三分损益模式下追求平均律的尝试:京房推到六十律  

An Attempt to Chase the Equal-tone of Fixed Musical Pitch by the Toning Method of the"Addition or Subtraction of One-third":Computative Sixty-note by Jing Fang

作　　者：马金 孙小淳 MA Jin;SUN Xiaochun(School of Humanities,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学人文学院,北京100049

出　　处：《广西民族大学学报（自然科学版）》2022年第1期11-21,32,共12页Journal of Guangxi Minzu University ：Natural Science Edition

摘　　要：古人认为音律是天、地、人三才所构成的宇宙之根本法则的体现。汉代是律学发展的重要时期,因三分损益法带来的音程不均值问题和十二律还宫困境困扰着律学家的同时也催生了律学理论的不断发展。为试图解决这些问题,易学家、律学家京房从宇宙论“气数一理”和蕴涵周而复始之义的“复”卦的启发下,突破了“仲吕极不生”的束缚,提出了六十律理论,对后世律学发展影响颇深。然而从六十律发端起,争议从未断绝。从音乐考古史料研究和三分损益数学模型的生律困境说起,认为在西汉律管律制面临困境时,京房构建的六十律比十二律更能反映音程差距之精细化,试图给出“构造六十律”的解。京房为拯救律值逻辑上数值不完全闭合的现象,使用了复卦、节气、五行等要素互相渗透相互佐证,形式上避免了宇宙论体系的崩塌,这也是他为追求音程平均值所进行的一次尝试。The ancients believed that the musical rhythm is the fundamental embodiment of the universe composed of the Heaven,Earth and Man.The Western Han Dynasty was an important period for the development of the musical rhythm.The unequal melody and the dilemma⁃cycle of twelve⁃note of fixed musical pitch caused by the toning method of the"Addition or Subtraction of One⁃third"bothered the scholars,but also led a continuous development of the musical pitch theory.To solve the former problems,Jing Fang,a scholar in Yi Scriptures,inspired by the homologous cosmology thought of"Qi"and"Shu"as well as the"Fu"hexagram,breaking through the shackle that"Zhong Lu pitch"is the last one,proposed a sixty⁃note of the fixed musical pitch theory which had a profound influence on the development of the musical pitch in later generations.However,the controversy was simultaneous with recognition.By the study of musical archaeology and the dilemma of the toning method of the"Addition or Subtraction of One⁃third",it may be concluded that the sixty⁃note of the fixed musical pitch theory,which needs a solution,can better reflect the refinement of the pitch interval gap than the twelve⁃tone in the Western Han dynasty.In order to save the uncycle phenomenon in logic,Jing Fang used the"Fu"hexagram,the solar terms and the five elements to mutually infiltrate and corroborate each other to avoid the collapse of the cosmological system in form for he aimed to chase the equal⁃tone of the fixed musical pitch.

关 键 词：京房 六十律 三分损益法 

分 类 号：N09[自然科学总论—科学技术哲学]