Observing Heaven, Keeping Time · A calendar you can move
Two clocks in heavenwrite one calendarfor human life.
月months · festivals
合日seasons · farming
One follows the Moon’s phases; the other follows the seasons. They do not run at the same speed. The Chinese calendar keeps them in long-term accord.
Begin with one day↓I · Find the first clock
Where does
a day come from?
Move through a day. Watch the Sun return to the sky.
One rotation of Earth makes one day.
II · Find the second clock
Where does
a month come from?
Move the Moon until it returns to new moon.
New Moon · almost invisible
The phases begin again: ≈ 29.53 days
III · Pull the view outward
Where does
a year come from?
Move the Sun along the ecliptic. When China and the Northern Hemisphere have summer, the Southern Hemisphere has winter.
Looking up from Earth · the Sun moves north and south of the celestial equator
Spring Equinox: the Sun crosses northward; day and night are nearly equal.
China · Northern Hemisphere
The north warms while the south cools
The seasons begin again: ≈ 365.24 days
IV · The problem appears
Do the two clocks
run at the same speed?
Push twelve lunar months to the end of a solar year. Watch the numbers separate.
Twelve lunar months are about 354 days: roughly 11 days short of the seasonal year.
V · Let the error accumulate
If we follow only the Moon,
where will Spring Festival go?
For the moment, add no leap month. Move through ten years and watch a lunar festival drift against the seasons.
0 days earlier against the seasons
Still in winterFollow the Moon alone, and a festival will eventually travel through every season.
VI · Bring the clocks together
What can we do?
Add one month.
When the accumulated difference nears one synodic month, put a month back into the year.
The clocks are still about 33 days apart.
The intuition: when the error grows close to a month, add a month and return toward the seasons.
VII · But which month is repeated?
There is no fixed “every third year.”
Look back to the Sun.
The 24 solar terms alternate between twelve sectional terms (jie, 节) and twelve principal terms (zhongqi, 中气). Lunar months run from one new moon to the next. When intercalation is needed, the calendar finds a month without a principal term.
one new moon to the next
Rain Water, Spring Equinox, Grain Rain …
- 1Fix Month 11
The lunar month containing the Winter Solstice is always Month 11.
- 2Count the months
From this Month 11 to the next: twelve months means no intercalation; thirteen means a leap month is required.
- 3Find the first month without a principal term
Among those thirteen months, move forward and find the first complete lunar month containing no zhongqi.
- 4Repeat the preceding month’s name
If the preceding month is Month 6, the extra month is called Leap Month 6; later month names shift accordingly.
The distinction: “no principal term” decides which month repeats; “thirteen months between two Winter-Solstice months” decides whether intercalation is needed.
The animation below shows Step 3How can a principal term cross a lunar boundary and leave one month empty?
Each lunar month currently contains a principal term.
VIII · Marks left by the Sun
Why do the
solar terms exist?
Two views of the same instant: Earth’s place in orbit, and the Sun north or south of the celestial equator. Every 15° of solar longitude lights another term.
🌱Spring begins; living things stirThe Sun is about 16.6° south of the celestial equator
Solar terms record the Sun’s position—not the Moon’s phase.
IX · Two clocks, one calendar
Draw the whole of
2026.
Both timelines share the same date. The solar line shows Gregorian months and solar terms; the lunar line shows new moons, lunar months, and traditional festivals.
It is not a purely “lunar” calendar. It is lunisolar: lunar phases determine months, the Sun’s position determines solar terms, and leap months keep the months in long-term agreement with the seasons.
Evidence and limits
Where do the numbers come from?
This page uses uniform circular motion and average periods to build intuition; it is not a date-calculation tool. The actual Chinese calendar is computed from real astronomical positions, with complete rules involving new moons, the Winter-Solstice month, and principal terms.