无商之圜钟与无徵之四旦

Bell Temperament without Shang and Si Dan without Zhi

明末方以智《东西均.开章》言及"无商之圜钟"、"无徵之四旦"。方以智所谓"无商之圜钟",是说传统钟律,有宫、徵、角、羽,而唯独无商。①方以智所谓"无徵之四旦",是说一均四旦,有宫、商、角、羽,而唯独无徵。方以智所说,乃是律度量衡一体、律历一也之中国传统乐律体系的核心之谜。《礼记.乐记》载,孔子问及:"声淫及商,何也?"宾牟贾对曰:"有司失其传也。"春秋以降,"无商之圜钟","无徵之四旦"的中国上古乐律,有司渐失其传。而"声淫及商"的新兴乐律,则开始大行其道。中国乐人代相传习之非单纯三分损益的律度量衡一体、律历一也之"无商之圜钟"、"无徵之四旦"的上古乐律体系,长期以来隐匿其身且一直未得正解。近代以来,又被西洋无明的所谓科学,蒙上了一层厚厚雾障。今日开解此谜,将不理会种种不切题之说,而直射鹄的。

As Fang Yizhi of the late Ming Dynasty noted in his book The Harmony of East and West,there were four basic sounds in the Chinese ancient bell temperament including gong,zhi,jue,yu (equivalent to do,sol,mi,la of the Western scale) without shang (corresponding to re of the Western scale) while si dan involves gong,shang,jue,yu with zhi excluded.Bell temperament without shang and si dan without zhi,as the very characteristic of traditional Chinese temperament,is also a magnificent puzzle for researchers.Howev...