What is the difference between Jing Fang's 8-Palace sequence (You Hun / Gui Hun) and the San Yuan Da Gua Inner-Outer transformation sequence?

Jing Fang's Western Han 8-Palace system changes lines sequentially from Line 1 up to Line 5, steps back to Line 4 (You Hun / Wandering Soul), and restores the lower trigram (Gui Hun / Returning Soul). San Yuan Xuan Kong Da Gua uses the symmetric Inner-Outer Trigram XOR operator (comparing Upper vs Lower trigrams directly) so that every hexagram and its vertical inversion share the exact same Star Period.

☯️ CHAPTER 03 · MATHEMATICAL MATRIX & MASTER TABLES 64 Hexagrams · 384 Yao Lines · Gua Qi & Gua Yun • Master Ung Khiem Monograph Series

The 64 Hexagrams & 384 Lines System in Xuan Kong Da Gua: Complete Gua Qi & Gua Yun Derivation

Q: How do you calculate the Gua Qi (1, 2, 3, 4, 6, 7, 8, 9) of any hexagram without looking at a compass?

Identify the Upper (Outer) Trigram of the hexagram (Lines 4, 5, 6) on the Outer Ring (or Lower Trigram on the Inner Ring), place it in its Early Heaven Bagua position, and read the corresponding Luo Shu number: Kun = 1 Water, Xun = 2 Fire, Li = 3 Wood, Dui = 4 Metal, Gen = 6 Water, Kan = 7 Fire, Zhen = 8 Wood, and Qian = 9 Metal.

Q: How do you calculate the Gua Yun (Star Period 1–9) of any hexagram from its six lines?

Compare the three lines of the Upper Trigram (Lines 4, 5, 6) with the three corresponding lines of the Lower Trigram (Lines 1, 2, 3). If the two trigrams are identical (0 line differences), it is a Period-1 Pure Parent Hexagram; if all 3 lines differ, it is a Period-9 Inverted Parent Hexagram; if only the bottom line differs, it is Period 8 (Gen); if only the middle line differs, it is Period 7 (Kan); if only the top line differs, it is Period 6 (Qian); if bottom and middle differ, it is Period 4 (Dui); if middle and top differ, it is Period 3 (Li); if bottom and top differ, it is Period 2 (Xun).

Q: Why is there no Gua Qi 5 or Gua Yun 5 among the 64 hexagrams?

Because there are 8 Trigrams (2^3 = 8) surrounding the Taiji Center and 64 Hexagrams (8 × 8 = 64) on the perimeter ring, the Central Palace 5 has no standalone trigram. Instead, 5 acts as the central Taiji pivot connecting opposite pairs into 10 and generative pairs by a difference of 5.

Q: How do the 384 Yao lines work in practical compass alignment?

Each of the 64 hexagrams spans 5.625 degrees and is subdivided into 6 individual yao lines of 0.9375 degrees each. On the Luo Pan's 384-line ring, specific lines are marked with red dots indicating auspicious moving lines (Dong Yao) whose transformation brings the hexagram into Pure One Qi or Sum-of-Ten harmony with the sitting/facing axis.

Throw away rote memorization. Once you understand the binary operator linking the Upper Trigram and the Lower Trigram of any six-line hexagram, you can look at any of the 64 Hexagrams (六十四大卦) and calculate its exact Gua Qi Five Phase (1–9) and Gua Yun Star Period (1–9) in under three seconds—without touching a lookup chart! Building on Chapter 02: Theoretical Foundations, this third monograph reveals the two great transformation engines of classical I Ching metaphysics—Jing Fang’s Eight-Palace Line Transformation (Ba Gong Bian Yao 八宮變爻) and the San Yuan Inner-Outer Trigram XOR Operator—provides the Complete 64-Hexagram Master Matrix across all eight trigram families, and explains how the 384 Individual Yao Lines (`0.9375°` each) operate in real-world site alignment.

Master Ung Khiem (Thầy Ưng Khiêm)

Classical Feng Shui & East Asian Metaphysics Master · UK MASTER ACADEMY

Published June 16, 2026 · Updated October 15, 2026
7,500-word Monograph · 29 min read
🇻🇳 Bản tiếng Việt

The 64 Hexagrams and 384 Lines System in Xuan Kong Da Gua: Complete Gua Qi and Gua Yun Tables

Monograph Dossier: Chapter 03 — 64 Gua & 384 Yao

Matrix Structure:

8 Trigram Palaces × 8 Transformations = 64 Great Hexagrams

Yao Resolution:

64 Hexagrams × 6 Lines = 384 Yao (0.9375° per line)

Gua Qi (Substance):

1, 2, 3, 4, 6, 7, 8, 9 (Determined by Leading Palace Trigram)

Gua Yun (Function):

Star Periods 1–9 (Determined by Upper vs. Lower Trigram XOR)

Parent Hexagrams:

8 Pure Gua (Period 1) + 8 Inverted Gua (Period 9) = 16 Fu Mu Gua

Descendant Gua:

48的子孫卦 (Zi Sun Gua) distributed across Periods 2, 3, 4, 6, 7, 8

Active Line Rule:

Dong Yao (動爻): Central Lines 2, 3, 4, 5 preferred over Edge Lines 1 & 6

✦ Core Formula: Every hexagram is a 6-bit binary vector [L1, L2, L3, L4, L5, L6]. Its Palace Trigram gives its Five-Phase Substance (Gua Qi); the XOR difference between Upper [L4,L5,L6] and Lower [L1,L2,L3] gives its Temporal Period (Gua Yun).

Executive Summary for Readers & AI Search (GEO Summary)

Two Coordinates of Every Hexagram: In Xuan Kong Da Gua, every one of the 64 hexagrams possesses two numbers from the set {1, 2, 3, 4, 6, 7, 8, 9}: (1) Gua Qi (卦氣 — Five-Phase Substance), which determines whether the hexagram belongs to 1–6 Water, 2–7 Fire, 3–8 Wood, or 4–9 Metal; and (2) Gua Yun (卦運 — Star Period Function), which determines its timeliness across the Nine Periods.
Instant Gua Qi Algorithm: Read the Leading Palace Trigram (the Upper/Outer Trigram on the standard Outer Ring) and map it to the Early Heaven Bagua on the Luo Shu: Kun ☷ = 1 Water, Xun ☴ = 2 Fire, Li ☲ = 3 Wood, Dui ☱ = 4 Metal, Gen ☶ = 6 Water, Kan ☵ = 7 Fire, Zhen ☳ = 8 Wood, Qian ☰ = 9 Metal.
Instant Gua Yun (Star Period) Algorithm: Compare the 3 lines of the Upper Trigram (`L4, L5, L6`) with the 3 lines of the Lower Trigram (`L1, L2, L3`). Where two corresponding lines are different, write a Yin line (0); where they are the same, write a Yang line (1)—or equivalently, check which lines of the Pure Parent Trigram changed to produce the second trigram: No change = Period 1; Line 1 & 3 change = Period 2; Line 2 & 3 change = Period 3; Line 1 & 2 change = Period 4; Line 3 changes = Period 6; Line 2 changes = Period 7; Line 1 changes = Period 8; All 3 lines change = Period 9.
16 Parent Hexagrams vs. 48 Offspring Hexagrams: The 8 Pure Hexagrams (Period 1) are the San Yuan Father Hexagrams; the 8 Inverted-Trigram Hexagrams (Period 9) are the San Yuan Mother Hexagrams; the remaining 48 Hexagrams are the Six Offspring Sons and Daughters (8 hexagrams each in Periods 2, 3, 4, 6, 7, and 8).
The 384 Yao Lines: Each hexagram’s 5.625° arc contains 6 lines of 0.9375° each, counted from Bottom Line 1 to Top Line 6 along the compass progression. Flipping a single Moving Line (Dong Yao) transforms a hexagram into its 6-line neighbor, unlocking advanced sitting-facing and water-mouth combinations.

1. Anatomy of a Six-Line Hexagram: Inner Host (Lower) vs. Outer Guest (Upper)

Six stacked lines. Two three-line trigrams. Before you can compute any formula in Xuan Kong Da Gua, you must see the internal architecture of a six-line hexagram (Da Gua 大卦) the way classical masters see it. Every hexagram is built from the ground upward, from Line 1 at the bottom (Chu Yao 初爻) to Line 6 at the top (Shang Yao 上爻), and divides naturally into two three-line halves:

The Lower / Inner Trigram (Xia Gua 下卦 or Nei Gua 內卦 — Lines 1, 2, 3): Represents the Host (Zhu 主), Earth, the internal foundation, the interior of the residence, and the quiet root of qi.
The Upper / Outer Trigram (Shang Gua 上卦 or Wai Gua 外卦 — Lines 4, 5, 6): Represents the Guest (Bin 賓), Heaven, the external manifestation, the approaching environment, and the active crown of qi.
The Three Cosmic Powers (San Cai 三才) Inside Every Hexagram: Within the six lines, Lines 1 and 2 belong to Earth (Di); Lines 3 and 4 belong to Humanity (Ren) standing at the threshold between inner and outer worlds; and Lines 5 and 6 belong to Heaven (Tian). Furthermore, Line 2 is the central ruler of the Lower Trigram, while Line 5 is the supreme imperial ruler (Jun Wei 君位) of the Upper Trigram—hence the classical I Ching praise for “Central and Correct” (Zhong Zheng 中正) lines!

Notice the correspondence between the Lower and Upper Trigrams: Line 1 corresponds to Line 4 (the bottom lines of the two trigrams); Line 2 corresponds to Line 5 (the middle lines of the two trigrams); and Line 3 corresponds to Line 6 (the top lines of the two trigrams). That exact 3-pair correspondence (`L1↔L4`, `L2↔L5`, `L3↔L6`) is the key to calculating every hexagram’s Star Period!

2. Deriving Gua Qi (1–9): The Eight Trigram Palaces & He Tu Five Phases

How do the 64 hexagrams divide into Eight Palace Families (Ba Gong 八宮) of 8 hexagrams each? In the San Yuan Xuan Kong Da Gua compass system, the 64 hexagrams are grouped by their Leading Trigram (the Upper / Outer Trigram on the standard Outer Ring, or the Lower / Inner Trigram on the inverted Inner Ring). Each of the 8 Trigram Palaces carries an immutable Gua Qi Number (卦氣數) and He Tu Five Phase (河圖五行):

1. Kun Palace Group (坤宮 ☷ — 8 Hexagrams): Early Heaven Kun sits at North (Luo Shu 1). Gua Qi = 1 · Yang Water (水).
2. Xun Palace Group (巽宮 ☴ — 8 Hexagrams): Early Heaven Xun sits at Southwest (Luo Shu 2). Gua Qi = 2 · Yin Fire (火).
3. Li Palace Group (離宮 ☲ — 8 Hexagrams): Early Heaven Li sits at East (Luo Shu 3). Gua Qi = 3 · Yang Wood (木).
4. Dui Palace Group (兌宮 ☱ — 8 Hexagrams): Early Heaven Dui sits at Southeast (Luo Shu 4). Gua Qi = 4 · Yin Metal (金).
5. Gen Palace Group (艮宮 ☶ — 8 Hexagrams): Early Heaven Gen sits at Northwest (Luo Shu 6). Gua Qi = 6 · Yin Water (水).
6. Kan Palace Group (坎宮 ☵ — 8 Hexagrams): Early Heaven Kan sits at West (Luo Shu 7). Gua Qi = 7 · Yang Fire (火).
7. Zhen Palace Group (震宮 ☳ — 8 Hexagrams): Early Heaven Zhen sits at Northeast (Luo Shu 8). Gua Qi = 8 · Yin Wood (木).
8. Qian Palace Group (乾宮 ☰ — 8 Hexagrams): Early Heaven Qian sits at South (Luo Shu 9). Gua Qi = 9 · Yang Metal (金).

Test yourself right now. Take the hexagram Heaven Water Song (天水訟 ䷅): its Upper Trigram is Heaven Qian ☰, so on the Outer Ring its Palace is Qian and its Gua Qi is 9 Metal! Take Water Heaven Xu (水天需 ䷄): its Upper Trigram is Water Kan ☵, so its Palace is Kan and its Gua Qi is 7 Fire! Simple. Instant. Unerring.

3. Jing Fang’s Eight-Palace Line Transformation (Ba Gong Bian Yao) Explained

During the Western Han Dynasty, the brilliant易學 (I Ching) scholar Jing Fang (京房, 77–37 BCE)—disciple of Jiao Yanshou—systematized the Eight-Palace Line Transformation Method (Ba Gong Gua 八宮卦) in his Jing Shi Yi Zhuan (京氏易傳). In Jing Fang’s classical divination system (which is also used in Na Jia Wen Wang Gua and referenced by several Ming–Qing geomantic schools), each of the 8 Palaces begins with its Pure Six-Line Hexagram (Ba Chun Gua 八純卦) and generates 7 descendant hexagrams by progressively changing lines from bottom to top:

Palace Root (Ben Gong Gua 本宮卦): The Pure Hexagram where Upper and Lower Trigrams are identical (e.g., Qian Wei Tian ䷀).
First-Generation Change (Yi Shi Gua 一世卦): Flip Bottom Line 1 (e.g., Qian ䷀ flips Line 1 → Tian Feng Gou ䷫).
Second-Generation Change (Er Shi Gua 二世卦): Flip Line 2 as well (e.g., Gou ䷫ flips Line 2 → Tian Shan Dun ䷠).
Third-Generation Change (San Shi Gua 三世卦): Flip Line 3 as well (e.g., Dun ䷠ flips Line 3 → Tian Di Pi ䷋).
Fourth-Generation Change (Si Shi Gua 四世卦): Flip Line 4 (e.g., Pi ䷋ flips Line 4 → Feng Di Guan ䷓).
Fifth-Generation Change (Wu Shi Gua 五世卦): Flip Line 5 (e.g., Guan ䷓ flips Line 5 → Shan Di Bo ䷖).
Wandering Soul (You Hun Gua 遊魂卦): Because flipping Line 6 would turn the hexagram into the Pure Hexagram of the opposite palace, the transformation steps backward and flips Line 4 again (e.g., Bo ䷖ flips Line 4 → Huo Di Jin ䷢).
Returning Soul (Gui Hun Gua 歸魂卦): Finally, the lower three lines (Lines 1, 2, 3) flip together back to the original Palace Root trigram (e.g., Jin ䷢ restores Lower Qian → Huo Tian Da You ䷍).

Why must a serious Xuan Kong Da Gua practitioner understand both Jing Fang’s Sequential Line Changes and the San Yuan Inner-Outer Trigram Transformation? Because in San Yuan Xuan Kong Da Gua, rather than changing Line 4 and Line 5 in the Upper Trigram (which alters the Upper Trigram in Generations 4, 5, You Hun, and Gui Hun), we keep the Leading Trigram fixed as the Gua Qi Palace and transform the three lines of the second trigram against the Leading Trigram in 8 combinations (`0, L1, L2, L3, L1+2, L2+3, L1+3, L1+2+3`) to generate the **8 Star Periods (Gua Yun 1, 8, 7, 6, 4, 3, 2, 9)**! Let us see how that works in Section 4.

Figure 3.1: The 8 Line-Transformation states between Upper and Lower Trigrams that generate the 8 Star Periods (Gua Yun 1, 8, 7, 6, 4, 3, 2, 9) across all 64 hexagrams.

4. Deriving Gua Yun (Star Periods 1–9): The Inner-Outer Trigram XOR Algorithm

Now let me teach you the 3-Second Mental XOR Trick that my advanced students at UK Master Academy use to compute the Gua Yun Star Period (卦運星運) of any hexagram on sight.

Look at the Upper Trigram (`Lines 4, 5, 6`) and the Lower Trigram (`Lines 1, 2, 3`) of any hexagram, and compare them position by position—Bottom (`L1 vs L4`), Middle (`L2 vs L5`), and Top (`L3 vs L6`)—to form a 3-line Resultant Trigram using this single rule:

Same Polarity (`Yang + Yang` or `Yin + Yin`) → Write a Broken Yin Line (- -) (no change = quiet = Yin).
Different Polarity (`Yang + Yin` or `Yin + Yang`) → Write a Solid Yang Line (—) (changed = active = Yang).

Now read the Early Heaven Luo Shu Gua Qi number of that 3-line Resultant Trigram! Let us verify all 8 possibilities:

Zero lines differ (`000` = Kun ☷): What is Kun’s Luo Shu number? 1! Every Pure Hexagram where Upper = Lower has Gua Yun = Period 1 (Greedy Wolf)!
All three lines differ (`111` = Qian ☰): What is Qian’s Luo Shu number? 9! Every Inverted Hexagram where Upper is the exact opposite of Lower (`Tai ䷊, Pi ䷋, Ji Ji ䷾, Wei Ji ䷿, Xian ䷞, Sun ䷨, Heng ䷟, Yi ䷩`) has Gua Yun = Period 9 (Right Assistant)!
Only the Bottom line differs (`L1 ≠ L4` → Bottom Yang `100` = Zhen ☳): What is Zhen’s Luo Shu number? 8! Every hexagram where only the bottom line of the two trigrams differs has Gua Yun = Period 8 (Left Assistant)!
Only the Middle line differs (`L2 ≠ L5` → Middle Yang `010` = Kan ☵): What is Kan’s Luo Shu number? 7! Every hexagram where only the middle line differs has Gua Yun = Period 7 (Broken Army)!
Only the Top line differs (`L3 ≠ L6` → Top Yang `001` = Gen ☶): What is Gen’s Luo Shu number? 6! Every hexagram where only the top line differs has Gua Yun = Period 6 (Martial Star)!
Bottom and Middle lines differ (`L1 ≠ L4` and `L2 ≠ L5` → `110` = Dui ☱): What is Dui’s Luo Shu number? 4! Every hexagram where Lines 1 & 2 differ (and Line 3 matches) has Gua Yun = Period 4 (Literary Star)!
Bottom and Top lines differ (`L1 ≠ L4` and `L3 ≠ L6` → `101` = Li ☲) / Middle and Top lines differ (`011` = Xun ☴): Note one vital classical nuance between the two double-line changes (`L1+L3` vs `L2+L3`): in the direct XOR mapping, `L1+L3` gives Li (`3`) and `L2+L3` gives Xun (`2`), whereas in Jing Fang’s Sequential Line-Change table (where changing 2 lines from the top downward leaves `L1` unchanged as the 2nd change and `L2` unchanged as the 3rd change), `L1+L3` is assigned Period 2 and `L2+L3` is assigned Period 3! Both conventions appear on classical compass rings (and we document both columns explicitly in the Master Tables below so you can read any mainland or Taiwan San Yuan Luo Pan effortlessly).

5. The 16 Parent Hexagrams (Fu Mu Gua): 8 Pure Period-1 & 8 Inverted Period-9

Before inspecting the 64-hexagram master tables, pause and honor the royal aristocracy of the 64 hexagrams: the 16 Parent Hexagrams (Shi Liu Fu Mu Gua 十六父母卦). Why did Grandmaster Yang Yun Song’s Tian Yu Jing declare that “East, West, and the Four Gua Perfect Combinations—specifically the Parent Gua—hold the supreme dragon-water mystery”?

The 8 Father Hexagrams (Period 1 — Ba Chun Qian Kun Zi): Formed when the Upper and Lower Trigrams are identical (`0` line changes): Pure Qian ䷀ (Qi 9, Yun 1), Pure Dui ䷹ (Qi 4, Yun 1), Pure Li ䷝ (Qi 3, Yun 1), Pure Zhen ☳ ䷲ (Qi 8, Yun 1), Pure Xun ☴ ䷸ (Qi 2, Yun 1), Pure Kan ☵ ䷜ (Qi 7, Yun 1), Pure Gen ☶ ䷳ (Qi 6, Yun 1), and Pure Kun ☷ ䷁ (Qi 1, Yun 1).
The 8 Mother Hexagrams (Period 9 — Ba Fou Tai Jiao Gua): Formed when the Upper and Lower Trigrams are 100% Yin-Yang Opposites (`3` line changes): Heaven Earth Pi ䷋ (Qi 9, Yun 9), Lake Mountain Xian ䷞ (Qi 4, Yun 9), Fire Water Wei Ji ䷿ (Qi 3, Yun 9), Thunder Wind Heng ䷟ (Qi 8, Yun 9), Wind Thunder Yi ䷩ (Qi 2, Yun 9), Water Fire Ji Ji ䷾ (Qi 7, Yun 9), Mountain Lake Sun ䷨ (Qi 6, Yun 9), and Earth Heaven Tai ䷊ (Qi 1, Yun 9).

Look at the numbers of those 16 Parent Hexagrams: every Father Hexagram has Gua Yun = 1, and every Mother Hexagram has Gua Yun = 9, so any Father paired with any Mother automatically achieves `1 + 9 = 10` Sum-of-Ten in Star Period (`He Shi Gua Yun`)! Even more remarkably, in our current Period 9 Fire Era (2024–2043), the 8 Mother Hexagrams (Period 9) are the Direct Spirit (Zheng Shen) Rulers, while the 8 Father Hexagrams (Period 1) are the Indirect Spirit (Ling Shen) Water Rulers! We will explore that Period 9 master strategy in depth in Chapter 06: Zheng Shen & Ling Shen in Da Gua.

6. Master Table Part I: The 32 Yang-Group Palaces (Qian 9, Dui 4, Li 3, Zhen 8)

Below is Part I of our complete reference matrix covering the first four Trigram Palaces—Qian Palace (Gua Qi 9 Metal), Dui Palace (Gua Qi 4 Metal), Li Palace (Gua Qi 3 Wood), and Zhen Palace (Gua Qi 8 Wood)—listing all 32 hexagrams, their Upper/Lower Trigrams, changing lines, Gua Qi Five Phases, and Gua Yun Star Periods:

Table 3.1: Complete Mathematical Matrix of the 32 Hexagrams in Qian (9), Dui (4), Li (3) & Zhen (8) Palaces
Palace & Gua Qi	Hexagram & Symbol	Chinese / Pinyin	Upper / Lower	Lines Changed (vs Upper)	Gua Qi Element	Gua Yun (Star Period)	Family Rank
Qian Palace ☰ Gua Qi 9 Yang Metal	1. Pure Qian ䷀	乾為天 · Qián Wéi Tiān	☰ / ☰	None (Pure)	9 Metal	Period 1	Father (Pure)
	2. Gou ䷫	天風姤 · Tiān Fēng Gòu	☰ / ☴	Line 1 (Bot)	9 Metal	Period 8	1st Line Change
	3. Tong Ren ䷌	天火同人 · Tiān Huǒ Tóng Rén	☰ / ☲	Line 2 (Mid)	9 Metal	Period 7	2nd Line Change
	4. Lu ䷉	天澤履 · Tiān Zé Lǚ	☰ / ☱	Line 3 (Top)	9 Metal	Period 6	3rd Line Change
	5. Dun ䷠	天山遯 · Tiān Shān Dùn	☰ / ☶	Lines 1 & 2	9 Metal	Period 4	Double Change A
	6. Wu Wang ䷘	天雷無妄 · Tiān Léi Wú Wàng	☰ / ☳	Lines 2 & 3	9 Metal	Period 3	Double Change B
	7. Song ䷅	天水訟 · Tiān Shuǐ Sòng	☰ / ☵	Lines 1 & 3	9 Metal	Period 2	Double Change C
	8. Pi ䷋	天地否 · Tiān Dì Pǐ	☰ / ☷	All 3 (1,2,3)	9 Metal	Period 9	Mother (Inverse)
Dui Palace ☱ Gua Qi 4 Yin Metal	9. Pure Dui ䷹	兌為澤 · Duì Wéi Zé	☱ / ☱	None (Pure)	4 Metal	Period 1	Father (Pure)
	10. Kun ䷮	澤水困 · Zé Shuǐ Kùn	☱ / ☵	Line 1 (Bot)	4 Metal	Period 8	1st Line Change
	11. Sui ䷐	澤雷隨 · Zé Léi Suí	☱ / ☳	Line 2 (Mid)	4 Metal	Period 7	2nd Line Change
	12. Guai ䷪	澤天夬 · Zé Tiān Guài	☱ / ☰	Line 3 (Top)	4 Metal	Period 6	3rd Line Change
	13. Cui ䷬	澤地萃 · Zé Dì Cuì	☱ / ☷	Lines 1 & 2	4 Metal	Period 4	Double Change A
	14. Ge ䷰	澤火革 · Zé Huǒ Gé	☱ / ☲	Lines 2 & 3	4 Metal	Period 3	Double Change B
	15. Da Guo ䷛	澤風大過 · Zé Fēng Dà Guò	☱ / ☴	Lines 1 & 3	4 Metal	Period 2	Double Change C
	16. Xian ䷞	澤山咸 · Zé Shān Xián	☱ / ☶	All 3 (1,2,3)	4 Metal	Period 9	Mother (Inverse)
Li Palace ☲ Gua Qi 3 Yang Wood	17. Pure Li ䷝	離為火 · Lí Wéi Huǒ	☲ / ☲	None (Pure)	3 Wood	Period 1	Father (Pure)
	18. Lu ䷷	火山旅 · Huǒ Shān Lǚ	☲ / ☶	Line 1 (Bot)	3 Wood	Period 8	1st Line Change
	19. Da You ䷍	火天大有 · Huǒ Tiān Dà Yǒu	☲ / ☰	Line 2 (Mid)	3 Wood	Period 7	2nd Line Change
	20.噬嗑 Shi He ䷔	火雷噬嗑 · Huǒ Léi Shì Hé	☲ / ☳	Line 3 (Top)	3 Wood	Period 6	3rd Line Change
	21. Jin ䷢	火地晉 · Huǒ Dì Jìn	☲ / ☷	Lines 1 & 2	3 Wood	Period 4	Double Change A
	22. Kui ䷥	火澤睽 · Huǒ Zé Kuí	☲ / ☱	Lines 2 & 3	3 Wood	Period 3	Double Change B
	23. Ding ䷱	火風鼎 · Huǒ Fēng Dǐng	☲ / ☴	Lines 1 & 3	3 Wood	Period 2	Double Change C
	24. Wei Ji ䷿	火水未濟 · Huǒ Shuǐ Wèi Jì	☲ / ☵	All 3 (1,2,3)	3 Wood	Period 9	Mother (Inverse)
Zhen Palace ☳ Gua Qi 8 Yin Wood	25. Pure Zhen ䷲	震為雷 · Zhèn Wéi Léi	☳ / ☳	None (Pure)	8 Wood	Period 1	Father (Pure)
	26. Yu ䷏	雷地豫 · Léi Dì Yù	☳ / ☷	Line 1 (Bot)	8 Wood	Period 8	1st Line Change
	27. Gui Mei ䷵	雷澤歸妹 · Léi Zé Guī Mèi	☳ / ☱	Line 2 (Mid)	8 Wood	Period 7	2nd Line Change
	28. Feng ䷶	雷火豐 · Léi Huǒ Fēng	☳ / ☲	Line 3 (Top)	8 Wood	Period 6	3rd Line Change
	29. Xiao Guo ䷽	雷山小過 · Léi Shān Xiǎo Guò	☳ / ☶	Lines 1 & 2	8 Wood	Period 4	Double Change A
	30. Da Zhuang ䷡	雷天大壯 · Léi Tiān Dà Zhuàng	☳ / ☰	Lines 2 & 3	8 Wood	Period 3	Double Change B
	31. Jie ䷧	雷水解 · Léi Shuǐ Jiě	☳ / ☵	Lines 1 & 3	8 Wood	Period 2	Double Change C
	32. Heng ䷟	雷風恆 · Léi Fēng Héng	☳ / ☴	All 3 (1,2,3)	8 Wood	Period 9	Mother (Inverse)

Figure 3.2: Grouping of the first 32 hexagrams into the He Tu 4–9 Metal Alliance (Qian 9 & Dui 4) and the He Tu 3–8 Wood Companionship (Li 3 & Zhen 8).

7. Master Table Part II: The 32 Yin-Group Palaces (Xun 2, Kan 7, Gen 6, Kun 1)

Now examine Part II of our complete reference matrix covering the remaining four Trigram Palaces—Xun Palace (Gua Qi 2 Fire), Kan Palace (Gua Qi 7 Fire), Gen Palace (Gua Qi 6 Water), and Kun Palace (Gua Qi 1 Water):

Table 3.2: Complete Mathematical Matrix of the 32 Hexagrams in Xun (2), Kan (7), Gen (6) & Kun (1) Palaces
Palace & Gua Qi	Hexagram & Symbol	Chinese / Pinyin	Upper / Lower	Lines Changed (vs Upper)	Gua Qi Element	Gua Yun (Star Period)	Family Rank
Xun Palace ☴ Gua Qi 2 Yin Fire	33. Pure Xun ䷸	巽為風 · Xùn Wéi Fēng	☴ / ☴	None (Pure)	2 Fire	Period 1	Father (Pure)
	34. Xiao Chu ䷈	風天小畜 · Fēng Tiān Xiǎo Chù	☴ / ☰	Line 1 (Bot)	2 Fire	Period 8	1st Line Change
	35. Jia Ren ䷤	風火家人 · Fēng Huǒ Jiā Rén	☴ / ☲	Line 2 (Mid)	2 Fire	Period 7	2nd Line Change
	36. Zhong Fu ䷼	風澤中孚 · Fēng Zé Zhōng Fú	☴ / ☱	Line 3 (Top)	2 Fire	Period 6	3rd Line Change
	37. Jian ䷴	風山漸 · Fēng Shān Jiàn	☴ / ☶	Lines 1 & 2	2 Fire	Period 4	Double Change A
	38. Guan ䷓	風地觀 · Fēng Dì Guān	☴ / ☷	Lines 2 & 3	2 Fire	Period 3	Double Change B
	39. Huan ䷺	風水渙 · Fēng Shuǐ Huàn	☴ / ☵	Lines 1 & 3	2 Fire	Period 2	Double Change C
	40. Yi ䷩	風雷益 · Fēng Léi Yì	☴ / ☳	All 3 (1,2,3)	2 Fire	Period 9	Mother (Inverse)
Kan Palace ☵ Gua Qi 7 Yang Fire	41. Pure Kan ䷜	坎為水 · Kǎn Wéi Shuǐ	☵ / ☵	None (Pure)	7 Fire	Period 1	Father (Pure)
	42. Jie ䷻	水澤節 · Shuǐ Zé Jié	☵ / ☱	Line 1 (Bot)	7 Fire	Period 8	1st Line Change
	43. Bi ䷇	水地比 · Shuǐ Dì Bǐ	☵ / ☷	Line 2 (Mid)	7 Fire	Period 7	2nd Line Change
	44. Zhun ䷂	水雷屯 · Shuǐ Léi Zhūn	☵ / ☳	Line 3 (Top)	7 Fire	Period 6	3rd Line Change
	45. Jing ䷯	水風井 · Shuǐ Fēng Jǐng	☵ / ☴	Lines 1 & 2	7 Fire	Period 4	Double Change A
	46. Xu ䷄	水天需 · Shuǐ Tiān Xū	☵ / ☰	Lines 2 & 3	7 Fire	Period 3	Double Change B
	47. Jian ䷦	水山蹇 · Shuǐ Shān Jiǎn	☵ / ☶	Lines 1 & 3	7 Fire	Period 2	Double Change C
	48. Ji Ji ䷾	水火既濟 · Shuǐ Huǒ Jì Jì	☵ / ☲	All 3 (1,2,3)	7 Fire	Period 9	Mother (Inverse)
Gen Palace ☶ Gua Qi 6 Yin Water	49. Pure Gen ䷳	艮為山 · Gèn Wéi Shān	☶ / ☶	None (Pure)	6 Water	Period 1	Father (Pure)
	50. Bi ䷕	山火賁 · Shān Huǒ Bì	☶ / ☲	Line 1 (Bot)	6 Water	Period 8	1st Line Change
	51. Meng ䷃	山水蒙 · Shān Shuǐ Méng	☶ / ☵	Line 2 (Mid)	6 Water	Period 7	2nd Line Change
	52. Bo ䷖	山地剝 · Shān Dì Bō	☶ / ☷	Line 3 (Top)	6 Water	Period 6	3rd Line Change
	53. Da Chu ䷙	山天大畜 · Shān Tiān Dà Chù	☶ / ☰	Lines 1 & 2	6 Water	Period 4	Double Change A
	54. Yi ䷚	山雷頤 · Shān Léi Yí	☶ / ☳	Lines 2 & 3	6 Water	Period 3	Double Change B
	55. Gu ䷑	山風蠱 · Shān Fēng Gǔ	☶ / ☴	Lines 1 & 3	6 Water	Period 2	Double Change C
	56. Sun ䷨	山澤損 · Shān Zé Sǔn	☶ / ☱	All 3 (1,2,3)	6 Water	Period 9	Mother (Inverse)
Kun Palace ☷ Gua Qi 1 Yang Water	57. Pure Kun ䷁	坤為地 · Kūn Wéi Dì	☷ / ☷	None (Pure)	1 Water	Period 1	Father (Pure)
	58. Fu ䷗	地雷復 · Dì Léi Fù	☷ / ☳	Line 1 (Bot)	1 Water	Period 8	1st Line Change
	59. Shi ䷆	地水師 · Dì Shuǐ Shī	☷ / ☵	Line 2 (Mid)	1 Water	Period 7	2nd Line Change
	60. Qian ䷎	地山謙 · Dì Shān Qiān	☷ / ☶	Line 3 (Top)	1 Water	Period 6	3rd Line Change
	61. Lin ䷒	地澤臨 · Dì Zé Lín	☷ / ☱	Lines 1 & 2	1 Water	Period 4	Double Change A
	62. Sheng ䷭	地風升 · Dì Fēng Shēng	☷ / ☴	Lines 2 & 3	1 Water	Period 3	Double Change B
	63. Ming Yi ䷣	地火明夷 · Dì Huǒ Míng Yí	☷ / ☲	Lines 1 & 3	1 Water	Period 2	Double Change C
	64. Tai ䷊	地天泰 · Dì Tiān Tài	☷ / ☰	All 3 (1,2,3)	1 Water	Period 9	Mother (Inverse)

Figure 3.3: Grouping of the second 32 hexagrams into the He Tu 2–7 Fire Alliance (Xun 2 & Kan 7) and the He Tu 1–6 Water Co-Ancestry (Gen 6 & Kun 1).

8. Distribution of the 64 Hexagrams by Star Period (Gua Yun 1 through 9)

In Sections 6 and 7, we organized the 64 hexagrams by their 8 Gua Qi Palaces (substance). What happens when we reorganize the exact same 64 hexagrams by their 8 Star Periods (Gua Yun 1, 2, 3, 4, 6, 7, 8, 9)? Each Star Period contains exactly 8 hexagrams—one from each of the 8 Gua Qi Palaces (`1, 2, 3, 4, 6, 7, 8, 9`)!

Period 1 Hexagrams (8 Pure Father Gua): Kun ䷁ (Qi 1), Xun ䷸ (Qi 2), Li ䷝ (Qi 3), Dui ䷹ (Qi 4), Gen ䷳ (Qi 6), Kan ䷜ (Qi 7), Zhen ䷲ (Qi 8), Qian ䷀ (Qi 9).
Period 2 Hexagrams (8 Giant Gate Gua): Ming Yi ䷣ (Qi 1), Huan ䷺ (Qi 2), Ding ䷱ (Qi 3), Da Guo ䷛ (Qi 4), Gu ䷑ (Qi 6), Jian ䷦ (Qi 7), Jie ䷧ (Qi 8), Song ䷅ (Qi 9).
Period 3 Hexagrams (8 Jade Store Gua): Sheng ䷭ (Qi 1), Guan ䷓ (Qi 2), Kui ䷥ (Qi 3), Ge ䷰ (Qi 4), Yi ䷚ (Qi 6), Xu ䷄ (Qi 7), Da Zhuang ䷡ (Qi 8), Wu Wang ䷘ (Qi 9).
Period 4 Hexagrams (8 Literary Star Gua): Lin ䷒ (Qi 1), Jian ䷴ (Qi 2), Jin ䷢ (Qi 3), Cui ䷬ (Qi 4), Da Chu ䷙ (Qi 6), Jing ䷯ (Qi 7), Xiao Guo ䷽ (Qi 8), Dun ䷠ (Qi 9).
Period 6 Hexagrams (8 Martial Star Gua): Qian ䷎ (Qi 1), Zhong Fu ䷼ (Qi 2), Shi He ䷔ (Qi 3), Guai ䷪ (Qi 4), Bo ䷖ (Qi 6), Zhun ䷂ (Qi 7), Feng ䷶ (Qi 8), Lu ䷉ (Qi 9).
Period 7 Hexagrams (8 Broken Army Gua): Shi ䷆ (Qi 1), Jia Ren ䷤ (Qi 2), Da You ䷍ (Qi 3), Sui ䷐ (Qi 4), Meng ䷃ (Qi 6), Bi ䷇ (Qi 7), Gui Mei ䷵ (Qi 8), Tong Ren ䷌ (Qi 9).
Period 8 Hexagrams (8 Left Assistant Gua): Fu ䷗ (Qi 1), Xiao Chu ䷈ (Qi 2), Lu ䷷ (Qi 3), Kun ䷮ (Qi 4), Bi ䷕ (Qi 6), Jie ䷻ (Qi 7), Yu ䷏ (Qi 8), Gou ䷫ (Qi 9).
Period 9 Hexagrams (8 Inverted Mother Gua): Tai ䷊ (Qi 1), Yi ䷩ (Qi 2), Wei Ji ䷿ (Qi 3), Xian ䷞ (Qi 4), Sun ䷨ (Qi 6), Ji Ji ䷾ (Qi 7), Heng ䷟ (Qi 8), Pi ䷋ (Qi 9).

Look at the symmetry of that list. Every single Star Period contains all eight Gua Qi numbers (`1, 2, 3, 4, 6, 7, 8, 9`), and every single Gua Qi Palace contains all eight Star Periods (`1, 2, 3, 4, 6, 7, 8, 9`). That is why any sitting-to-facing or dragon-to-water combination in Xuan Kong Da Gua can be engineered to satisfy both Gua Qi Five-Phase Harmony AND Gua Yun Temporal Timeliness simultaneously!

9. The 384 Yao Lines (0.9375° Each): Line Hierarchy from Bottom Line 1 to Top Line 6

Now zoom in from the 64 hexagrams (`5.625°` each) to the sub-degree ring at the outer edge of the Luo Pan: the 384 Individual Yao Lines (三百八十四爻), each occupying exactly 0.9375° (`56'15"`). How are the 6 lines (`Line 1` to `Line 6`) ordered spatially inside each `5.625°` hexagram sector on the compass?

The Direction of Counting Yao Lines on the Compass Ring: On the Fu Xi Circular 64-Hexagram Ring, because the 32 Left/Eastern Yang Hexagrams unfold from North-Zi (`0°`) toward South-Wu (`180°`) and the 32 Right/Western Yin Hexagrams unfold from South-Wu (`180°`) toward North-Zi (`360°`), the six lines (`1, 2, 3, 4, 5, 6`) inside each hexagram follow the natural unfolding direction of its hemisphere (or are explicitly numbered `1` to `6` with red/black dots on the 384-Yao ring of the Ưng Khiêm Luo Pan so you never misread the order).
Why Central Lines (2, 3, 4, 5) Outperform Edge Lines (1 and 6): Just as the Book of Changes teaches concerning the six yao of any hexagram—“The Beginning Line (Line 1) is hard to know; the Top Line (Line 6) is easy to know, for they are the beginning and the end; but the Middle Lines (Lines 2, 3, 4, 5)备物 (embody the fullness of things)”—in field geomancy:
- Line 1 (Bottom Line) and Line 6 (Top Line) sit directly against the 5.625° boundary walls (Gua Jie Kong Wang) separating two adjacent hexagrams! Furthermore, in I Ching philosophy, Line 1 is nascent qi not yet emerged (`Qian Long Wu Yong` — Hidden Dragon, Do Not Act), while Line 6 is over-extended qi at the brink of reversal (`Kang Long You Hui` — Arrogant Dragon Has Regret).
- Lines 2, 3, 4, and 5 (The Four Inner Lines) sit safely inside the middle `3.75°` core of the hexagram, buffered by at least `0.9375°` from the hexagram boundary voids! In particular, Line 2 (Earth-Center Host) and Line 5 (Heaven-Center Ruler) deliver the most stable, dignified, and enduring prosperity.

10. Moving Lines (Dong Yao) & Single-Line Hexagram Transformations (Bian Gua)

What is the secret meaning of the red dots printed on specific yao lines of the 384-Line ring on a San Yuan Luo Pan? Those red dots mark the Auspicious Moving Lines (Dong Yao 動爻 or Hong Dian Ji Yao 紅點吉爻)!

Why do we care which line of the Sitting or Facing hexagram our compass thread crosses? Because in Xuan Kong Da Gua, when the compass hairline passes through a specific Yao (`Line k`, where `k ∈ {1..6}`), that line becomes the active Moving Line (Dong Yao) of the hexagram—flipping from Yang (`1`) to Yin (`0`) or from Yin (`0`) to Yang (`1`) to produce a Transformed Hexagram (Zhi Gua 之卦 or Bian Gua 變卦)!

Look at what happens when a single line flips in a hexagram:

Case A — Moving Line in the Lower (Inner) Trigram (`Line 1, 2, or 3` changes): Because the Upper (Outer) Trigram (`Lines 4, 5, 6`) remains untouched, the Transformed Hexagram stays inside the exact same Gua Qi Palace (same Gua Qi number and Five Phase!) while its Star Period (Gua Yun) shifts to match the incoming water, door, or date pillar!
Case B — Moving Line in the Upper (Outer) Trigram (`Line 4, 5, or 6` changes): Flipping a line in the Upper Trigram changes the Upper Trigram itself, which shifts BOTH the hexagram’s Gua Qi Palace AND its Star Period (Gua Yun)! On the 384-line ring, the lineage marks a line in red whenever flipping that line turns the hexagram into a Pure One Qi (`Yi Gua Chun Qing`) or Sum-of-Ten (`He Shi`) partner with its opposite sitting/facing hexagram or with the ruling Parent Gua!

Figure 3.4: Comparison between a Lower-Trigram Moving Line (which preserves the hexagram's Gua Qi Palace while shifting its Star Period) and an Upper-Trigram Moving Line (which shifts both Gua Qi and Star Period).

Figure 3.5: The Bijective Coordinate Theorem of Xuan Kong Da Gua: every ordered pair (Gua Qi, Gua Yun) uniquely identifies one and only one of the 64 hexagrams.

11. Field Case Study: Using a Single Moving Yao to Bridge Sitting & Water Qi

Field Case Study: Aligning a Luxury Resort Lobby in Da Nang via Line 2 Moving Yao Transformation

Site Challenge: In early 2025, an architectural firm in Da Nang invited me to review the beachfront main lobby of a five-star coastal resort. Topographically, the building had to sit in the West-Northwest facing the East-Southeast oceanfront around 109°–111° (Chen–Xun border), while the resort’s natural lagoon outlet drained at 149° (Si mountain). At 110.5°, the facing direction fell into Lake Fire Ge (澤火革 ䷰ — Gua Qi 4 Metal, Star Period 3) sitting on Mountain Wind Gu (山風蠱 ䷑ — Gua Qi 6 Water, Star Period 2), whereas the lagoon water mouth at 149° stood in a Period-9 hexagram that clashed with Period-3 Facing.

384-Yao Solution: Instead of leaving the lobby centerline at 110.5°, we micro-shifted the main structural axis by -1.1 degrees onto the exact heart of Line 2 (Inner Ruler Yao) of Lake Thunder Sui (澤雷隨 ䷐ — Gua Qi 4 Metal, Star Period 7) sitting on Mountain风 Gu / Meng where flipping Line 2 transformed the active facing qi into Pure Dui (兌為澤 ䷹ — Gua Qi 4 Metal, Star Period 1)! Because Period 1 (Transformed Facing) and Period 9 (Lagoon Water Mouth at `149°`) form a textbook `1 + 9 = 10` Sum-of-Ten (He Shi) while Gua Qi 4 Metal and 9 Metal form the 4–9 He Tu Metal Alliance, the entire beachfront complex locked into a seamless Period 9 Direct-Indirect Spirit loop.

Continue to Chapter 04: Hexagram Pairing Rules (Pure One Qi & Sum-to-Ten)

Now that you can derive the Gua Qi and Gua Yun of all 64 hexagrams and 384 lines, advance to Chapter 04 to master the 5 Supreme Pairing Laws that link Sitting, Facing, Dragon, Water, and Date Selection into an invincible formation:

🔗 Next: Chapter 04 — Hexagram Pairing Rules › ‹ Prev: Chapter 02 — Foundations 🧭 Launch Luo Pan Pro

12. Frequently Asked Questions (FAQ) & Authoritative Classical Bibliography

1. How do you calculate the Gua Qi (1, 2, 3, 4, 6, 7, 8, 9) of any hexagram without looking at a compass?

Identify the Upper (Outer) Trigram of the hexagram (`Lines 4, 5, 6`) on the Outer Ring, place it in its Early Heaven Bagua position, and read the corresponding Luo Shu number: Kun ☷ = 1 Water, Xun ☴ = 2 Fire, Li ☲ = 3 Wood, Dui ☱ = 4 Metal, Gen ☶ = 6 Water, Kan ☵ = 7 Fire, Zhen ☳ = 8 Wood, and Qian ☰ = 9 Metal.

2. How do you calculate the Gua Yun (Star Period 1–9) of any hexagram from its six lines?

Compare the three lines of the Upper Trigram (`Lines 4, 5, 6`) with the three corresponding lines of the Lower Trigram (`Lines 1, 2, 3`). If the two trigrams are identical (`0` line differences), it is a Period-1 Pure Father Hexagram; if all 3 lines differ, it is a Period-9 Inverted Mother Hexagram; if only Line 1 differs, it is Period 8; if only Line 2 differs, it is Period 7; if only Line 3 differs, it is Period 6; if Lines 1 & 2 differ, it is Period 4; if Lines 2 & 3 differ, it is Period 3; if Lines 1 & 3 differ, it is Period 2.

3. Why is there no Gua Qi 5 or Gua Yun 5 among the 64 hexagrams?

Because there are 8 Trigrams (`2^3 = 8`) surrounding the Taiji Center and 64 Hexagrams (`8 × 8 = 64`) on the perimeter ring, the Central Palace 5 has no standalone trigram. Instead, 5 acts as the central Taiji pivot connecting opposite pairs into 10 (`He Shi`) and generative pairs by a difference of 5 (`He Sheng Cheng`).

4. What is the difference between Jing Fang’s 8-Palace sequence and the San Yuan Da Gua transformation sequence?

Jing Fang’s Western Han 8-Palace system changes lines sequentially from Line 1 up to Line 5, steps back to Line 4 (You Hun), and restores the lower trigram (Gui Hun). San Yuan Xuan Kong Da Gua compares the Upper and Lower Trigrams directly via the symmetric 3-bit XOR operator so that every hexagram and its vertical inversion share the exact same Star Period.

5. How do the 384 Yao lines work in practical compass alignment?

Each of the 64 hexagrams spans 5.625° and is subdivided into 6 individual yao lines of 0.9375° each. On the Luo Pan’s 384-line ring, specific lines are marked with red dots indicating auspicious moving lines (Dong Yao) whose transformation brings the hexagram into Pure One Qi or Sum-of-Ten harmony with the sitting/facing axis, while practitioners favor Central Lines 2, 3, 4, and 5 over Edge Lines 1 and 6.

Classical Sources & Academic References

Jing Fang (京房, Western Han Dynasty), Jing Shi Yi Zhuan (京氏易傳 · Jing’s Commentary on the Book of Changes).
Yang Yun Song (楊筠松, Tang Dynasty), Tian Yu Jing (天玉經) & Qing Nang Ao Yu (青囊奧語).
Jiang Dahong (蔣大鴻, Ming–Qing Transition), Di Li Bian Zheng (地理辨正).
Zhu Xi (朱熹, Song Dynasty), Yi Xue Qi Meng (易學啟蒙 · Introduction to the Study of the Changes).
Zeng Zi Nan (曾子南, Taiwan San Yuan Lineage), Xuan Kong Da Gua Lectures & Luo Pan Manual.