An entry in a Chinese daily almanac — the 黄历, the 通勝 — looks like the work of a specialist weighing each day. It names the day's stem and branch, a day officer, a lunar mansion, a clash, and two lists: activities the day suits and activities it should avoid.
Most of that entry is arithmetic, and can be computed from the date alone. One part is not. This article separates the two, computes the first for a real day, and then shows what happens to the second when you read it from more than one publisher. It explains how the entry is built; it takes no view on whether any day is auspicious.
The day's stem and branch is a count that never resets
Each day carries one of sixty stem-and-branch pairs. The sequence of sixty runs continuously, unbroken by the end of a month, the turn of a year, or even a leap month.
That makes it a formula. Given the Julian Day Number of a date — a running count of days used by astronomers — the position in the sixty is (JDN + 49) mod 60, with 0 as 甲子. For Monday 21 September 2026, that gives 34, which is 戊戌. So does every published almanac for that date. The same formula returns 戊午 for 1 January 2000 and 辛巳 for 1 January 1970, both matching the published record.
The day officer, and the day it repeats
The twelve day officers — 建 除 满 平 定 执 破 危 成 收 开 闭 — cycle day by day, and the rule for which one applies is set by the month. 建 falls on the day whose branch matches the month's branch, and the rest follow in order:
officer = (day branch − month branch) mod 12
The "month" in this rule is not the lunar month. It is the month defined by the solar terms, which changes on the day of each 节, the twelve terms that open a month.
For 21 September 2026 the month is the 酉 month, opened by 白露 on 7 September. The day branch is 戌. 戌 minus 酉 is one step, so the officer is 除. Every almanac consulted agreed.
The rule has a consequence that looks like an error and is not. On 8 October 2026 the solar term 寒露 begins, and the month changes from 酉 to 戌. Work the officer on either side:
| Date | Day | Month branch | Officer |
|---|---|---|---|
| 7 October | 甲寅 | 酉 | 执 |
| 8 October | 乙卯 | 戌 | 执 |
The result is two consecutive days with the same officer. The day branch advanced by one, but so did the month branch, keeping the difference between them the same. A Kangxi-era treatise on calendrical practice states this directly: at each change of solar-term month, two consecutive days share an officer. It happens twelve times a year, and it is how the twelve-day cycle stays locked to the solar year rather than drifting against it.
There is one point of disagreement in this calculation. If the day a solar term falls is split at the exact moment of the term, rather than assigned wholly to the new month, the morning of 8 October would belong to the old month and take a different officer. Software libraries that compute almanacs expose this as a setting, a sign that practice differs.
The lunar mansion is a weekday in disguise
The twenty-eight lunar mansions also run as a continuous daily count, and the formula is (JDN + 11) mod 28, with 0 as 角. For 21 September 2026 it returns 心, matching the almanacs.
Twenty-eight is four sevens. Because the mansion cycle is exactly four weeks long, each mansion always falls on the same day of the week. 房, 虚, 昴 and 星 are always Sundays. Running the formula over five dates spread across fifty-six years, the weekday the mansion implies matched the calendar's weekday every time. 心 always falls on a Monday, and 21 September 2026 is a Monday.
So the mansion carries no information the weekday does not. It is the seven-day week, renamed four times over.
The clash
The clash follows from the day's branch by a fixed opposition: the opposing branch is six places on. A 戌 day clashes with 辰, the Dragon, and the full clashing pair shown in almanacs is the day's stem advanced four and its branch advanced six; for 戊戌, that is 壬辰. The direction printed beside it comes from which of four three-branch groups the day belongs to.
The part that is not arithmetic
The suitable and avoid lists — 宜 and 忌 — are the part a reader actually uses, and they are built differently.
The imperial Qing compilation 《協紀辨方書》, commissioned under Qianlong and finished between 1739 and 1741, set out which spirits favour or forbid which activities, and then tabulated the result for every combination of twelve months and sixty days. So the lists are the output of a rule system, but that output was published as a table. A modern open-source library that computes almanacs reproduces this faithfully: its suitable and avoid lists are a lookup keyed on the month and the day, with no formula inside.
A table can be copied, abridged or replaced. Which is what the published almanacs show.
One day, two opposite answers
For 21 September 2026, seven almanac sites give the same suitable list, which includes 开市 — opening a business. A weekly almanac published by a major Chinese news portal two days earlier gives, for the same date, an avoid list that includes 开业 — opening a business.
That is a direct contradiction on the one activity a reader is most likely to be checking. The second source is working from a simplified tradition that assigns each day a meaning from its officer alone, rather than from the full table. Neither is misprinting. They are consulting different systems and printing both under the same name.
The agreement among the seven sites is revealing. Their lists match so exactly that they almost certainly draw on one shared dataset. Seven sources agreeing, in this case, is closer to one source repeated seven times than to independent confirmation.
Smaller differences appear on the same day as well: one site places the day's fetal spirit to the south of the room where the others place it at the centre, and one lists an additional inauspicious spirit that the others omit.
This disagreement is not new, and the old almanac makers knew it. One nineteenth-century almanac publisher's preface set out a rule for the case: if its own almanac conflicted with the imperial one, follow the imperial one. If one listed an activity as suitable and the other as to be avoided, take the avoidance.
Who makes the almanac people actually buy
In Hong Kong, the almanac most widely sold comes from a family firm founded in Guangzhou in 1891 by a former official of the imperial astronomical bureau. Its twentieth-century head moved it to Hong Kong and published it for decades, and it now sells close to a million copies a year, with the family licensing its annual lists to other publishers. It was listed as provincial intangible heritage in 2013.
That firm also grades days on its own scale of fortune, which is its own editorial judgement layered on top of the traditional rules — a further way the same date can read differently depending on whose almanac is on the table.
Where these came from
The formulas for the day's stem and branch, the officer, the mansion and the clash were computed here and checked against published almanacs for 21 September 2026, for 7 and 8 October 2026 across the solar term, and for 1 January 2000 and 1 January 1970. The date of the 寒露 solar term is the Hong Kong Observatory's. The rule that two days share an officer at each change of month is stated in a Kangxi-era calendrical treatise. The structure of the suitable and avoid tables is from a master's thesis on the 協紀辨方書 and from the source code of an open-source almanac library. The conflicting lists for 21 September 2026 were read from the sites named in the working notes on 21 September 2026. The history of the Hong Kong almanac firm is from published profiles of it.
Two dates are left as ranges rather than chosen. The 協紀辨方書 is dated to 1739 by some sources and 1741 by others; the 1780 date often attached to it is when the imperial library edition was checked, not when it was written. And when the lunar mansions first came to be used as a daily count could not be pinned to a firm date.
