玄ZenTellATLAS OF WISDOM TRADITIONS

Foundations / ENCYCLOPEDIA

Sexagenary cycle

干支历

The sexagenary cycle advances ten stems and twelve branches together, returning after sixty steps. It is a naming cycle used within calendrical systems.

Introductory article2 min readUpdated 2026-09-30AI-assisted · Editorially checked

At a glance

Period
Sixty steps
Arithmetic
Advance both sequences together
Why the cycle has sixty pairsStarting at Jia–Zi, both lists advance one place. They align again after sixty steps, rather than using every one of the 120 arbitrary combinations.10 stems and 12 branches advance togetherLeast common multiple: lcm(10,12) = 60甲子 → 乙丑 → 丙寅 → … → 癸亥 → 甲子
Why the cycle has sixty pairsStarting at Jia–Zi, both lists advance one place. They align again after sixty steps, rather than using every one of the 120 arbitrary combinations.

Definition and terminology

The cycle starts Jia-Zi, Yi-Chou and Bing-Yin and ends Gui-Hai. Both sequences advance together, giving sixty permitted pairs rather than all 120 theoretical combinations. Parity is preserved, so Jia-Chou is excluded. Years and days can both carry these labels, but their cycles are distinct.

Structure and rules

Sixty is the least common multiple of ten and twelve. With a reliable starting point, modular arithmetic gives later pairs. Practical day naming still needs a trusted epoch. Month boundaries must be specified, month stems derive from year stems, and hour stems derive from day stems in the traditional conversion scheme.

Worked reading

In a teaching sequence beginning Jia-Zi, the second pair is Yi-Chou, the eleventh Jia-Xu and the thirteenth Bing-Zi. Stems and branches return at different intermediate steps; both reset together at step sixty-one. Separate columns make the procedure transparent. A fictional starting point should never be used to date an actual event.

Context and limits

Year boundaries can differ by use: lunar New Year and the Start of Spring are both encountered, while natal practice commonly uses solar-term boundaries. Day rollover at 23:00 versus midnight is another convention. Calendar conversion is checkable; a correct conversion does not independently validate interpretations of a person’s future.

References & further reading

Historical sources document ideas and rules of their time, not empirical proof of predictive accuracy. Source notes identify the nature and scope of each reference.

  1. Hong Kong Observatory: Heavenly Stems and Earthly BranchesInstitutional / reference source

    Official calendar reference for sequences and double hours; does not validate natal divination.