Enoch Calendar · Leap Week Reference

The Leap Week

Key numbers, trigger rule, and seven-thousand-year statistics for the solar intercalation mechanism of the Enoch Calendar

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Ordinary Year

364

days — exactly 52 weeks
no days left over

Leap Year

371

days — exactly 53 weeks
weekly cycle intact

Drift Window

±3.5_d

from noon on Tekufah Spring
equinox must stay inside

Average Gap

5.635_yr

between Leap Weeks
long-term average year = 365.242 d

Trigger Rule

Each Year — Check

Would next year’s equinox fall more than +3.5 days past noon on the Tekufah Spring day?

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If Yes — Act

Insert a Leap Week this year (year N). The current year becomes 371 days.

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Result

Next Nisan 1 shifts 7 days later. The equinox lands on the early side of the window — within 3.5 days before noon.

The rule fires one year early — in year N based on a projection of year N+1. The check uses the actual computed equinox position from the JPL ephemeris rather than an assumed fixed year length, so the calendar adapts automatically to long-term variations in the tropical year including Earth’s axial precession.

Gap Distribution — AM Years 1–7,000

Gap length	Count	Share
5 years between Leap Weeks	453	36.5%
6 years between Leap Weeks	789	63.5%
Total Leap Weeks inserted	1,243	AM 1–7000

Gaps are always either 5 or 6 years — never 4, never 7. The variation arises from short-term fluctuations in the solar year and from the one-year-early trigger. The average converges to 7 ÷ (365.242 − 364) = 5.635 years, giving a long-term average year length of exactly 365.242 days — equal to the tropical year by construction.

Closest the Equinox Came to the Boundary

Side	Extreme Drift	AM Year	Margin
Before noon	−3d 11h 58m 4s	1832 AM	1 min 56 sec
After noon	+3d 11h 59m 14s	5844 AM	46 seconds

In both cases the equinox remained inside the one-week window. Neither extreme was a failure or a near-miss by design — the algorithm does not know or care how close it comes. These are the two tightest outcomes produced by the rule operating unchanged across 7,000 years.

Data source: NASA JPL DE441 ephemeris — sub-minute precision across the full span.