TL;DR: Quái khí is a Han dynasty method that maps the 64 hexagrams of the Chu Dịch onto the 365.25 day year. The four cardinal hexagrams Khảm, Ly, Chấn and Đoài stand outside the 60 hexagram cycle, ruling the four seasons and the solstices and equinoxes; the remaining 60 hexagrams each govern six days and seven parts. This is a convention of a Han dynasty Yi school, not an astronomical fact, and some later texts rejected it.
What Is Quái khí and Why Divide Hexagrams by Days?
Quái khí (卦氣) is the method of spreading the 64 hexagrams of the Chu Dịch across the calendar year, with each hexagram governing a period of time, in order to observe whether the qi of heaven and earth flows smoothly or adversely and thereby judge auspicious and inauspicious matters. This method is associated with the names Mạnh Hỷ (孟喜) and Kinh Phòng (京房) of the Han dynasty, and is recorded in Qing dynasty works on Dịch Hán học and in the Dịch vĩ Kê lãm đồ. Mạnh Hỷ's own book does not survive; what we know comes from later books, such as the remark of Nhất Hạnh of the Tang that the twelve month hexagrams come from Mạnh's commentary, quoted by Huệ Đống[1].
The mechanism is very simple in numerical terms. A solar year has 365 and 1/4 days. The four hexagrams Khảm, Ly, Chấn and Đoài are set apart as the four cardinal hexagrams (四正卦), each governing one season and one solstice or equinox marker. The remaining sixty hexagrams share the remaining time. Dividing 365.25 by 60 gives 6.0875 days, that is, six days and seven eightieths of a day. This is the figure "six days and seven parts" (六日七分) that Han learning texts repeatedly mention.
Huệ Đống records Mạnh's quái khí chart: Khảm, Ly, Chấn and Đoài are the four cardinal hexagrams, and the remaining 60 hexagrams each govern six days and seven parts, together exactly matching the celestial cycle[1]. He also records the view that the 12 sovereign hexagrams (Thái, Đại Tráng, Quải, Kiền, Cấu, Độn, Bĩ, Quan, Bác, Khôn, Phục, Lâm) are king hexagrams, the rest are minister hexagrams, and the four cardinal hexagrams are regional lords. This assignment of roles is a school convention, not a result of measurement.
How Are Six Days and Seven Parts Calculated?
Six days and seven parts is a shorthand for six days plus seven eightieths of a day. One day is divided into eighty parts, each hexagram governs six days and seven parts, that is 6 + 7/80 days. Multiplying by 60 hexagrams: 60 × 6 = 360 days, plus 60 × 7/80 = 5.25 days, totaling 365.25 days, exactly matching one year.
This book records a rebuttal: if one hexagram governs six days and seven parts, then 64 hexagrams would amount to 389-odd days, not matching one year[3]; and it holds that dividing hexagrams by days is Kinh Phòng's technique for divining calamities and anomalies, not the original intent of the sages. This is where the schools disagree, and it should be stated clearly: the six days and seven parts method is a convention of the Quái khí school, not a calendar calculation accepted by all Yi scholars.
Why Seven Parts and Not Another Number?
Because 360 days shared among 60 hexagrams give each six days, leaving five and a quarter days. With a day divided into eighty parts, five and a quarter days are 420 parts, and 420 shared among 60 hexagrams gives exactly seven parts each. The seven parts are thus an exact division, not a rounding.
What Are the Four Cardinal Hexagrams and What Do They Govern?
The four cardinal hexagrams are Khảm, Ly, Chấn and Đoài. They are not part of the 60-hexagram day cycle, but stand apart to govern the four seasons and the four major markers of the year.
| Cardinal Hexagram | Direction | Season | Solstice/Equinox Marker |
|---|---|---|---|
| Khảm | North | Winter | Winter Solstice |
| Chấn | East | Spring | Spring Equinox |
| Ly | South | Summer | Summer Solstice |
| Đoài | West | Autumn | Autumn Equinox |
Where the books differ is the time given to these four hexagrams. In the Mạnh method all sixty hexagrams get six days and seven parts, and the four cardinal hexagrams only distribute their lines over the twenty four solar terms. Kinh Phòng instead gives seventy three eightieths of the first day of the winter solstice, spring equinox, summer solstice and autumn equinox to Khảm, Chấn, Ly and Đoài, and cuts the four hexagrams Di, Tấn, Tỉnh and Đại Súc to five days and fourteen parts[1].
Huệ Đống records the view that the four cardinal hexagrams govern the four seasons, the 24 lines govern the 24 solar terms, the 12 sovereign hexagrams govern the 12 months, and the remaining 60 hexagrams govern 365 and 1/4 days. He cites both Kinh Phòng and Han dynasty texts to prove that this method was once used to predict rain and sunshine, not merely to expound the Kinh Dịch.
In What Order Are the Sixty Hexagrams Assigned to Days?
The sixty hexagrams are not arranged in the order of the 64 hexagrams in the classic, but in a separate order beginning with Trung Phu (中孚). Huệ Đống quotes the Dịch vĩ Kê lãm đồ: the quái khí of the Giáp Tý day begins at Trung Phu, each hexagram taking six days and seven eightieths of a day; Trịnh Khang Thành's commentary explains that eighty parts make one day[1].
This is a Han dynasty apocryphal text, with commentary traditionally attributed to Trịnh Huyền, while passages beginning with the character 按 are editorial notes by Qing dynasty scholars when compiling texts from the Vĩnh Lạc đại điển. The extant text therefore cannot be taken as an intact original from the Han dynasty.
The order of the 60 hexagrams in the Quái khí method also differs from the order of the 64 hexagrams in the classic. Each solar month has five hexagrams, and Huệ Đống records their roles after the Chính Quang calendar of the Wei: Trung Phu is the three dukes, Phục the Son of Heaven, Truân the feudal lords, Khiêm the grand master and Khuê the nine ministers[1].
Why Was Quái khí Important in Han Dynasty Yi Learning?
Because it transformed the Kinh Dịch from a divination book into a tool for measuring the qi of heaven and earth. Han scholars used Quái khí to predict rain and sunshine, drought and flood, and to explain why the same hexagram encountered at different times yields different results.
The Hán thư records the response of Cốc Vĩnh: when the king follows the Way, Quái khí is orderly; when he loses the Way, Quái khí is chaotic. The Hậu Hán thư records Trương Hành's memorial also saying that the laws of calendar and Quái khí have verification. These are evidence that the Quái khí method was once used in Han dynasty court politics, not merely a matter for diviners[1].
Huệ Đống concludes that the Han scholars all used quái khí for prognostication, but that from the Song and Yuan onward Han learning faded until hardly anyone knew what quái khí was[1].
How Do Schools Rebut the Quái khí Method?
There are at least two major lines of rebuttal. The first holds that dividing hexagrams by days is Kinh Phòng's technique for divining calamities and anomalies, not the original intent of the sages. The second holds that the six days and seven parts calculation is itself mathematically flawed, because multiplying 64 hexagrams does not match one year.
This book records the rebuttal: if one hexagram governs six days and seven parts, then 64 hexagrams would amount to 389-odd days, not matching one year; and it holds that dividing hexagrams by days is Kinh Phòng's technique for divining calamities and anomalies, not the original intent of the sages. This rebuttal is valid mathematically, but it should be noted: the Quái khí method does not divide all 64 hexagrams by days, but sets aside the four cardinal hexagrams first, dividing only 60 hexagrams. If calculated correctly in that way, the numbers match.
Vương Sung of the Eastern Han criticized the custom of selecting days and believing in Thái Tuế. According to him, the lifespan of life and death, and the fate of nobility and wealth, are endowed at birth through qi, and cannot be changed by selecting days. He does not discuss quái khí itself, but his words show that already in the Han some rejected judging affairs by days.
How Does Quái khí Differ from Other Methods of Assigning Hexagrams to Days?
There are many methods of assigning hexagrams to days, not only Quái khí. Tiền Trừng Chi's Điền Gian Dịch học records the method of Tiêu Diên Thọ: each hexagram governs one day, starting from Kiền on Giáp Tý day, Khôn on Ất Sửu day, to Vị Tế on Quý Hợi day, completing 60 days; the four cardinal hexagrams govern the four solstice and equinox days, not part of the 60-hexagram cycle[4]. This method differs from Kinh Phòng's in that Kinh Phòng governs six days and seven parts, while Tiêu Diên Thọ governs one day.
The book records the words of Hạng Bình Am: Tiêu Diên Thọ's method follows the order of the 64 hexagrams in the classic, each governing one day; Kinh Phòng's method uses the order of the Thái Huyền, each governing six days and seven parts. The two methods differ in hexagram order and in the length of time each hexagram governs.
This difference shows that even in the Han dynasty there were at least two ways of assigning hexagrams to days, and later texts record both without reconciling them. Readers should not take one way as the only correct one.
How Should We Understand the Hexagram of the Day According to Quái khí Today?
Nhật Nguyệt's suggestion: if you encounter a lookup page saying "today's hexagram is hexagram X," you should ask which method that page uses. There are at least three different methods: Kinh Phòng's Quái khí, Tiêu Diên Thọ's method, and the method of Mai Hoa Dịch số. Each gives a different result, and none is considered a universal standard.
If you want to look it up yourself using the Quái khí method, you need the table of the 60 hexagrams starting from Trung Phu and the starting day. This table is in the Dịch vĩ Kê lãm đồ and in Qing dynasty Han learning texts. But remember: this is a convention of one school, not an astronomical fact, and later texts have refuted this calculation. Using it for reference is fine; using it to decide major matters is not advisable.
This book teaches how to obtain hexagrams by time, but does not use the Quái khí method. The book records: "旺者，如寅卯之月日則木旺，巳午之月日火旺", meaning in the months and days of Dần and Mão, wood is prosperous; in the months and days of Tị and Ngọ, fire is prosperous. This is the method of obtaining hexagrams by the five elements of the time, quite different from the Quái khí method of dividing hexagrams by days.
In Summary
Quái khí is the method of assigning the 64 hexagrams to the calendar year, originating in the Han dynasty, associated with the names Mạnh Hỷ and Kinh Phòng. The four cardinal hexagrams Khảm, Ly, Chấn and Đoài stand outside the 60-hexagram cycle, governing the four seasons and the four solstice and equinox markers; the remaining 60 hexagrams share 365 and 1/4 days, each governing six days and seven parts. This is a convention of a Yi learning school, not an astronomical fact, and later texts have refuted this calculation. Readers should know clearly which method is being used when looking up the hexagram of the day.
