6*6*10 or 6×6×10 is a perennial solar calendar with:
- 6 months per year
- 6 weeks per month
- 10 days per week
Every month ends with a blank day, except for of the last month in non-leap years. Blank days are intercalary days and can be treated as holidays.
| Week | Days | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| W0 | 00 | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 |
| W1 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| W2 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
| W3 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
| W4 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |
| W5 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 |
| Blank | 60 | |||||||||
Nice attributes of the 6*6*10 calendar[]
The units are regular:
- Every year is the same (except leap years).
- Every month is the same (in leap years).
A regular calendar simplifies scheduling.
Days of the month are decimal zero-based numbering:
- One's place corresponds to the weekday number.
- Ten's place corresponds to the month's week number.
Thus, dates are easy to compute and visualize in your head.
The units are divisible (ignoring blank days):
- All units are divisible by half – ½ year, ½ month, ½ week.
- All units are divisible a second way – ⅓ year, ⅓ month, ⅕ week.
Divisibility allows flexibility. For example, if weeks (10 days) are too long for a recurring schedule, then use half weeks (5 days).
Month-week-day format:
- Explicitly states the week number and weekday (no need to consult a calendar to look up the weekday).
- MWD consumes only three digits (which is more compact than Gregorian's MMDD four digits).
MWD format[]
Complete year with dates in MWD format:
000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060
100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260
300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360
400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460
500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 (if leap year)
Calendar-app format[]
The first two months of the year displayed in a calendar app:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 00 | |||||||||
| 01 | |||||||||
| 02 | |||||||||
| 03 | |||||||||
| 04 | |||||||||
| 05 | |||||||||
| 06 | |||||||||
| 10 | |||||||||
| 11 | |||||||||
| 12 | |||||||||
| 13 | |||||||||
| 14 | |||||||||
| 15 | |||||||||
| 16 |
The header row labels the week days. The left cells contain the first day of the week and list the month and week in MW format.
Why 6 months per year[]
A solar year is about 365.2 days. 360 is a superior highly composite (very divisible) number.
360 is 5 to 6 days short of a solar year. So the calendar has 5 or 6 months per year with one intercalary day at the end of each month
- if 5 months per year, then leap years would have a month with 2 intercalary days
- if 6 months per year, then non-leap years would have a month with 0 intercalary days
0 intercalary days per month is more regular than 2 intercalary days per month. Therefore 6 months per year is used.
Why 10 days per week[]
With 6 months per year, there are 61 days per month. 6 is a superior highly composite (very divisible) number. Most humans use the base 10 number system.
So, days per week is either 6 or 10
- 6m/y * 10w/m * 6d/w
- 6m/y * 6w/m * 10d/w
The latter is used because
- Base 10 occurs 36 times for 36w/yr (vs. only 10 times for 10m/y).
- Adding an intercalary day to 10d/w makes the week 10% longer (vs. 17% longer for a 6d/w). Therefore, 10d/w has more uniform intervals.
- Grouping base-6 units in adjacent places.
Why a 6*6*10 reform calendar hasn't been proposed[]
It seems that serious proposed reform calendars prioritize (from high to low)
- accuracy
- minimize changes
- regularness and divisibility
There is a limit to the amount of change that humans tolerate. The 6*6*10 calendar is too radical; it departs from the customary number of months and weekdays.
Supporting evidence, from the calendar reform article at Wikipedia: All governments eventually implement calendar reforms for accuracy. All calendars mentioned on that page either retain 12-13 months per year or retain a 7-day week. (The Calendar of Romulus had 10 months/year and 8 days/week, but 61 days during winter were not assigned to any month.)
It's been known since the 2nd century BC that the solar year is about 365.2 days.
From Tropical year#Early value, precession discovery:
Hipparchus … reckoned the length of the year to be 1/300 of a day less than 365.25 days.
Using the 6*6*10 calendar in fiction[]
The 6*6*10 calendar would be suitable for a fictional story featuring Earthlings that value regularity more than avoiding change.