calendar-calculation-method

name	calendar-calculation-method
description	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.

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