Archive:Xhovian calendar

The Xhovian Calendar is the most widely used civil calendar of South Baredina. The reformed version used today was devised in 1480 by the Haldian mathematician and astronomer Ajkkën Veuttinec.

It is a solar calendar beginning on the Gregorian date of the 21st of June, in accordance with the occurrence of the summer solstice. An additional day is inserted between the Gregorian dates of the 20th and 21st of June every leap year, which in terms of the Xhovian calendar is defined as being every year divisible four, excluding any year that is also divisible by 100 and yields a remainder of 200 or 600 when divided by 900.

The Xhovian calendar does not split the year up into months, and so the date is typically written in the formats of DDD/YY, DDD/YYYY, or more rarely, YYYY/DDD.

Arithmetic

The following are Gregorian minus Xhovian date differences, calculated for the beginning of March in each century year, which is where differences arise or disappear, until 10000 AD. These are exact arithmetic calculations, not depending on any astronomy. A negative difference means that the proleptic Xhovian calendar was behind the proleptic Gregorian calendar. The Xhovian calendar is the same as the Gregorian calendar from 1 March 1600 to 28 February 2800. A positive difference means that the Xhovian calendar will be ahead of the Gregorian calendar, which will first occur on 1 March 2800:

Gregorian minus Xhovian date differences

Century Difference	100 0	200 −1	300 −1	400 0	500 0	600 −1	700 −1	800 0	900 0	1000 0
Century Difference	1100 −1	1200 0	1300 0	1400 0	1500 −1	1600 0	1700 0	1800 0	1900 0	2000 0
Century Difference	2100 0	2200 0	2300 0	2400 0	2500 0	2600 0	2700 0	2800 +1	2900 0	3000 0
Century Difference	3100 0	3200 +1	3300 0	3400 0	3500 0	3600 +1	3700 +1	3800 0	3900 0	4000 +1
Century Difference	4100 +1	4200 0	4300 0	4400 +1	4500 +1	4600 +1	4700 0	4800 +1	4900 +1	5000 +1
Century Difference	5100 0	5200 +1	5300 +1	5400 +1	5500 +1	5600 +1	5700 +1	5800 +1	5900 +1	6000 +1
Century Difference	6100 +1	6200 +1	6300 +1	6400 +2	6500 +1	6600 +1	6700 +1	6800 +2	6900 +1	7000 +1
Century Difference	7100 +1	7200 +2	7300 +2	7400 +1	7500 +1	7600 +2	7700 +2	7800 +1	7900 +1	8000 +2
Century Difference	8100 +2	8200 +2	8300 +1	8400 +2	8500 +2	8600 +2	8700 +1	8800 +2	8900 +2	9000 +2
Century Difference	9100 +2	9200 +2	9300 +2	9400 +2	9500 +2	9600 +2	9700 +2	9800 +2	9900 +2	10000 +3

The Xhovian leap rule omits seven of nine century leap years, leaving 225−7 = 218 leap days per 900-year cycle. Thus the calendar mean year is 365+²¹⁸⁄₉₀₀ days, but this is actually a double-cycle that reduces to 365+¹⁰⁹⁄₄₅₀ = ~365.242 days, or exactly 365 days 5 hours 48 minutes 48 seconds, which is exactly 24 seconds shorter than the Gregorian mean year of 365.2425 days, so in the long term on average the Xhovian calendar pulls ahead of the Gregorian calendar by one day in 3600 years.

The number of days per Xhovian calendar cycle = 900 × 365 + 218 = 328,718 days. Taking mod 7 leaves a remainder of 5, so unlike the Gregorian calendar, the Xhovian calendar cycle does not contain a whole number of weeks. Therefore, a full repetition of the Xhovian leap cycle with respect to the seven-day weekly cycle is seven times the cycle length = 7 × 900 = 6300 years.

Conversion

The following is a table listing the conversion of all dates of the year from the Gregorian to the Xhovian calendar, excluding during leap years.
It is read from left to right in pairs in columns, so for example, the Gregorian date January 1^st is the Xhovian date '196^th'.

January	Xhovian	February	Xhovian	March	Xhovian	April	Xhovian	May	Xhovian	June	Xhovian	July	Xhovian	August	Xhovian	September	Xhovian	October	Xhovian	November	Xhovian	December	Xhovian
1	196	1	227	1	255	1	286	1	316	1	347	1	12	1	43	1	74	1	104	1	135	1	165
2	197	2	228	2	256	2	287	2	317	2	348	2	13	2	44	2	75	2	105	2	136	2	166
3	198	3	229	3	257	3	288	3	318	3	349	3	14	3	45	3	76	3	106	3	137	3	167
4	199	4	230	4	258	4	289	4	319	4	350	4	15	4	46	4	77	4	107	4	138	4	168
5	200	5	231	5	259	5	290	5	320	5	351	5	16	5	47	5	78	5	108	5	139	5	169
6	201	6	232	6	260	6	291	6	321	6	352	6	17	6	48	6	79	6	109	6	140	6	170
7	202	7	233	7	261	7	292	7	322	7	353	7	18	7	49	7	80	7	110	7	141	7	171
8	203	8	234	8	262	8	293	8	323	8	354	8	19	8	50	8	81	8	111	8	142	8	172
9	204	9	235	9	263	9	294	9	324	9	355	9	20	9	51	9	82	9	112	9	143	9	173
10	205	10	236	10	264	10	295	10	325	10	356	10	21	10	52	10	83	10	113	10	144	10	174
11	206	11	237	11	265	11	296	11	326	11	357	11	22	11	53	11	84	11	114	11	145	11	175
12	207	12	238	12	266	12	297	12	327	12	358	12	23	12	54	12	85	12	115	12	146	12	176
13	208	13	239	13	267	13	298	13	328	13	359	13	24	13	55	13	86	13	116	13	147	13	177
14	209	14	240	14	268	14	299	14	329	14	360	14	25	14	56	14	87	14	117	14	148	14	178
15	210	15	241	15	269	15	300	15	330	15	361	15	26	15	57	15	88	15	118	15	149	15	179
16	211	16	242	16	270	16	301	16	331	16	362	16	27	16	58	16	89	16	119	16	150	16	180
17	212	17	243	17	271	17	302	17	332	17	363	17	28	17	59	17	90	17	120	17	151	17	181
18	213	18	244	18	272	18	303	18	333	18	364	18	29	18	60	18	91	18	121	18	152	18	182
19	214	19	245	19	273	19	304	19	334	19	365	19	30	19	61	19	92	19	122	19	153	19	183
20	215	20	246	20	274	20	305	20	335	20	1	20	31	20	62	20	93	20	123	20	154	20	184
21	216	21	247	21	275	21	306	21	336	21	2	21	32	21	63	21	94	21	124	21	155	21	185
22	217	22	248	22	276	22	307	22	337	22	3	22	33	22	64	22	95	22	125	22	156	22	186
23	218	23	249	23	277	23	308	23	338	23	4	23	34	23	65	23	96	23	126	23	157	23	187
24	219	24	250	24	278	24	309	24	339	24	5	24	35	24	66	24	97	24	127	24	158	24	188
25	220	25	251	25	279	25	310	25	340	25	6	25	36	25	67	25	98	25	128	25	159	25	189
26	221	26	252	26	280	26	311	26	341	26	7	26	37	26	68	26	99	26	129	26	160	26	190
27	222	27	253	27	281	27	312	27	342	27	8	27	38	27	69	27	100	27	130	27	161	27	191
28	223	28	254	28	281	28	313	28	343	28	9	28	39	28	70	28	101	28	131	28	162	28	192
29	224	---	---	29	283	29	314	29	344	29	10	29	40	29	71	29	102	29	132	29	163	29	193
30	225	---	---	30	284	30	315	30	345	30	11	30	41	30	72	30	103	30	133	30	164	30	194
31	226	---	---	31	285	---	---	31	346	---	---	31	42	31	73	---	---	31	134	---	---	31	195