Chinese Music Theory

by Jonathan Service

Chinese culture has a long tradition of theoretical reflection on music that connects the sounding phenomenon to both mathematical principles and philosophical concepts. Traditional Chinese music theory takes its starting point from numbers: the salient musical numbers are twelve, five and eight.

The number twelve refers to the number of pitches from which scales can be constructed. In the Chinese classic Master Lü’s Spring and Autumn Annals, or Lüshi chunqiu 呂氏春秋, dating from 239 BCE, can be found the story of Ling Lun. The Yellow Emperor ordered Ling Lun to bring order to music and Ling Lun obediently traveled to the mountains where he collected bamboo with thick and even nodes. Blowing on one of these like a pipe, he found its sound agreeable and named it the “Yellow Bell,” or huangzhong 黄鐘, the lowest of the twelve pitches. His attention was then drawn by the sound of phoenixes singing in the valley. The male and female phoenix each sang six tones. Ling Lun cut his bamboo pipes so that the sound produced by them matched the pitches of the phoenixes. He ended up with twelve pitch pipes, divided into two sets: six from the male phoenix and six from the female: these were called in Chinese the lülü 律呂 or later the shierlü 十二律.

This story is mythical, but it does demonstrate two things. First, it shows the centrality of the twelve so-called “pitch pipes,” or lükuan 律管, in theoretical discussions of pitch. Music theorists developed other methods of determining pitch that were either more durable (bells) or more easily measurable and manipulated (monochords), but the pitch pipe always maintained its preeminence in the cultural imagination. Second, the way that Ling Lun divided the twelve tones into two sets (male and female) hints at the method through which these tones were generated. This is the “Method of Subtracting and Adding Thirds,” or sanfen sunyi 三分損益. This method involved alternately rising a fifth and descending a fourth through the subtraction or addition of a third of the length of the preceding pitch pipe. For example, the first application of the method involved taking Ling Lun’s “Yellow Bell” pitch pipe, dividing it into thirds, subtracting one of the thirds from the total length, and cutting a new pitch pipe to match the remaining (two thirds) length. This new pitch pipe produced a pitch a fifth above (the length of the pipes are in the ratio 3:2). This pitch pipe in turn was divided into thirds and this time a third of the length was added. When the next pitch pipe was cut matching this new length, it produced a tone a fourth below the preceding tone: that is, a whole tone above the “Yellow Bell.” This method was repeated until a complete set of twelve pitches had been generated. The theoretical provenance of the twelve pitches can be discerned by the fact that the pitches produced by adding a third (and descending a fourth) were referred to by Sima Qian 司馬遷 in the Records of the Grand Historian, or Shiji 史記 (91 BCE), as pitches of “superior generation,” that is, the pitches of Ling Lun’s male phoenix; the pitches produced by subtracting a third (and ascending a fifth) were referred to as pitches of “inferior generation,” that is, the pitches of Ling Lun’s female phoenix.

Later theorists were troubled by the way the Method of Subtracting and Adding Thirds failed to close the octave. Jing Fang 京方, a Han Dynasty music theorist whose work is recorded in the Book of Han, or Hanshu 漢書, dating from 111 CE, increased the number of pitches within a single octave by extending the process of rising a fifth and falling a fourth sixty times. The last note generated by his method was virtually indistinguishable from the octave above the Yellow Bell but remained slightly different in terms of its mathematical ratio. This problem was famously solved by the Ming Dynasty music theorist Zhu Zaiyu 朱載堉 who discovered the formula for the twelve-tone equal division of the octave (equal temperament) and published his result in New Theories in the Study of Pitch, or Lüxue xinshuo 律學新說 in 1584.

The number five refers to the number of tones of the scale most commonly used in China, the pentatonic scale. Initially, the five tones seem to have represented a series of tonal relations, not a gamut of pitches. In the Record of Music, or Yueji (5th – 3rd century BCE, recompiled in the Classic of Rites, or Liji 樂記, after the Burning of Books and Burying of Scholars fenshu kengru 焚書坑儒 in 213 BCE), mention is made of the five tones and how they hold certain precise “social” relations. The central tone, gong 宮, is the prince; shang 商 is the minister; jue 角 is the people; zhi 徵 represents affairs; yu 羽 represents things. As this conception developed, the “governing” gong tone moved from the middle to become the lowest tone in the scale. Very early on, in the 5th – 4th century BCE, a seven-tone (heptatonic) scale was developed: the ancient Chinese history Discourses of the States, or Guoyu 國語, mentions as much. However, the theoretical emphasis remained on a five-tone structure. This can be discerned in the fact that the additional two tones were not given names in their own right, rather they were called “altered” tones: there was a biangong 變宮 and a bian-zhi 變徵. The two tones were understood, in effect, as “lowered” or flat variations of the tone above.

In the Huainanzi 淮南子, dating from the 2nd century BCE, reference is made to the way in which the five tones, when they came to be placed within the structure of the twelve absolute pitches, could generate an elaborate system of sixty musical modes. Because the twelve pitches were not evenly spaced, when each of the five tones took it in turn to function as the “keynote,” a slightly different arrangement of intervals was produced. Five musical modes were thereby generated for each pitch. The Huainanzi also makes explicit the connection between the five tones and the “Five Phases,” or Wuxing 五行: Wood, Fire, Earth, Metal and Water. In the great structure of analogies developed in ancient China, the five tones were identified via Five Phase Theory with the five flavors, the five colors, the five grains, et cetera. These analogies were further supplemented by Yin-Yang Theory 陰陽 whereby the cold, wet, feminine Yin found its musical correlate in the six pitches of “inferior generation,” that is, the pitches of Ling Lun’s female phoenix and the hot, hard, and masculine Yang found its musical correlate in the six pitches of “superior generation,” that is, the pitches of Ling Lun’s male phoenix.

The number eight refers to the number of different “sounds” or sound sources. Ancient Chinese music theorists were acutely sensitive to variations in timbre. They devised a system of “organological” classification that identified eight different sound sources, the so-called “eight sounds,” or bayin 八音: stone, metal, silk, bamboo, wood, skin, gourd, earth. These sound sources were actualized in the ancient Court orchestra: stone chimes (stone); bells (metal); zithers or lutes (silk strings); flutes or pipes (bamboo); a hollowed and carved “Tiger-box” (wood); drums (skin); the “reed organ” sheng (gourd); globular flutes (earth). These eight sound sources were identified early on with the eight winds and through this long association with eight directions (the four cardinal points and the points equidistant between them) and with the seasons (again, the four seasons and points halfway between them). Timbral associations were key: bells were rung during military retreats; bells were associated with autumn when days and the yang force declines; bells were associated with the Western compass point, the direction in which the sun sets. The sound source of metal therefore, actualized in bells, carried rich connotations for the “man of learning.”

Born and raised in Vancouver, Jonathan Service spent fours years in Japan after college studying the language and culture. He came to Harvard in 2006 where he was able to bring his twin passions (East Asia and Music) together in a dissertation on the musical culture of late nineteenth century Japan. After receiving his Ph.D. in 2012, he became a Research Associate at the Japan Centre, SOAS, London.