Tam nguyên and the 18 Ju of Qimen: How to Derive the Ju Number from Solar Terms According to the Source Texts

What is Tam nguyên in Qimen Dunjia?

Tam nguyên is the division of each solar term into three five-day segments, each called a nguyên: upper nguyên, middle nguyên, and lower nguyên. Each nguyên lasts five days, that is sixty hours, and is assigned one ju number. The three nguyên of a solar term use three different ju numbers, read from the verses in the section below. This concept is the foundation for setting up a Qimen board, because the ju number determines the starting positions of the six yi and the three qi on the earth plate.

The Hiệp kỷ biện phương thư (欽定協紀辨方書), compiled by Doãn Lộc and colleagues in 1741 by imperial order, states in volume 35: “五日六十時為一元” (five days and sixty hours make one nguyên), and “甲巳日必甲子時故以甲巳日為符首” (a Giáp or Kỷ day necessarily has a Giáp Tý hour, so Giáp and Kỷ days are taken as fu shou)^[1]. This means the fu shou is the starting day of each nguyên, and every five days the nguyên changes once.

The Yên ba điếu tẩu ca, the foundational verse of Qimen, also confirms this principle in the line: “陰陽二遁分順逆，一氣三元人莫測。五日都來接一元，接氣超神為準則” (yin and yang dun divide forward and reverse, one qi has three nguyên which people cannot fathom; five days all come to connect one nguyên, tiếp khí and siêu thần are the standard rules)^[2]. That is, each solar term (one qi) comprises three nguyên, every five days the nguyên changes, and adjustment by tiếp khí or siêu thần is a mandatory rule.

Why does each solar term have three nguyên?

A solar term lasts about fifteen days, which is exactly divisible by five days, so it fits exactly three nguyên. This is the natural reason why tam nguyên is tightly bound to the solar term. The Hiệp kỷ biện phương thư explains: “一節十五日三元既周則下節叧起也” (one term of fifteen days, when the three nguyên are complete the next term begins separately)^[1].

However, twenty-four terms of fifteen days make only 360 days, while a year is longer than 365 days, so the fu shou of the terms gradually drifts away from the term day. The text states: “又有置閏之法乃由氣盈而生” (there is also the method of placing intercalation, arising from the surplus of qi)^[1]. When the accumulated deviation becomes large enough, one must use siêu thần, tiếp khí, or trí nhuận to adjust, otherwise the ju will become increasingly incorrect over time.

Which verses give the table of tam nguyên ju by solar term?

Volume 35 of the Hiệp kỷ biện phương thư records, right after the Kỳ Môn tam nguyên ca (the verse other editions call the Yên ba điếu tẩu ca), two short verses, the Dương độn ca and the Âm độn ca. Each line gives all three ju numbers, for the upper, middle and lower nguyên, of one or two solar terms, for example “冬至驚蟄一七四” (Đông Chí, Kinh Trập: one, seven, four)^[1]. Looking at the numbers, in yang dun each nguyên equals the previous one plus six, and in yin dun the previous one minus six, counted cyclically within the nine palaces.

Yang dun verse:

• Đông Chí, Kinh Trập: 1, 7, 4
• Tiểu Hàn: 2, 8, 5
• Đại Hàn, Xuân Phân: 3, 9, 6
• Lập Xuân: 8, 5, 2
• Vũ Thủy: 9, 6, 3
• Thanh Minh, Lập Hạ: 4, 1, 7
• Cốc Vũ, Tiểu Mãn: 5, 2, 8
• Mang Chủng: 6, 3, 9

Yin dun verse:

• Hạ Chí, Bạch Lộ: 9, 3, 6
• Tiểu Thử: 8, 2, 5
• Đại Thử, Thu Phân: 7, 1, 4
• Lập Thu: 2, 5, 8
• Xử Thử: 1, 4, 7
• Sương Giáng, Tiểu Tuyết: 5, 8, 2
• Hàn Lộ, Lập Đông: 6, 9, 3
• Đại Tuyết: 4, 7, 1

The table below summarizes the upper, middle, and lower nguyên ju numbers for each term according to the two verses above:

This table is taken directly from the Dương độn ca and the Âm độn ca in volume 35 of the Hiệp kỷ biện phương thư^[1].

How to determine the nguyên from the fu shou day?

To know which nguyên a specific day belongs to, one relies on the nearest fu shou day before it. The fu shou is a Giáp or Kỷ day, because according to the Hiệp kỷ biện phương thư, “甲巳日必甲子時” (a Giáp or Kỷ day necessarily has a Giáp Tý hour)^[1]. The text classifies:

• Upper nguyên: the days Giáp Tý, Giáp Ngọ, Kỷ Mão, Kỷ Dậu
• Middle nguyên: the days Giáp Dần, Giáp Thân, Kỷ Tị, Kỷ Hợi
• Lower nguyên: the days Giáp Thìn, Giáp Tuất, Kỷ Sửu, Kỷ Mùi

The text gives the example of a term that uses yang dun ju 1 in its upper nguyên: the Giáp Tý day is the upper nguyên, with the Giáp Tý hour starting at the Khảm palace 1; the Kỷ Tị day is the middle nguyên, with the Giáp Tý hour starting at the Đoài palace 7; the Giáp Tuất day is the lower nguyên, with the Giáp Tý hour starting at the Tốn palace 4; and on the Kỷ Mão day the upper nguyên returns^[1]. The ju number is also the palace where Mậu is placed on the earth plate: in yang dun ju 1 the text sets Mậu at Khảm 1, Kỷ at Khôn 2, Canh at Chấn 3, Tân at Tốn 4, Nhâm at the centre 5 lodged at Khôn, Quý at Càn 6, then Đinh at Đoài 7, Bính at Cấn 8 and Ất at Ly 9^[1].

Siêu thần, tiếp khí, and trí nhuận: what to do when the fu shou drifts from the term?

Because each year runs more than five days beyond the 360 days of the twenty-four terms, the fu shou of the following year usually does not coincide with the term day. The Hiệp kỷ biện phương thư takes the Đông Chí term as its example and gives four cases^[1]:

• Chính thụ (正授): the fu shou coincides exactly with the term day. The text's example: this year Đông Chí falls on a Giáp Tý day, so the upper nguyên of Đông Chí is used at once.
• Siêu thần (超神): the fu shou arrives before the term. Next year Đông Chí falls on a Kỷ Tị day, the Giáp Tý fu shou stands five days before Đông Chí, and from that Giáp Tý day the upper nguyên of Đông Chí is already used.
• Trí nhuận (置閏): the year after, Đông Chí falls on a Giáp Tuất day; the Giáp Tý fu shou stands ten days before the term and the Kỷ Mão fu shou five days after it, far before and near after. The Giáp Tý, Kỷ Tị and Giáp Tuất days then use again the upper, middle and lower nguyên of the Đại Tuyết term. The text calls this intercalating one qi, that is, repeating all three nguyên of the preceding term, and says: “置閏必在二至之前超不過十接不過五” (intercalation must be before the two solstices, siêu not exceeding ten, tiếp not exceeding five)^[1].
• Tiếp khí (接氣): the fu shou arrives after the term. In the example above, only on the Kỷ Mão day after Đông Chí is the upper nguyên of Đông Chí used.

The text also notes: “然此乃以平氣正授起算若以定氣而論盈縮各有不同當以逺近為斷” (but this is calculated by mean qi and chính thụ; if calculated by true qi, the surplus and deficit differ, and one must judge by distance)^[1]. This shows that even in ancient texts there is a distinction between two methods of calculating solar terms, and the handling may differ according to method.

Do the schools agree on how to calculate the ju?

Not entirely. The Hiệp kỷ biện phương thư records two variant views in small notes, one on the path of the nine stars and one on the names of the eight spirits: “一説九星亦是順行八卦” (one theory says the nine stars also proceed forward through the eight trigrams) and “一説白虎作勾陳元武作朱雀” (one theory replaces White Tiger with Hook Chen, Dark Warrior with Vermilion Bird)^[1]. This shows that even within the same book, the author recorded variant versions without arbitrarily choosing one side.

Regarding the calculation of ju from solar terms, the ju table of the Dương độn ca and the Âm độn ca is shared; where practitioners differ is in how they handle a fu shou that has drifted from the term. The Hiệp kỷ biện phương thư follows siêu thần, tiếp khí and trí nhuận, and mentions another method, splitting and patching the ju (拆局補局), which uses the lower nguyên of the current term first, adding the words “不可從” (not to be followed)^[1]. With true qi, the text says to judge by distance: if the earlier fu shou is seven days before the term and the later one eight days after it, siêu thần is still used; if eight days before and seven after, trí nhuận is applied^[1]. The text also explains the root of the ju table: Đông Chí at Khảm, Lập Xuân at Cấn, Xuân Phân at Chấn and Lập Hạ at Tốn belong to yang dun and run forward; Hạ Chí at Ly, Lập Thu at Khôn, Thu Phân at Đoài and Lập Đông at Càn belong to yin dun and run in reverse; the upper nguyên of Đông Chí uses ju 1, so Tiểu Hàn uses ju 2 and Đại Hàn ju 3, and the upper nguyên of Hạ Chí uses ju 9, so Tiểu Thử uses ju 8 and Đại Thử ju 7^[1].

Gợi ý của Nhật Nguyệt

To look up the Qimen ju for a given hour, three things are determined in order: the current solar term, the nearest fu shou day, and the nguyên corresponding to that day. When the fu shou has drifted from the term, one must check whether the case is siêu thần, tiếp khí or trí nhuận, because each gives a different ju. This is where the texts differ, so when reading a Qimen board one needs to know which method its maker followed. This article only reports how the old texts calculate the ju number of a traditional divination art.