by An Liu
The ancient Chinese kept track of periodic time by means of a cycle of sixty quasi-numerals, the ganzhi sexagenary cycle. This cycle was calculated from two sets of ordinals: the ten heavenly stems (gan ) and the twelve earthly branches (zhi ). In very ancient times, these two sets were probably used separately for different purposes. During the Shang period (ca. 1550–1046 B.C.E.), the ten stems denoted a ten-day “week” used primarily to keep track of which royal ancestors were to receive sacrifices on which days. From very early times, the twelve branches were probably used to keep track of the lunar months and perhaps also of the twelve years of the Jupiter cycle. At some point, at least as early as the Shang and perhaps many centuries before that, the two sets began to be combined in the form 1, i; 2, ii; . . . 10, x; 1, xi; 2, xii; 3, i. . . . This system produced a sequence of sixty binomes, which was used to keep a continuous count of days. Much later, during the early imperial period, the sexagenary cycle also began to be used to keep track of years repeating at sixty-year intervals. Table 4 shows the heavenly stems, the earthly branches, and the sexagenary binomes.
TABLE 4 Stems, Branches, and the Sexagenary Cycle
Heavenly Stems (tian gan ) Earthly Branches (di zhi )
1. jia 1. Zi
2. yi 2. chou
3. bing 3. yin
4. ding 4. mao
5. wu 5. chen
6. ji 6. si
7. geng 7. wu
8. xin 8. wei
9. ren 9. shen
10. gui 10. you
11. xu
12. hai
The Sexagenary Cycle
1. jiazi
2. yichou
3. bingyin
4. dingmao
5. wuchen
6. jisi
7. gengwu
8. xinwei
9. renshen
10. guiyou
11. jiaxu
12. yihai
13. bingzi
14. dingchou
15. wuyin
16. jimao
17. gengchen
18. xinsi
19. renwu
20. guiwei
21. jiaxin
22. yiyou
23. bingxu
24. dinghai
25. wuzi
26. jichou
27. gengyin
28. xinmao
29. renchen
30. guisi
31. jiawu
32. yiwei
33. bingshen
34. dingyou
35. wuxu
36. jihai
37. gengzi
38. xinchou
39. renyin
40. guimao
41. jiachen
42. yisi
43. bingwu
44. dingwei
45. wushen
46. jiyou
47. gengxu
48. xinhai
49. renzi
50. guichou
51. jiayin
52. yimao
53. bingchen
54. dingsi
55. wuwu
56. jiwei
57. gengshen
58. xinyou
59. renxu
60. guihai
Calendars
The task, and the fundamental problem, of calendars in early China, as elsewhere in the ancient world, was to keep track of and attempt to reconcile two incommensurable periods: the (approximately) 354-day lunar year of twelve lunar months, and the 365.25-day solar year. The basic technique for reconciling the lunar and solar years was the so-called Metonic cycle (named for its Greek discoverer in the Western world), according to which seven additional (intercalary) months were added at intervals during each nineteen-year period. Other adjustments were built into the calendar to take account of various anomalies that accumulated during repeated Metonic cycles. The main goal of the calendar reforms that were undertaken by imperial regimes from time to time was to identify and deal with such anomalies.
Both the government and ordinary people used the resulting lunar–solar calendar for ritual purposes. In practice, especially in making decisions about the times of planting and harvesting crops, people also used a separate solar calendar, keyed to the solstices, equinoxes, and the regular annual round of meteorological phenomena and agricultural activities (table 5).
TABLE 5 The Solar Year Agricultural Calendar
Name Translation Approximate Date
1. Lichun Spring Begins February 4 or 5 (winter solstice, plus forty-six days)
2. Yushui Rainwater February 19 or 20
3. Jingzhe Insects Awaken March 6 or 7
4. Chunfen Spring Equinox March 20 or 21
5. Qingming Clear and Bright April 5 or 6
6. Guyu Grain Rain April 20 or 21
7. Lixia Summer Begins May 6 or 7
8. Xiaoman Small Grain May 21 or 22
9. Mangzhong Grain in Ear June 6 or 7
10. Xiazhi Summer Solstice June 20 or 21
11. Xiaoshu Lesser Heat July 7 or 8
12. Dashu Great Heat July 23 or 24
13. Liqiu Fall Begins August 8 or 9
14. Chushu Abiding Heat August 23 or 24
15. Bailu White Dew September 8 or 9
16. Qiufen Autumn Equinox September 22 or 23
17. Hanlu Cold Dew October 9 or 10
18. Shuangjiang Frost Descends October 24 or 25
19. Lidong Winter Begins November 8 or 9
20. Xiaoxue Slight Snow November 23 or 24
21. Daxue Great Snow December 7 or 8
22. Dongzhi Winter Solstice December 21 or 22
23. Xiaohan Slight Cold January 6 or 7
24. Dahan Great Cold January 21 or 22
The calendar was composed of twenty-four “nodes” (jie ), or fortnights.
Reconciling Three Calendars
Three calendars were being used at the time the Huainanzi was written and throughout the imperial period: (1) the astronomical calendar, in which the months were denoted by the twelve earthly branches and the year (defined, for example, by the reciprocal waxing and waning of yin and yang) began with the month (designated zi) in which the winter solstice occurred; (2) the agricultural calendar of twenty-four “solar nodes” outlined in table 5; and (3) the civil calendar (also called the Xia calendar), in which the months were numbered (zheng yue , er yue , etc. [that is, “beginning month,” “second month,” and so on]) and the year began in the third astronomical month (designated yin), that is, at the second new moon following the month in which the winter solstice occurred. The first civil month was undoubtedly designated so as to keep the civil calendar and the agricultural calendar in approximate alignment. The astronomical months and the civil months are, of course, the same except for their designations. Both are correlated in the same way (for astrological purposes) with the twelve pitch-pipe notes of the duodecatonic scale and the same compass directions plotted around the horizon. Table 6 shows approximately how the three calendars relate to one another.
Correlative Cosmological Terms
The Huainanzi ’s cosmology is based on the idea that all things in the world are made of qi and that those things sharing similar qi are likely to respond strongly to one another through the principle of resonance (ganying, “stimulus and response” [see appendix A]). Correlative categories therefore became important as a way both to classify phenomena and to predict which phenomena would be likely to be in strongly resonant relationships with one another. The two most important correlative categories are yin–yang and the Five Phases (wuxing). Tables 7 and 8 are lists (not exhaustive) of yin–yang and Five-Phase correlates that appear in the Huainanzi; other categories could be added on the basis of other texts. Note that some of the Five-Phase correlates (for example, directions and colors) were standardized, whereas others (for example, visceral orbs) often varied among different textual traditions.
In addition to yin–yang dualism and the Five Phases were other numerical correlative categories. For example, the twelve earthly branches correlated with months, di
rections, musical notes, the years of the Jupiter cycle, and other cosmological phenomena. Less important categories were based on ten (the heavenly stems) and eight (directions, winds). Interestingly, the Huainanzi does not use the eight trigrams of the Changes as a correlative category, although the Changes itself is frequently quoted as a canonical text.1
Music and Mathematical Harmonics
The Huainanzi cites the two ancient Chinese sequences of notes: the pentatonic scale (seen as correlated with the Five Phases) and the duodecatonic scale (seen as correlated with the earthly branches, months, and so on). The names of the pentatonic notes—gong, zhi, shang, yu, and jue —are customarily not translated, although they could be, because they seem to have been understood as sound words on the order of “do, re, mi.” The names of the notes of the duodecatonic scale usually are translated, however, although at least some of them probably should not be (as they may be transcriptions of non-Sinitic words). The twelve notes are defined by the sounds of a set of twelve pitch pipes (lü ) of standard lengths.
Table 6 Relationship of the Three Calendars
Table 7 Yin–Yang Correlates
Table 8 Five-Phase Correlates
The two scales correlate with each other because their fundamental notes (gong and Yellow Bell) are defined as having the same pitch. In turn, that pitch is defined as the sound of a pitch pipe nine inches (chi) long. But because the length of an inch in ancient China varied from place to place and over time, it is no longer possible to say with any confidence what the pitch value of that tone might have been. The following two lists arbitrarily assign a hypothetical value of C to the fundamental, but this is an artificial value for illustrative purposes only and should not be assumed as corresponding to the actual pitch value of gong /Yellow Bell in ancient China. (Evidence from inscribed bell-sets from the middle Zhou period suggests, however, that the Chinese of that era did have the concept of absolute pitch and that their fundamental note was rather close to the value of C.)
The twelve notes of the pitch-pipe scale were generated from the fundamental by means of a procedure known as “ascending and descending thirds.” The numerical value of each of the notes is multiplied by either 2/3 or 4/3, beginning with 81 (the square of the length of the Yellow Bell pitch pipe). Thus 81 × 2/3 = 54; 54 × 4/3 = 72; 72 × 2/3 = 48; and so on. There is one break in the sequence (both Responsive Bell and Luxuriant are multiplied by 4/3), allowing the notes generated to stay within a single octave. The sequence thus produced is as follows:
Yellow Bell (× 2/3 =)
Forest Bell (× 4/3 =)
Great Budding (× 2/3 =)
Southern Regulator (× 4/3 =)
Maiden Purity (× 2/3 =)
Responsive Bell (× 4/3 =)
Luxuriant (× 4/3 =)
Great Regulator (× 2/3 =)
Tranquil Pattern (× 4/3 =)
Pinched Bell (× 2/3 =)
Tireless (× 4/3 =)
Median Regulator
The difficulty with this procedure is that because of small increments of flatness at each step, after twelve steps the scale has gone flat by a half tone. That is, taking the fundamental note as a hypothetical C, Median Regulator (the twelfth step in the ascending and descending thirds sequence) winds up as F. If the next step were taken (Median Regulator × 2/3), the resulting note would be about a half tone short of completing the octave at C. The ascending and descending thirds method, in other words, produces an untempered scale. Whether the ancient Chinese also had a tempered scale is a matter of some dispute, and we will touch on this again later.
Rearranging the twelve pitch-pipe notes into an ascending scale, again with the fundamental set arbitrarily and hypothetically at C, we can see the relationship between the duodecatonic and pentatonic scales:
Yellow Bell C gong
Great Regulator C-sharp
Great Budding D shang
Pinched Bell D-sharp
Maiden Purity E jue
Median Regulator F
Luxuriant F-sharp
Forest Bell G zhi
Tranquil Pattern G-sharp
Southern Regulator A yu
Tireless A-sharp
Responsive Bell B
Yellow Bell C gong
In the terminology of early Chinese music, some notes (or scales or tuning systems) are sometimes described as qing , “clear,” and others as zhuo , “muddy” or “turbid.” It is not at all obvious, and much disputed, what these terms mean when applied to music. (The same terms also are used to describe different grades or qualities of qi [see appendix A].) Sometimes qing and zhuo seem to refer to high notes and low notes; sometimes to tonic and flattened notes (or scales or tunings); sometimes perhaps to notes played on an open or a stopped string. As some musicologists have pointed out, these terms also suggest the intriguing possibility of a tempered scale in early Chinese music. That would mean that the pitch-pipe notes derived from the ascending and descending thirds method would subsequently and systematically be altered (tempered) to be slightly sharp, so the numerical value of the last note of the series of twelve could be multiplied by 2/3 to produce a note one octave above the fundamental note (C above middle C, in the hypothetical values we are using here), thus completing the octave. In other words, the meaning (or a meaning) of qing and zhuo might be “notes of a tempered scale” and “notes of an untempered scale.” The two would sound quite different from each other, and that difference could account for some of the debates in Warring States and Han times about moral, proper, antique ritual music versus licentious popular music.
Weights and Measures
Weights and measures were standardized by the regime of Qin Shihuangdi as part of the Qin dynasty’s program of nationalizing reforms. The Han dynasty adopted the Qin standards, but they were changed again during the Wang Mang interregnum. Over the long course of imperial history, the values of weights and measures changed greatly. For example, the Han “foot” (chi) measured about nine English inches, but in the twentieth century, under the Republic of China, it had grown to thirteen inches. Table 9 gives rough approximations of the value of weights and measures in the early Han period. Many such tables give conversion figures specified to two or three decimal places.2 Aside from the practical difficulties of computing values with such precision on the basis of textual records and archaeological artifacts, such spurious accuracy can be confusing rather than enlightening. The real utility of tables like these, we feel, is to create a practical mental image of the values of weights and measures mentioned in the text.
TABLE 9 Weights and Measures
Weight
1 fen Weight of 12 millet grains: ~ 0.05 gram
12 fen = 1 shu Approximately 0.6 gram
12 shu = 1 ban liang” “Half ounce” (the weight of a standard Han coin): approximately 7.5 grams, or ¼ ounce
2 ban liang = 1 liang “Ounce”: approximately 15 grams, or 1/2 ounce
16 liang = 1 jin “Catty”: approximately 245 grams, or a bit more than 1/2 pound
30 jin = 1 jun Approximately 7.4 kilograms, or 16 pounds
4 jun = 1 dan (note special pronunciation of , usually pronounced shi) Approximately 29.5 kilograms, or 65 pounds
Volume
1 ge Approximately 20 cubic centimeters, or 4 teaspoons
10 ge = 1 sheng Approximately 200 cubic centimeters, or 7/8 cup
10 sheng = 1 dou Approximately 2 liters, or 1/2 gallon
10 dou = 1 hu “Bushel”: approximately 20 liters, or 5 gallons
Length
1 fen Approximately 0.23 centimeter, or 1/10 inch
10 fen = 1 cun “Inch”: approximately 2.3 centimeters, or 29/32 inch
10 cun = 1 chi “Foot”: approximately 23 centimeters, or 9 inches
6 chi = 1 bu “Double-pace”: approximately 140 centimeters, or 54 inches
8 chi = 1 xun (or ren ) “Fathom”: approximately 185 centimeters, or 6 feet
10 chi = 1 zhang Sometimes (loosely) “fathom”: Approximately 230 centimeters, or 71/2
feet
2 xun = 1 chang Approximately 370 centimeters, or 12 feet
4 zhang = 1 pi Approximately 920 centimeters, or 30 feet (the length of a standard [2 chi-wide] bolt of silk for tax purposes)
1 li Approximately 0.4 kilometer, or 1/3 mile
Area
1 mu (or mou) Approximately 67 square meters, or 1/6 acre (7,300 square feet)
100 mu = 1 qing Approximately 6,700 square meters (6.7 hectares), or 16.7 acres
John S. Major
1. For diagrams of the various correlative systems found in the cosmological chapters of the Huainanzi, see Major 1993.
2. See, for example, Denis Twitchett and Michael Loewe, eds., The Ch ’in and Han Empires, 221 b.c.–a.d. 220, vol. 1 of The Cambridge History of China (Cambridge: Cambridge University Press, 1986).
Appendix C
A CONCISE TEXTUAL HISTORY OF THE HUAINANZI AND A BIBLIOGRAPHY OF HUAINANZI STUDIES
ANUMBER of observations about the textual history of the Huainanzi can be made with relative certainty.1 The first is that the surviving evidence testifies to a continuous transmission of the text from the time of its creation and presentation to Han emperor Wu in 139 B.C.E. Prior to the evidence provided by the many editions from the early Ming period (1368–1644), the testimony to this transmission comes principally from historical sources such as the Shiji and Han shu and the bibliographical monographs (yiwenzhi ) of the dynastic histories. These sources mention a work in twenty-one chapters being produced at the court of Huainan during the decade of the 140s B.C.E. as one of a trilogy of philosophical works (“inner,” “middle,” and “outer” books) written at Huainan and the only one to have been presented to the imperial court in Chang’an. Early copies of the work included this imperial recension and others recovered and taken to the imperial library by Liu De , father of the famous bibliographer Liu Xiang , after the fall of Huainan in 122 B.C.E. Liu Xiang is said to have combined the extant copies into one recension that undoubtedly was the one transmitted through the Han and into later periods. Earlier scholarly debate on whether or not the entire work was written by one person, Liu An, or by the team of eight scholars mentioned in the Gao You preface under the direction of Liu An, has now been resolved in favor of the latter position.2 After our many years of working on the Huainanzi, we also agree with this conclusion, although we think it likely that the last chapter, the postface, was written by Liu.