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calendar-calculation-method

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Use when calculating calendars, determining seasonal timing, or establishing the correct 正朔. Covers leap month intercalation using the 19-year Metonic cycle, solstice measurement via shadow length (晷景), and dynastic calendar differences.

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Calendar Calculation Method (历法推算)

This method describes how to calculate and maintain an accurate calendar for agricultural and ceremonial purposes.

Core Principles

  • 履端於始: Begin calculations from the correct starting point
  • 举正於中: Establish the middle correctly
  • 归邪於终: Return errors to the end

Key Calculations

Determining the Year Start (正朔)

Different dynasties used different months:

  • 夏正以正月
  • 殷正以十二月
  • 周正以十一月

Leap Month Calculation

  • Track discrepancy between lunar and solar years
  • Insert leap month when discrepancy reaches one month
  • 周襄王二十六年闰三月 - Example of incorrect leap month placement

Seasonal Determination

Four Key Points:

  1. 冬至 - Shortest day
  2. 夏至 - Longest day
  3. 春分 - Equal day/night (spring)
  4. 秋分 - Equal day/night (autumn)

Calculation Steps

Step 1: Establish Base Point

  • Use winter solstice as anchor
  • Measure shadow length (晷景)
  • Confirm with natural signs:
    • 鹿解角
    • 兰根出
    • 泉水跃

Step 2: Track Celestial Movement

  • Observe sun's position against stars
  • Note moon phases
  • Record planetary positions

Step 3: Calculate Intercalation

  • 19 years = 235 lunar months (Metonic cycle)
  • Insert 7 leap months in 19-year cycle

Step 4: Verify and Adjust

  • Compare predictions with observations
  • Adjust calculations as needed
  • Document all anomalies

Recording Format

Document for each year:

  • 岁名
  • 月名
  • 日得
  • 大馀/小馀

Expected Outcomes

  • Accurate seasonal predictions
  • Proper timing for agricultural activities
  • Correct scheduling of ceremonies

Validation

  1. Confirm the winter solstice anchor point is verified by both shadow length measurement (晷景) and natural signs (鹿解角, 兰根出, 泉水跃)
  2. Verify the 19-year Metonic cycle is applied correctly — 7 leap months inserted per 19-year cycle, producing 235 lunar months
  3. Check that predictions are compared with actual celestial observations and discrepancies are documented for future adjustment