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