During the Song Dynasty, there was a man named Qian Lezhi, who studied the theoretical musicology of Jing Fang and developed three hundred musical scales. Scholar Shen Zhongzhong from the Liang Dynasty stated in his "Lü Yi": "The Book of Changes uses three hundred and sixty hexagrams to correspond to the number of days in a year, which is the numerical foundation of the musical system. The Huainanzi says: 'One scale produces five sounds, twelve scales produce sixty sounds, multiplied by six, is three hundred and sixty sounds, corresponding to the number of days in a year. The numerical basis of the musical system is the law of the movement of heaven and earth.' Therefore, the method for deriving these three hundred and sixty scales has been established since ancient times." Shen Zhongzhong calculated three hundred and sixty scales based on the numbers in the Huainanzi, using Jing Fang's method. Each month uses a primary scale as the base scale, the number of days contained in each solar term as the sub-number, and the primary scale to determine the sub-number. According to the number of days, each scale corresponds to different days and fractions.
According to this method of allocating seven sounds, the scale corresponding to the winter solstice is as follows: Huangzhong is the tonic, Taicu is the subtonic, Linzhong is the mediant, Nanlu is the dominant, Guxi is the subdominant, Yingzhong is the leading tone, Ruibin is the submediant. In this way, the five tones and seven pitches are complete. The scales corresponding to the following days are then run in sequence. The scale corresponding to the day is the tonic, and the subtonic and mediant are also arranged in order. Using this method to study sound and qi, distinguish the timing, and all things should follow the solar terms. From Huangzhong to Zhuangjin, there are a total of one hundred and fifty scales, all generated by the method of decreasing by one-third; from Yixing to Yizhao, there are a total of two hundred and nine scales, all generated by the method of increasing by one-third; only the Anyun scale is the final one, and no new scales are generated. The lengths of these scales are all based on the actual length of Huangzhong, which is 177,147, using three-ninths as the ratio to calculate their lengths, accurate to inches, tenths, and hundredths, and the remaining remainder is discarded. This is the length of each scale. The arrangement of these scales establishes the order of the tonic and mediant. Now I will briefly mention their names.
Huangzhong:
Baoyu, Hanwei, Dide, Guangyun, Xiaoji, Kezhong, Zhish, Woji, Chishu, Huangzhong, Tongs, Qiansheng, Qiansheng
Yin Pu Jing Sheng Zi Meng Guang Bei Xian Heng Nai Wen Nai Sheng Wei Yang Fen Dong Sheng Qi Yun Fan Yu Yan
Sheng Yin Tun Jie Kai Yuan Zhi Wei E Mei Bu Jian Xiang Zhong Yu Zhu Diao Feng
One part of the Right Huang Zhong, consisting of thirty-four tunes. (Each tune is divided into thirty-four segments, with each segment corresponding to thirty-one days.)
Da Lu:
At the beginning, experiencing the vastness of heaven and earth, full of vitality, assisting the times, rectifying and aiding, distinguishing between good and evil, flourishing and prosperous, yet also meticulous and cautious, giving up some unrealistic hopes, striving to uphold justice and remain steadfast, not fearing darkness, following the light, grasping the deeper significance of life, striving for progress, wisely seizing opportunities, being flexible, speaking less and doing more, working together with others in unity, receiving blessings, inheriting and promoting the glorious tradition.
This is the Da Lu palace tune, consisting of twenty-seven tunes, each corresponding to one day, and also including one-third of a day's worth of three-thirds.
Next is the Tai Cu palace tune.
Unaware of one's own abilities yet determined to make a mark, being as upright as a righteous person, as swift as the wind, working hard from the beginning, reaping rewards when the time is right, understanding the meaning of life, playing the paiban instrument, the initial angle appears, the gentle essence of Shaoyang, the low pitch of Shang tone, supporting the weak, continuing the previous efforts, both animals and plants thriving, developing together, stopping at the right time, following the changes of the seasons, the dragon soaring, Gou Mang overseeing the seasonal order, green seedlings growing, flowers blooming, spreading and expanding, just laws and a clear hierarchy, spring plowing begins, praising the harvest, removing obstacles, all things withering.
This is the Tai Cu palace tune, consisting of thirty-four tunes.
Then comes the Jia Zhong palace tune.
Everyone helping each other, yin energy nourishing all things, wind assisting in growth, policies being implemented, all things reviving, spring arriving, the virtue of reverberation, riding the spring breeze, fragrant and overflowing, the sun shining brightly, the spring breeze bringing joy, united in heart, all things flourishing and developing independently, free and unrestrained, benevolence and dignity coexisting, spring moving towards the south, the rising sun in the east, all things growing, rejuvenated.
This is the Jiazhong Gong melody, made up of twenty-seven lines.
Next is the Guxia Gong tune.
Good news comes from the south, reminiscing about ancestors, worshiping deities, showcasing a beautiful scene, carrying the breath of spring, washing away the dust of the old year, changing old habits, displaying new vitality, auspicious energy rising, clouds appearing, beautiful mountains, clearing paths, following the seasons, traveling day and night, accumulating strength, the hot summer winds start to blow, tender branches start to bear fruit, the laws come into effect, all things gather, vegetation flourishes, crops mature, light shines bright, thriving, as downward brings peace and upward brings nurturing, making fewer choices, following the right path, dressed in vermilion robes, making a name at court, and upholding purity.
This is the Guxia Gong tune, consisting of thirty-four verses.
Then comes the Zhonglü Gong tune.
The Vermilion Bird star appears, signaling a new beginning, the warm spring breeze, all things begin to grow, warmth from the south, spring arrives, guiding farmers in their work, orderly and methodical, the southern star appears, respectfully worshiping, mutually promoting, keeping purity within, red vegetation shines brightly, yielding to the rules, light shines bright, the Snake Hour arrives, the weather is refreshing and warm, all things thrive, advising people not to waste, fallen leaves return to their roots, the virtue of purity, heaven blesses the Zhou Dynasty.
This is the Zhonglü Gong tune, consisting of twenty-seven verses.
Finally, we have the Ruibin Gong tune.
Affairs of the south (the final principles of Jingfang), quiet and peaceful, choosing the right moment, flowers bloom, full of vitality, latent power, tremendous changes, guests are at peace, reminiscing about the distant past, sounds spread in all directions, the trajectory is the same, the sea is calm, eliminating disasters, leaving hometown, living and working in peace, brightness is noble, gazing into the future, rising to a higher realm, the phoenix soars, the sun rises, seizing the moment, auspicious signs abound, the Quanhua star appears, order is well-maintained, flames rise high, radiating brilliance.
Wow, this is packed with classical texts! Let me break it down for you into modern language, line by line.
First, "右蕤宾一部，二十七律。林钟：" means that what follows is a piece of music from Ruibin Palace, with a total of twenty-seven lines. The name of the piece is "Lin Zhong," which features phrases like humility in service, respect for virtue, sticking to principles, being capable, rising yin energy, absence of evil, elimination of destruction, fading brilliance, friends celebrating, clouds filling the sky, shared burdens, admiration for achievements, tolerance and peace, passing through safely, equal virtues, no obstacles, complete rituals, profound wisdom, serious responsibility, pure loyalty, returning to goodness, beautiful sounds, warm winds, following the seasons, blooming Mei Jia flowers, beautiful Xiuling mountains, no distinction between good and bad, Jingkou (place name), Yaojing (place name), radiant sunlight, overlapping wheels, and prosperous wealth. In simpler terms: this piece from Ruibin Palace is called "Lin Zhong," consisting of 27 lines, and the lyrics talk about humility, following rules, being capable, good winning over evil, friends gathering, fairness, calmness, smoothness, virtue, wisdom, being responsible, goodness, good weather, and beautiful scenery—basically, it’s all about good fortune and everything going well.
Next is "Right Lin Zhong," one section with thirty-four lines: "Yi Ze." This means that the following is a musical piece in the Lin Zhong mode, consisting of thirty-four lines. The name of the piece is "Yi Ze," and the content includes: Sheng Shang mode (a type of musical scale), refreshing, pure in spirit, hidden merits, storage, adherence to etiquette, reduction of punishments, chastity and fortitude, Heavenly Sovereign (referring to the supreme deity), Liu Xian (a legendary figure), following the Dao, returning to benevolence and righteousness, Yin Qi companion, leaving the south, dissipating Yin Qi, gentle yet diligent, extending Yi Geng (referring to time), free from weeds, Yi Jin (referring to beauty), building wealth, Kong Xiu (referring to Confucian cultivation), embodying the Nine Virtues (referring to nine kinds of virtues), everyone follows, contributing to peace in the world. In simpler terms, this piece in the Lin Zhong mode is called "Yi Ze," consisting of 34 lines, and the lyrics talk about good weather, good morals, adhering to rules, reducing punishment, being a good person, building wealth, being a cultivated person, and ultimately bringing peace to the world.
Next is "Right Yi Ze," one section with twenty-seven lines: "Nan Lü." This means that the following is a musical piece in the Yi Ze mode, consisting of twenty-seven lines. The name of the piece is "Nan Lü," and the content includes: Bai Lü (a type of pitch), abandoning superficiality, being genuine and grounded, a simple atmosphere, strong matters, abundant harvests for chieftains, unity, fertile land, weakness in the middle, plenty of sunlight, resisting external enemies, moderation, returning to deadlines, virtues in the middle, kingly strategies, completely blocking evil, Ru Shou (mythical figure), restraining the reins, falling leaves, no marks, quality is approachable, ample distribution, Taoist cultivation, chastity and strength, halting accumulation, returning to calmness, eliminating sweat, evenly distributing justice, happily serving, without toil, peace in the world, and a time of glory and prosperity. In simpler terms, this piece in the Yi Ze mode is called "Nan Lü," consisting of 27 lines, and mainly talks about being practical and hardworking, abundant harvests, unity, resisting enemies, moderation, doing good deeds, and ultimately bringing peace and prosperity to the world.
"Right Nan Lu, 34 lines. Wu She:" means that the next section is the Nan Lu tune, with a total of 34 lines. The name of the tune is "Wu She," and the content consists of: reflecting on impulses, embracing humility, respect, simplicity, and frugality, cultivating well-being, caring for the people, eliminating misfortunes, self-discipline, abundant harvest, deep concealment, sunshine's warmth, the arrival of spring, sacrificing livestock, the bright Kuixing star, harmonious communities, adhering to principles, great wealth, thriftiness, offering support to those in need, taking a break, without boundaries, seeking protection, long life, autumn landscapes, dark moon, and clear skies. In short, this "Wu She" piece, with 34 lines, talks about humility, diligence, caring for the people, praying for a good harvest, national prosperity, and longevity.
"Right Wu She, 27 lines. Ying Zhong:" means that the next section is the Wu She tune, with a total of 27 lines. The name of the tune is "Ying Zhong," and the content consists of: transparent distribution, tracing back to the source, understanding the beginnings, reaching success, stable leadership, peace and calm, slow and measured approach, leading through non-action, peace throughout the land, Gusheshan, the legendary mountain of immortals, serious and profound, the balance of action and stillness, heeding omens, no procreation, everything, everlasting longevity, endless and eternal, gradual improvement, gradual establishment, without rest, vast lands, countless people, and stable functioning. This "Ying Zhong" piece, with 27 lines, expresses the idea that governing a country must start from the fundamentals, be peaceful and tranquil, ensure long-term stability, and achieve peace throughout the land, leaving a lasting legacy.
Finally, "Right Ying Zhong, 28 lines." means that the next section is the Ying Zhong tune, with a total of 28 lines. This section does not have specific lyrics, so it cannot be translated.
According to the "Records of the Grand Historian," "Yu of Xia used his body as a measure and his voice as a musical pitch." The "Book of Rites" states, "A man's outstretched hand's width is one chi." In "Zhou Guan," it is written: "the Bi Xian measurement." Zheng Sinong explains that "Xian" refers to length. The diameter of this bi is one chi, serving as a standard for measurement. In "Yi Wei Tong Gua Yan," it is stated, "The width of ten horse tails is regarded as one fen." In "Huainanzi," it says, "At the autumn equinox, the awns of the grain ears become fixed, indicating that the grains are ripe. The number of musical pitches, twelve awns of grain ears' width equals one grain, twelve grains equal one cun." Here, "rui" refers to the awn on the grain ear. Furthermore, in "Shuo Yuan," it is said, "The standard of measurement comes from grains; one grain is considered one fen." In "Sunzi Arithmetic," it is recorded: "The silk spit out by silkworms is called 'hu,' ten hus make a miao, ten miaos make a hao, ten haos make a li, ten lis make a fen." These represent the origins of measurement; however, the statements contradict each other and lack consistency. Only the "Book of Han" provides a more reliable account: "Measurement tools are used to measure length, and the initial standard was based on the length of the Huang Zhong. Using medium-sized grains known as ju shu for measurement, the width of one ju shu is considered one fen, and the length of ninety ju shu equals that of the Huang Zhong. One shu is one fen, ten fen is one cun, ten cun is one chi, ten chi is one zhang, ten zhang is one yin, and thus the five types of measurements are determined." Later authors formulated measurements based on this account and derived various calculation methods based on the size of ju shu, so these proportions are still applicable. However, the size of ju shu varies, and the size of grains varies between years of good and poor harvests. The calibration of ancient measurements often differed, coupled with oral transmission among the people, errors inevitably occurred, leading to gradual changes in the values of measurements. Now, I will briefly list fifteen types of measurements from various dynasties along with their differing accounts: The "Book of Han" records the bronze hu chi established by Liu Xin during Wang Mang's reign.
The bronze ruler during the Jianwu period of the Later Han Dynasty;
The legal ruler established by Xun Xu during the tenth year of the Taishi period of the Jin Dynasty, which is the ruler before the Jin Dynasty;
The bronze ruler passed down by Zu Chongzhi.
It is said that in the ninth year of the Taishi period of Emperor Wu of Jin, Xun Xu, the supervisor of the Imperial Library, inspected the eight sounds of the palace and found that the musical tones were not harmonious. Upon investigation, it was found that the rulers from the Eastern Han Dynasty to the Wei Dynasty were over four fen longer than the ancient rulers. Xun Xu instructed the compiler Liu Gong to remake the rulers according to the standards of the "Rites of Zhou," which is the ancient ruler. Then, they used this ancient ruler to recast the bronze tuning pipes to adjust the musical tones. When measuring ancient musical instruments with this ancient ruler, the dimensions were completely consistent with the original inscriptions. Interestingly, someone in Jijun illegally excavated the tomb of King Wei Xiang and unearthed jade tuning pipes and chimes from the Zhou Dynasty, which remarkably sounded similar to the newly cast tuning pipes! At that time, Han Dynasty bells were also discovered in various places, and when tested with the newly made tuning pipes, they all matched perfectly.
Emperor Wu of the Liang Dynasty recorded in his "Treatise on Bells and Tuning Pipes" that the bronze ruler handed down by Zu Chongzhi had an inscription that read: "In the tenth year of Taishi of Jin, the supervisor of the Imperial Library examined ancient artifacts, measured and compared the current rulers, and found them to be four and a half fen longer. The seven ancient standards verified include: Guxi jade tuning pipes, Xiaolu jade tuning pipes, Xijing bronze measuring rules, Jincuo measuring rules, bronze hu, ancient coins, and Jianwu bronze rulers. Guxi jade tuning pipes are slightly higher, Xijing bronze measuring rules are slightly lower, and the rest are the same as this ruler." The inscription consists of eighty-two characters. This ruler is the one remade by Xun Xu; while the ruler currently in use is the one by Du Kui. In the "Illustrated Treatise on Bells and Tuning Pipes" drawn by Lei Cizong and He Yinzhi, the text documenting Xun Xu's calibration of the ancient ruler exactly matches this inscription. However, the music scores of Xiao Ji state that these are the seven standards verified by the Liang Dynasty, which is incorrect. We should now use this ruler as the standard to correct rulers from previous dynasties.
The ruler of the Liang Dynasty was actually one chi and seven fen longer than the rulers before the Jin Dynasty.
Once upon a time, an old farmer dug up a jade measuring stick from the Zhou Dynasty in the field. It was reputed to be the national standard for measurement. Xun Xu compared it with the gold, stone, silk, and bamboo artifacts he made and found that his items were all one meter shorter than the standard. Emperor Liang Wu's work "Zhong Lu Wei Cheng" also recorded this incident, stating that there were a bronze ruler and eight ancient jade laws from the Zhou Dynasty in the imperial palace. The bronze ruler was originally worn as part of the emperor's clothing, and Dong Hun Hou even used it as a token of trust, but it eventually went missing. One of the jade laws was damaged, and the remaining seven were used as musical scales, with previous inscriptions on them. Emperor Liang Wu then made a new ruler based on these jade laws for mutual verification. He used the finest millet grains to measure, repeatedly calibrating, making it the most accurate method of the time, even surpassing Zu Chongzhi's ruler by half a millimeter! He then crafted four musical instruments known as "Tong" with this new ruler. He also made a flute according to the new ruler to verify the pitch of the ancient bells, blowing out the Yi Ze notes in accordance with the scale, and then using the flute to determine the pitch of the Yin He rhyme, resulting in the Yi Ze notes and Yin He rhyme matching up. As you can see, the lengths of these two measuring sticks are nearly identical.
Xiao Ji noted in his writings: "This method comes from the 'Sima Fa.' The Liang Dynasty inscribed the ruler's scale on the shadow gauge to measure the sun's shadow." He referred to the bronze sundial crafted by Zuxun at the court's request. After the Chen Dynasty fell, this artifact became part of the imperial collection. During the Sui Dynasty, a proposal was made to restore the ancient standards, so they used this shadow gauge to calibrate the musical scales and create eight types of instruments, including bells and chimes. During the Jin Dynasty, an individual in Shiping County unearthed an ancient bronze measuring stick from the ground.
Xiao Ji said in "Music Scores": "During the reign of Emperor Zhang of Han, the literary historian Xi Jing from Lingling County dug up a set of jade rulers under the Shun Temple in Lingling County, and then made this ruler based on it." Fu Chang said in "Praise of Various Officials of Jin": "The musical tuning made by Ge Xu was considered very accurate by people at that time; only Ruan Xian from Chenliu said that its pitch was too high. Later, an ancient bronze ruler was dug up in Shiping County, almost completely rusted. When compared with Xu Xu's ruler, it was found to be a quarter shorter. People at that time all agreed with Ruan Xian." The lengths of these two rulers are also similar.
In the fourth year of the reign of King Jingyuan of Wei Chenliu, Liu Hui said in his annotations to "Nine Chapters on the Mathematical Art" that the measuring vessels and rulers used by Liu Xin during the Wang Mang period were four and a half centimeters shorter than the rulers at that time, and compared with the rulers of the Wei Dynasty, the depth of that vessel was nine inches, five minutes, and five seconds. This is the same as what Xu Xu of the Jin Dynasty said, "Du Kui's ruler is four and a half centimeters longer than the current ruler."
Xiao Ji noted that this ruler was used in Jiangdong during the Jin Dynasty.
The market ruler of the Later Zhou Dynasty was one foot, nine centimeters and three centimeters shorter than the jade ruler.
The official ruler of the Kaihuang period was an iron ruler measuring one foot and two inches long.
After that, from the early Wei Dynasty to the division of the Eastern and Western Wei, until the Later Zhou Dynasty stopped using the jade ruler, people commonly mixed and used these rulers.
Zhen Luan's "Arithmetic" says: "The market ruler of the Zhou Dynasty is a nine-centimeter, two-centimeter jade ruler." It is said that this ruler was made by Zhi Gong Dao Ren during the Liang Dynasty, and that he sent it to the Zhou Dynasty, giving it to an old man of great age. Emperor Taizu of the Zhou Dynasty and Emperor Gaozu of the Sui Dynasty both believed that this ruler was made for them, but in reality, it had always been in use among the common people of the Zhou Dynasty. During the Kaihuang period, the government ordered it to be established as the official ruler, and all departments used this ruler, up until the Renshou period. During the Daye period, it was also privately used by some people.
This jade ruler was constructed by Zhongwei Yuan Yanming of the Wei Dynasty, using the width of half a millet grain, and this method was later adopted by the Qi Dynasty. Wei Shou wrote in "Book of Wei · Records of Law and Calendars": "During the Yongping period, Gongsun Chong created a new ruler, using the length of one millet grain as the unit. Later, the Minister of Ceremonies, Liu Fang, was tasked with revising the musical standards, using the width of a medium-sized millet grain as a unit. Zhongwei Yuan Kuang used the width of one millet grain plus the space of two millet grains to define a unit. The three parties had differing opinions and debated for a long time without reaching a conclusion. In the nineteenth year of Dahe, the emperor decreed that the width of one millet grain would serve as a unit, and the length of ninety millet grains would be used for determining the bronze ruler. The relevant departments reported that the previous decree matched both Liu Fang's ruler and the emperor's ruler; therefore, the laws governing weights and measures were revised based on Liu Fang's ruler. Until the Wuding period, there was no further discussion on the law." The jade ruler from the Later Zhou Dynasty was longer by one foot, one inch, five fen, and eight li than those from before the Jin Dynasty. Also passed down from ancient times is a bronze yue, inlaid with silver, with an inscription: "Yue, the palace of Huangzhong, nine inches long, nine fen in circumference, can hold one thousand two hundred millet grains, weighing twelve zhu, with two zhu making one he. Three points of loss or gain, turning into twelve laws." Zuxiaosun said, "It is said that this bronze yue was made by Cai Yong." During the Baoding era of the Later Zhou Dynasty, the emperor commanded Grand Zongbo Lu Jingxuan, Shangdang Gong Changsun Shaoyuan, Qiguo Gong Husizheng, and others to create rulers using accumulated millet grains, but the dimensions remained uncertain. Later, while repairing the granary, workers unearthed an ancient jade measuring vessel, which was used as a standard for establishing laws and measurements. This ruler was then used to grant amnesty across the country and to transition the era to Tianhe, and all departments began to use this ruler until the conclusion of the Daxiang period. The Huangzhong musical standards of this legal system are identical to those of Cai Yong's ancient yue. The Song ruler is one foot, six fen, and four li longer than the rulers before the Jin Dynasty. Additionally, there is Qian Lezhi's celestial globe ruler, as well as the iron ruler from the Later Zhou Dynasty.
In the early years of the Kaihuang era, the standards for tuning bells and measurements were revised. After pacifying the Chen Dynasty, the standards for tuning bells and the water measuring stick were revised again. This ruler refers to the type commonly used by the populace during the Song Dynasty, which later spread to the Qi, Liang, and Chen Dynasties for making musical instruments and determining musical scales. Its length is approximately comparable to the rulers used after the Jin Dynasty, as well as those used by the common folk in the Liang Dynasty and the ruler on Liu Yao's armillary sphere. This is likely because the rulers used by the common folk would inevitably wear out and vary over time. In the sixth year of Jiande during the Zhou Dynasty, after defeating the Qi Dynasty, this ruler was employed to standardize laws and measurements nationwide, which were then enacted for use across the realm. Later, during Emperor Xuan's reign, Daxi Zhen and Niu Hong discussed this issue.
Speaking of the issue of measurements and weights, as it relates to national matters, it is essential to study it thoroughly and understand its origins and evolution. We carefully investigated and found that the iron ruler currently in use was made by order of Emperor Taizu based on the ruler created by Su Chuo from the Book of Documents during the time of the Former Zhou! When we measured it, we found that this iron ruler is roughly the same length as the rulers from the Song Dynasty, which were initially used to calibrate musical pitches and also for land measurement. Now, we're testing it with millet from Shangdang, following the method described in the "Book of Han: Treatise on Law and Calendar." If we pile up large millet grains, it just reaches one foot, but when placed into the Huangzhong tube, we have to shake it vigorously to fit it in. If we use medium-sized millet grains, although they are a bit sparse, they fit perfectly into the Huangzhong tube without any shaking. These two scenarios differ mainly because of the uneven sizes of the millet grains, so we still need to determine the accuracy of this iron ruler. Moreover, the millet from Shangdang differs from that of other regions; it is black and shiny, and the grains are round and heavy, so using it for measurement is certainly not arbitrary. After all, different regions have varying rainfall and drought conditions, and the fertility of the land differs, leading to different sizes of millet, making it difficult to find a perfect match. Xu Shen explained that the large millet, referred to as jushuo, differs from regular millet. I suspect that the large millet we have now is indeed jushuo, and it takes one hundred grains to make a foot, which is consistent with ancient practices. Besides the one foot that fits perfectly, there are still about a dozen grains left, which could be due to the millet not being packed tightly or the dimensions of the tube being slightly off. However, the idea of shaking it to fill it up, as we did earlier, is reasonable. We also checked ancient coins from the Zhou and Han Dynasties, and their sizes are quite consistent; the size of the Song Dynasty's armillary sphere is also consistent. The "Huainanzi" states that twelve grains of millet piled together equal one inch, which indicates that the standards established by previous kings, upon careful verification and calculation by law, yield consistent results. The "Book of Han: Treatise on Food and Money" states: "A square of gold measuring one inch weighs one pound." We are now casting gold to verify, and the iron ruler is the closest match. From both the literature and practical situations, there are many points of agreement. Furthermore, the use of this iron ruler began in the Pingqi period, and continuing to use it now is quite appropriate. As for measuring millet with a jade ruler, due to the varying lengths of the millet grains, there will be leftovers when piled up, and it cannot be filled completely. After reviewing ancient and modern literature, it seems this method is not feasible. The rulers from the Jin and Liang Dynasties are too short; when millet is placed into the tube, it simply cannot fill it up. If we calibrate musical pitches based on this, the sound would certainly be shrill and piercing. The harmony of the eight tones is a hallmark of wise and virtuous rulers, and unified laws and measurements are the governing strategy of enlightened monarchs. We have carefully studied previous literature and combined it with current practical situations, concluding that the iron ruler is the more suitable choice.
Before they had enough time to finalize the details, Emperor Gaozu passed away. Niu Hong, Xin Yanzhi, Zheng Yi, He Tuo, and a few others discussed for half a day but reached no conclusion. After pacifying the Chen Dynasty, the emperor felt that the music of ancient China was the best, saying, "This is the music of ancient Huaxia. Although it has changed with the times, it still largely follows the ancient methods." Emperor Zu Xiaosun said, "After pacifying the Chen Dynasty, the jade尺 (yu chi) and律吕 (lülü) of the Zhou Dynasty were abolished, and iron尺 (chi) and律吕 (lülü) were used instead, stipulating that one尺 (chi) and two寸 (cun) equal one市尺 (shìchǐ)."
In the tenth year of the Kaihuang era, the water尺 (shuǐchǐ) of lülü manufactured by Wan Baochang was actually one尺 (chi), one寸 (cun), eight分 (fēn), and six厘 (lì) longer than the尺 (chi) before the Jin Dynasty. "The current Taiyue Library and the inner collection of copper律 (lü) are all made by Wan Baochang, called水尺律 (shuǐchǐ lü). Its黄钟律 (huángzhōng lü) is said to be twice the pitch of the南吕 (nán lü) from the iron尺 (chi). The南吕 (nán lü) is the feather tone of the黄钟 (huángzhōng), hence it is called水尺律 (shuǐchǐ lü)."
Currently, both the Taiyue Library and the palace house a set of copper律吕 (lülü) made by Wan Baochang, which is known as水尺律 (shuǐchǐ lü). The book states that its黄钟律 (huángzhōng lü) corresponds to double the pitch of the南吕 (nán lü) from the iron尺 (chi).南吕 (nán lü) is the feather tone of黄钟 (huángzhōng), so it is called水尺律 (shuǐchǐ lü).
Among the various尺 (chi), the土圭尺 (tǔguī chǐ) used in Zhao Liuyao's Hunyuan Instrument is four分 (fēn) and three厘 (lì) longer than the Liang Dynasty's legal尺 (chi) and one尺 (chi) and five分 (fēn) longer than the尺 (chi) before the Jin Dynasty. "The土圭尺 (tǔguī chǐ) of Zhao Liuyao's Hunyuan Instrument is four分 (fēn) and three厘 (lì) longer than the Liang legal尺 (chi) and one尺 (chi) and five分 (fēn) longer than the尺 (chi) before the Jin Dynasty."
Fifteen, the commonly used ruler in the Liang Dynasty is six fen and three li longer than the Liang Dynasty's legal ruler, two fen longer than the ruler used in Liu Yao's armillary sphere, and actually one foot, seven fen, and one li longer than the rulers that were in use before the Jin Dynasty. The Emperor Wu of Liang mentioned in the "Zhonglü Wei": "After Emperor Wu of Song pacified the Central Plains, he sent the armillary sphere and the gnomon, claiming they were made by Zhang Heng. However, based on the inscription on the armillary sphere, it was produced in the fourth year of Guangchu, and the gnomon was made in the eighth year of Guangchu. Both were made by Liu Yao, not Zhang Heng. The ruler used is four fen and three li longer than the current new ruler, and two fen shorter than the commonly used ruler." In this context, the "new ruler" refers to the Liang Dynasty's legal ruler.
Goodness, this article discusses ancient measurements and weights, tracing from the Zhou Dynasty all the way to the Han Dynasty, and the content is quite complex! Let's go through it sentence by sentence.
First, the "Rites of Zhou" states that the Zhen clan was responsible for crafting measuring instruments. This measuring instrument has a depth of one foot, with an inner square of one foot on each side and a circular outer shape, with a capacity of one dou; its base has a diameter of one inch, also with a capacity of one dou; its handle is three inches long, which holds one sheng; the total weight is one jun; it produces a sound that harmonizes with the pitch of the Huangzhong; and it is exempt from tax. The inscription reads: "In time, literature contemplates, and it reaches its peak. The excellent measures have been established, to observe the four states. May it be passed on forever, this instrument is the standard." This inscription speaks for itself; it is quite imposing.
Then, the "Zuo Zhuan" (Commentary of Zuo) from the "Spring and Autumn Annals" mentions four types of measuring vessels from the Qi state: dou, qu, hu, and zhong. Four sheng equal one dou, and so on; four dou equal one hu, and six dou and four sheng equal one hu; ten hu equal one zhong, which is sixty-four dou. Zheng Xuan believed that the area of a square foot is one thousand cun, which differs from the calculations in the "Nine Chapters on the Methods of Grain," which is short by two sheng and eighty-one fen, or one twenty-second of the total. Zu Chongzhi recalculated using a different method, and the recalculated result was 1562.5 cun. If it is a square with a side length of one foot, and a circular shape is made outside, subtracting a small amount from the edge, the diameter is approximately one foot, four cun, one fen, four miao, and two hu, with a depth of one foot; this measurement represents the standard for the ancient hu.
The "Nine Chapters on Commercial Methods" states that the volume of one hu of millet is 2700 cun, one hu of rice is 1620 cun, and one hu of beans and hemp wheat is 2430 cun. The pricing varies based on the weight of the grain, yet the prices remain consistent; this pricing method is quite ingenious. Using the rice hu as a standard is consistent with what is written in the "Book of Han."
The "Sunzi Suanshu" states that six grains of millet equal one gui, ten gui equal one miao, ten miao equal one pinch, ten pinches equal one spoon, and ten spoons equal one he. Ying Shao said that gui is a natural shape, that the beginning of yin and yang, and four gui equal one pinch; Meng Kang noted that sixty-four grains of millet equal one gui.
The "Book of Han" states that the measuring instruments include the yue (a type of measuring vessel), he, sheng, dou, and hu, used to measure quantities. Initially, they were made based on the yue of the Huangzhong pitch, using a standardized ruler for measuring volume, filling the yue with one thousand two hundred millet grains, and then calibrating with well water. One yue equals one he; ten he equals one sheng; ten sheng equals one dou; and ten dou equals one hu, completing these five measuring instruments. The method of making them involves copper, shaped into a square with a side length of one foot, featuring a round exterior and side handles. The top is hu, the bottom is dou, the left handle is sheng, and the right handle is he and yue. The shape resembles a jue, which symbolizes official rank. Three above and two below symbolize heaven and earth; the round shape envelops the square shape, with one on the left and two on the right, symbolizing yin and yang. The round shape represents a compass, weighing two jun, containing quantities of various materials, each amounting to eleven thousand five hundred twenty. The sound corresponds with the Huangzhong pitch, starting from Huangzhong and repeating. The inscription on the hu reads: "The principle of good measurement for the hu, square inside and round outside, with a side of nine li and five hao, depth of one foot, accumulating one thousand six hundred twenty cun, holding ten dou." The mathematician Zu Chongzhi calculated using pi, determining that the diameter of this hu should be one foot, four inches, three tenths, six hundredths, one millimeter, nine seconds, and two tenths of a millimeter; the width of the handle is about one tenth and nine hao. Liu Xin estimated the handle width to be one li and four hao shorter, due to his imprecise calculations. In summary, the ancients were indeed meticulous in their approach to measurement! In the fourth year of Wei Jingyuan, Liu Hui wrote in "Nine Chapters on the Mathematical Art": The hu used by the current Minister of Agriculture has a diameter of one foot, three inches, five and five-tenths, with a depth of one foot, holding one thousand four hundred forty-one inches in thirty parts. The copper hu from the Wang Mang period, calculated using today's measurements, has a depth of nine inches, five tenths, five hundredths, and a diameter of one foot, three inches, six tenths, eight hundredths, and seven hao. Using Liu Hui's method of calculation, the volume of the copper hu from the Wang Mang period is just slightly over nine dou, seven sheng, and four he compared to the current hu. Thus, it can be concluded that the hu of the Wei dynasty were relatively larger, and their rulers were also longer; the hu of the Wang Mang period were relatively smaller, and their rulers were also shorter.
The Liang Dynasty and the Chen Dynasty used ancient units of measurement for length. Meanwhile, the Qi Dynasty used five ancient units of sheng to create one dou.
In the first year of the reign of Emperor Wudi of the Later Zhou Dynasty (561 AD), in May, when the Jin State was building a warehouse, they discovered an ancient jade measuring vessel. By the fifth year of Emperor Wudi's reign (565 AD), in October, he ordered the reform of bronze laws and weights and measures, ultimately achieving uniformity and consistency. By repeatedly measuring with millet, the capacity of the jade vessel exactly matched the new bronze weights and measures, so a bronze measuring vessel was cast based on this standard and distributed for use throughout the country. The inscription on the bronze vessel read: "In the first year of Emperor Wudi of the Great Zhou Dynasty, when the Jin State was repairing the warehouse, they found this jade vessel, which was well-formed and an ancient standard measuring instrument. The Grand Preceptor of the Jin State reported to the court, and the Emperor ordered it to be stored in the imperial treasury. By the fifth year of Emperor Wudi's reign, he ordered careful calibration and verification to ensure accuracy. Bronze vessels were then cast, modeled after the jade vessel, and distributed throughout the country to standardize weights and measures." The inner diameter of this bronze vessel was seven inches and one fen, with a depth of two inches and eight fen, and a weight of seven jin and eight liang. On the fifteenth day of the first month of the second year of Tianhe (567 AD), the bronze vessel was calibrated again and placed as a standard object in the government office. The inscription on the jade vessel read: "In the first year of Emperor Wudi of the Great Zhou Dynasty, when the Jin State government was repairing the warehouse, they found this jade vessel, which was well-formed and seemed to be an ancient standard measuring instrument. The Grand Preceptor of the Jin State reported to the court, and the Emperor ordered it to be stored in the imperial treasury. By the fifth year of Emperor Wudi's reign, he ordered careful calibration and verification to ensure accuracy. Bronze vessels were then cast, modeled after the jade vessel, and distributed throughout the country to standardize weights and measures." Calculating the volume, the jade vessel measured slightly over one hundred and ten inches and eight fen, equivalent to one thousand one hundred and eighty-five minutes seven centimeters three millimeters nine seconds. According to Zhen Luan in "Arithmetic," one sheng of the jade vessel is equivalent to one sheng, three he, and four shao of the government's measuring vessel. Therefore, the jade vessel is larger than the government's measuring vessel. Based on calculations, Zhen Luan said that the government's measuring vessel of the Later Zhou Dynasty had a volume of slightly over ninety-seven inches, equivalent to nine hundred and seventy-seven inches. The Later Zhou's jade vessels, along with matching bronze vessels and the gold-inlaid bronze vessels of the sixth year of Jiande (577 AD), were all measured using millet. When using the jade vessel for measurement, one sheng weighed six jin and thirteen liang.
During the reign of Emperor Kaihuang, the ancient unit of measurement "three sheng" was defined as "one sheng." During the reign of Emperor Daye, the capacity of the ancient unit "dou" was reinstated. "Heng" means balance, and "quan" means weight. The function of "heng" is to bear weight, used to measure the weight of things. The construction of "heng" involves using a base to ensure vertical alignment and a rope to determine its straightness. Turning left reveals a compass, while turning right reveals a square. The function of "heng" in the sky is to support the Xuanji (an ancient astronomical instrument), consider and adjust the Jianzi, which refers to specific star constellations, and coordinate the seven celestial bodies (sun, moon, and five planets), hence it is called "Yuheng." "Quan" refers to weight units such as zhu, liang, jin, jun, and dan. Using a scale allows for accurate weight measurement. In ancient times, there were also weight units such as shu, lei, chui, zi, huan, gou, lue, and yi, with varying standards across different dynasties. According to the "Book of Han," the origin of "quan" was based on the weight of the Huangzhong (an ancient musical instrument). One yue (an ancient capacity unit) could hold 1200 grains of shu, weighing 12 zhu. 24 zhu make one liang, 16 liang make one jin, 30 jin make one jun, and 4 jun make one dan. The craftsmanship of these five weights is highly precise, with their standards established based on reason and calibrated with physical objects. The remaining size differences are adjusted based on weight. Form a circle around it, ensuring it is slightly thicker, creating a continuous loop. When the weight and object achieve equilibrium, a balance is established, the operation of which gives rise to a compass, the circular shape of the compass produces a square, the square shape of the ruler establishes a guideline, and the straightness of the rope establishes a guideline. When the guideline is correct, the balance is balanced, and the weight is accurate. These five basic principles are embodied in the balance, which serves as the primary standard.
According to the "Zhao Book," in the eighteenth year of the reign of Shi Le, in July, when the Jiande Hall was under construction, a round stone resembling a water mill was obtained. It bore an inscription: "Stone of the Law, weighing four jun, in accordance with the standards of weights and measures. Made by the Xin family." The Xuxianyi is believed to be from the Wang Mang period. During the Jingming period of the Northern Wei Dynasty, Wang Xianda from Beizhou presented an ancient bronze weight with an inscription of 81 characters. The inscription stated: "Stone of the Law, weighing four jun." It also said: "The Yellow Emperor, the first ancestor, virtue extended to Yu. Yu, the first ancestor, virtue extended to Xin. In the year of Daliang, the dragon gathered in Wuchen. Wuchen directly determined, heaven's mandate has come. Based on the virtue of the earth, the correct number is true. Changing the correct to Jiachou, longevity and prosperity. In accordance with the standards of weights and measures, inspecting the people. The dragon is in Jisi, the year is truly sinking, the first to establish order in the world, all nations forever obey. Descendants for generations, enjoying the tradition for billions of years." This was also produced during the Wang Mang period. At that time, the Taile Ling, Gong Sun Chong, based on the "Han Book," first adjusted the ruler. When he saw this weight, he used a new ruler to measure it, and the weight was 120 catties. The new ruler and this weight matched perfectly. So he handed it over to Gong Sun Chong to adjust the music. During the period of Emperor Xiaowen, the weights and measures were crafted according to the standards of the "Han Book." It is said that during the Liang and Chen dynasties, they used old scales. During the Qi Dynasty, one jin was equivalent to eight taels now. In the Zhou Dynasty, one jin of jade was four taels, equivalent to four and a half old scales. During the Kaihuang period of Emperor Wen of Sui, it was stipulated that one jin was equivalent to three jin of the old scale. During the Daye period of Emperor Yang of Sui, the old scale was restored. Thus, the weight units varied across different dynasties, which was quite perplexing. The Liang and Chen dynasties used old scales, one jin in the Qi Dynasty was eight taels, in the Zhou Dynasty, one jin of jade was four taels, equivalent to four and a half old scales. Emperor Wen of Sui said that from now on, one jin would be equal to three jin of the old scale! As a result, Emperor Yang of Sui changed it back and used the old scale again. Oh, all this fuss over weights is truly baffling!
