中国历法中的闰周与“谐月”

On the Cycle of Intercalary Month and the“Xieyue”in Traditional Chinese Calendar

阐明中国历法的"趋同原理",考察农历千百年的共同特征;分析闰周的内涵并扩大了它的外延,提出"谐月"等概念;应用算术化方法建立符号和公式系统,根据回归年和朔望月数据,通过精确计算,将有关的周期性质表述成连分数和渐近分数;并列举历谱中千百年间的诸多实例予以验证,为认识传统历法提供新视角和新判据。

This paper illustrates＂the Principle of inclination to uniformity＂. It investigates the common properties of Chinese lunar calendars in the past thousands of years, analyzes the connotation of the cycle of intercalary month and extends its denotation. The concept of＂Xieyue＂is proposed here, and the arithmetical methods are being applied to establish a system of symbols and formulae. Based on the data of tropical years as well as crescent moon and full moon（plenilune）, the paper makes a precise calculation, and the concerning properties of periodicity are expressed in the form of continued fraction and approximate fraction. The paper supports this idea with many examples in the lunar calendars in history. It provides a new point of view and new evidence for the understanding of traditional calendar.