On 4 February this year, the day of "Spring Commences", a friend asked: "What year is it today?" My simple and quick response was "2018", an answer that did not quite meet his expectation. He actually wanted to test my knowledge in the details of using "Heavenly Stems and Earthly Branches" (also known as Celestial Stems and Terrestrial Branches, or simply "Gan-Zhi") to denote the year in Chinese calendar. The concept was presented by my colleague Mr Wong Wai-kwong through his web article "Changeover of Gan-Zhi in Chinese Calendar" ^[1] published early this year. Here, I extracted some main points from his article with supplementary information added.

There are 10 heavenly stems, beginning with "Jia" and ending at "Gui"; and 12 earthly branches following the sequence from "Zi" to "Hai" ^[2]. Each heavenly stem is paired with an earthly branch to form the Gan-Zhi sexagenary cycle that starts with Jia-Zi and ends at Gui-Hai. Each year is therefore represented by a Gan-Zhi pair and the cycle is repeated every 60 years.

The Gan-Zhi year denotation has been used for more than two thousand years. Although it attracts less interest in modern society, it still generates a lot of attention and discussion in the Chinese community around the time of Chinese New Year. For example, in 2018, the solar term "Spring Commences" fell on 4 February while the first day of the first Chinese calendar month (commonly known as "Lunar New Year's Day" in Hong Kong) was on 16 February. The question then was whether the changeover of Gan-Zhi should happen on the day of "Spring Commences" or on "Lunar New Year's Day"?

The Hong Kong Observatory, being the authority responsible for the compilation of calendars in Hong Kong, has long been using the first day of the first Chinese calendar month to mark the changeover of Gan-Zhi. Such a practice has been described in the chapter on astronomy in the ancient book "Records of the Grand Historian", in which the first day of the first Chinese calendar month was defined as the beginning of a year and "Spring Commences" signaled the start of the four seasons.

Let me give a brief explanation here about the relationships among year, month and solar terms in the Chinese calendar. Based on changes in the moon phase, each Chinese calendar month has 29 or 30 days, approximately the number of days between two successive occurrences of new moon or full moon. This comes from the lunar calendar (Yinli) and provides a convenient way to count the days by observing the moon phases (i.e., new moon -> first quarter -> full moon -> last quarter -> new moon), even in the absence of advanced time instruments and clocks. Comparatively speaking, the cycle of a Chinese calendar year is a bit more complicated, each comprising 12 Chinese calendar months in a normal year and 13 months in a leap year, and the extra month is called a "leap month". The 24 solar terms come from the solar calendar (Yangli) and are defined based on the revolution of the Earth around the Sun. Each cycle of the 24 solar terms corresponds exactly to one year, or more precisely, one “tropical year”. Starting with “Spring Commences”, it effectively describes the seasonal cycle and provides guidance for farming and daily routines in the ancient times. One can see that there is no direct relationship between Yinli and Yangli and one tropical year is actually longer than 12 Chinese calendar months combined. To harmonize the two calendars, the day of the second new moon of the Chinese calendar month (leap month not to be counted) after “Winter Solstice” is defined as the Lunar New Year's Day, i.e. the beginning of the Chinese calendar year, and the Metonic cycle of 7 leap months in 19 years is adopted.

For more than a century, the Gregorian calendar has been widely adopted and there has been a lack of detailed authoritative guidelines for compiling the Chinese calendar. This has led to the emergence of popular Chinese folk calendars compiled by different users in accordance with their own specific needs or purposes. For instance, fortune tellers or fortune-telling enthusiasts tend to use "Spring Commences" as the time mark for the changeover of Gan-Zhi, in contrast to the common practice adopted for the official calendars. It should be noted, however, that the Chinese Government has since issued a standards document "Calculation and promulgation of the Chinese calendar" dated 12 May 2017. The guidelines for compilation of Chinese calendar and the definition of the beginning of the Chinese calendar year given in the document are consistent with the Observatory's practice. The Observatory has compiled a Gregorian-Chinese Calendar Conversion Table covering the period from 1901 to 2100 for general reference at
https://www.hko.gov.hk/en/gts/time/conversion.htm