五合化氣 5 Duo-Stems
甲與己合乙與庚合丙與辛合丁與壬合戊與癸合
甲己化土乙庚化金丙辛化水丁壬化木戊癸化火○考原曰五合者即五位相得而各有合也河圖一與六二與七三與八四與九五與十皆各有合以十干之次言之一為甲六為己故甲與己合二為乙七為庚故乙與庚合三為丙八為辛故丙與辛合四為丁九為壬故丁與壬合五為戊十為癸故戊與癸合又年起月日起時越五則花甲周而復始而月時同干亦即五合之義
按化氣之理沈括據黄帝素問論之最明素問有五運六氣所謂五運者
甲己為土運乙庚為金運丙辛為水運丁壬為木運戊癸為火運也黄帝問岐伯五運之所始岐伯引太始天元冊文曰始于戊己之分所謂戊己分者奎壁角軫也奎壁角軫天地之門戶也王冰注引遁甲六戊為天門六己為地戶天門在戌亥之間奎壁之分地戶在辰巳之間角軫之分隂陽皆始于辰五運起于角軫者亦始于辰也
- 甲己之歲戊己
黅天之氣經于角軫角屬辰軫屬己其歲得戊辰己巳干皆土故為土運- 乙庚之歲庚辛
素天之氣經于角軫其歲得庚辰辛巳干皆金故為金運- 丙辛之歲壬癸
元天之氣經于角軫其歲得壬辰癸巳干皆水故為水運- 丁壬之歲甲乙
蒼天之氣經于角軫其歲得甲辰乙巳干皆木故為木運- 戊癸之歲丙丁
丹天之氣經于角軫其歲得丙辰丁巳干皆火故為火運運臨角軫則氣在奎壁氣與運常司天地之門戶
- 戊己在角軫則甲乙在奎壁甲己歲必甲戌乙亥也故素問曰
土位之下風氣承之- 庚辛在角軫則丙丁在奎壁乙庚歲必丙戌丁亥也故曰
金位之下火氣承之- 壬癸在角軫則戊巳在奎壁丙辛歲必戊戌己亥也故曰
水位之下土氣承之- 甲乙在角軫則庚辛在奎壁丁壬歲必庚戌辛亥也故曰
風位之下金氣承之- 丙丁在角軫則壬癸在奎壁戊癸歲必壬戌癸亥也故曰
相火之下水氣承之五行家以戊寄於己巳寄於午六壬家以戊寄於己巳寄於未惟素問以戊寄於戌己寄於辰遁甲以六戊為天門六己為地戶與素問同水土相隨水金子也
陽土故居金行之末以為亥始水木母也巳金祖也隂土故居水行之墓以為巳始故曰天地之門戶而萬物所從出星家有逢龍則化之說亦本於此此十干化氣之源也

| 五合化氣 5 Duo-Stems | 天干 Heavenly Stem | 天干 Heavenly Stem | 河圖之象 HE-TU | 河圖之象 HE-TU | 氣 Qi |
|---|---|---|---|---|---|
| ㊏EARTH | S0甲 | S5己 | 一⑴ | 六⑹ | 黅天之氣 |
| ㊎METAL | S1乙 | S6庚 | 二⑵ | 七⑺ | 素天之氣 |
| ㊌WATER | S2丙 | S7辛 | 三⑶ | 八⑻ | 元天之氣 |
| ㊍WOOD | S3丁 | S8壬 | 四⑷ | 九⑼ | 蒼天之氣 |
| ㊋FIRE | S4戊 | S9癸 | 五⑸ | 十⑽ | 丹天之氣 |
Kaoyuan (Investigation of Origins) ctext states: Five DUO-HARMONIES arises from the mutual compatibility of five positions. According to the HE-TU: 1 pairs with 6, 2 pairs with 7, 3 pairs with 8, 4 pairs with 9, and 5 pairs with 10. Applying this to the Ten Heavenly Stems:
- 1 is S0甲⊕WOOD, 6 is S5己⊖EARTH, hence S0甲⊕WOOD and S5己⊖EARTH are DUO-HARMONY.
- 2 is S1乙⊖WOOD, 7 is S6庚⊕METAL are DUO-HARMONY, hence S1乙⊖WOOD and S6庚⊕METAL are DUO-HARMONY.
- 3 is S2丙⊕FIRE, 8 is S7辛⊖METAL, hence S2丙⊕FIRE and S7辛⊖METAL are DUO-HARMONY.
- 4 is S3丁⊖FIRE, 9 is S8壬⊕WATER, hence S3丁⊖FIRE and S8壬⊕WATER.
- 5 is S4戊⊕EARTH, 10 is S9癸⊖WATER, hence S4戊⊕EARTH and S9癸⊖WATER.
Five YEARs covers 60 SEXAGENARY-CYCLE of MONTHs, Five DAYs covers 60 SEXAGENARY-CYCLE of HOURs, and cycles restart after completion, forming Five DUO-HARMONIES.