### On the Periodicity of Chinese Sexagenary Indices

I have written a short note on the periodicity of Chinese sexagenary indices (traditionally known as bazi 八字) after I read the book by Hee on the same subject, many years ago. I was motivated primarily by a section of her book. In page 22, Hee wrote:

...because of the numerous possible combinations, it takes 60 years for the same set of year pillars to repeat itself (by comparison, a set of month pillars repeats itself after just five years). Therefore, if you have a certain day and time, the set of four pillars will repeat itself in 60 years. However, since the same day may not appear in exactly the same month - and even if it is in the same month, the day may not be found in the same half month - it takes 240 years before the identical four pillars appear again. Basically, Hee's claims are as follows:

When considered independently, the periodicity of the year-index is 60 years, which is obviously correct.When considered independently, the periodicity of the month-index is 5 …

...because of the numerous possible combinations, it takes 60 years for the same set of year pillars to repeat itself (by comparison, a set of month pillars repeats itself after just five years). Therefore, if you have a certain day and time, the set of four pillars will repeat itself in 60 years. However, since the same day may not appear in exactly the same month - and even if it is in the same month, the day may not be found in the same half month - it takes 240 years before the identical four pillars appear again. Basically, Hee's claims are as follows:

When considered independently, the periodicity of the year-index is 60 years, which is obviously correct.When considered independently, the periodicity of the month-index is 5 …