Debt ledger
10.88 days
235 lunar months nearly match 19 tropical years- 12 lunar months
- 354.37 d
- Tropical year
- 365.24 d
- 19-year gap
- 0.09 d
- Leap months
- 7 in 19
Islamic
Never pays the solar debt. Twelve lunar months stay honestly lunar, so 1 Muharram walks backward through Gregorian seasons.
Hebrew
Pays on a fixed arithmetic pattern. Seven leap months in a 19-year Metonic cycle keep festivals near their seasonal anchors.
Chinese
Pays from sky rules. Leap months are tied to solar terms, so the rhythm often lands near seven in nineteen years but is not just a stored table.
Across 40 Gregorian years, 1 Muharram moves from 2020-08-20 to 2059-06-11 and wraps through the seasons 1 time.
In 2020-2038, browser ICU data shows 7 Hebrew leap-month years and 7 Chinese leap-month years. The theoretical Metonic debt asks for 7 extra lunar months because 235 - (19 x 12) = 7.
Method
Synodic month = 29.530588861 days. Mean tropical year = 365.242189 days. The walk and ledger read Islamic Umm al-Qura, Hebrew and Chinese labels from ECMAScript Intl/ICU calendar data in the browser.
Trust boundary
This is an explanatory CalculationTime instrument, not an official religious calendar or moon-sighting authority. Observed Islamic dates can differ from civil Umm al-Qura labels by location and authority.