M03 · LESSONS 20–33

Module 3 · Heavenly Stems and Earthly Branches (Lessons 20–33)

The Ten Heavenly Stems and Twelve Earthly Branches are repeating symbols used for dates, months, hours, directions, and many traditional calculation systems. Their earliest documented uses as date markers must be distinguished from the yin-yang, Five-Phase, and image associations added in later traditions. This module builds the sixty-pair cycle, shows how to calculate year, month, day, and hour labels, and introduces the relationships and auxiliary tables used by later lessons.

Lesson 20 · The Ten Heavenly Stems#

Learning goals#

Memorize the yin-yang, Five-Phase, and directional assignments of the Ten Stems.
Understand stem imagery as analogy within a tradition.
Distinguish early date notation from later divinatory interpretation.

Lesson#

The Ten Stems—Jia through Gui—form a repeating sequence. Shang oracle-bone inscriptions provide evidence that stems and stem-branch combinations were used to record days. That evidence does not show that all later destiny-calculation meanings already existed at the time. Yin-yang, Five-Phase, direction, and image associations were additional interpretive layers.

Stem	Yin or yang	Phase	Direction	Traditional image
Jia	Yang	Wood	East	Tall tree, timber
Yi	Yin	Wood	East	Flowering plant, vine
Bing	Yang	Fire	South	Sun
Ding	Yin	Fire	South	Lamp or spark
Wu	Yang	Earth	Center	Mountain, wall, embankment
Ji	Yin	Earth	Center	Garden soil, cultivated earth
Geng	Yang	Metal	West	Blade, worked iron
Xin	Yin	Metal	West	Jewel, ornament
Ren	Yang	Water	North	River or sea
Gui	Yin	Water	North	Rain, dew, spring water

Mnemonic: Jia and Yi are eastern wood; Bing and Ding southern fire; Wu and Ji central earth; Geng and Xin western metal; Ren and Gui northern water. In this lesson’s table, odd positions are yang and even positions yin. The images are teaching analogies, not measurements of a person’s character.

To unpack “Geng metal,” first count Geng as the seventh stem, so it is yang under the lesson’s convention; next, note that Geng and Xin are assigned to metal; only then use a particular author’s imagery, such as an axe or unworked iron. The National Museum of China’s inscribed “stem-branch table” ox bone is an artifact associated with the sixty-pair cycle. It supports the historical use of the notation, not a claim that later destiny meanings were already present.

Practice#

Recreate the first four columns of the table from memory.
Make ten stem flashcards.
Find five objects that can serve as images for different stems, explaining the analogy.

Check your understanding#

What are Xin’s yin-yang and phase assignments?
Which stems are assigned to the center?
What is the traditional image for Ren?

Answers: 1. Yin metal. 2. Wu and Ji. 3. A river or sea.

Lesson 21 · The Twelve Earthly Branches#

Learning goals#

Memorize the attributes associated with the Twelve Branches.
Understand the historical use of zodiac-animal correspondences.
Use the hand diagram as a memory aid.

Lesson#

The Twelve Branches—Zi through Hai—form a cycle used for months, double hours, directions, and zodiac animals. These correspondences have their own rules. Yin can name a month branch, a time interval, or the branch paired with the tiger; do not merge those uses simply because the label is the same. Early Qin Rishu (“daybooks”), including material from Shuihudi, contain animal-branch pairings that are not identical to the modern zodiac table.

Branch	Yin or yang	Phase	Zodiac animal	Direction	Month begins at	Double hour
Zi	Yang	Water	Rat	North	Major Snow / 11th month	23:00–01:00
Chou	Yin	Earth	Ox	North-northeast	Minor Cold / 12th month	01:00–03:00
Yin	Yang	Wood	Tiger	East-northeast	Beginning of Spring / 1st month	03:00–05:00
Mao	Yin	Wood	Rabbit	East	Awakening of Insects / 2nd month	05:00–07:00
Chen	Yang	Earth	Dragon	East-southeast	Pure Brightness / 3rd month	07:00–09:00
Si	Yin	Fire	Snake	South-southeast	Beginning of Summer / 4th month	09:00–11:00
Wu	Yang	Fire	Horse	South	Grain in Ear / 5th month	11:00–13:00
Wei	Yin	Earth	Goat	South-southwest	Minor Heat / 6th month	13:00–15:00
Shen	Yang	Metal	Monkey	West-southwest	Beginning of Autumn / 7th month	15:00–17:00
You	Yin	Metal	Rooster	West	White Dew / 8th month	17:00–19:00
Xu	Yang	Earth	Dog	West-northwest	Cold Dew / 9th month	19:00–21:00
Hai	Yin	Water	Pig	North-northwest	Beginning of Winter / 10th month	21:00–23:00

The branches Zi, Wu, Mao, and You are the Four Cardinal branches; Yin, Shen, Si, and Hai are called the Four Birth branches; Chen, Xu, Chou, and Wei are the Four Storage branches, assigned to the end of each season. A hand diagram places the twelve branches around the finger joints as a way to remember their order and relationships. It is a memory tool, not another calendar.

With the civil double-hour table, 06:20 falls in Mao hour because Mao runs from 05:00 to 07:00. A chart calculation needs further assumptions about location, time zone, true solar time, and the day boundary.

Practice#

Recreate the table’s phase, animal, direction, and month columns.
Make twelve branch flashcards.
On your hand, point out the Four Cardinal, Four Birth, and Four Storage branches.

Check your understanding#

What phase and animal are assigned to Xu?
Which branches are the Four Storage branches?
Which solar term begins the Yin month?

Answers: 1. Earth and dog. 2. Chen, Xu, Chou, and Wei. 3. The Beginning of Spring.

Lesson 22 · The Sexagenary Cycle and Year Designations#

Learning goals#

Understand how the sixty stem-branch pairs are formed.
Calculate a year’s sexagenary designation.
Apply the correct year boundary for a chart.

Lesson#

The sexagenary cycle pairs the Ten Stems and Twelve Branches while both advance one place at a time. Their least common multiple is sixty, so the sequence returns to Jia-Zi after sixty pairs. The cycle pairs yang stems with yang branches and yin with yin; Jia-Chou is not a pairing. Each group of ten starts with Jia, yielding six “decades” or xun.

Xun	Ten pairs
Jia-Zi	Jia-Zi, Yi-Chou, Bing-Yin, Ding-Mao, Wu-Chen, Ji-Si, Geng-Wu, Xin-Wei, Ren-Shen, Gui-You
Jia-Xu	Jia-Xu, Yi-Hai, Bing-Zi, Ding-Chou, Wu-Yin, Ji-Mao, Geng-Chen, Xin-Si, Ren-Wu, Gui-Wei
Jia-Shen	Jia-Shen, Yi-You, Bing-Xu, Ding-Hai, Wu-Zi, Ji-Chou, Geng-Yin, Xin-Mao, Ren-Chen, Gui-Si
Jia-Wu	Jia-Wu, Yi-Wei, Bing-Shen, Ding-You, Wu-Xu, Ji-Hai, Geng-Zi, Xin-Chou, Ren-Yin, Gui-Mao
Jia-Chen	Jia-Chen, Yi-Si, Bing-Wu, Ding-Wei, Wu-Shen, Ji-You, Geng-Xu, Xin-Hai, Ren-Zi, Gui-Chou
Jia-Yin	Jia-Yin, Yi-Mao, Bing-Chen, Ding-Si, Wu-Wu, Ji-Wei, Geng-Shen, Xin-You, Ren-Xu, Gui-Hai

For a quick year-name calculation, the lesson’s mnemonic maps the final digit of the Gregorian year to the stem: 0 Geng, 1 Xin, 2 Ren, 3 Gui, 4 Jia, 5 Yi, 6 Bing, 7 Ding, 8 Wu, 9 Ji. For the branch, subtract 4 from the year and take the remainder after division by 12: 0 Zi, 1 Chou, through 11 Hai. Thus 2026 ends in 6, giving Bing; 2026 − 4 = 2022, which leaves a remainder of 6 when divided by 12, giving Wu. The year label is Bing-Wu.

That calculation gives a Gregorian year’s sequence label. A BaZi year pillar uses the stem-branch calendar and generally changes at the exact Beginning of Spring, not at January 1 or Lunar New Year. A birthday before that year’s solar-term boundary is assigned to the previous stem-branch year. The formula also needs adjustment for BCE years because there is no year zero.

Practice#

Memorize the sixty-pair table, or at least the first and last pair of every xun.
Calculate the year names for 1949, 1984, 2000, and 2030.
Calculate a family member’s birth-year label, checking whether the birthday fell before that year’s Beginning of Spring.

Check your understanding#

What was the sexagenary designation of 1984?
What is the last pair in the Jia-Shen xun?
A person was born on January 25, 2027. Which stem-branch year applies before the 2027 Beginning of Spring?

Answers: 1. Jia-Zi. 2. Gui-Si. 3. Bing-Wu, because the Beginning of Spring in 2027 was on February 4.

Lesson 23 · Month Stems and the Five Tigers Method#

Learning goals#

Learn the Five Tigers mnemonic and its derivation.
Calculate a month’s stem-branch within a given year.

Lesson#

The four pillars are stem-branch pairs assigned to a person’s year, month, day, and hour. The month branch is established from the solar-term month: Yin begins at the Beginning of Spring, Mao at Awakening of Insects, and so on. The month stem is then derived from the year stem using the Five Tigers method (Wuhu Dun). First establish the year designation, use the mnemonic to find the stem of Yin month, and then advance both stems and branches one step per month.

The mnemonic is:

For Jia and Ji, Bing is the head; for Yi and Geng, Wu begins.
For Bing and Xin, seek Geng; for Ding and Ren, Ren flows from Yin.
For Wu and Gui, ask where it starts: Jia-Yin is the place to begin.

Year stem	Stem combination	Phase produced	Yin-month pillar
Jia or Ji	Jia-Ji	Earth	Bing-Yin
Yi or Geng	Yi-Geng	Metal	Wu-Yin
Bing or Xin	Bing-Xin	Water	Geng-Yin
Ding or Ren	Ding-Ren	Wood	Ren-Yin
Wu or Gui	Wu-Gui	Fire	Jia-Yin

Within this system, the Five Tigers rule is explained through the Five-Phase relationships of the stem combinations. This shows how the rule is made internally coherent; it does not mean that an astronomical solar-term boundary physically causes a particular stem.

For a Bing-Wu year, the Yin month begins Geng-Yin. Advancing the sequence gives Xin-Mao, Ren-Chen, Gui-Si, Jia-Wu, Yi-Wei, Bing-Shen, Ding-You, Wu-Xu, Ji-Hai, Geng-Zi after Major Snow, and Xin-Chou after Minor Cold. The solar-term boundary—not the lunar first day—determines when the month pillar changes.

Practice#

Memorize the Five Tigers mnemonic, then reconstruct it from the table.
Write all twelve month pillars for Ding-Wei year 2027.
Find your birth month pillar by locating the two solar nodes that bound your birth date.

Check your understanding#

What is the Yin-month pillar in a Wu year?
What is the month pillar from Major Snow until Minor Cold in 2026?
How does the Five Tigers rule relate to the Ten Stem combinations?

Answers: 1. Jia-Yin. 2. Geng-Zi. 3. The stem combination’s associated phase determines the generating phase used for the Yin-month stem in this traditional derivation.

Lesson 24 · Day Stems and Branches: Calculating from a Base Date#

Learning goals#

Calculate a day’s stem-branch from a verified base date.
Track the date difference accurately, including leap days.

Lesson#

Day stems and branches advance one place through the sixty-pair cycle on each successive civil date. Choose a base date whose day pillar has been independently verified, calculate the number of elapsed calendar days, add that difference to the base sequence number, and reduce it modulo sixty. Do not count the base date twice; use the actual number of days in each month, including February 29 in a leap year.

The lesson numbers the cycle from Jia-Zi = 1 through Gui-Hai = 60. If the stem number is g (Jia = 1 through Gui = 10) and branch number is z (Zi = 1 through Hai = 12), its index is the remainder of (6g − 5z) divided by 60; add 60 if the result is negative and treat remainder zero as 60. For Ding-Hai, g = 4 and z = 12: 24 − 60 = −36; adding 60 gives index 24.

To advance from a base date, add the elapsed days to its index and reduce modulo sixty. The lesson offers 2000-01-01 as Wu-Wu, index 55; 2026-11-09 as Ding-Hai, index 24; and 1949-10-01 as Jia-Zi, index 1. Verify a base date independently before using it. For example, March 1, 2000 is sixty days after January 1 in leap year 2000, so its day pillar returns to Wu-Wu.

The output is a date label. It does not decide which time zone to use or how a birth during Zi hour crosses the day boundary. State those conventions separately when calculating a chart.

Practice#

Memorize one verified base date.
Calculate your next birthday’s day pillar, then compare it with a reliable calendar.
Calculate the day pillar for 2027-01-01 using a stated base date.

Check your understanding#

What is the index of Wu-Wu?
Which pair has index 44?
What day pillar occurs sixty days after a given day pillar?

Answers: 1. For Wu-Wu, g = 5 and z = 7: 30 − 35 = −5; adding 60 gives 55. 2. Index 44 is Ding-Wei. 3. The same pillar.

Lesson 25 · Hour Stems and Branches: Five Rats and Empty Branches#

Learning goals#

Use the Five Rats method to calculate hour pillars.
Find the empty branches (xunkong) for a day’s xun.

Lesson#

The hour pillar has a stem and branch. First determine the branch from the double-hour interval; then use the day stem and the Five Rats rule (Wushu Dun) to set the stem of Zi hour, advancing both in sequence for each subsequent double hour.

For Jia and Ji, begin with Jia; for Yi and Geng, start with Bing.
For Bing and Xin, begin at Wu; for Ding and Ren, Geng sits at Zi.
For Wu and Gui, where does it begin? Ren-Zi is the true path.

Day stem	Stem combination	Phase produced	Zi-hour pillar
Jia or Ji	Jia-Ji	Earth	Jia-Zi
Yi or Geng	Yi-Geng	Metal	Bing-Zi
Bing or Xin	Bing-Xin	Water	Wu-Zi
Ding or Ren	Ding-Ren	Wood	Geng-Zi
Wu or Gui	Wu-Gui	Fire	Ren-Zi

For example, on a Jia day, Zi hour is Jia-Zi. Advancing through Chou, Yin, Mao, Chen, and Si gives Yi-Chou, Bing-Yin, Ding-Mao, Wu-Chen, and Ji-Si; Wu hour is Geng-Wu. Writing each step makes it easier to catch a skipped branch.

Xunkong (empty branches) are the two branches omitted from each ten-day xun. A xun advances ten stems but twelve branches, leaving two branch positions without a stem in that segment:

Xun	Jia-Zi	Jia-Xu	Jia-Shen	Jia-Wu	Jia-Chen	Jia-Yin
Empty branches	Xu-Hai	Shen-You	Wu-Wei	Chen-Si	Yin-Mao	Zi-Chou

For example, Xin-Mao belongs to the Jia-Wu xun, whose empty branches are Chen and Si. In Liuyao and date selection, an empty branch can be interpreted as unrealized, insubstantial, or temporarily absent within that system. It does not mean the branch or related real-world thing does not exist.

Practice#

Memorize the Five Rats mnemonic and reconstruct its table.
Calculate the hour pillars for Ding day at Shen hour, Jia day at Wu hour, and Gui day at Hai hour.
Find the empty branches for today’s day pillar.

Check your understanding#

What is the hour pillar at Wu hour on a Geng day?
What are the empty branches of Jia-Wu xun?
Which branches are empty on a Gui-You day?

Answers: 1. Ren-Wu. 2. Chen and Si. 3. Gui-You is in Jia-Yin xun, so the empty branches are Zi and Chou.

Lesson 26 · Assessment: Calculating Stem-Branch Combinations#

Review method#

This assessment switches between classification, sequence arithmetic, and astronomical boundaries. A four-pillar chart uses a pair for year, month, day, and hour. The year pillar changes at the Beginning of Spring; the month pillar changes at a solar node; the day pillar advances through calendar days under a stated day-boundary convention; the hour pillar uses the time branch and the day stem. To check an answer, write the full chain rather than comparing only the final result with software.

Use a verified base date for calculation problems, state the time zone and solar-term moment for boundary problems, and return to the cited text for historical questions. When software and hand calculation disagree, compare calendar, time zone, true-solar-time setting, and Zi-hour convention before assuming an arithmetic error.

Closed-book assessment#

Suggested time: 40 minutes. Passing score: 80 out of 100.

Give the yin-yang and Five-Phase assignments of the Ten Stems, and the phases and zodiac animals of the Twelve Branches. (16 points)
Write the first and last pairs of each of the six xun. (6 points)
Calculate the year designations for 1990, 2008, and 2031. (9 points)
Write the Five Tigers and Five Rats mnemonics and explain each rule in one sentence. (16 points)
Find the month pillars for the Chen and You months of Ding-Wei year 2027. (8 points)
Given that 2000-01-01 is Wu-Wu, calculate the day pillar on 2000-03-01. (12 points)
Find the hour pillar at Si hour on the date in Question 6, and that day’s empty branches. (12 points)
List the empty branches for all six xun. (12 points)
Why does the stem-branch year change at the Beginning of Spring in this calendar? (9 points)

Answer key for supplied items: 3. Geng-Wu, Wu-Zi, Xin-Hai. 5. Jia-Chen and Ji-You. 6. January has 31 days and February 29 in leap year 2000, a total of 60 days; the day pillar returns to Wu-Wu. 7. On a Wu day, Zi hour begins Ren-Zi; advancing to Si gives Ding-Si. Wu-Wu is in Jia-Yin xun, whose empty branches are Zi and Chou. 9. The stem-branch calendar follows solar terms; the Beginning of Spring is at the sun’s apparent ecliptic longitude of 315 degrees and marks the Yin-month year beginning.

Lesson 27 · Five Stem Combinations and Four Clashes#

Learning goals#

Memorize the Five Combinations and their traditional transformations.
Identify the Four Clashes.
Distinguish a combination from a transformation.

Lesson#

The Five Stem Combinations pair Jia-Ji, Yi-Geng, Bing-Xin, Ding-Ren, and Wu-Gui. Traditional tables associate them with earth, metal, water, wood, and fire, respectively. The Four Clashes pair Jia-Geng, Yi-Xin, Bing-Ren, and Ding-Gui. Wu and Ji are central in the directional scheme and are not included in the Four Clashes.

Combination	Traditional transformation
Jia-Ji	Earth
Yi-Geng	Metal
Bing-Xin	Water
Ding-Ren	Wood
Wu-Gui	Fire

In a destiny-calculation tradition, “combination” means two stems form a paired relation in the rule table; “transformation” is a further judgment that the relationship changes into another phase. A combination does not automatically transform. A school may require support from the month command, position, and the absence of interference. When conditions have not been checked, “Jia and Ji combine; transformation into earth is undecided” is more precise.

For a fictional chart with Jia in the year stem and Ji in the month stem, first mark the Jia-Ji combination. To judge transformation, state which school’s rules you are using and check its conditions. The Four Clashes are likewise symbolic relationships; the word “clash” alone does not establish a real-world conflict or disaster. These are later destiny-calculation rules and should not be projected back onto early stem notation.

Practice#

Memorize the Five Combinations and Four Clashes.
Find stem-branch pairs in the sixty-cycle whose branch’s principal stem forms a combination with the stem.
Explain how the Five Tigers and Five Rats rules use the Five Combinations.

Check your understanding#

Which stem combines with Ding, and what phase is assigned to their combination?
Which stem clashes with Bing?
How does combination differ from transformation?

Answers: 1. Ren; wood. 2. Ren. 3. Combination is the paired relation; transformation is a conditional judgment that the relationship changes phase.

Lesson 28 · Six Clashes and Six Combinations of the Branches#

Learning goals#

Memorize the Six Clashes and Six Combinations.
Locate them on the branch hand diagram.

Lesson#

The Six Clashes pair branches six positions apart on the twelve-branch circle: Zi-Wu, Chou-Wei, Yin-Shen, Mao-You, Chen-Xu, and Si-Hai. The Six Combinations are another traditional set of paired relations:

Combination	Traditional transformation
Zi-Chou	Earth
Yin-Hai	Wood
Mao-Xu	Fire
Chen-You	Metal
Si-Shen	Water
Wu-Wei	Fire or earth, depending on the source

“Clash” and “combination” are structural labels within a model. Neither is inherently good or bad, nor does it by itself predict that people or events will change. In a fictional chart, or when reading an almanac phrase such as “clashes with the rabbit,” first translate the animal to its branch (rabbit = Mao), then find Mao’s clash (You). If the day is indeed You, the label has been decoded; that is not a prediction about a rabbit-year person’s day. Full destiny or almanac judgments may also use positions, seasonal strength, jianchu, or spirits, and need their own rules.

Some manuals describe a combination as restraining a branch and a clash as opening it, but the sequence for resolving overlapping relations depends on the system. Do not treat “combination” as automatic transformation; Wu-Wei in particular has differing transformation explanations.

Practice#

Point out the Six Clashes and Six Combinations on the hand diagram.
Find the branches corresponding to your family’s zodiac animals and list their clashes and combinations.
Identify which zodiac animal is traditionally paired with today’s day branch’s clash.

Check your understanding#

Which branch clashes with Si, and which combines with it?
What phase is assigned to the Mao-Xu combination?
If an almanac says “clashes with the rabbit,” what day branch is implied?

Answers: 1. Hai clashes with Si; Shen combines with it. 2. Fire. 3. You.

Lesson 29 · Three Harmonies and Three Meetings#

Learning goals#

Memorize the Four Three-Harmony combinations and Four Three-Meeting groups.
Understand the “birth, peak, tomb” pattern in Three Harmonies.
Distinguish a half combination from an arched combination.

Lesson#

The Three Harmonies and Three Meetings are different three-branch groupings. A Three-Harmony combination uses birth, peak, and tomb positions: Shen-Zi-Chen forms the water group, for example. A Three-Meeting group collects branches assigned to one season and direction.

Three-Harmony group	Birth	Peak	Tomb	Phase
Shen-Zi-Chen	Shen	Zi	Chen	Water
Hai-Mao-Wei	Hai	Mao	Wei	Wood
Yin-Wu-Xu	Yin	Wu	Xu	Fire
Si-You-Chou	Si	You	Chou	Metal

The pattern starts with one of the Four Birth branches, peaks at one of the Four Cardinal branches, and ends at one of the Four Storage branches. If two branches appear without the third, systems may call a pair containing the peak branch a half combination (banhe) and a pair missing the peak an arched combination (gonghe). These names describe incomplete groupings; whether either counts as a formed combination depends on the school, month command, and positions.

Three-Meeting group	Direction and phase
Yin-Mao-Chen	East, wood
Si-Wu-Wei	South, fire
Shen-You-Xu	West, metal
Hai-Zi-Chou	North, water

Some traditions regard a Three-Meeting group as stronger than a Three-Harmony group, but this is not a rule that removes the need to examine context.

Practice#

Write the Three-Harmony and Three-Meeting groups from memory.
Find the four triangles formed by the Three-Harmony groups on the hand diagram.
Name the Three-Harmony and Three-Meeting groups that include your zodiac branch.

Check your understanding#

Which Three-Harmony and Three-Meeting groups include Wu?
What is the term for Shen and Chen without Zi under this lesson’s convention?
What do the middle branches of the Four Three-Harmony groups have in common?

Answers: 1. Yin-Wu-Xu, fire; and Si-Wu-Wei, south/fire. 2. An arched combination, because the peak branch Zi is missing. 3. They are the Four Cardinal branches: Zi, Wu, Mao, and You.

Lesson 30 · The Twelve Growth Stages#

Learning goals#

Memorize the Twelve Growth Stages.
Derive a stem’s stages from its starting branch.
Recognize variation in yin-stem and earth conventions.

Lesson#

The Twelve Growth Stages (shier changsheng) assign a sequence of symbolic conditions to a stem or phase across the twelve branches. The names borrow the imagery of a life cycle: Birth, Bath, Cap and Belt, Official Position (also called Establishing Rank), Prosperity, Decline, Sickness, Death, Tomb, Extinction, Conception, and Nourishment. Texts differ in their detailed interpretations. These are symbolic labels, not forecasts of literal life or illness.

Under this lesson’s convention, wood is born at Hai, fire at Yin, metal at Si, and water at Shen; earth is associated with fire in one convention and with water in another. The birth branch is the first branch of the corresponding Three-Harmony group. For Jia wood, which proceeds forward in the yang-stem convention, Hai is Birth, Zi Bath, Chou Cap and Belt, Yin Official Position, Mao Prosperity, then onward through the cycle until Shen is Extinction.

Stem	Birth	Prosperity	Tomb	Direction
Jia	Hai	Mao	Wei	Forward
Bing, Wu	Yin	Wu	Xu	Forward
Geng	Si	You	Chou	Forward
Ren	Shen	Zi	Chen	Forward
Yi	Wu	Yin	Xu	Reverse
Ding, Ji	You	Si	Chou	Reverse
Xin	Zi	Shen	Chen	Reverse
Gui	Mao	Hai	Wei	Reverse

Many tables say yang stems proceed forward and yin stems backward (“yang is born where yin dies; yin is born where yang dies”). Other traditions let yin and yang share the same birth and death positions. State which table you use. Birth, Prosperity, or Death cannot by itself determine whether a chart is favorable; the day master, month command, and the rest of the system matter.

Practice#

Memorize the twelve-stage sequence.
Write the full Jia wood sequence starting from Hai.
Write the Geng metal sequence from its birth branch.

Check your understanding#

Where is Bing fire’s Prosperity stage?
Where is Ren water’s Tomb stage?
Why is a Five-Phase birth branch the first branch of its Three-Harmony group?

Answers: 1. Wu. 2. Chen. 3. In this model, the birth, peak, and tomb positions of the phase align with the Three-Harmony pattern.

Lesson 31 · Punishments, Harms, Breaks, and Hidden Stems#

Learning goals#

Memorize the Three Punishments, Six Harms, and Six Breaks.
Learn the hidden-stem table.

Lesson#

Punishment, harm, and break are three categories of branch relations in traditional tables. “Punishment” (xing) refers to specified patterns of restraint or discord; “harm” (hai) to six pairs described as covertly obstructive; and “break” (po) to six pairs described as disruptive. The ethical names “ungrateful,” “relying on power,” and “disrespectful” are symbolic labels from later traditions, not objective descriptions of people. Self-punishment is assigned when Chen, Wu, You, or Hai repeats with itself. Systems differ in how these relations are applied and weighted; none automatically indicates actual injury.

The Three Punishments are Yin-Si-Shen (ungrateful), Chou-Xu-Wei (relying on power), and Zi-Mao (disrespectful), plus self-punishment for Chen-Chen, Wu-Wu, You-You, and Hai-Hai. The Six Harms are Zi-Wei, Chou-Wu, Yin-Si, Mao-Chen, Shen-Hai, and You-Xu. The Six Breaks are Zi-You, Chou-Chen, Yin-Hai, Mao-Wu, Si-Shen, and Wei-Xu.

Hidden stems (canggan) are another table that places stems inside branches. The first entry is usually called the principal qi; later entries are secondary qi. They are levels within a system, not literal matter hidden inside a branch.

Branch	Hidden stems	Branch	Hidden stems
Zi	Gui	Wu	Ding, Ji
Chou	Ji, Gui, Xin	Wei	Ji, Ding, Yi
Yin	Jia, Bing, Wu	Shen	Geng, Ren, Wu
Mao	Yi	You	Xin
Chen	Wu, Yi, Gui	Xu	Wu, Xin, Ding
Si	Bing, Geng, Wu	Hai	Ren, Jia

The Four Cardinal branches (Zi, Wu, Mao, You) have fewer hidden stems in this table. The Four Storage branches (Chen, Xu, Chou, Wei) hold three. Chen is also called the water storehouse because it is the tomb branch in the Shen-Zi-Chen water group; this is a Three-Harmony metaphor, not the same rule as the hidden-stem table.

Practice#

Memorize the Three Punishments, Six Harms, and Six Breaks.
Memorize the hidden stems.
Explain why Chen is called the water storehouse and Xu the fire storehouse.

Check your understanding#

What punishment is assigned to Yin-Si-Shen?
Which stems are hidden in Wei?
What relation links Zi and Wei?

Answers: 1. The ungrateful punishment. 2. Ji, Ding, Yi. 3. A Six Harm.

Lesson 32 · An Overview of Auxiliary Stars (Shensha)#

Learning goals#

Recognize several frequently used auxiliary stars.
Understand their place and debated weight within divination systems.

Lesson#

Shensha are auxiliary labels calculated from stem-branch combinations. Their names and calculation methods vary by tradition. Tianyi Nobleman is often interpreted as assistance from benefactors; Prosperity (lu) as salary or foundation; Yang Blade as sharpness or force; Peach Blossom as social or romantic appeal; Traveling Horse as movement; Canopy as solitude, art, or religion; and Literary Star as writing ability. A label is not a fact about someone’s future just because its name sounds auspicious or ominous.

Before calculating a star, decide which pillar is the reference point and which table applies. For the Shen-Zi-Chen group, this lesson’s Traveling Horse rule takes Shen and then its opposing branch, Yin. That is a reproducible lookup; it does not prove that the person will move house or travel. The received Ziping Zhenquan includes a chapter titled “Stars Do Not Determine the Structure,” expressing one internal critique of making auxiliary stars govern the chart. Editions and commentaries differ, so identify the text you are citing.

Auxiliary star	Lookup rule	Common traditional interpretation
Tianyi Nobleman	Jia, Wu, Geng see Chou/Wei; Yi, Ji see Zi/Shen; Bing, Ding see Hai/You; Ren, Gui see Mao/Si; Xin sees Wu/Yin	Help from benefactors
Prosperity (lu)	Jia-Yin, Yi-Mao, Bing/Wu-Si, Ding/Ji-Wu, Geng-Shen, Xin-You, Ren-Hai, Gui-Zi	Salary, foundation
Yang Blade	Jia-Mao, Bing/Wu-Wu, Geng-You, Ren-Zi	Force, risk of injury
Peach Blossom	Shen-Zi-Chen see You; Yin-Wu-Xu see Mao; Si-You-Chou see Wu; Hai-Mao-Wei see Zi	Social or romantic appeal
Traveling Horse	Shen-Zi-Chen see Yin; Yin-Wu-Xu see Shen; Si-You-Chou see Hai; Hai-Mao-Wei see Si	Travel or movement
Canopy	Shen-Zi-Chen see Chen; Yin-Wu-Xu see Xu; Si-You-Chou see Chou; Hai-Mao-Wei see Wei	Solitude, art, religion
Literary Star	Jia-Si, Yi-Wu, Bing/Wu-Shen, Ding/Ji-You, Geng-Hai, Xin-Zi, Ren-Yin, Gui-Mao	Literary ability

Peach Blossom is associated with the bath position of the Three-Harmony group; the Traveling Horse is opposite its first branch; Canopy is the group’s tomb/storage branch. These are mnemonic patterns in the system, not empirical claims.

Practice#

Memorize the Tianyi Nobleman mnemonic: “Jia, Wu, and Geng see ox and goat; Yi and Ji see rat and monkey; Bing and Ding see pig and rooster; Ren and Gui hide rabbit and snake; Xin meets horse and tiger.”
Calculate Peach Blossom, Traveling Horse, and Canopy from your year or day branch, naming the reference point.
Explain why the Shen-Zi-Chen Traveling Horse is Yin.

Check your understanding#

Which two branches are Tianyi Nobleman for a Geng day?
Where is Peach Blossom for the Yin-Wu-Xu group?
What position does Ziping Zhenquan assign to auxiliary stars?

Answers: 1. Chou and Wei. 2. Mao. 3. They should not determine the overall chart structure.

Lesson 33 · Assessment: Branch Relationships#

Review method#

This assessment moves among several tables: clashes are opposite positions, combinations are paired relations, punishments, harms, and breaks are other traditional relation labels, Three Harmonies group birth-peak-tomb branches, Three Meetings group a season and direction, and the Twelve Growth Stages require a stated starting point and direction. An auxiliary star also requires a named reference pillar. Write the rule name before listing members or performing a calculation; note a school difference when it matters.

When checking a complete chart, distinguish “the branch can relate to X” from “X is present in the chart.” Wu’s relationship lookup may list Zi, Wei, Yin-Wu-Xu, Si-Wu-Wei, Wu-Wu, Chou, and Mao, but absent branches do not form relations in a particular chart. The exercise checks symbolic calculation, not a prediction of fortune.

Closed-book assessment#

Suggested time: 45 minutes. Passing score: 80 out of 100.

Write the Five Stem Combinations and transformations, and the Four Clashes. (10 points)
Write the Six Clashes and Six Combinations. (12 points)
Write the Four Three-Harmony and Four Three-Meeting groups. (12 points)
Give the birth branches for Jia, Bing, Geng, Ren, Yi, and Gui in the Twelve Growth Stages. (12 points)
Write the Three Punishments and Six Harms. (12 points)
Write the hidden stems for the Twelve Branches. (12 points)
List all branches related to Wu by clash, combination, Three Harmony, Three Meeting, punishment, harm, and break. (10 points)
Write the Tianyi Nobleman mnemonic. (10 points)
Explain the difference between “combination” and “transformation,” and between a half combination and an arched combination. (10 points)

Answer key for supplied items: 4. Jia-Hai, Bing-Yin, Geng-Si, Ren-Shen, Yi-Wu, Gui-Mao. 7. Clash: Zi; combination: Wei; Three Harmony: Yin-Wu-Xu; Three Meeting: Si-Wu-Wei; self-punishment: Wu-Wu; harm: Chou; break: Mao. 9. Combination is a paired relation, while transformation is a conditional change of phase; a half combination includes the peak branch, while an arched combination lacks it.

Module outcome#

You are ready to continue when you can explain the difference between the earliest calendrical use of stem-branch notation and later symbolic interpretation, calculate each pillar under stated conventions, and identify branch relationships without treating a lookup table as a guaranteed prediction.

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