Why the cycle contains sixty pairs
Gan-Zhi advances one position through ten Heavenly Stems and one through twelve Earthly Branches at each step. HKO’s sequence begins Jia-Zi, then Yi-Chou, and reaches Gui-Hai at its sixtieth position.
An arithmetic way to inspect the pattern is to number steps from zero: the stem position is the remainder after division by 10, and the branch position is the remainder after division by 12. Both counters first return together after 60 steps. This produces 60 pairs, not every one of the 120 possible combinations of the two lists.
A cycle index needs an anchor
The same pair can label a year, month, day or hour. Its position in the sequence does not by itself give a Gregorian date. A calculation also needs a reference point, a calendar unit and its boundary convention.
In the Atlas receipt, inspect the solar year for the year pillar and the cycle date for the day pillar. The hour stem depends on the selected day stem. Do not transfer a year-cycle index directly into the day or hour calculation.
Compare full pairs and full receipts
When comparing reports, first check that both refer to the same kind of pillar. Next compare the input, timezone, clock convention and rollover. Only then compare the two Chinese characters and their romanized names.
A matching animal alone does not establish agreement: the animal identifies the branch, while the full pair also includes a stem. A repeated pair later in the cycle likewise does not establish identical birth circumstances or an identical reading.
Use the cycle to inspect the calendar result. Interpretive meaning belongs to a named method using that result; the repeating arithmetic alone does not supply a personality assessment or prediction.
Word origin · etymology
Latin-derived numerical adjective.
Sexagenary comes from Latin sexagenarius, of sixty. The cycle name describes sixty successive stem–branch combinations.
Merriam-Webster: sexagenary ↗Hong Kong Observatory: Heavenly Stems and Earthly Branches ↗
How we know · epistemology
Modular calendar arithmetic
Advancing both sequences together produces sixty distinct stem–branch pairs. The cycle is mathematically reproducible, but assigning it to a year, day or hour still needs a calendar anchor and an explicit rollover rule.
Hong Kong Observatory: Heavenly Stems and Earthly Branches ↗
Explore it in your atlas
Connected concepts
Read alongside this entry
Terms used in this explanation
Mentioned in 3 other entries
These links connect subjects and terminology. They do not establish a shared historical origin.
Sources & provenance
Use the citations beside each section to distinguish a calculation convention, a historical teaching and an editorial example.