Introduction to the 10 Heavenly Stems

The Heavenly Stems (天干) are a set of ten characters used in ancient Chinese calendar systems and astrology.

10-HEAVENLY-STEMS 十干 {#10-heavenly-stems}

Duduan (Independent Judgment) of Cai Yong _wiki states, there are 10 HEAVENLY-STEMS _wiki

^S0甲_⊕WOOD (jiǎ)
^S1乙_⊖WOOD (yǐ)
^S2丙_⊕FIRE (bǐng)
^S3丁_⊖FIRE (dīng)
^S4戊_⊕EARTH (wù)
^S5己_⊖EARTH (wù)
^S6庚_⊕METAL (gēng)
^S7辛_⊖METAL (xīn)
^S8壬_⊕WATER (rén)
^S9癸_⊖WATER (guǐ)

10-HEAVENLY-STEMS correspondance with 4-SEASONS {#10-heavenly-stems-x-4-seasons}

The Liji (Book of Rites), Yueling (Monthly Ordinances) _ctext states:

In spring months, the days are ^S0甲_⊕WOOD and ^S1乙_⊖WOOD
In summer months, the days are ^S2丙_⊕FIRE and ^S3丁_⊖FIRE
In the central ㊏_EARTH phase, the days are ^S4戊_⊕EARTH and ^S5己_⊖EARTH
In autumn months, the days are ^S6庚_⊕METAL and ^S7辛_⊖METAL
In winter months, the days are ^S8壬_⊕WATER and ^S9癸_⊖WATER

Five DUO-HARMONIES 五合化氣 {#-heavenly-stems-duo-harmonies}

^S0甲_⊕WOOD and ^S5己_⊖EARTH are DUO-HARMONY, transform into ㊏_EARTH
^S1乙_⊖WOOD and ^S6庚_⊕METAL are DUO-HARMONY, transform into ㊎_METAL,
^S2丙_⊕FIRE and ^S7辛_⊖METAL are DUO-HARMONY, transform into ㊌_WATER,
^S3丁_⊖FIRE and ^S8壬_⊕WATER are DUO-HARMONY, transform into ㊍_WOOD,
^S4戊_⊕EARTH and ^S9癸_⊖WATER are DUO-HARMONY, transform into ㊋_FIRE.

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.