Daily hexagram by the Gua Qi method, 1900 to 2100

Conventions taken

This is a hexagram ASSIGNED BY THE CALENDAR under the Han-dynasty Gua Qi method as transmitted by Meng Xi, not a cast hexagram: there is no moving line, no changed hexagram, and the line ruling the day is not a moving line. How to recompute a row. (1) Take the latest winter solstice not after 12:00 noon of that day, Vietnam time UTC+7 (column dong_chi, same engine as the moc-tiet-khi-1900-2100 dataset). (2) Count the minutes from that moment to 12:00 noon of that day (column phut_tu_dong_chi). The day's hexagram is the one in force at noon. (3) Each hexagram rules for 6 days and 7 parts, a day being divided into 80 parts, i.e. 6 7/80 days, exactly 8,766 minutes; sixty hexagrams make 365.25 days. The position equals the integer part of phut_tu_dong_chi divided by 8,766, plus 1. The tropical year is about eleven minutes shorter than 365.25 days, so the next solstice arrives before hexagram 60 has run its full share and the cycle restarts at position 1. Each year is re-anchored at the true solstice and the whole difference falls on hexagram 60 (Nourishment). Measured over 1900 to 2100: hexagram 60 is cut short in all 201 years, by 10.5 minutes on average and 7 to 13 minutes in range, never lengthened; the sources do not say how to handle the difference, so this is the site's choice. The mo_hinh column records the version code of this method.(4) Look that position up in the table of sixty hexagrams (dataset thu-tu-60-que-quai-khi), which starts with Inner Truth at the winter solstice. (5) Take the remainder of the division in step 3, divide by 1,440 and add 1 to the integer part: that is the day within the hexagram (1 to 7). Each line rules one day, from the bottom line up. After six lines 7/80 of a day remains; a noon falling in that remainder is day 7, and the site assigns the remainder to the top line, so the ruling line equals the day within the hexagram except that day 7 is line 6. The sources do not say which line owns the remainder; this is the site's choice. (6) The four cardinal hexagrams Kan, Zhen, Li and Dui do not rule days but the four seasons, one line per solar term: Kan from the winter solstice (bottom line) to Awakening of Insects (top line), Zhen from the vernal equinox, Li from the summer solstice, Dui from the autumnal equinox. The solar term is taken at noon. Sources: the order of the sixty hexagrams follows the table in the Dayan calendar's fa lian shu, New Book of Tang, juan 28A; starting Inner Truth at the winter solstice and one cardinal line per solar term follow Yixing's Gua Yi, New Book of Tang, juan 27A; 6 days 7 parts per hexagram and one day per line follow Kong Yingda's subcommentary on hexagram Fu in the Zhouyi Zhengyi, quoting the Yiwei Jilantu. Both juan of the New Book of Tang were read on Wikisource. Where the schools differ. Jing Fang gives the first 73/80 of a day at each solstice and equinox to the cardinal hexagram and shortens Nourishment, Progress, The Well and Great Taming to 5 days 14 parts; the Gua Yi rejects this, and the site follows Meng Xi. Some texts restart the count at each mid-month solar term instead of counting evenly from the solstice: with the old mean solar terms the two agree, with true astronomical terms as used here they drift apart, most around the vernal equinox (2.33 days in 2026). The site counts evenly from the true solstice and re-anchors once a year. Under those conventions a day near a changeover can land on the neighbouring hexagram. The engine's solar term moments differ from the astronomical values by at most 14 minutes, 3.2 minutes early on average (measured over all 24 terms, see the moc-tiet-khi-1900-2100 dataset); the sat_giao_que column flags days whose noon is less than 15 minutes from a changeover, where the hexagram may be the neighbouring one.