The Twelve Lu

The twelve lu are twelve pitch standards, not twelve keys and not equal temperament

Related

The Twelve LüXuangong (Rotating the Gong)GongdiaoBianzhong

Time and place

The twelve lu took shape in the pre-Qin period. The key texts are the Guanzi and the Lushi Chunqiu. The bells from Marquis Yi of Zeng's tomb at Suizhou, buried around 433 BCE, carry inscriptions listing lu names and octave relations. Later theorists from Jing Fang to Zhu Zaiyu worked on the same set of names.

What happened

The pitches are generated by sanfen sunyi, alternately subtracting and adding one third of a pipe or string length. Starting from Huangzhong, the series yields Dalu, Taicu, Jiazhong, Guxi, Zhonglu, Ruibin, Linzhong, Yize, Nanlu, Wuyi and Yingzhong. The twelfth step does not return to the starting pitch, so Han and later writers added more lu, Jing Fang sixty and Qian Lezhi three hundred and sixty. In 1584 Zhu Zaiyu's Luxue Xinshuo derived twelve equal divisions of the octave by root extraction.

Musical features

The twelve lu are pitch standards, not a scale. Pentatonic and heptatonic melodies draw their notes from this grid, and the same tune can sit at different absolute heights. Pipe length and string length fix the pitch, and the absolute pitch of Huangzhong changed across dynasties; equating it with C is a modern convenience. Nor are the twelve lu twelve keys: a key combines the position of the gong with a mode.

What to listen for

Begin with Yangguan Sandie, whose pentatonic frame is clear and whose phrases tend to close on zhi or yu. Then hear the chant Jing Yun, where intonation drifts and the written lu names sit at a distance from actual singing. Finally hear the piano piece titled Yayue E Jue Mode, where a lu name has become a key label, far from pre-Qin tuning.

Common misunderstandings

The usual error is to treat the twelve lu as twelve-tone equal temperament. The sanfen sunyi series produces unequal steps and cannot be rotated freely. Zhu Zaiyu calculated equal temperament only in the late sixteenth century, and European theorists made similar calculations late in the same century. It is equally wrong to call the twelve lu twelve keys, or to claim the Zeng bells prove equal temperament.

Sources

• 《吕氏春秋·音律》与《管子·地员》— 三分损益生律记载核对，未引用
• The New Grove Dictionary of Music and Musicians, 2nd ed., entry "China" — tuning framework checked, not quoted

Used for fact-checking only; all prose is original.