Difference between revisions of "Archive:Xhovian calendar"
m |
Protondonor (talk | contribs) m (Protondonor moved page Xhovian calendar to Archive:Xhovian calendar) |
(No difference)
|
Latest revision as of 06:20, 20 October 2021
This article or section is out of date. A country/countries relevant to this article have been removed from Sahar and have been retconned. Not everything here may still be considered canonical. This page was last edited by Protondonor (talk | contribs) 2 years ago. (Update) |
Part of a series on |
Xhovians |
---|
Nations |
|
Languages |
Monarchy |
Other |
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 winter 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 specify divisions of weeks, although 73 weeks of 5 days are often used, and the year is not split up into months, 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 synchronised with Gregorian calendar from 1 March 1600 to 28 February 2800. A positive difference means that the Xhovian calendar will be ahead relative to the Gregorian calendar, which will first occur on 1 March 2800 (excluding the basic difference of ~240 years between the two calendars):
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 relative to 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, and taking mod 5 leaves a remainder of 3, so the Xhovian calendar cycle does not contains neither a whole number of Gregorian 7 day weeks nor optional Xhovian 5 day weeks. Therefore, a full repetition of the Xhovian leap cycle with respect to the five-day weekly cycle is seven times the cycle length = 5 × 900 = 4500 years.
Conversion
The epoch of the Xhovian calendar is June 21st, 240 BCE, so in order to convert a date from Gregorian to Xhovian, observe the following process:
- Add 240 to the Gregorian year, or if it is a date before the 21st of June in the Gregorian calendar, add 239 (value y)
- Find the month then day of the Gregorian date in the table below, and find the value in the cell on its right (value d)
- Write the date in the format [d]/[y]
Example - conversion of Gregorian date 1st September 2017 to Xhovian calendar:
- September 1st is after June 21st in a Gregorian year, so add 240 to the Gregorian year to give the Xhovian year of 2257
- '73' is the value right of September 1st in the table, so the day is the 73rd
- The full Xhovian date is therefore 73/2257, also commonly written as 73/57
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 of columns, so for example, the Gregorian date January 1st is the Xhovian date '195th'.
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 | 195
|
1 | 226
|
1 | 254
|
1 | 287
|
1 | 317
|
1 | 346
|
1 | 11
|
1 | 42
|
1 | 73
|
1 | 103
|
1 | 134
|
1 | 164
|
2 | 196
|
2 | 227
|
2 | 255
|
2 | 286
|
2 | 316
|
2 | 347
|
2 | 12
|
2 | 43
|
2 | 74
|
2 | 104
|
2 | 135
|
2 | 165
|
3 | 197
|
3 | 228
|
3 | 256
|
3 | 287
|
3 | 317
|
3 | 348
|
3 | 13
|
3 | 44
|
3 | 75
|
3 | 105
|
3 | 136
|
3 | 166
|
4 | 198
|
4 | 229
|
4 | 257
|
4 | 288
|
4 | 318
|
4 | 349
|
4 | 14
|
4 | 45
|
4 | 76
|
4 | 106
|
4 | 137
|
4 | 167
|
5 | 199
|
5 | 230
|
5 | 258
|
5 | 289
|
5 | 319
|
5 | 350
|
5 | 15
|
5 | 46
|
5 | 77
|
5 | 107
|
5 | 138
|
5 | 168
|
6 | 200
|
6 | 231
|
6 | 259
|
6 | 290
|
6 | 320
|
6 | 351
|
6 | 16
|
6 | 47
|
6 | 78
|
6 | 108
|
6 | 139
|
6 | 169
|
7 | 201
|
7 | 232
|
7 | 260
|
7 | 291
|
7 | 321
|
7 | 352
|
7 | 17
|
7 | 48
|
7 | 79
|
7 | 109
|
7 | 140
|
7 | 170
|
8 | 202
|
8 | 233
|
8 | 261
|
8 | 292
|
8 | 322
|
8 | 353
|
8 | 18
|
8 | 49
|
8 | 80
|
8 | 110
|
8 | 141
|
8 | 171
|
9 | 203
|
9 | 234
|
9 | 262
|
9 | 293
|
9 | 323
|
9 | 354
|
9 | 19
|
9 | 50
|
9 | 81
|
9 | 111
|
9 | 142
|
9 | 172
|
10 | 204
|
10 | 235
|
10 | 263
|
10 | 294
|
10 | 324
|
10 | 355
|
10 | 20
|
10 | 51
|
10 | 82
|
10 | 112
|
10 | 143
|
10 | 173
|
11 | 205
|
11 | 236
|
11 | 264
|
11 | 295
|
11 | 325
|
11 | 356
|
11 | 21
|
11 | 52
|
11 | 83
|
11 | 113
|
11 | 144
|
11 | 174
|
12 | 206
|
12 | 237
|
12 | 265
|
12 | 296
|
12 | 326
|
12 | 357
|
12 | 22
|
12 | 53
|
12 | 84
|
12 | 114
|
12 | 145
|
12 | 175
|
13 | 207
|
13 | 238
|
13 | 266
|
13 | 297
|
13 | 327
|
13 | 358
|
13 | 23
|
13 | 54
|
13 | 85
|
13 | 115
|
13 | 146
|
13 | 176
|
14 | 208
|
14 | 239
|
14 | 267
|
14 | 298
|
14 | 328
|
14 | 359
|
14 | 24
|
14 | 55
|
14 | 86
|
14 | 116
|
14 | 147
|
14 | 177
|
15 | 209
|
15 | 240
|
15 | 268
|
15 | 299
|
15 | 329
|
15 | 360
|
15 | 25
|
15 | 56
|
15 | 87
|
15 | 117
|
15 | 148
|
15 | 178
|
16 | 210
|
16 | 241
|
16 | 269
|
16 | 300
|
16 | 330
|
16 | 361
|
16 | 26
|
16 | 57
|
16 | 88
|
16 | 118
|
16 | 149
|
16 | 179
|
17 | 211
|
17 | 242
|
17 | 270
|
17 | 301
|
17 | 331
|
17 | 362
|
17 | 27
|
17 | 58
|
17 | 89
|
17 | 119
|
17 | 150
|
17 | 180
|
18 | 212
|
18 | 243
|
18 | 271
|
18 | 302
|
18 | 332
|
18 | 363
|
18 | 28
|
18 | 59
|
18 | 90
|
18 | 120
|
18 | 151
|
18 | 181
|
19 | 213
|
19 | 244
|
19 | 272
|
19 | 303
|
19 | 333
|
19 | 364
|
19 | 29
|
19 | 60
|
19 | 91
|
19 | 121
|
19 | 152
|
19 | 182
|
20 | 214
|
20 | 245
|
20 | 273
|
20 | 304
|
20 | 334
|
20 | 365
|
20 | 30
|
20 | 61
|
20 | 92
|
20 | 122
|
20 | 153
|
20 | 183
|
21 | 215
|
21 | 246
|
21 | 274
|
21 | 305
|
21 | 335
|
21 | 1
|
21 | 31
|
21 | 62
|
21 | 93
|
21 | 123
|
21 | 154
|
21 | 184
|
22 | 216
|
22 | 247
|
22 | 275
|
22 | 306
|
22 | 336
|
22 | 2
|
22 | 32
|
22 | 63
|
22 | 94
|
22 | 124
|
22 | 155
|
22 | 185
|
23 | 217
|
23 | 248
|
23 | 276
|
23 | 307
|
23 | 337
|
23 | 3
|
23 | 33
|
23 | 64
|
23 | 95
|
23 | 125
|
23 | 156
|
23 | 186
|
24 | 218
|
24 | 249
|
24 | 277
|
24 | 308
|
24 | 338
|
24 | 4
|
24 | 34
|
24 | 65
|
24 | 96
|
24 | 126
|
24 | 157
|
24 | 187
|
25 | 219
|
25 | 250
|
25 | 278
|
25 | 309
|
25 | 339
|
25 | 5
|
25 | 35
|
25 | 66
|
25 | 97
|
25 | 127
|
25 | 158
|
25 | 188
|
26 | 220
|
26 | 251
|
26 | 279
|
26 | 310
|
26 | 340
|
26 | 6
|
26 | 36
|
26 | 67
|
26 | 98
|
26 | 128
|
26 | 159
|
26 | 189
|
27 | 221
|
27 | 252
|
27 | 280
|
27 | 311
|
27 | 341
|
27 | 7
|
27 | 37
|
27 | 68
|
27 | 99
|
27 | 129
|
27 | 160
|
27 | 190
|
28 | 222
|
28 | 253
|
28 | 281
|
28 | 312
|
28 | 342
|
28 | 8
|
28 | 38
|
28 | 69
|
28 | 100
|
28 | 130
|
28 | 161
|
28 | 191
|
29 | 223
|
--- | ---
|
29 | 281
|
29 | 313
|
29 | 343
|
29 | 9
|
29 | 39
|
29 | 70
|
29 | 101
|
29 | 131
|
29 | 162
|
29 | 192
|
30 | 224
|
--- | ---
|
30 | 283
|
30 | 314
|
30 | 344
|
30 | 10
|
30 | 40
|
30 | 71
|
30 | 102
|
30 | 132
|
30 | 163
|
30 | 193
|
31 | 225
|
--- | ---
|
31 | 284
|
--- | ---
|
31 | 345
|
--- | ---
|
31 | 41
|
31 | 72
|
--- | ---
|
31 | 133
|
--- | ---
|
31 | 194
|
Xhovian calendrical calculations
The calendrical arithmetic discussed here is adapted from Gregorian and Julian calendar arithmetic published by Dershowitz and Reingold.[1] They define the MOD operator as x MOD y = x − y × floor(x / y), because that expression is valid for negative and floating point operands, returning the remainder from dividing x by y while discarding the quotient.[2] Expressions like floor(x / y) return the quotient from dividing x by y while discarding the remainder.
Leap rule
isLeapYear = (year MOD 4 = 0)
IF isLeapYear THEN
- IF year MOD 100 = 0 THEN
- Century = (year / 100) MOD 9
- isLeapYear = (Century=2) OR (Century=6)
- END IF
END IF
References
- ↑ Dershowitz, Nachum; Reingold, Edward M. (2008). Calendrical Calculations (3rd ed.). Cambridge University Press. p. 47, footnote 3.
- ↑ Dershowitz, Nachum; Reingold, Edward M. (2008). Calendrical Calculations (3rd ed.). Cambridge University Press. p. 18, equation 1.15.