.83 . β0.81 . β0.54
865 sun AI: on the Kalend . . β0.81 β1.00 β0.93 . .
1023 sun AI: black cloud . . β0.60 β0.98 β0.92 . β0.83
1039 sun AI β0.54 β0.85 . β0.89 β0.63 β0.41 β0.83
fits by offset: {-1042: 6, -532: 7, -521: 8, 0: 11, 521: 8, 532: 5, 1042: 7} (visible only: {-1042: 7, -532: 8, -521: 11, 0: 11, 521: 12, 532: 6, 1042: 10}) of 17
C. THE KALENDS COMB: 295 year-lines with a weekday and a moon's age for 1 January. At each offset: weekday matches (exact), moon's age matches (Β±1 day, true sky), both. 532 is the computus' own cycle; 521 is the sky's.
offset -1042: weekday 140/295 moon age 164/295 both 84/295
offset -532: weekday 5/295 moon age 149/295 both 1/295
offset -521: weekday 73/295 moon age 158/295 both 42/295
offset +0: weekday 5/295 moon age 149/295 both 2/295
offset +521: weekday 3/295 moon age 134/295 both 1/295
offset +532: weekday 5/295 moon age 10/295 both 1/295
offset +1042: weekday 2/295 moon age 124/295 both 1/295
(lines per annal: {'Annals of Ulster': 295})
D. THE KALENDS COMB SCANNED FINELY around 0, Β±521, Β±532, Β±1042: weekday matches / moon-age matches / both, of 295
-1046: weekday 0 age 0 both 0
-1045: weekday 3 age 20 both 0
-1044: weekday 1 age 0 both 0
-1043: weekday 76 age 0 both 0
-1042: weekday 140 age 164 both 84 β best both
-1041: weekday 0 age 2 both 0
-1040: weekday 0 age 1 both 0
-1039: weekday 2 age 2 both 0
-1038: weekday 1 age 0 both 0
-536: weekday 0 age 0 both 0
-535: weekday 2 age 4 both 0
-534: weekday 1 age 0 both 0
-533: weekday 217 age 0 both 0
-532: weekday 5 age 149 both 1
-531: weekday 0 age 0 both 0
-530: weekday 3 age 0 both 0
-529: weekday 1 age 24 both 0
-528: weekday 3 age 0 both 0
-525: weekday 0 age 0 both 0
-524: weekday 3 age 27 both 0
-523: weekday 2 age 0 both 0
-522: weekday 148 age 0 both 0
-521: weekday 73 age 158 both 42
-520: weekday 0 age 2 both 0
-519: weekday 1 age 1 both 0
-518: weekday 1 age 3 both 1
-517: weekday 1 age 0 both 0
-8: weekday 1 age 20 both 0
-7: weekday 76 age 0 both 0
-6: weekday 140 age 1 both 0
-5: weekday 0 age 2 both 0
-4: weekday 0 age 0 both 0
-3: weekday 2 age 41 both 0
-2: weekday 1 age 0 both 0
-1: weekday 217 age 0 both 0
+0: weekday 5 age 149 both 2
+1: weekday 0 age 2 both 0
+2: weekday 3 age 2 both 0
+3: weekday 1 age 3 both 1
+4: weekday 3 age 0 both 0
+5: weekday 211 age 4 both 4
+6: weekday 2 age 0 both 0
+7: weekday 0 age 0 both 0
+8: weekday 3 age 160 both 2
+517: weekday 1 age 0 both 0
+518: weekday 1 age 47 both 0
+519: weekday 1 age 0 both 0
+520: weekday 283 age 0 both 0 β best weekday
+521: weekday 3 age 134 both 1
+522: weekday 0 age 2 both 0
+523: weekday 3 age 2 both 0
+524: weekday 1 age 3 both 1
+525: weekday 76 age 0 both 0
+528: weekday 0 age 0 both 0
+529: weekday 2 age 169 both 1
+530: weekday 1 age 1 both 0
+531: weekday 217 age 0 both 0
+532: weekday 5 age 10 both 1
+533: weekday 0 age 0 both 0
+534: weekday 3 age 2 both 0
+535: weekday 1 age 2 both 1
+536: weekday 3 age 0 both 0
+1038: weekday 3 age 0 both 0
+1039: weekday 1 age 60 both 0
+1040: weekday 3 age 0 both 0
+1041: weekday 211 age 0 both 0
+1042: weekday 2 age 124 both 1
+1043: weekday 0 age 2 both 0
+1044: weekday 3 age 1 both 0
+1045: weekday 2 age 3 both 1
+1046: weekday 148 age 0 both 0
weekday matches by century of entry, at offset 0 and at +520:
400s: n= 40 at 0: 3 at +520: 36 at +1: 0 at -1: 28
500s: n= 63 at 0: 0 at +520: 60 at +1: 0 at -1: 47
600s: n= 58 at 0: 1 at +520: 56 at +1: 0 at -1: 44
700s: n= 1 at 0: 0 at +520: 1 at +1: 0 at -1: 1
900s: n= 6 at 0: 0 at +520: 4 at +1: 0 at -1: 2
1000s: n= 97 at 0: 1 at +520: 96 at +1: 0 at -1: 72