The Ten-Day Xun and Void
Last updated 10/7/2026
The 60 Ganzhi pairs divide into six groups of ten called xun. Each xun uses all ten stems but only ten of the twelve branches. The two branches left outside that ten-pair window are the void pair.
This lesson calculates the state. Later lessons decide what a void selected line can do and when the state may change.
The six xun
| Xun beginning | Pair positions | Void branches |
|---|---|---|
| Jia-Zi | 1–10 | Xu, Hai |
| Jia-Xu | 11–20 | Shen, You |
| Jia-Shen | 21–30 | Wu, Wei |
| Jia-Wu | 31–40 | Chen, Si |
| Jia-Chen | 41–50 | Yin, Mao |
| Jia-Yin | 51–60 | Zi, Chou |
Arithmetic check
Number the stems 1–10 and branches 1–12. For a valid day pair with stem position s and branch position b:
- calculate
11 - s + b; - calculate
12 - s + b; - wrap each result into the 1–12 branch range.
Those two positions are the void branches.
Case 00035
Ji-Mao uses stem position 6 and branch position 4:
11 - 6 + 4 = 9→ Shen;12 - 6 + 4 = 10→ You.
So Ji-Mao belongs to the Jia-Xu xun and has Shen/You void. On the primary Hexagram 3 chart, line 4 carries Shen and is tagged void; no primary line carries You.
Mechanics supplement: Case 00115
The source record asks when an awaited 文书 would be received. Its document type and historical stakes are unknown, so this course does not call it official, legal, financial, or low-stakes. Only its verified calendar input is used here.
Ren-Chen uses stem position 9 and branch position 5:
11 - 9 + 5 = 7→ Wu;12 - 9 + 5 = 8→ Wei.
The result is Wu/Wei void, matching the documented record catalogued here as Case 00115. No source outcome is needed to verify this calculation.
Failure controls
- The day branch alone cannot determine the xun; use the full stem-branch pair.
- Check that the pair is valid before calculating. Opposite polarities do not form a day in the 60-pair cycle.
- Void does not erase a line from the chart. Record the branch and add a separate void flag.
- Do not infer release timing here. Calculation, effect, and timing are three different page jobs.
For the effect of void on a selected line, continue later to the Void strength lesson. For candidate release timing, use the Void Timing lesson.
Source note
The formula and complete six-pair table make the void assignment reproducible from the declared day pair. Case 00115 is bounded by Zengshan Buyi, volume 2, 飞伏神章, checked PDF printed p. 53 / physical p. 54 and CText anchors p79–p86; the number is a UAYA course catalogue label, not a traditional-edition case number.
Next: Continue to The Five Phases and add element relations to the line table.