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ISO-Uncia Leap Week Calendar

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Disclaimer: The use of the term “ISO” in the title and body of this article is not meant to suggest or imply any formal approval or recommendation of this proposal by the ISO. It is meant simply to signify that the proposal is compatible with the week numbering scheme of ISO 8601.


The ISO Uncia Calendar is a proposal to incorporate the week numbering rules of ISO 8601 into an auxiliary calendar format that can be put to use at any time by anyone, because it serves to supplement the existing Gregorian calendar and ISO 8601 rules without changing them.

Quarters Edit

The year is first divided into four equal quarters of 91 days/13 weeks (the last quarter will have 98 days in leap years). Each quarter begins on Monday of W01, W14, W27, and W40 of the ISO week numbering system. The leap week will be added whenever ISO 8601 specifies a 53rd week.

Uncias Edit

Each quarter is further divided into 3 divisions which are called uncia (Latin for twelfth). They are called such so that they will not be confused with the months of the Gregorian calendar, which they will not replace, and with which they will not precisely correspond.

Each uncia will have 30 days, except the third, which will have 31. (The very last, or 12th, will have 38 days in a leap year.) The longer unciaeis at the end of each quarter. In this way, the first 90 days of the quarter can be easily divided into useful day-groups of 3, 5, 6, 9, 10, 15, 30 or 45 days, which can conveniently fit into the 90-day scheme of 3 unciae, minus the last day (or last week of the leap week year). Of course, with the 91st day, the quarter can be divided into 13 7-day weeks.

The unciae will always begin on Monday, Wednesday or Friday, depending upon whether the uncia is respectively the 1st, 2nd or 3rd unica of a quarter.

Numbering Edit

The unciae will simply be identified by ordinal numbering (1st thru 12th). As an option, for those who prefer names, they can be called by ordinal numbers in Latin:

  1. Prima
  2. Secunda
  3. Tertia
  4. Quarta
  5. Quinta
  6. Sexta
  7. Septima
  8. Octava
  9. Nona
  10. Decima
  11. Undecima
  12. Duodecima

They can be numbered in a format similar to the ISO day numbering scheme as ccyy-Uuu-dd, wherein Uuu – with initial literal capital ‘U’ – represents the uncia, such that U03 would represent the 3rd uncia, or Tertia, and dd would represent the day number of that particular uncia.

1st quarter
Uncia Week 1 2 3 4 5 6 7
Mon Tue Wed Thu Fri Sat Sun
Prima 01 01 02 03 04 05 06 07
02 08 09 10 11 12 13 14
03 15 16 17 18 19 20 21
04 22 23 24 25 26 27 28
Secunda 05 29 30 31 32 33 34 35
06 36 37 38 39 40 41 42
07 43 44 45 46 47 48 49
08 50 51 52 53 54 55 56
Tertia 09 57 58 59 60 61 62 63
10 64 65 66 67 68 69 70
11 71 72 73 74 75 76 77
12 78 79 80 81 82 83 84
13 85 86 87 88 89 90 91
2nd quarter
Uncia Week 1 2 3 4 5 6 7
Mon Tue Wed Thu Fri Sat Sun
Quarta 14 092 093 094 095 096 097 098
15 099 100 101 102 103 104 105
16 106 107 108 109 110 111 112
17 113 114 115 116 117 118 119
Quinta 18 120 121 122 123 124 125 126
19 127 128 129 130 131 132 133
20 134 135 136 137 138 139 140
21 141 142 143 144 145 146 147
Sexta 22 148 149 150 151 152 153 154
23 155 156 157 158 159 160 161
24 162 163 164 165 166 167 168
25 169 170 171 172 173 174 175
26 176 177 178 179 180 181 182
3rd quarter
Uncia Week 1 2 3 4 5 6 7
Mon Tue Wed Thu Fri Sat Sun
Septima 27 183 184 185 186 187 188 189
28 190 191 192 193 194 195 196
29 197 198 199 200 201 202 203
30 204 205 206 207 208 209 210
Octava 31 211 212 213 214 215 216 217
32 218 219 220 221 222 223 224
33 225 226 227 228 229 230 231
34 232 233 234 235 236 237 238
Nona 35 239 240 241 242 243 244 245
36 246 247 248 249 250 251 252
37 253 254 255 256 257 258 259
38 260 261 262 263 264 265 266
39 267 268 269 270 271 272 273
4th quarter
Uncia Week 1 2 3 4 5 6 7
Mon Tue Wed Thu Fri Sat Sun
Decima 40 274 275 276 277 278 279 280
41 281 282 283 284 285 286 287
42 288 289 290 291 292 293 294
43 295 296 297 298 299 300 301
Undecima 44 302 303 304 305 306 307 308
45 309 310 311 312 313 314 315
46 316 317 318 319 320 321 322
47 323 324 325 326 327 328 329
Duodecima 48 330 331 332 333 334 335 336
49 337 338 339 340 341 342 343
50 344 345 346 347 348 349 350
51 351 352 353 354 355 356 357
52 358 359 360 361 362 363 364
53 365 366 367 368 369 370 371

Days Edit

Every day of each uncia will always correspond to a particular week-day number in the ISO week numbering scheme. For instance, U05-19 (19th day of Quinta), will always correspond to W20-7, a Sunday. U10-10 (10th day of Decima), will correspond to W41-3, a Wednesday. And so on, for every day of the ISO week numbering system. There will never be a difference, as long as the ISO rules are not changed.

Properties Edit

Given that the ISO-Uncia Calendar is an auxiliary, or supplemental calendar, rather than a proposal to replace the existing Gregorian calendar, or change any current ISO standard, or modify the sequence of weekdays, it does not require any authorization from any legislature, standards setting body, or religious denomination. Anyone who finds the Calendar useful, is free to implement it anytime that they want in their own way.

A couple of added bonuses of the ISO Uncia calendar:

  1. The format is very similar to the ancient Enoch calendar, and to several proposed leap week calendars.
  2. There are no Friday the 13th's!

See also Edit

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