Nayin (纳音) refers to a theory that integrates the five tones and twelve pitches into the traditional Chinese calendar system based on the five elements and the Ganzhi (干支). Besides its application in musicology and calendar studies, it is also used in traditional Chinese medicine, Yi studies, and numerology.
The "yin" in "Nayin" refers to the five tones determined by ancient Chinese people based on different musical scales. The five tones are a highly abstract summary of the natural sound patterns by the ancients. The Nayin five elements are formed by combining the ancient five tones and twelve musical pitches, used to describe more precisely the characteristics of the five elements after the combination of Heavenly Stems (天干) and Earthly Branches (地支). The original Ganzhi five elements are called the true five elements, while the Nayin five elements are called the borrowed five elements, as they are formed by borrowing the ancient five tones (Gong, Shang, Jiao, Zhi, Yu) and twelve musical pitches.
The Nayin numerology is traditionally attributed to Guiguzi, and named by Dongfang Shuo. A text marked "Yu Xuyu" in the Qin bamboo slips of Shuihudi's "Day Book" contains the earliest known material on the Nayin five elements, proving that the theory of the sixty Jiazi (甲子) Nayin appeared no later than the late Warring States period. Its content uses the date, time, and five elements after Nayin, combined with the daily morning and evening hours, to divine the auspiciousness of travel.
Shen Kuo introduced the "Sixty Jiazi Nayin" in "Mengxi Bitan", stating that "the sixty Jiazi have Nayin, few understand its meaning, it is the method of rotating the sixty pitches as Gong, each pitch contains five tones, twelve pitches contain sixty tones", which is the earliest detailed exposition of this concept available. Tao Zongyi recorded the discussion on the sixty Jiazi Nayin in the "Nancun Chuo Geng Lu" from the "Rijia Yishu" he saw.
Mnemonic Verse
Jiazi Yichou Haizhong Jin (甲子乙丑海中金)
Bingyin Dingmao Luzhong Huo (丙寅丁卯炉中火)
Wuchen Jisi Dalin Mu (戊辰己巳大林木)
Gengwu Xinwei Lubang Tu (庚午辛未路傍土)
Renshen Guiyou Jianfeng Jin (壬申癸酉剑锋金)
Jiaxu Yihai Shantou Huo (甲戌乙亥山头火)
Bingzi Dingchou Jianxia Shui (丙子丁丑涧下水)
Wuyin Jimao Chengtou Tu (戊寅己卯城头土)
Gengchen Xinsi Baila Jin (庚辰辛巳白蜡金)
Renwu Guiwei Yangliu Mu (壬午癸未杨柳木)
Jiashen Yiyou Quanzhong Shui (甲申乙酉泉中水)
Bingxu Dinghai Wushang Tu (丙戌丁亥屋上土)
Wuzi Jichou Pilihuo (戊子己丑霹雳火)
Gengyin Xinmao Songbai Mu (庚寅辛卯松柏木)
Rencheng Guisi Changliu Shui (壬辰癸巳长流水)
Jiawu Yiwei Shazhong Jin (甲午乙未砂中金)
Bingshen Dingyou Shanxia Huo (丙申丁酉山下火)
Wuxu Jihai Pingdi Mu (戊戌己亥平地木)
Gengzi Xinchou Bishang Tu (庚子辛丑壁上土)
Renyin Gui Mao Xibo Jin (壬寅癸卯锡箔金)
Jiachen Yisi Fudeng Huo (甲辰乙巳覆灯火)
Bingwu Dingwei Tianhe Shui (丙午丁未天河水)
Wushen Jiyou Dayi Tu (戊申己酉大驿土)
Gengxu Xinhai Chaichuan Jin (庚戌辛亥钗钏金)
Renzi Guichou Sangtuo Mu (壬子癸丑桑拓木)
Jiayin Yimao Daxi Shui (甲寅乙卯大溪水)
Bingchen Dingsi Shazhong Tu (丙辰丁巳沙中土)
Wuwu Jiwei Tianshang Huo (戊午己未天上火)
Gengshen Xinyou Shiliu Mu (庚申辛酉石榴木)
Renxu Guihai Dahai Shui (壬戌癸亥大海水)