Huangji Calendar

皇极历 Sui · Liu Zhuo

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Overview

Made by Liu Zhuo, it created the method of the “true solar term,” used second-order interpolation to find the sun’s position, and took precession as one degree in 75 years. Never promulgated; used only for eclipse computation.

Key data

ItemDetail
PeriodSui (604–617)
CompilerLiu Zhuo
Tropical year365.2445 days
PrecessionOne degree in 75 years

Liu Zhuo and the Huangji calendar

The Huangji calendar was made by Liu Zhuo of the Sui, the foremost calendrist of the age. Though never formally promulgated, its methods were taken up by the Tang Dayan calendar and others, with lasting effect.

Three innovations

1. The method of the true solar term (dingqi). Terms were divided by the sun’s actual position rather than by equal time — dingqi against pingqi — and used to compute the sun’s place.

2. Second-order interpolation at equal intervals. Since the sun’s motion is uneven, Liu used a second-order interpolation to find its position at any moment — an early use of interpolation in the calendar.

3. Precession at one degree in 75 years, adjusted after Zu Chongzhi and closer to the truth.

A calendar never promulgated

Blocked by the powerful, it was never promulgated and served only for computing eclipses.

That an unpromulgated calendar should deeply influence those that followed is rare — evidence that merit is not lost by a temporary rejection.

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Compiled and arranged by Chujia Kuang.