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[Diagram of the Generating and Completing Numbers of the Five Elements]
The song states:
One and Six generate Water, Two and Seven generate Fire,
Three and Eight are always assisted by Wood.
Four and Nine generate Metal, Earth generates at Five and reaches its limit,
Because there is no completing number for Ten (Earth), it is difficult to fixate (referring to the special status of Earth in the generating numbers).
When the Five Movements are insufficient, one can deduce from the generating numbers;
If encountering excess, the completing numbers will inevitably follow.
The generating and functional aspects of the Six Qi can verify the orthodox transformations;
The completing numbers combined with opposing transformations leave no doubt.

The Classic states: To the right of Xianming (meaning midday, i.e., the Mao position), is the position of Ministerial Fire; to the right of Ministerial Fire (Chen position), moving back one step (one step equals 60 days and 87.5 ke), it is governed by Executive Fire; moving back another step, it is governed by Earth Qi; moving back another step, it is governed by Metal Qi; moving back another step, it is governed by Water Qi; moving back another step, it is governed by Wood Qi. This constitutes the main positions of the Six Qi. Starting from the major solar term Great Cold in the twelfth month, the initial Qi of Wood is exchanged; then arriving at the major solar term Spring Equinox in the second month, the second Qi of Ministerial Fire is exchanged (i.e., the aforementioned position of Ministerial Fire); then arriving at Minor Fullness in the fourth month, the third Qi of Executive Fire is exchanged (i.e., the aforementioned right of Ministerial Fire, moving back one step, governed by Executive Fire); then arriving at the major solar term Great Heat in the sixth month, the fourth Qi of Earth is exchanged; then arriving at the major solar term Autumn Equinox in the eighth month, the fifth Qi of Metal is exchanged; then arriving at the major solar term Light Snow in the tenth month, the sixth Qi of Water is exchanged. Each Qi governs for 60 days and 87.5 ke, totaling 365 days and 25 ke, perfectly circling one year. If (the character "Ruo" is interpreted as "Chu", meaning subtract, which seems more logical.) the remaining days outside the year, (the remainder is obtained by subtracting five days from 365 days.) and the days of the small months, (small months have six days which are also subtracted.) then it falls short. (Subtracting the previous five remainder days and the six days of small months, a total of eleven days are subtracted, leaving only 354 days, which is less than 365 days.) However, when calculating the calendar days based on solar terms and exchanging Qi, they commonly serve as the main Qi of dryness, dampness, cold, heat, wind, and fire for each year. This is the regular record of the Six Qi. This is referred to as the Yin and Yang of the Earth, static Qi with fixed positions.

Due to different correspondences of Qi, there are also the Guest Qi of Si Tian (Heavenly Stewardship), Zai Quan (Earthly Abode), and the four interstitial Guest Qi on the left and right. (For example, in the Zi and Wu years, Shaoyin Ministerial Fire is Si Tian, so Miao and You Yangming Dryness Metal must be Zai Quan. The right interstitial of Zi is Jueyin Hai Wood; the left interstitial of Zi is Taiyin Chou Earth; the right interstitial of Miao is Shaoyang Yin Executive Fire; the left interstitial of Miao is Taiyang Chen Water. The Classic states: Left and Right are the pathways of Yin and Yang, this is what is meant.) Guest Qi also has transformations of cold, heat, dryness, dampness, wind, and fire. It is the wheel of heavenly mandate rotating through the year, residing above the Main Qi. The Main Qi should only obey the heavenly mandate of the Guest Qi, moving without cessation. (Broadly speaking, Si Tian governs the first half of the year, and Zai Quan governs the second half. Specifically, each Qi governs for over 60 days, with the remainder being 87.5 ke.) If Guest Qi overcomes Main Qi, it follows; if Main Qi overcomes Guest Qi, it is contrary. In these two cases, there is overcoming but no retaliation. Every year, the position three steps before Si Tian is Zai Quan, and the fourth position is the Initial Qi. For example, if Zi is Shaoyin Ministerial Fire Si Tian, the position three steps before Zi, Miao, is Yangming Dryness Metal Zai Quan, and the fourth position, Chen, is the Initial Qi. Chen and Xu are opposite, both belonging to Taiyang Cold Water. (Governing from after Great Cold to Spring Equinox, over 60 days.) Chen is the left interstitial of Miao. Next, Si is the Second Qi, Si and Hai are opposite, both belonging to Jueyin Wood. (Governing from after Spring Equinox to Minor Fullness, over 60 days.) Si is the right interstitial of Wu. Next, Wu is the Third Qi, Wu and Zi are opposite, both belonging to Shaoyin Fire. (Governing from after Minor Fullness to Great Heat, over 60 days.) Wei is the left interstitial of Wu. Next, You is the Fifth Qi, You and Miao are opposite, both belonging to Shaoyang Executive Fire. (Governing from after Autumn Equinox to Light Snow, over 60 days.) Shen is the right interstitial of You. Next, You is the Final Qi, You and Miao are opposite, both belonging to Yangming Dryness Metal. (Governing from after Light Snow to Great Cold, over 60 days.) This is the Zai Quan Qi.

Commentary: When the Six Qi are Si Tian, the governing year position is in the South, so one faces North to speak of left and right. When Zai Quan, the position is in the North, so one faces South to speak of left and right. For instance, in Chou and Wei years, Earth is Si Tian, facing North to speak of left and right; the left interstitial of Chou is Executive Fire Yin, and the right interstitial is Ministerial Fire Zi. Chen and Xu Water are Zai Quan, facing South to speak of left and right; the left interstitial of Chen is Jueyin Si Wood, and the right interstitial is Yangming Miao Metal. Thus it is said: Left Jueyin, Right Yangming. In this year, the Initial Qi of Guest Qi is Jueyin Hai Wood, the Second Qi is Shaoyin Zi Fire, the Third Qi is Si Tian Chou Earth, the Fourth Qi is Shaoyang Executive Fire Yin, the Fifth Qi is Yangming Miao Metal, and the Final Qi is Zai Quan Chen Water. This refers to Si Tian, Zai Quan, and the four interstitial Guest Qi; the four interstitial Guest Qi are superimposed upon the Main Qi, and the rest follow this pattern.

Master Wu of Caolu () stated: The operation of Yin and Yang of Heaven and Earth comes and goes, Wood, Fire, Earth, Metal, Water, beginning and ending cyclically, like following a track. This is the order of generation among the Six Qi. The annual Qi begins in Zi and ends in Zi. Thus it is said: At the midpoint of Winter Solstice in Zi, the Heart of Heaven does not shift. In Zi and Wu years, it starts with Dryness Metal at Winter Solstice, then passes to Cold Water, up to Executive Fire, each day lasting sixty days five times, and after Light Snow, thirty days remain, finally returning to Dryness Metal. In Chou and Wei years, it starts with Cold Water at Winter Solstice, thirty days later then passes to Wind Wood, up to Dryness Metal, each day lasting sixty days five times, and after Light Snow, thirty days remain, finally returning to Cold Water. The same applies to Yin, Shen, and below. Thus, for sixty years or even millions of years, the sequence of Qi generates continuously without interruption. It is not that at the end of Minor Cold, there is nowhere to transmit; nor at the beginning of Great Cold, is there nowhere to receive. Rather, it skips one Qi, not connecting continuously, thereby cutting off Great Cold as the head of the Initial Qi of the next year. This is the wonder of creation. The *Neijing* kept it secret and unexpressed, Qixuanzi (Wang Bing) omitted it and did not speak of it. Recently, Yang Zijian deduced and obtained it. This theory contradicts the Classic but is extremely reasonable. I respectfully attach it here so that learners may know.