Hey /his/torians, I have a question to ask about the Chinese

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Hey /his/torians, I have a question to ask about the Chinese traditional calendar. I know that the Daoist concept of the universe can be surmised by the following excerpt:

>The Limitless (無極; wuji) produces the delimited (有極; youji), and this demarcation is equivalent to the Absolute (太極; taiji).
The Taiji (the two opposing forces in embryonic form) produces two forms, named yin-yang (陰陽) which are called Liangyi (the manifested opposing forces).
These two forms produce four phenomena: named lesser yin (少陰, shaoyin), greater yin (太陰; taiyin, which also refers to the Moon), lesser yang (少陽, shaoyang), and greater yang (太陽; taiyang, which also refers to the Sun).
The four phenomena (四象; Sìxiàng) act on the eight trigrams (八卦; Bagua).
Eight 'eights' results in sixty-four hexagrams.

I know the years were based off of titular years devised by the imperial court. How exactly did East Asia use this stuff above to record the months and days?