Module 3
The eight trigrams: from one line to three
Goal of this module
Understand how the trigrams are generated from yin and yang lines, and be able to work back from structure to name.
Count them first
One line has two possibilities, yin or yang.
What about two lines? When the first is yang, the second can be either: two. When the first is yin, the second can again be either. Altogether 2×2 = 4.
With three lines, on top of each of those the third can again be either. 2×2×2 = 8.
So the eight trigrams are what 2³ ＝ 8 produces. Nobody in antiquity settled on eight; three lines can only be arranged in eight ways, not one more and not one fewer. By the same reasoning, stacking two trigrams gives 8×8 = 64 — the number of hexagrams is derived as well.
Why from the bottom up
The three positions are called the bottom, middle and top lines.
What matters is that a trigram is generated from the bottom up. The first result you get when casting goes at the bottom, the second above it, and so on. That is why the lowest line of a six-line figure is called the “initial” line: initial means first.
Because it is generated bottom-up, it is read bottom-up too. This runs against our habit of writing downward, and it is the easiest thing in the whole course to get wrong. From here on, every time you look at a figure, confirm it to yourself first: the bottom line is the first line.
Flip them yourself
Each of the three lines below can be switched. Try all eight combinations and watch the structural note beside them — see the pattern for yourself before reading on.
Kun
kūn
Earth
supporting, receiving, accommodating
all three lines yin
Click any line to switch it between yin and yang. Try all eight combinations before reading on.
The pattern: look for the odd one out
If you have flipped through all eight, you have probably noticed it already: six of the eight trigrams contain exactly one “minority” line.
The remaining two are the extremes: three yang lines is Qian, three yin lines is Kun.
| Minority line | At the bottom | In the middle | At the top |
|---|---|---|---|
| The single yang line | Zhen | Kan | Gen |
| The single yin line | Xun | Li | Dui |
Identifying any three-line figure takes two steps: is the minority line yin or yang, and which position does it hold? There is no need to remember eight shapes.
The names of these six and the natural images behind them (thunder, water, mountain, wind, fire, lake) are left to module 5. For now, structure only — this is what “understand the structure first, memorize the names later” looks like in practice.
Three names for the same thing
Chinese has three words here — 三爻卦, 經卦, 單卦 — and they all point at the same object: a figure made of three lines. There are several names because two of these will later be stacked into a six-line figure, and at that point a word is needed for “the three-line figure acting as a component”, which is what 經卦 (component trigram) and 單卦 (single trigram) supply.
On this site, “trigram” means one of the eight, and “component trigram” means one of them in its role as part of a hexagram.
Exercises
1Three lines, each with two possibilities. How many combinations in all?
One line gives 2. Add another, and each of those branches into 2 again.
That step went astray. 6 is 3×2 — multiplying “three lines” by “two states”. But those are not parallel: every possibility for the second line has to be counted once under every possibility for the first, so it is a branching that multiplies, 2×2×2.
Right. 2×2×2 = 2³ = 8. The first line gives 2; under each of those the second gives 2 more, making 4; under each of those the third gives 2 more, making 8. The eight trigrams were not decreed — three lines simply cannot make any more.
That step went astray. 9 is 3² — base and exponent swapped. This is “2 states repeated 3 times”, not “3 states repeated 2 times”.
The point of this question is not the arithmetic. It is that the number of trigrams is derived, not decreed. The same holds for the hexagrams: 8×8 = 64.
2In a three-line figure, which line is settled first?
Right. Right. A trigram is generated from the bottom up: the first result you get when casting goes at the bottom, and the rest stack upward from there. So it is read from the bottom up as well.
That step went astray. Reading habits pull the eye downward from the top, which is exactly the beginner’s classic mistake. Both the generation and the reading run bottom-up, and the lowest line is called the “initial” line — initial meaning first.
That step went astray. The middle line is structurally special, as you will see when you meet “holding the centre”. But in order of generation it is the second, not the first.
3Bottom line yang, middle line yin, top line yin. Which trigram is this?
Do not reach for the name. Ask first: which of yin and yang appears only once, and where is it?
Right. One yang line only, and it sits at the bottom: that is Zhen. Identifying a figure by “where is the single odd line” is far quicker than memorizing eight shapes, and far harder to mix up.
That step went astray. Gen also has just one yang line, but at the top. Zhen and Gen are the pair most easily confused, and the only difference is where that yang line sits.
That step went astray. Kan’s single yang line is in the middle. Zhen, Kan and Gen are structurally the same kind of figure, differing only in whether the yang line is at the bottom, middle or top.
Six of the eight trigrams contain exactly one “minority” line. Check whether the minority is yin or yang, then check its position: two steps to fix any trigram, with no symbols to memorize.
Common mistakes
These are not filler. They are the specific places beginners go wrong.
Reading the three lines from the top down.
A trigram is generated from the bottom up, and the bottom line is settled first — which is why it is called the “initial” line. Read it backwards and Zhen becomes Gen, Xun becomes Dui: each turns into precisely its counterpart. This is the number-one error across the whole course.
Thinking the count is 3×2 = 6.
The three lines are not three parallel choices but a branching. Under each possibility for the first line the second has two, and under each of those the third has two again. Hence 2×2×2 = 8.
Trying to memorize the eight shapes by brute force.
Six of the eight contain exactly one “minority” line: check whether it is yin or yang, then whether it sits at the bottom, middle or top, and the trigram is fixed in two steps. Memorizing shapes is slower, and it guarantees that Zhen/Gen and Xun/Dui end up confused.
Thinking the trigrams rank against each other, better and worse.
The eight trigrams are all the combinations of three lines, and they stand on equal footing. Qian comes first because three yang lines are the easiest place to begin an explanation, not because it is the best — module 1’s value-judgment habit, once again.
You have it when
You can explain why there are exactly eight trigrams (not six, not nine), state correctly in which direction three lines are generated and read, and work back from structure to a trigram’s name without consulting a table.
Your progress is kept only in this browser, on this device: the site has no accounts and uploads nothing to a server. Clearing site data, changing devices or browsing privately will lose it. Export and backup will come in a later version.
The prose, examples and exercises on this page are written for this site (L4). Passages quoted from the Zhou Yi and the Ten Wings are L1/L2 and in the public domain; per-passage sourcing is given on the hexagram pages.