The 45 hui positions on the qin (harmonics 諧波位) 節四十五 同者 十有四 得位者 三十有一
折紙求徽法 folding paper to find hui positions
西麓堂琴統 卷一 中的
十則
琴有十則 節四十五 同者 十有四 得位者 三十有一
終於搞懂 (就是在講泛音位, 十三徽之外還有的泛音位)
此31個徽位 著實很有用
Footnote:
My WP qin, which is an imitation of the Tang dynasty Qin "Da Sheng Yi Yin," has a string length of 110cm.
According to XLTQT V1 " 十則 十而分之各得四寸五分"
110 divided by 10 is 11 cm, and
If 11cm = 4 cùn and 5 fēn = 4.5 inches, then 1 inch = 2.44cm.
Therefore, this measurement is closer to the units of measurement used during the Jin dynasty and Northern and Southern dynasties.
I have a feeling that the look of the qin we are playing now (with 13 hui dots) might invented not in Han dynasty but after Han and before Northern and Southern dynasties, probably during the Jin Dynasty (265-420). As of now, no 'qin hui' (琴徽), which could serve as harmonic nodal markers, has been found among the archaeological discoveries of musical artifacts from the Han Dynasty, including physical objects and images.
Please see https://mp.weixin.qq.com/s/OwhgDEVqn1GCnoPKOo8bpQ , article in Chinese.
Debates on the Issue of Qin Hui (Chapter of New Interpretation) by Wu Yaohua: [New Explanation of the Character "徽 Hui"]
Also, a group of brick paintings depicting the Seven Sages of the Bamboo Grove" and Rong Qiqi, excavated from the Palace Mountain Grand Tomb in Xishanqiao, Nanjing, Jiangsu, dated around Southern Dynasties (420-589) shows two 5-stringed qin with hui dots.
The 'Seven Sages of the Bamboo Grove' refers to seven prominent scholars during the Wei and Jin periods, while Rong Qiqi was a distinguished figure from the Spring and Autumn period. In the painting, Ji Kang is portrayed with a double-knotted hairstyle, gazing at a distance, and playing a five-stringed qin. Rong Qiqi, with flowing hair and long beard, is depicted in a contemplative pose also playing a five-stringed qin.
https://www.njmuseum.com/en/zoomPreview?id=465&n=0
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