M04 · LESSONS 34–39
Module 4 · Hetu, Luoshu, Na Yin, and Date Selection (Lessons 34–39)
This module brings together several kinds of traditional correspondences: the Hetu and Luoshu number diagrams, musical pitch systems, Na Yin labels, and almanac rules. They share inputs such as stems, branches, directions, or dates, but they developed in different contexts. A symbol’s presence in an almanac does not make all the rules one ancient, unified system.
Lesson 34 · Hetu, Luoshu, and the Nine Palaces#
Learning goals#
- Draw the traditional Hetu and Luoshu diagrams.
- Understand the diagrammatic terms “generating number” and “completing number.”
- Match Luoshu numbers with the Later Heaven trigrams and practice the nine-palace route.
Lesson#
The Yijing, “Appended Statements A,” says, “The River brought forth the Diagram; the Luo brought forth the Writing; the sages took these as models.” The passage preserves a legend but does not draw the familiar black-and-white dot diagrams. The standard diagrams took shape in Song-period Yijing studies. Liu Mu’s Northern Song Yishu gouyin tu called the nine-number diagram the Hetu and the ten-number diagram the Luoshu. Zhu Xi and Cai Yuanding’s Original Meaning of the Changes used the reverse naming; Zhu Xi’s version became more common in later teaching. Mention of “River Diagram and Luo Writing” in an early text does not prove that the later diagrams were already in use. The Shandong University Center for Zhouyi Studies describes Liu Mu’s scheme as an innovation in Song Yijing studies, helping distinguish an ancient legend from the documented history of the diagrams.
The Hetu arranges one through ten into five number-pairs. In each pair, a “generating number” from one through five is matched with a “completing number” five higher. For example, north is one and six, associated with water; east is three and eight, associated with wood. “Generating” and “completing” name positions in the diagram; they are not experimental descriptions of how matter forms.
| Direction | Number pair | Phase | Traditional formula |
|---|---|---|---|
| North | 1, 6 | Water | Heaven 1 generates water; Earth 6 completes it |
| South | 2, 7 | Fire | Earth 2 generates fire; Heaven 7 completes it |
| East | 3, 8 | Wood | Heaven 3 generates wood; Earth 8 completes it |
| West | 4, 9 | Metal | Earth 4 generates metal; Heaven 9 completes it |
| Center | 5, 10 | Earth | Heaven 5 generates earth; Earth 10 completes it |
The Luoshu is not a set of five pairs. It places each number from one to nine once in a three-by-three square. With the top treated as south, every row, column, and diagonal sums to fifteen. The mnemonic “Nine on the head, one beneath; three left, seven right; two and four as shoulders, six and eight as feet; five in the center” describes the layout.
The Nine Palaces divide a plane into a center and eight surrounding directions. The Later Heaven trigrams arrange eight trigrams by direction and sequence, leaving the center for five. Combining the Luoshu numbers and Later Heaven trigrams gives Kan 1, Kun 2, Zhen 3, Xun 4, center 5, Qian 6, Dui 7, Gen 8, and Li 9.
| Southwest: 2, Kun | South: 9, Li | Southeast: 4, Xun |
|---|---|---|
| West: 7, Dui | Center: 5 | East: 3, Zhen |
| Northwest: 6, Qian | North: 1, Kan | Northeast: 8, Gen |
“Flying stars” describes procedures that move the nine numbers through the palaces along a set route. In the Luoshu pattern, five enters the center; then numbers one through nine are placed center, northwest, west, northeast, south, north, southwest, east, southeast. For a practice sequence with nine in the center, follow the same route: center 9, northwest 1, west 2, northeast 3, south 4, north 5, southwest 6, east 7, southeast 8. Xuan Kong feng shui and Qimen Dunjia use nine-palace movement rules, but the calculation alone does not prove that a direction causes a real-world outcome.
Practice#
- Draw the Hetu and Luoshu from memory.
- Verify that all eight Luoshu rows, columns, and diagonals sum to fifteen.
- Place nine in the center and fill the grid by following the nine-palace route.
Check your understanding#
- What phase and direction do the Hetu numbers four and nine represent?
- Which number and trigram are in the Luoshu’s south palace?
- In which period did the standard Hetu and Luoshu diagrams take shape?
Answers: 1. Metal, west. 2. Nine, Li. 3. Song-period Yijing studies.
Lesson 35 · The Five Tones, Pitch Standards, and Na Yin#
Learning goals#
- Learn the traditional associations of the Five Tones and Twelve Pitch Standards.
- Understand Na Yin as a separate layer of stem-branch classification.
- Recognize historical explanations without mistaking them for modern acoustics.
Lesson#
The Five Tones, pitch standards (lü), and Na Yin all involve sound, but they are different levels of classification. Gong, Shang, Jiao, Zhi, and Yu are the five tones of the traditional scale, associated respectively with earth, metal, wood, fire, and water. The Twelve Pitch Standards—Huangzhong, Dalu, Taicu, Jiazhong, Guxian, Zhonglü, Ruibin, Linzhong, Yize, Nanlü, Wuyi, and Yingzhong—are standard pitch names. They were also paired with the twelve earthly branches and months in ritual-calendar schemes.
The ancient “three-part loss and gain” method (sansun sunyi) generated pitches from pipe lengths by multiplying by two-thirds or four-thirds, producing intervals related to fifths. The Yueling (“Monthly Ordinances”) pairs months with pitch names, showing how ritual, music, and calendrical order were thought to correspond. This is historical music theory, not modern acoustic proof of Five-Phase attributes.
| Tone | Gong | Shang | Jiao | Zhi | Yu |
|---|---|---|---|---|---|
| Assigned phase | Earth | Metal | Wood | Fire | Water |
| Branch | Zi | Chou | Yin | Mao | Chen | Si | Wu | Wei | Shen | You | Xu | Hai |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Pitch standard | Huangzhong | Dalu | Taicu | Jiazhong | Guxian | Zhonglü | Ruibin | Linzhong | Yize | Nanlü | Wuyi | Yingzhong |
| Lunar month | 11th | 12th | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th |
Na Yin takes each adjacent pair in the sixty-pair cycle and assigns it a phase label and image, such as “Metal in the Sea” or “Fire in the Furnace.” Shen Kuo’s Dream Pool Essays, “Pitch Standards,” explains Na Yin through “the twelve pitch standards rotating as palace”: each of the twelve standards in turn serves as the gong (the central tone of a tonal set), generating five tones, for sixty sound positions matched with the sixty stem-branch pairs. This is a Song-period explanation of the correspondence, not a derivation accepted by modern acoustics.
| Xun | Pair 1 | Pair 2 | Pair 3 | Pair 4 | Pair 5 |
|---|---|---|---|---|---|
| Jia-Zi | Jia-Zi / Yi-Chou · Metal in the Sea | Bing-Yin / Ding-Mao · Fire in the Furnace | Wu-Chen / Ji-Si · Wood of the Great Forest | Geng-Wu / Xin-Wei · Earth by the Road | Ren-Shen / Gui-You · Sword-Edge Metal |
| Jia-Xu | Jia-Xu / Yi-Hai · Fire on the Mountain | Bing-Zi / Ding-Chou · Water in the Ravine | Wu-Yin / Ji-Mao · Earth on the City Wall | Geng-Chen / Xin-Si · White Wax Metal | Ren-Wu / Gui-Wei · Willow Wood |
| Jia-Shen | Jia-Shen / Yi-You · Water from a Spring | Bing-Xu / Ding-Hai · Earth on the Roof | Wu-Zi / Ji-Chou · Thunder Fire | Geng-Yin / Xin-Mao · Pine and Cypress Wood | Ren-Chen / Gui-Si · Long-Flowing Water |
| Jia-Wu | Jia-Wu / Yi-Wei · Metal in Sand | Bing-Shen / Ding-You · Fire at the Foot of the Mountain | Wu-Xu / Ji-Hai · Wood on the Plain | Geng-Zi / Xin-Chou · Earth on a Wall | Ren-Yin / Gui-Mao · Gold Foil |
| Jia-Chen | Jia-Chen / Yi-Si · Covered-Lamp Fire | Bing-Wu / Ding-Wei · Water of the Heavenly River | Wu-Shen / Ji-You · Earth on the Great Road | Geng-Xu / Xin-Hai · Hairpin Metal | Ren-Zi / Gui-Chou · Mulberry and Zhe Wood |
| Jia-Yin | Jia-Yin / Yi-Mao · Water of the Great Stream | Bing-Chen / Ding-Si · Earth in Sand | Wu-Wu / Ji-Wei · Fire in the Sky | Geng-Shen / Xin-You · Pomegranate Wood | Ren-Xu / Gui-Hai · Water of the Great Sea |
For memorization, begin with the phase sequences: Jia-Zi and Jia-Wu rows follow metal, fire, wood, earth, metal; Jia-Xu and Jia-Chen follow fire, water, earth, metal, wood; Jia-Shen and Jia-Yin follow water, earth, fire, wood, water. Then learn the images. The 2026 Bing-Wu and 2027 Ding-Wei pairs share the Na Yin label “Water of the Heavenly River,” even though the stems and branches of Bing-Wu are assigned to fire in the ordinary stem-branch Five-Phase table. Stem/branch phase and Na Yin are different classification layers.
Na Yin appears in classical destiny-calculation texts, date selection, marriage matching, and popular “what element is my birth year?” questions. It is not the sole method in BaZi traditions that center the day stem. Zi Wei Dou Shu uses a “Five-Phase Bureau” as a chart classification; traditional rules derive it from the Na Yin of the Life Palace’s stem-branch. The role of Na Yin differs across applications. These labels describe traditional schemes, not scientific measurements of personality or fate.
Practice#
- Memorize the three recurring Five-Phase sequences, then attach the imagery.
- Find the Na Yin labels for 1990, 2026, and your birth year.
- Name the phase assigned to each of the Five Tones and hum a familiar five-tone melody.
Check your understanding#
- What is the Na Yin of Jia-Zi?
- What is the Na Yin assigned to 2026?
- Which branch and month are paired with Huangzhong?
Answers: 1. Metal in the Sea. 2. Water of the Heavenly River. 3. Zi, the eleventh lunar month.
Lesson 36 · The Almanac I: The Twelve Officers#
Learning goals#
- Memorize the Twelve Officers (jianchu).
- Calculate an officer from the month branch and day branch.
Lesson#
The Twelve Officers are a date-selection method that pairs the month branch with each day branch to assign one of twelve labels. “Officer” here is a traditional calendar category, not a claim that twelve entities can be observed. Bamboo slips from the Qin tomb at Shuihudi, excavated in 1975, preserve a systematic jianchu calendar scheme, showing that such practices were recorded by the late Warring States or Qin period. Later almanacs use different versions, so state the month-branch and calendar convention.
The yuejian (month branch) is traditionally set by the solar-term boundary, not simply by the lunar first day. The day branch comes from the day’s stem-branch pair. Set the day whose branch matches the month branch as Establish; then proceed through the branch sequence assigning Remove, Full, Balance, Set, Grasp, Break, Danger, Complete, Receive, Open, and Close. For Hai month:
| Day branch | Hai | Zi | Chou | Yin | Mao | Chen | Si | Wu | Wei | Shen | You | Xu |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Officer | Establish | Remove | Full | Balance | Set | Grasp | Break | Danger | Complete | Receive | Open | Close |
Thus, in Zi month, the Wu day is Break because it is six positions from Zi and clashes with it. This explains a relation in the table; it does not mean a Wu day inevitably ruins an undertaking.
| Officer | Common gloss |
|---|---|
| Establish | Begin, establish |
| Remove | Clear away, remove the old |
| Full | Abundance, completion |
| Balance | Ordinary, level |
| Set | Stabilize |
| Grasp | Hold, take control |
| Break | Clash or break; often treated cautiously |
| Danger | Risk; proceed carefully |
| Complete | Accomplish; often favorable |
| Receive | Gather, receive |
| Open | Open, begin |
| Close | Close, store, conclude |
Using the lesson’s checked examples: 2026-12-01 is a Ji-You day in Hai month and is Open; December 2 is Geng-Xu and is Close; December 22 is Geng-Wu in Zi month and is Break; and January 6, 2027 is Yi-You in Chou month and is Complete. For dates near a solar-term boundary, use the exact time and stated calendar convention.
Practice#
- Memorize the Twelve Officers in order.
- Derive the officers for all day branches in Zi month.
- Calculate today’s officer and compare it with an almanac, noting the month-boundary convention.
Check your understanding#
- Which day branch is Establish in Zi month?
- What is the officer for You day in Chou month?
- Why does Break always oppose the month branch in this scheme?
Answers: 1. Zi day. 2. Complete. 3. Break is six positions after Establish, opposite the month branch.
Lesson 37 · The Almanac II: Clashes, Sha Directions, and Grand Treasurer#
Learning goals#
- Read “clash” and “sha direction” as different kinds of almanac labels.
- Understand the modern folk categories of “offending Taisui.”
Lesson#
“Clash” and “sha” answer different questions in an almanac. Clash compares the day branch with the branch opposite it: You day clashes with Mao, so an almanac may say “clashes with the rabbit.” The “sha direction” is calculated from the day branch’s Three-Harmony group and a direction rule.
| Day-branch group | Three-Harmony phase | Sha direction in this lesson |
|---|---|---|
| Shen, Zi, Chen | Water | South |
| Yin, Wu, Xu | Fire | North |
| Si, You, Chou | Metal | East |
| Hai, Mao, Wei | Wood | West |
The Grand Treasurer (Taisui) began as a calendrical concept related to Jupiter and the passage of years, then developed into a deity associated with each sexagenary year in popular religion. Modern “offending Taisui” lists group a person’s zodiac branch with the year’s branch through relations such as matching, clash, harm, break, or punishment. These are separate relations, not one uniform fortune algorithm.
For 2026, Bing-Wu year: Wu matches the year branch; Zi clashes with Wu; Chou harms Wu; Mao breaks Wu; and Wu is sometimes listed as self-punishing. For 2027, Ding-Wei year: Wei matches the year branch; Chou clashes with Wei; Zi harms Wei; Xu breaks Wei; and Chou, Wei, and Xu form the Three Punishments. Such lists may vary, particularly for punishments. They are folk classifications, not guarantees of harm or misfortune.
| Category | 2026, Bing-Wu | 2027, Ding-Wei |
|---|---|---|
| Year branch / matches Taisui | Wu, Horse | Wei, Goat |
| Clash | Zi, Rat | Chou, Ox |
| Harm | Chou, Ox | Zi, Rat |
| Break | Mao, Rabbit | Xu, Dog |
| Punishment | Wu, Horse (self-punishment) | Wei, Chou, Xu (Three Punishments) |
For another year, first decide whether the year changes at the Beginning of Spring or Lunar New Year, then check each relation separately. To “appease Taisui” is a customary ritual at the start of the year; it expresses belief and hope, not a technique shown to eliminate real-world risk.
Practice#
- Memorize the four sha-direction groups.
- Calculate the folk “offending Taisui” list for 2028, Wu-Shen year, using the relations in this lesson.
- Find today’s clash and sha direction in an almanac; record its date and convention.
Check your understanding#
- What is the sha direction for Xu day?
- Which zodiac animal is listed as harmed by the 2027 Wei year?
- Why are punishment categories especially complex?
Answers: 1. North (the Yin-Wu-Xu fire group). 2. Rat (Zi is harmed by Wei). 3. There are several Three Punishments groups and self-punishment; lists may differ by convention.
Lesson 38 · Reading an Almanac and the Tradition of Date Selection#
Learning goals#
- Identify the different sources of information on a traditional almanac page.
- Learn the place of the Xieji Bianfang Shu and historical criticism of date selection.
Lesson#
An almanac page combines several kinds of information. The lunar date and stem-branch date come from calendar calculation; Na Yin, the Twelve Officers, clash and sha, and the Officer of the Day come from separate date-selection rules; “suitable” and “avoid” summarize rules from one almanac tradition. Readers may assume the columns independently confirm one another, but they often share the same date, stem-branch, or solar-term inputs.
Some names are easy to mistake for observable astronomical facts. “Officer of the Day” is a rotating calendar label. The Twelve Officers of the Day are divided into “Yellow Path” and “Black Path” categories in the traditional scheme; these do not describe the sun’s physical route among constellations. The Twenty-Eight Mansions are historical sky divisions, while a mansion assigned to a date is a calendar marker. The “Pengzu Hundred Taboos” pair a day stem or branch with a cautionary phrase. “Auspicious spirits” and “inauspicious sha” are categories of names in date-selection books. The “fetal spirit” is a folk claim about a changing direction, not a medical fact. “Suitable” and “avoid” are recommendations made by that almanac’s compilation rules.
The Twelve Yellow-Path Officers are Azure Dragon, Bright Hall, Heavenly Punishment, Vermilion Bird, Golden Coffer, Heavenly Virtue, White Tiger, Jade Hall, Heavenly Jail, Black Tortoise, Director of Fate, and Hooked Array. The traditional scheme places Azure Dragon, Bright Hall, Golden Coffer, Heavenly Virtue, Jade Hall, and Director of Fate in the Yellow-Path category. The Qing imperial Xieji Bianfang Shu is a systematic compilation of date-selection rules and shensha, but modern almanacs do not all rely on it as their single source.
Wang Chong’s Eastern Han Lunheng, “Criticizing Day Selection,” criticizes deciding actions by day-stem and day-branch fortune. This shows that date-selection claims were also contested in antiquity; it does not mean that people stopped using the practice.
| Almanac column | Example | Source or rule layer |
|---|---|---|
| Lunar date | 23rd day of the tenth month | Lunar calendar |
| Stem-branch date | Bing-Wu year, Ji-Hai month, Ji-You day | Stem-branch calendar |
| Na Yin | Great-Road Earth for the day | Na Yin table |
| Twelve Officer | Open | Lesson 36 |
| Clash and sha | Clashes with Rabbit (Gui-Mao); sha east | Lesson 37 |
| Officer of the Day | Vermilion Bird (Black Path) | Rotating spirits |
| Mansion of the day | Zui | Date-assigned mansion |
| Pengzu taboo | “Ji avoids breaking contracts; You avoids receiving guests” | Day-stem/branch maxim |
| Auspicious spirits | Month Virtue, Heavenly Grace, Mother Storehouse | Date-selection list |
| Inauspicious spirits | Calamity Sha, Heavenly Fire, Five Separation, Vermilion Bird | Date-selection list |
| Suitable | Open a market, receive wealth, travel, sacrifice, study, build | Almanac compilation |
| Avoid | Move house, enter a new residence, burial | Almanac compilation |
| Fetal spirit | At the main gate, outside northeast | Folk directional belief |
Read “suitable for opening a market” in two layers. Descriptively, this edition of the almanac lists the activity as suitable. Analytically, ask which rules were combined and whether there is independent evidence that the date predicts business results. Shared customs can help families coordinate; that social function is different from a claim that date selection predicts commercial success.
Practice#
- Open an almanac page for today and identify which earlier lesson supplies each column.
- Read the opening of Wang Chong’s “Criticizing Day Selection” and summarize the argument.
- Find the Yellow-Path days in the current month, noting the calendar source.
Check your understanding#
- Which six names are classified as Yellow-Path Officers?
- What is the Xieji Bianfang Shu?
- What determines the Pengzu Hundred Taboos?
Answers: 1. Azure Dragon, Bright Hall, Golden Coffer, Heavenly Virtue, Jade Hall, Director of Fate. 2. A Qing imperial compilation of date-selection rules. 3. The day stem and day branch.
Lesson 39 · Assessment: Hetu, Na Yin, and Date Selection#
Review#
This assessment combines Song-period number diagrams, traditional pitch systems and Na Yin, daybook jianchu labels, almanac clashes and sha, and the layout of a traditional calendar. They may share branches, directions, and dates, but derive from different historical texts and rules. For each problem, state the inputs and show the steps. When a term has competing versions, name the convention used in this module.
For example, on Wu day, the branch clashes with Zi, so the almanac phrase is “clashes with Rat.” Wu belongs to the Yin-Wu-Xu fire group, so this lesson assigns sha north. To calculate a Twelve Officer, you also need the month branch; to calculate Na Yin, you need the complete day stem-branch pair. One branch participates in several systems, but one system’s output is not automatically another’s input.
Closed-book assessment#
Suggested time: 40 minutes. Passing score: 80 out of 100.
- Draw the Luoshu Nine Palaces and assign the Later Heaven trigrams. (12 points)
- Write the Hetu generating/completing-number mnemonic. (10 points)
- Give the nine-palace route; fill the grid with eight in the center. (12 points)
- Match the Five Tones with the Five Phases; which month is paired with Huangzhong? (8 points)
- Give the three Na Yin phase sequences; find the Na Yin of 1990 and 2026. (12 points)
- Write the Twelve Officers; what is the officer for Mao day in Zi month? (12 points)
- What does Wu day clash with, and what is its sha direction? (6 points)
- Which zodiac animals are listed as offending Taisui in 2028? (10 points)
- Name the six Yellow-Path Officers. (8 points)
- Summarize Wang Chong’s criticism of date selection. (10 points)
Answer key for supplied items: 3. Center 8, northwest 9, west 1, northeast 2, south 3, north 4, southwest 5, east 6, southeast 7. 5. Geng-Wu is Roadside Earth; Bing-Wu is Water of the Heavenly River. 6. Zi is Establish, Chou Remove, Yin Full, Mao Balance. 7. Wu clashes with Zi (Rat); the Yin-Wu-Xu fire group gives sha north. 8. Year branch Monkey (value), Tiger (clash), Pig (harm), Snake (break), and Tiger/Snake (punishment), under this lesson’s convention.
Module outcome#
You are ready to continue when you can distinguish historical number diagrams from their later forms, separate the Five Tones, pitch standards, and Na Yin, calculate an almanac label from its actual inputs, and explain date-selection customs without treating their claims as empirical guarantees.