Which Hexagrams Are Derived From One Hexagram: Changing Hexagram, Nuclear Hexagram, Opposite Hexagram, Reversed Hexagram, and How to Read by the Number of Moving Lines

The four derivations and why one hexagram gives rise to others

In the I Ching, a hexagram does not stand still. From one original hexagram, several derived hexagrams can be inferred by rule-based transformations. The four most common are the changing hexagram, the nuclear hexagram, the opposite hexagram and the reversed hexagram. Each answers a different question about the same situation, so they are usually read as four layers of one story rather than four separate verdicts.

In the common presentation, a hexagram consists of six stacked lines, counted from the bottom up: line one at the bottom, line six at the top. Each line is either yang (a solid stroke) or yin (a broken stroke). The six lines combine into two three-line trigrams: the inner trigram below and the outer trigram above. Eight trigrams combine to give 64 hexagrams. All the derivations below operate on those six lines.

What is the changing hexagram and why is it used most?

The changing hexagram is obtained by flipping the state of the moving line while keeping the other five lines unchanged. A moving yang line becomes yin, a moving yin line becomes yang. If several lines move together, all moving lines are flipped.

The changing hexagram is used most because it is tied directly to the moving line, and the moving line is the focus of the whole hexagram. When casting, the moving line shows where change is occurring. The changing hexagram shows where the situation leans if that momentum continues. In other words, the original hexagram is the present, the changing hexagram is the direction.

One point to note: the moving line does not exist in isolation. It may generate, control, combine with or clash with other lines in the hexagram, so when interpreting the changing hexagram people usually read it together with the relationship between the moving line and the changed line, not just the new hexagram shape.

What is the nuclear hexagram and which lines is it taken from?

The nuclear hexagram is built from the core of the original hexagram: lines 2, 3, 4 form the inner trigram and lines 3, 4, 5 form the outer trigram. Therefore the nuclear hexagram is always calculated from the original hexagram, fixed across all six lines, and does not change with the moving line.

A very common mistake among beginners is calculating the nuclear hexagram from the changing hexagram. That is wrong. The nuclear hexagram must be drawn from the original hexagram. The nuclear hexagram shows the hidden current running beneath the surface, the forces not yet revealed when only looking at the original hexagram. In many readings, the original hexagram is the current context, the nuclear hexagram is the latent process, the changing hexagram is the expected outcome.

There is also a broader theory called "one hexagram mutually produces five hexagrams": from one hexagram, five different hexagrams can be inter-generated by taking consecutive line groups. For example, with the hexagram Zhun, people successively draw the hexagrams Jian, Bi, Bo, Yi, Fu from different line groups. This method is not called the nuclear hexagram but the miscellaneous hexagram, and it belongs to a separate style of analysis, not the standard nuclear hexagram construction rule.

How do the opposite hexagram and the reversed hexagram differ?

These two are often confused, so they need to be clearly separated.

The opposite hexagram, also called the opposing hexagram or the complementary hexagram, is built by flipping the state of all six lines: yang to yin, yin to yang, entirely. The result is a hexagram completely opposite in shape to the original. For example, Qian opposes to Kun, Kan opposes to Li.

The reversed hexagram, also called the inverted hexagram or the overturned hexagram, is built by turning the whole hexagram upside down. Line one becomes line six, line two becomes line five, and vice versa. This keeps the number of yin and yang lines the same, only changing their positions.

These two give different perspectives. The opposite hexagram shows the opposing side, what is completely contrary to the situation under consideration. The reversed hexagram shows that same situation but seen from the other side, like a mirror. In the commentary tradition, it is observed that among the 64 hexagrams, every two form a pair, either as reversed hexagrams of each other or as opposite hexagrams of each other. This shows that the reversed and opposite derivations are tools for pairing and reading correspondences.

Table of the four derivations: how to build and usual meaning

Reading rules by the number of moving lines that casting tools apply

When casting, the number of moving lines can be zero, one, two, three, four, five or six. Each case has a different reading method. The most common method is recorded in Zhu Xi's Yixue Qimeng, and this is the convention most casting tools today apply.

• No moving lines: read the hexagram text (guaci), take the whole hexagram as the subject.
• One moving line: read the line text of that moving line as the main point.
• Two moving lines: read both line texts, take the upper line as the subject.
• Three moving lines: read the original hexagram text and the changing hexagram text, take the original as the subject, the changing as secondary.
• Four moving lines: read the two non-moving line texts below, take the lowest of the two as the subject.
• Five moving lines: read the text of the single non-moving line.
• Six moving lines: for the Qian hexagram, read Yong Jiu; for the Kun hexagram, read Yong Liu. Other hexagrams read the changing hexagram text.

It must be stated clearly: this rule belongs to one school, not all schools follow it. Some practitioners use a simpler reading, where knowing the moving line is enough to interpret, without reading all the other lines. Others use a different method for cases with many moving lines. So when reading a hexagram, one should first identify which convention the tool or book follows.

How do schools differ in reading the changing and nuclear hexagrams?

The three major schools use the nuclear and changing hexagrams very differently.

Mei Hua Yi Shu, systematized by Shao Kangjie in the Song dynasty, reads the hexagram in three stages: subject, nuclear, changing. The subject hexagram is the current situation, the nuclear hexagram is the inner development, the changing hexagram is the result. Mei Hua also uses the Ti-Yong pair: the trigram containing the moving line is Yong, the other trigram is Ti. Yong represents the matter, Ti represents the querent. The five-element relationship between Ti and Yong indicates whether the situation is favorable or unfavorable. Mei Hua mainly builds hexagrams by numbers or by observing external signs, so the nuclear and changing hexagrams play an important role in interpretation.

Liu Yao, that is Najia, almost never uses the nuclear hexagram. This school assigns Heavenly Stems, Earthly Branches, the six relations and the six spirits to each line, then interprets generation and control, combination and clash, prosperity and decline according to the monthly and daily influences. The changing hexagram is still used, but the nuclear hexagram almost never appears in its interpretive system.

Zhu Xi's method in Yixue Qimeng leans toward reading the classic text, that is the guaci and yaoci, so his moving-line-count rule is tied to choosing which sentence to read in the book. This is a very different reading from Mei Hua and Liu Yao, which lean toward image-number and five elements.

Hexagrams that are self-reversed

An easily overlooked point: not every hexagram reversed gives a different hexagram. There are eight hexagrams that keep the same shape when reversed, that is they are self-reversed. They are Qian, Kun, Kan, Li, Yi, Zhong Fu, Da Guo and Xiao Guo.

These eight are regarded as the pillars of the Upper and Lower Classics. The remaining 56 hexagrams inter-generate and shift among each other, playing the role of "function" in the structure of the classic. With the eight self-reversed hexagrams, the reversal method does not produce a new hexagram, so when interpreting their reversed hexagram, one must use the opposite method instead or note that the reversed hexagram coincides with the original.

Reading the four layers as one thread

Once all four hexagrams are available, the reading is usually presented as one continuous line: the original hexagram shows where you are, the nuclear hexagram shows what is really happening inside, the changing hexagram shows where you are heading, while the opposite and reversed hexagrams add two perspectives of opposition and mirroring. Not every reading needs all four. Depending on the question and the school, the interpreter may use only the original and changing hexagrams, or add the nuclear hexagram when needing to look into the hidden current.

It must be emphasized that no hexagram is absolutely auspicious or absolutely inauspicious. The same hexagram, placed in different contexts, different times, gives different advice. Schools also do not agree on the meaning of each hexagram and each line, so the reader should treat this as a tool for reflecting on the situation, not a fixed verdict about the future.

Table of opposite, reversed and nuclear hexagrams of the 64 hexagrams

The table is calculated by the same method that the casting tool of Nhat Nguyet uses: the opposite hexagram flips yin and yang of all six lines, the reversed hexagram turns the hexagram upside down, the nuclear hexagram takes lines 2, 3, 4 as the lower trigram and lines 3, 4, 5 as the upper trigram. For the eight hexagrams that reverse to themselves, the reversed hexagram coincides with the original.

FAQ

1. Which lines of the original hexagram is the nuclear hexagram built from?

The nuclear hexagram is built from lines 2, 3, 4 as the inner trigram and lines 3, 4, 5 as the outer trigram of the original hexagram. It is always calculated from the original, not from the changing hexagram.

2. How do the opposite hexagram and the reversed hexagram differ?

The opposite hexagram flips the state of all six lines, yang to yin and yin to yang, producing a completely opposite shape. The reversed hexagram turns the whole hexagram upside down, keeping the number of yin and yang lines the same but changing their positions.

3. Do all schools follow Zhu Xi's reading rule by the number of moving lines?

No. Zhu Xi's rule in Yixue Qimeng is the most common and is applied by most casting tools, but some schools use a simpler reading where knowing the moving line is enough, and others use different methods for cases with many moving lines. One should identify which convention the tool or book follows.