Astronomical Terms
In early China, as in other ancient societies, no distinction was made between astronomy and astrology. The task of locating periodical phenomena (the sun, moon, and planets that could be seen with the naked eye) and occasional portents (such as comets and meteors) was directed at ascertaining their astrological significance. Special attention was paid to the location of Jupiter, which was invested with particular astrological potency. The principal means of determining the location of heavenly bodies was with reference to the twenty-eight lunar lodges.
The Twenty-eight Lunar Lodges, with Angular Extensions
The twenty-eight lunar lodges (xiu 
) are a set of constellations denoting unequal segments of a celestial circle approximating the ecliptic and the celestial equator. The system is very ancient, attested in full from the early fifth century B.C.E. and possibly dating back as far as the late third millennium B.C.E. The lunar lodge system provides a means of locating the sun, moon, and visible planets among the fixed stars (table 1). For example, the location of heavenly bodies in the portion of the sky below the horizon can be calculated using the lunar lodges. The list of lodges begins in the east with Horn (jue 
), whose determinative star is Alpha Virginis, and proceeds westerly around the celestial circle (table 2).
Table 1 The Five Visible Planets
Sui xing  |
Year Star | Jupiter |
Ying huo  |
Sparkling Deluder | Mars |
Zhen xing  |
Quelling Star | Saturn |
Tai bo  |
Great White | Venus |
Chen xing  |
Chronograph Star | Mercury |
Table 2 The Twenty-eight Lunar Lodges
The Jupiter Cycle
The planet Jupiter takes approximately twelve years to complete a single orbit around the sun. The twelve years of Jupiter’s cycle had particular astrological significance. The names of the years apparently are from some unidentified non-Sinitic language; their origin is an unsolved mystery of the history of Chinese astrology. The Jupiter years also were correlated with the twelve earthly branches (table 3). At some time, perhaps as early as the fourth century B.C.E., the earthly-branch designations came to be associated with twelve animal names. These animal names do not appear in the Huainanzi, but subsequently became the usual way to refer to cyclical years. These names, too, have an unknown and mysterious origin.
TABLE 3 The Jupiter Cycle
| Year Name | Cyclical Character (branch, zhi  ) |
Animal (not in HNZ) |
Shetige  |
zi  |
Rat |
Ming’e  |
chou  |
Ox |
Zhixu  |
yin  |
Tiger |
Dahuangluo  |
mao  |
Rabbit |
Dunzang  |
chen  |
Dragon |
Xiexia  |
si  |
Snake |
Tuntan  |
wu  |
Horse |
Zuo’e  |
wei  |
Sheep |
Yanmao  |
shen  |
Monkey |
Dayuanxian  |
you  |
Rooster |
Kundun  |
xu  |
Dog |
Chifenruo  |
hai  |
Pig |
Calendrical Terms
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, directions, 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).