Early history of Chinese calendar

The earliest evidence of the Chinese calendar is found on oracle bones of the Shang dynasty (late second millennium BC), which seem to describe a lunisolar year of twelve months, with a possible intercalary thirteenth, or even fourteenth, added empirically to prevent calendar drift. The Sexagenary cycle for recording days was already in use. Tradition holds that, in that era, the year began on the first new moon after the winter solstice.
Early Eastern Zhou texts, such as the Spring and Autumn Annals, provide better understanding of the calendars used in the Zhou dynasty. One year usually had 12 months, which were alternately 29 and 30 days long (with an additional day added from time to time, to catch up with "drifts" between the calendar and the actual moon cycle), and intercalary months were added in an arbitrary fashion at the end of the year.
These arbitrary rules on day and month intercalation caused the calendars of each state to be slightly different, at times. Thus, texts like the Annals will often state whether the calendar they use (the calendar of Lu) is in phase with the Royal calendar (used by the Zhou kings).
Although tradition holds that in the Zhou, the year began on the new moon which preceded the winter solstice, the Spring and Autumn Annals seem to indicate that (in Lu at least) the Yin calendar (the calendar used in Shang dynasty, with years beginning on the first new moon after the winter solstice) was in use until the middle of the 7th century, and that the beginning of the year was shifted back one month around 650 BC.
By the beginning of the Warring States, progress in astronomy and mathematics allowed the creation of calculated calendars (where intercalary months and days are set by a rule, and not arbitrarily). The sìfēn四分 (quarter remainder) calendar, which began about 484 BCE, was the first calculated Chinese calendar, so named because it used a solar year of 365¼ days (the same as the 1st century BCE Julian Calendar of Rome), along with a 19-year (235-month) Rule Cycle, known in the West as the Metonic cycle. The year began on the new moon preceding the winter solstice, and intercalary months were inserted at the end of the year.
In 256 BC, as the last Zhou king ceded his territory to Qin, a new calendar (the Qin calendar) began to be used. It followed the same principles as the Sifen calendar, except the year began one month before (the second new moon before the winter solstice, which now fell in the second month of the year).