PRECISION

Two Paths To Accuracy

Every solar calendar must correct for the mismatch between day-cycles and year-cycles. HEKA offers two approaches: one for coordination, one for astronomical purity.

I. THE TWO MODES

SYNC vs TRUE

COORDINATION

SYNC Mode

Aligns with Gregorian leap years

March has 30 days when the Gregorian calendar has a leap year (Feb 29). HEKA April 1st realigns with Gregorian April 1st every year. Perfect for coordinating with the civil world.

Leap March when:
Gregorian year is leap

Realignment:
April 1st, annually
  • ✓ Matches civil calendar exactly
  • ✓ April 1st always aligned
  • ✓ Recommended for most users
ASTRONOMICAL

TRUE Mode

Follows pure astronomical precision

Uses the "4-year, except 128th" rule. March has 30 days every 4 years, except every 128th year which has 29.

Leap March when:
Year ÷ 4 = whole
EXCEPT year ÷ 128
  • ✓ Astronomical precision
  • ✓ Mean year: 365.242188 days
  • ✓ For purists and long-term

The Difference Over Time

In daily life, you won't notice the difference between SYNC and TRUE. Over centuries, TRUE mode drifts from the Gregorian calendar by a tiny amount, about 1 day every 450,000 years. For most users, SYNC mode provides the best balance of astronomical accuracy and civil coordination.

II. THE MATHEMATICS

Why 365.242188 Days?

365 + 1 4 1 128 = 365.242188

This expression yields exactly 365 + 31/128, matching the tropical year (the time from one vernal equinox to the next).

The Components

365 days
Base year (12 months × 28 + March 29)
+ 0.25 days
The Julian correction (1 day every 4 years)
− 0.0078 days
The precision term (skip every 128th)

The Result

365.242188
Mean year length

The tropical year is approximately 365.24219 days. HEKA's TRUE mode achieves 365.24219, a difference of less than 0.00001 days per year.

III. COMPARISON

How Calendars Measure Up

45 BCE

Julian

Roman
365.250000 days/year
Drift: 128 years
+0.0078 day error
1582 CE

Gregorian

Civil
365.242500 days/year
Drift: 3,216 years
+0.0003 day error
Now

HEKA

TRUE Mode
365.242188 days/year
Drift: ~450,000 years
−0.0000022 day error

Tropical year: 365.2421897 days (IAU 2000 standard)