Calendar science and institutions in the Tang period
The Dayan (大衍历) calendar brought together observation, instrument-making and mathematical work at the Tang court. Its principal designer, the Buddhist monk Yixing, worked with court scholars and technical specialists to revise the calculation of celestial events. The calendar entered official use in 729, after his death.
Yixing's work at court
Failures in eclipse prediction prompted an order for a new calendar in 721. Yixing's draft was completed in 727, the year he died. Zhang Yue and the calendar official Chen Xuanjing then organized the material. The completed work was submitted in 728 and issued for use from 729.
Yixing was a monk with substantial learning in the Chinese classics. His reform formed part of Emperor Xuanzong's revival of state ritual, with the Jixian Academy providing an important institutional setting. The intensive work of 724–725 accompanied preparations for major imperial sacrifices. Observation and ritual shared personnel and patronage, and a successful calendar supported the court's claim to govern in accordance with the heavens.
The completed work combined calculation procedures with discussions of earlier calendars and their shortcomings. A new calendar needed instructions that other specialists could follow, as well as an explanation of why its methods should replace those already in use.
Instruments and astronomical calculation
Yixing collaborated with Liang Lingzan on instruments, including a water-powered armillary sphere completed in 725. An armillary sphere represents celestial circles through an arrangement of rings. The reform also drew on observations from different locations and investigated the changing lengths of day and night. These activities connected positions in the sky with the observer's place and season.
A gnomon provided another way to measure the seasonal cycle. Its noontime shadow changed as the Sun's height changed. Comparisons across observing sites required known instrument dimensions and consistent procedures. Repeated measurements helped establish the solstices, while observations at different latitudes showed how the same seasonal event appeared from different places.
The Dayan procedures distinguished several astronomical cycles. The values below are rounded expressions of its historical calculation parameters.
| Quantity in the Dayan system | Approximate length | What it tracks |
|---|---|---|
| Seasonal, or tropical, year | 365.24441 days | The seasonal cycle |
| Sidereal year | 365.25625 days | The Sun's cycle relative to the stars |
| Mean lunar month | 29.530592 days | The average interval between successive new moons |
The distinction between the first two quantities reflects precession: the seasonal reference points shift gradually relative to the stars. Chinese calendar-makers had considered precession before Yixing, although its inclusion was not continuous in every intervening system. Dayan helped establish its lasting place in subsequent calendrical calculation.
New-moon calculations also accounted for variations in the apparent motions of the Sun and Moon. A mean lunar month gives an average interval between conjunctions. Corrections for uneven motion place an individual conjunction earlier or later than that average sequence would suggest, potentially changing the day assigned to a month beginning.
Dayan still used pingqi (平气), or mean solar terms, spaced at equal time intervals within the adopted seasonal year. Its corrections for solar motion did not extend to assigning solar terms by equal steps of longitude. That later change was introduced into the official Chinese calendar in the seventeenth century.
Adoption and later influence
Dayan faced criticism after adoption. Opponents alleged that it had borrowed incompletely from the Indian-derived Jiuzhi astronomical system. An official comparison with observing records favoured Dayan, and the challenge was rejected. The dispute brought technical performance, competing specialists and court authority together.
The calendar remained in official use in China from 729 to 761. It was also adopted in Japan in 764 and continued in use, later alongside the Goki calendar, until its replacement by the Xuanming (Senmyō) calendar in 862. Its influence outlasted these periods of use through the procedures and explanations preserved in the Tang histories and studied by later calendar-makers.
Yixing's later reputation extended beyond his calendrical work. Astrological and magical texts were attributed to him after his lifetime, and legends grew around his name. These later attributions belong to the history of his reputation rather than to the securely identified work behind the Dayan calendar.