A rational basis for a calendar upon 61 day periods
The Gregorian calendar is a 400-year-old hack job. February's weird. July-August breaks the pattern, and no one can remember which months have 31 days. But there's a better way, hidden in prime factorization.
- Solar day (roughly 24 hours for the earth to rotate)
- Solar year (365.2425 solar days for the earth to orbit the sun)
- Lunar cycle (29.53 days for 8 distinct moon phases, roughly 12x annually)
It's impossible to coordinate or synchronize these 3 cycles perfectly. But we can devise a system to accommodate them and minimize tradeoffs. We also want to consider historical calendars, particularly the current Gregorian calendar and less so the prior Julian calendar.
If a solar year is considered to be 366 days, this factors to 61 * 3 * 2, which naturally suggests (6) 61-day periods, or alternately (61) 6-day periods. Perhaps we should have 6 day weeks, but that will be for another proposal.
We can split each 61-day period into alternating months of 30 and 31 days, in either order. This provides some alignment with the lunar cycle as well as traditional calendars.
- 61 is prime; indivisible, mathematically fundamental
- Each of 6 periods of 61 days can be split into pairs of months, 30 + 31
- 12 months matches the lunar cycle of roughly 30 days
- 12 months allows clean divisibility by 4 (seasons, business quarters)
- 12 months matches tradition
- Resist entropy: a regular pattern of pairs in a predictable order
We can retain the Gregorian approach to leap years, which solves the problem of accounting for the remaining 0.2425 days in a solar year as years go by. We'll pick one month out of twelve that will have an extra day roughly every 4 years. If 366 days is our starting basis, then the leap month will have a one-day deficit in most years.
For explication, a leap year is considered the base case, and a "normal year" is handled specially, in some sense, even though leap years are less frequent.
- Always alternate 30-31
| Month | Length |
|---|---|
| Jan | 30 |
| Feb | 31 |
| Mar | 30 |
| Apr | 31 |
| May | 30 |
| Jun | 31 |
| Jul | 30 |
| Aug | 31 |
| Sep | 30 |
| Oct | 31 |
| Nov | 30 |
| Dec | 31 |
| Total | 366 |
- August through December retain their traditional lengths
- Halloween, Oct 31
- New Year's Eve, Dec 31
- February has a day removed
| Month | Length |
|---|---|
| Jan | 30 |
| Feb | 30 |
| Mar | 30 |
| Apr | 31 |
| May | 30 |
| Jun | 31 |
| Jul | 30 |
| Aug | 31 |
| Sep | 30 |
| Oct | 31 |
| Nov | 30 |
| Dec | 31 |
| Total | 365 |
- Retain all base case benefits
- February continues as the traditional leap month
- Start the year with 30-30-30 and alternate after that
- Most February weirdness is gone
- Gregorian July-August flip
- Gregorian starts big-small, pairwise
- August is due to be small but is big
- Pattern is small-big after that
- Pairwise: 3x big-small, 1x big-big, 2x small-big
- Rational Prime maintains 30-31 throughout
- August through December are identical to Gregorian month lengths
- January through July mismatch the Gregorian pattern
| Month | Gregorian | Rational Prime |
|---|---|---|
| Jan | 31 | 30 |
| Feb | 28/29 | 30/31 |
| Mar | 31 | 30 |
| Apr | 30 | 31 |
| May | 31 | 30 |
| Jun | 30 | 31 |
| Jul | 31 | 30 |
| Aug | 31 | 31 |
| Sep | 30 | 30 |
| Oct | 31 | 31 |
| Nov | 30 | 30 |
| Dec | 31 | 31 |
| Total | 365/366 | 365/366 |
- Predictable patterns (no more "30 days hath September" mnemonics)
- Business quarters are equalized
- Cultural continuity (Halloween, New Year's Eve preserved)
- Mathematical elegance
Preserved from Gregorian calendar:
- 12 month structure
- Months of alternating 30 and 31 lengths
- August-December lengths (dates like Halloween and New Year's Eve)
- Leap year frequency and concept
- February as the leap month
Fixed from Gregorian calendar:
- February: awkward 28/29 becomes rational 30/31
- July-August 31-31 pattern reversal becomes logical 30-31 within pattern
- Unpredictable patterns become clean alternation
This proposal is deliberately intended as a replacement for the Gregorian calendar, primarily within the Western cultural tradition. Other cultural traditions or calendars are welcomed yet will probably be considered out of scope.
This proposal is not intended to address local or global adoption. The intention is merely to lay out a more desirable scheme than the status quo. Adoption will have both costs and benefits.