Seeking the Winter Solstice Jiazi Direct Grant in Qimen Dunjia

From the perspective of Qimen Dunjia intercalation, casting configurations includes the concept of "direct grant" (zheng shou), with one configuration per hour, totaling 4320 configurations. Qimen Dunjia's 4320 configurations can actually be simplified to 1080 configurations, and 1080 can further be simplified to 72 configurations. The 72 configurations correspond to the seventy-two evenly divided states of the year, that is, the seventy pentads — this is beyond doubt.

However, there is a very crucial issue here: the Earth revolves around the Sun, and this time is a tropical year; yet the Earth also rotates on its axis, with an average angular velocity of 4.167×10⁻³ degrees/second, and a rotational linear speed at the equator of 465 meters/second. The Earth takes 23 hours and 56 minutes to rotate once, and approximately every ten years the rotation period increases or decreases by three to four thousandths of a second.

Modern astronomy uses the vernal equinox point as the standard reference point for calculation; this equinox is the Sun's position on the ecliptic. However, each time the Earth rotates to the same point on the ecliptic, its rotation is not exactly synchronized, so the equinox's transition moment does not fall at a fixed time each year.

Looking at the ancient method: Qimen first values the day. The day of the Winter Solstice is when the first yang is born. If it happened to be the perfect direct grant — that is, a Jiazi day at the Winter Solstice — then regardless of the time of day within that Jiazi day, one would begin Yang Dun One from the zi hour of that day.

Reasoning backwards, we know that a perfect Qimen direct-grant configuration should begin at the zi hour of the Jiazi day of the Winter Solstice. Once this time point is found, one can locate a relatively original upper-yuan start time for Qimen. This time is December 22, 1899, 0:56 AM, at which the Winter Solstice term transitioned in — it was a Jiazi day at the zi hour.

It is clearly noticeable that 0:56 AM — this zi hour was almost already past; how can it be used as a basis? So we look further back, to December 21, 1693, 0:43:22 AM, a bit earlier than the previous time; but this is obviously not enough, so we must keep searching slowly on and on.

Then we can find a relatively perfect time: December 13, 1384, 0:06:33 AM, which is only six minutes away from the mid-point of the Winter Solstice zi hour. Going further back is December 18, 606, 11:24:38 PM — too far from the mid-point of the Winter Solstice zi hour; but if the start of the zi hour is taken as 23:00, then this time is relatively more fitting. Searching further back, we reach December 25, 344 BCE, 0:20:39 AM — the deviation is clearly larger again; then, because computational ability is limited and going further back is more complex, we won't continue calculating.

If these are to serve as the accumulated days of the upper yuan for Qimen Dunjia, then the times of December 18, 606, 23:24:38 and December 13, 1384, 0:06:33 are both relatively fitting. If the mid-point of the zi hour is used to set the configuration — looking at the zi hour on a twelve-part day, it covers the range from 23:00 to 01:00 — then taking December 13, 1384, 0:06:33 as the center, with the zi hour enclosing it as the midpoint to mark the birth of Yang Dun, is theoretically justified.

There is also a more important issue: fixing the yin hour. If judged from celestial phenomena, the yin hour must be when the sun rises at yin, so that the day can perfectly represent the person's subject in the Four Pillars; thus the fixing of the yin hour should take into account the time of sunrise. The reason the yin hour is called "level dawn" (pingdan) is that it refers to the time of sunrise. This means that, since the Sun has been re-fixed to the vernal equinox using the fixed-qi method, the yin hour should also be re-fixed: likewise setting the Winter Solstice point at 270 degrees, so the zi hour is also fixed at 270 degrees, with yin as 0 degrees — that is, the moment of sunrise is the mid-point of yin. In this way the twelve double-hours are re-established, and accuracy will be greatly improved.

Later generations, because seeking a Winter Solstice Jiazi was inconvenient and intercalation was rather troublesome, made modifications — for example, five days difference in the first year, ten days difference in the second year, and so on. If one intercalated once per jiazi (sixty years), one would need nearly nine years before each intercalation could begin — this error is clearly too large, so one jiazi was not used as the interval for intercalation. Instead, intercalated nodes were adopted: taking fifteen days as one cycle, and when the error accumulated to ten days, one intercalation was made, and the following year realigned again; this way the error could be controlled within five years.

However, actually the earliest Qimen method used day-intercalation, which meant that in every three years the second year would undergo one intercalation — thus forming a closed three-year cycle.