Tag Archives: Sanfen sunyi

Triple Divisions—Key Points from the Treatises on Music (c. 680), Chapter 5:4 “On the Paradigm of Mutual Generations” and Chapter 5:5 “On ‘triple division with one part subtracted or added’ being applicable to strings and pipes”

This is the third part of my translation of Key Points from the Treatises on Music (c. 680), or “Empress Wu’s Music Theory Primer.” These two chapters continue to discus the seven sheng, yet it also “previews” a significant concept in Chinese tuning theory in relation to the twelve tuning pitch pipes (or lü), before their proper treatment in juan 6 of the treatise: sanfen sunyi “triple division with one part subtracted or added.” This latter phrase describes the canonical method of computing the lengths of the twelve tuning pitch pipes, in which one pipe generates another in succession: specifically through the compounding multiplications by 2/3 and 4/3.