六十甲子
the sexagenary cycle — the clock of the chart
Stems and branches turn together like two gears: ten teeth and twelve teeth. They pair only same-parity — yang stem with yang branch, yin with yin — so the full cycle is 60 pairs, from 甲子 to 癸亥, and then it repeats. (10 × 12 would be 120, but parity halves it to 60 — the least common multiple of the two gears, divided by the parity lock.)
This 60-step clock runs everywhere in the system. Years ride it: 1984 was 甲子, 2024 is 甲辰, 2044 will be 甲子 again. Days ride it independently: every date since the calendar's epoch has a day pillar, computed by a pure count — no astronomy needed, nothing to believe. Hours and months ride a variant, keyed off the day and year pillars by the 五鼠遁 and 五虎遁 rules (module 6).
how the cycle turns
The gears mesh like this: the stem advances one step, the branch advances one step — 甲子, 乙丑, 丙寅, 丁卯 … 癸酉, then the stems exhaust and restart: 甲戌, 乙亥, 丙子 … and after 60 steps, 甲子 returns. Because both gears always advance together, same-parity pairs are the only ones that ever occur: you will never see 甲丑 or 乙子. When someone hands you a "ganzhi" that breaks parity, it is not a real ganzhi.
The 60 pairs are also the skeleton of the 纳音 nayin (below) and of the 旬 xún — the six ten-day weeks the tradition divides the cycle into, each with two void branches (空亡, used in module 8's 冲空则实).
纳音 — the thirty element-tones — 纳音
Each ganzhi pair carries a poetic phase-name, two pairs sharing one name — 30 names across the 60 pairs. They are the tradition's most lyrical layer: 海中金 "metal in the sea," 炉中火 "fire in the furnace," 大林木 "timber of the great forest," 天上火 "fire in the heavens." Each name reads the pair's phase as situated somewhere — in the sea, the mountain, the street — a flavor, not a fortune. The app prints the nayin of all four pillars under the chart grid.
| nayin name | the pairs it covers |
|---|---|
| 海中金 metal in the sea | 甲子 乙丑 |
| 炉中火 fire in the furnace | 丙寅 丁卯 |
| 大林木 timber of the forest | 戊辰 己巳 |
| 路旁土 earth by the roadside | 庚午 辛未 |
| 剑锋金 sword-blade metal | 壬申 癸酉 |
| 山头火 fire on the mountain | 甲戌 乙亥 |
| 涧下水 water in the ravine | 丙子 丁丑 |
| 城头土 earth on the rampart | 戊寅 己卯 |
| 白蜡金 wax-white metal | 庚辰 辛巳 |
| 杨柳木 willow wood | 壬午 癸未 |
| 泉中水 spring water | 甲申 乙酉 |
| 屋上土 earth on the roof | 丙戌 丁亥 |
| 霹雳火 thunderbolt fire | 戊子 己丑 |
| 松柏木 pine and cypress | 庚寅 辛卯 |
| 长流水 long flowing water | 壬辰 癸巳 |
| 沙中金 metal in the sand | 甲午 乙未 |
| 山下火 fire below the mountain | 丙申 丁酉 |
| 平地木 wood on level ground | 戊戌 己亥 |
| 壁上土 earth on the wall | 庚子 辛丑 |
| 金箔金 gold-foil metal | 壬寅 癸卯 |
| 覆灯火 lamp-light fire | 甲辰 乙巳 |
| 天河水 river of heaven | 丙午 丁未 |
| 大驿土 earth of the great highway | 戊申 己酉 |
| 钗钏金 hairpin metal | 庚戌 辛亥 |
| 桑柘木 mulberry wood | 壬子 癸丑 |
| 大溪水 water of the great stream | 甲寅 乙卯 |
| 沙中土 earth in the sand | 丙辰 丁巳 |
| 天上火 fire in the heavens | 戊午 己未 |
| 石榴木 pomegranate wood | 庚申 辛酉 |
| 大海水 water of the great sea | 壬戌 癸亥 |
the day pillar is public math
The day pillar needs no astronomical table and no doctrine: it is the Julian day number of the birth date, taken mod 60, anchored at one known point — 2000-01-01 was 戊午 (index 54). Anyone with a calculator can verify every day pillar in this app by hand. This is the core of the project's promise: "computed, not generated." The day pillar is the anchor the rest of the chart is built around, and it is checkable down to the arithmetic.