Ancient people studied numbers, saying: "Things must come into being to have a shape; with a shape comes growth, and with growth comes quantity." Therefore, when heaven and earth began to form, humans and all things appeared, and the practice of counting was born. It is recorded that the ancient scholar Da Rao invented the sexagenary calendar, and Li Shou created counting methods. With the advent of these two innovations, they could be used to compare calendars and manage various matters.
You see, everyone uses numbers like one, ten, hundred, thousand, and ten thousand; while terms like length, capacity, weight, and measures each have their own specific uses. For measuring length, we use a ruler; for measuring quantity, we use containers; for weighing objects, we use scales; for coordinating sounds, we use musical notes; and for recording the movements of the sun, moon, and stars, we use calendars. This way, we can grasp the hidden and subtle changes in the world.
After the establishment of the Han Dynasty, Marquis Zhang Cang of Beiping was responsible for formulating music scales and calendars. During the reign of Emperor Wu of Han, music was highly valued, and an official position for music coordination was established to manage music affairs. During the Xin Dynasty under Wang Mang, experts in music theory were widely recruited to study the significance of musical scales. At that time, Liu Xin recorded and reported findings, while historian Ban Gu incorporated this information into the historical texts.
During the reign of Emperor Han Yuan, there was a court physician named Jing Fang (style name Junming), who was very knowledgeable about the five tones and the six pitches. The emperor asked the Prince's Tutor Wei Xuancheng and the Chief Councillor Zhang to conduct a series of assessments on Jing Fang in the music court. Jing Fang replied, "I learned from Huang Ling Jiao Yanshou. The principle behind the generation of the sixty lü is: the upper lü gives birth to the lower lü, both follow a pattern of three giving rise to two; the lower lü gives birth to the upper lü, both are three giving birth to four. The yang lü gives birth to the yin lü, the yin lü gives birth to the yang lü, ultimately resulting in the central lü, and the twelve lü are complete. The central lü gives birth to the starting note, the starting note gives birth to the ending note, the interaction between the upper and lower notes leads ultimately to the southern lü, and the sixty lü are complete. The transformation of the twelve pitches into sixty is like the transformation of the eight trigrams into sixty-four hexagrams. Fuxi authored the 'I Ching', recording the initial state of yang qi, and based on this established the law of lü. Starting from the winter solstice, Huang Zhong is designated as the tonic, Tai Cu as the subdominant, Gu Xi as the mediant, Lin Zhong as the dominant, Nan Lü as the submediant, Ying Zhong as the variable tonic, and Rui Bin as the variable dominant. These are the fundamentals of sound, the standards of the five tones. Therefore, each tone corresponds to a day. The rest of the tones run in order, and the tone corresponding to the day becomes the tonic, with the subdominant and dominant following suit. The 'Li Yun Pian' states 'the five tones, six lü, and twelve pipes all serve as the tonic', which is what it means. Using the sixty lü to divide the days of a year, starting from the winter solstice with Huang Zhong until the winter solstice ends, the signs of yin and yang, cold and heat, and wind and rain are all encompassed within. By standardizing various sounds in this way, assessing the pitch of these sounds, as long as it is not the sound of plants, the corresponding lü and tones can be identified. The 'Book of Documents' states 'lü and sound', which is what it means."
Jing Fang said, "The sound of bamboo pipes cannot be used to determine pitch, so standard instruments must be made to determine pitch values. This standard instrument is shaped like a stringed instrument, one zhang long, with thirteen strings spaced nine chi apart, corresponding to the length of nine cun of the yellow bell pitch; with a central string, marked with increments below, used to indicate the purity and impurity of the sixty pitches." Jing Fang's discussion on pitch is more detailed than Liu Xin's memorial, and his method was adopted by the historiographers and the Ministry of Rites (the department in charge of astronomy and calendar calculations). Due to the extensive nature of the content, not everything can be recorded. Therefore, I have summarized its main points to supplement the deficiencies of the "History of the Former Han Dynasty."
"The Art of Pitch" says, the yang qi, in round shape, is characterized by movement; the yin qi, in square shape, is characterized by stillness. The number representing movement is three, while the number representing stillness is two. When using yang to generate yin, multiply by two; when using yin to generate yang, multiply by four: both must be divided by three. Yin generated from yang is termed 'lower generation,' and yang generated from yin is termed 'upper generation.' The upper generation cannot exceed the muddiness of the yellow bell pitch, and the lower generation cannot be lower than the clarity of the yellow bell pitch. This adheres to the principle of the circular heavens and square earth, the generation of yin and yang, and the principle of six pairs carrying one odd number. "Yellow Bell" is the foundation of the pitches, and it can generate the other eleven pitches. The rules of their mutual generation are three parts subtracted or added to again. Therefore, the sum of the values of the twelve pitches is 177,147, which is the true value of the yellow bell pitch. Multiply by two and divide by three to get the actual value of the lower generation Lin bell pitch; multiply by four and divide by three to get the actual value of the upper generation Tai bell pitch. By this method, the values of the sixty pitches can be determined. Multiply by nine and three to get 19,683 as the standard value. In pitch, it is cun; in tuning, it is chi. If the value is insufficient, multiply by ten to obtain fen; if still not enough, multiply by ten to get li. Use the remaining numbers to adjust its strength.
Yellow Bell: 177,147.
Lower Generation Lin Bell: Yellow Bell as the tonic, Tai Bell as the supertonic, and Lin Bell as the mediant.
On the first day, the pitch measures nine cun, and the tuning measures nine chi.
Se Huang: 176,776.
Lower Generation Qiantai: Se Huang as the tonic, unknown as the supertonic, Qiantai as the mediant.
On the sixth day, the pitch is eight inches and nine points, with eight micro-strong divisions, and it is exactly eight feet nine inches, fifteen thousand nine hundred and seventy-three. Starting value is one hundred seventy-four thousand seven hundred sixty-two. Birth, death, and dissolution. Starting from the beginning as the palace, resting on the time, death and dissolution as the corresponding note.
On the sixth day, the pitch is eight inches and eight points, with seven major strong divisions, and it is exactly eight feet eight inches, fifteen thousand five hundred and sixteen. Bing Sheng is one hundred seventy-two thousand four hundred ten. Birth, peace, and progress. Bing Sheng as the palace, bending to the time, peace, and progress as the corresponding note.
On the sixth day, the pitch is eight inches and seven points, with six micro-weak divisions, and it is exactly eight feet seven inches, eleven thousand six hundred and seventy-nine. Moving division is one hundred seventy-eight thousand eighty-nine. Birth, return, and praise. Moving division as the palace, following the time, return and praise as the corresponding note.
On the sixth day, the pitch is eight inches and six points, with four strong divisions, and it is exactly eight feet six inches, eight thousand one hundred and fifty-two. Quality end is one hundred sixty-seven thousand eight hundred. Birth, negation, and agreement. Quality end as the palace, forming the time, negation, and agreement as the corresponding note.
On the sixth day, the pitch is eight inches and five points long, with a slight increase. The standard length is eight feet five inches, and the frequency is four thousand nine hundred forty-five. The frequency of the Da Lu is one hundred sixty-five thousand eight hundred eighty-eight. Next is the birth of Yi Ze. Da Lu as the palace tone, Jia Zhong as the commercial tone, Yi Ze as the corresponding note.
On the eighth day, the pitch is eight inches and four points long, with a slight increase. The standard length is eight feet four inches, and the frequency is five thousand five hundred eight. The frequency of Fen Fou is one hundred sixty-three thousand six hundred fifty-four. Next is the birth of Jie Xing. Fen Fou as the palace tone, Kai Shi as the commercial tone, Jie Xing as the corresponding note.
On the eighth day, the pitch is eight inches and three points long, with a slight increase. The standard length is eight feet three inches, and the frequency is two thousand eight hundred fifty-one. The frequency of Ling Yin is one hundred sixty-one thousand four hundred fifty-two. Next is the birth of Qu Nan. Ling Yin as the palace tone, Zu Jia as the commercial tone, Qu Nan as the corresponding note.
On the eighth day, the pitch is eight inches and two points long, with a slight decrease. The standard length is eight feet two inches, and the frequency is five hundred fourteen. The frequency of Shao Chu is one hundred fifty-nine thousand two hundred eighty. Next is the birth of Fen Ji. Shao Chu as the palace tone, Zheng Nan as the commercial tone, Fen Ji as the corresponding note.
On the sixth day, the pitch is eight inches long, with many small increments. The standard length is eight feet, and the frequency is 18,160. The frequency of the Tai Cu is 157,464. Then comes the Xia Sheng Nan Lü. The Tai Cu serves as the Gong sound, Gu Xi serves as the Shang sound, and Nan Lü serves as the Zhi tone.
On the first day, the pitch is eight inches long. The standard length is eight feet. The unknown frequency serves as the Gong sound. Then comes the Xia Sheng Bai Lü. The unknown frequency serves as the Gong sound, Nan Shou serves as the Shang sound, and Bai Lü serves as the Zhi tone.
On the sixth day, the pitch is seven inches and nine tenths of an inch long, with many small increments. The standard length is seven feet and nine inches, and the frequency is 16,383. The frequency of Shi Xi is 155,344. Then comes the Xia Sheng Jie Gong. Shi Xi serves as the Gong sound, Bian Yu serves as the Shang sound, and Jie Gong serves as the Zhi tone.
On the sixth day, the pitch is seven inches and eight tenths of an inch long, with a slight increase. The standard length is seven feet and eight inches, and the frequency is 18,166. The frequency of Qu Qi is 153,253. Then comes the Xia Sheng Gui Qi. Qu Qi serves as the Gong sound, Lu Shi serves as the Shang sound, and Gui Qi serves as the Zhi tone.
On the sixth day, the pitch is seven inches and seven tenths of an inch long, with a little less. The standard length is seven feet and seven inches, and the frequency is 16,939. The frequency of Sui Qi is 151,190. Then comes the Xia Sheng Wei Mao. Sui Qi serves as the Gong sound, Xing Shi serves as the Shang sound, and Wei Mao serves as the Zhi tone.
On the sixth day, the pitch is seven inches and six tenths of an inch long, with a slight increase. The standard length is seven feet and six inches, and the frequency is 15,992. The frequency of Xing Jin is 149,156.
Now, let's discuss the Yi Han Gong scale. You see, it starts from Yi Han, which is the Gong scale, with Xing Shang as the Shang sound, and Yi Han Zhi as the Zhi tone. This spans a total of six days. The pitch is seven inches and five tenths of an inch long, with small divisions of eight weak pulses. The standard length is seven feet and five inches, with a frequency of 15,335, and the interlocking frequencies are 147,456.
Next is the Wushigong Diao. The Gong Diao is Jia Zhong, the Shang Yin is Zhong Lu, and the Zheng Yin is Wu She. This lasts for six days. The tuning length is seven inches and four minutes, the small tuning is nine strong, the standard length is seven feet and four inches, the number is 18,118, and the opening time is 145,470.
Next is the Bi Yan Gong Diao. The Gong Diao is the opening time, the Shang Yin is Nan Zhong, and the Zheng Yin is Bi Yan. This lasts for eight days. The tuning length is seven inches and three minutes, the small tuning is nine slightly strong, the standard length is seven feet and three inches, and the family number is 143,513.
Next is the Lin Qi Gong Diao. The Gong Diao is the family's joy, the Shang Yin is Nei Fu, and the Zheng Yin is Lin Qi. This lasts for eight days. The tuning length is seven inches and two minutes, the small tuning is nine slightly strong, the standard length is seven feet and two inches, the number is 17,954, and competing for the south is 141,582.
Next is the Qi Bao Gong Diao. The Gong Diao is competing for the south, the Shang Yin is Wu Ying, and the Zheng Yin is Qi Bao. This lasts for eight days. The tuning length is seven inches and one minute, the small tuning is nine strong, the standard length is seven feet and one inch, the number is 18,327, and Gu Xi is 139,968.
Next is the Ying Zhong Gong Diao. The Gong Diao is Gu Xi, the Shang Yin is Rui Bin, and the Zheng Yin is Ying Zhong. This lasts for only one day. The tuning length is seven inches and one minute, the small tuning is one slightly strong, the standard length is seven feet and one inch, the number is 2,187, and Nan Shou is 139,674.
Next is the Fen Wu Gong Diao. The Gong Diao is Nan Shou, the Shang Yin is Nan Shi, and the Zheng Yin is Fen Wu. This lasts for six days. The tuning length is seven inches, the small tuning is nine strong, the standard length is seven feet, the number is 18,930, and Bian Yu is 138,084.
Next is the Chi Nei Gong Diao. The Gong Diao is Bian Yu, the Shang Yin is Sheng Bian, and the Zheng Yin is Chi Nei. This lasts for six days. The tuning length is seven inches, the small tuning is one half strong, the standard length is seven feet, the number is 3,030, and Lu Shi is 136,225.
Finally, we have the Wei Yu Gong Diao. The Gong Diao is Lu Shi, the Shang Yin is Li Gong, and the Zheng Yin is Wei Yu. This lasts for six days. The tuning length is six inches and nine minutes, the small tuning is two slightly strong, the standard length is six feet and nine inches, the number is 4,123, and Xing Shi is 134,392.
Finally, we have the Chi Shi Gong Diao, where the Gong Diao is Xing Shi, the Shang Yin is Zhi Shi, and the Zheng Yin is Chi Shi.
On the fifth day, the length of the tuning tube is six inches and eight tenths, with a small deviation of three tenths weak. The standard pitch is six feet and eight inches, with a frequency of five thousand four hundred and seventy-six. The total pitch count is one hundred and thirty-two thousand five hundred and eighty-two. That day is the upper birth of the color education, using the color education scale, approaching the commercial tone with humility, and the color education is the note of the Dorian mode.
On the seventh day, the length of the tuning tube is six inches and seven tenths, with a small deviation of three tenths strong. The standard pitch is six feet and seven inches, with a frequency of seven thousand fifty-nine. The total pitch count of the Zhonglü tone is one hundred and thirty-one thousand seven hundred and twenty. That day is the upper birth of the beginning, using the Zhonglü palace tone, eliminating the commercial tone, and the beginning is the note of the Dorian mode.
On the eighth day, the length of the tuning tube is six inches and six tenths, with a small deviation of six tenths weak. The standard pitch is six feet and six inches, with a frequency of eleven thousand six hundred and forty-two. The total pitch count of the southern middle tone is one hundred and twenty-nine thousand three hundred and eight. That day is the upper birth of Bing Sheng, using the southern middle palace tone, treating the commercial tone calmly, and Bing Sheng is the note of the Dorian mode.
On the seventh day, the length of the tuning tube is six inches and five tenths, with a small deviation of seven tenths weak. The standard pitch is six feet and five inches, with a frequency of thirteen thousand six hundred and eighty-five. The total pitch count of the inner negative tone is one hundred and twenty-seven thousand five hundred and sixty-seven. That day is the upper birth of Fendong, using the inner negative palace tone, approaching the commercial tone with obedience, and Fendong is the note of the Dorian mode.
On the eighth day, the length of the tuning tube is six inches and four tenths, with a small deviation of eight tenths strong. The standard pitch is six feet and four inches, with a frequency of fifteen thousand nine hundred and fifty-eight. The total pitch count of the object-resonant tone is one hundred and twenty-five thousand eight hundred and fifty. That day is the upper birth of Zhi Mo, using the object-resonant palace tone, rejecting the commercial tone, and Zhi Mo is the note of the Dorian mode.
On the seventh day, the length of the tuning tube is six inches and three tenths, with a small deviation of nine tenths strong. The standard pitch is six feet and three inches, with a frequency of eighteen thousand four hundred and seventy-one. The total pitch count of the Ruibin tone is one hundred and twenty-four thousand four hundred and sixteen. That day is the upper birth of Dalü, using the Ruibin palace tone, treating the commercial tone as the tonic note, and Dalü is the note of the Dorian mode.
On the first day, the length of the tuning tube is six inches and three tenths, with a small deviation of two tenths strong. The standard pitch is six feet and three inches, with a frequency of four thousand one hundred and thirty-one. The total pitch count of the Nanshi tone has been exhausted, there is no commercial tone and Dorian mode, therefore, it is not considered a scale.
On the seventh day, the length of the pitch pipe is six inches and three tenths, with the minor fraction being slightly weak. The standard pitch is six feet and three inches, with a frequency of one thousand five hundred and eleven. The palace mode of total pitch variation is one hundred and twenty-two thousand seven hundred and forty-one. That day, the upper birth division corresponds to the zhi sound, using the total pitch variation palace mode to unlock the physical treatment of the commercial sound.
On the seventh day, the length of the pitch pipe is six inches and two tenths, with the minor fraction being slightly strong. The standard pitch is six feet and two inches, with a frequency of seven thousand sixty-four. The pitch of the detached palace is one hundred and twenty-one thousand and eighty-nine. That day, the upper birth division corresponds to Lingyin, using the detached palace mode, removing the southern sound for the commercial sound, and the Lingyin corresponds to the zhi sound.
On the seventh day, the length of the pitch pipe is six inches and one tenth, with the minor fraction being slightly strong. The standard pitch is six feet and one inch, with a frequency of twelve thousand two hundred and twenty-seven. Initially, the value was one hundred and nineteen thousand four hundred and sixty. At this point, the upper birth is diminished, taking this number as the palace mode; the commercial mode represents the accumulation of births, and the zhi mode is the decrease. It lasted a total of eight days. The law is six inches plus one minor fraction and seven weak, and the standard is six feet plus thirteen thousand six hundred and twenty.
Next is the Linzhong, with a value of one hundred and eighteen thousand nine hundred and ninety-eight. This time, the upper birth is too dense; Linzhong is the palace mode, Nanlv is the commercial mode, and the too dense corresponds to the zhi mode. It lasted for one day. The law is six inches, and the standard is six feet.
Next is modesty, with a value of one hundred and seventeen thousand eight hundred and fifty-one. The upper birth corresponds to an unknown sound; modesty is the palace mode, Bailv is the commercial mode, and the unknown sound corresponds to the zhi mode. It lasted for five days. The law is five inches and nine tenths plus one minor fraction and nine weak, and the standard is five feet and nine inches plus seventeen thousand two hundred and thirteen.
Next is extinction, with a value of one hundred and sixteen thousand five hundred and eight. When the upper birth is in a state of rest, extinction is the palace mode, Jiegong is the commercial mode, and at rest corresponds to the zhi mode. It lasted for seven days. The law is five inches and nine tenths plus one minor fraction and two weak, and the standard is five feet and nine inches plus three thousand seven hundred and eighty-three.
Next is tranquility, with a value of one hundred and fourteen thousand nine hundred and forty. When the upper birth is bent, tranquility is the palace mode, the return phase represents the commercial mode, and the bent corresponds to the zhi mode. It lasted for six days. The law is five inches and eight tenths plus one minor fraction and four very weak, and the standard is five feet and eight inches plus seven thousand seven hundred and eighty-six.
After that is the return of Guijia, with a numerical value of 113,393. Shang Sheng is associated with Qi; Guijia should be in Gong tuning, Wei Mao is in Shang tuning, and Qi is in Zhi tuning. This lasted for six days. The tuning is 5.7 plus a small increment of 0.6, which is weak; the standard measurement is 5.7 plus 11,999.
Next is the matter of, with a numerical value of 111,867. Shang Sheng takes the form of Jin; the matter should be in Gong tuning, Yi Han is in Shang tuning, and Jin is in Zhi tuning. This lasted for five days. The tuning is 5.6 plus a small increment of 0.8, which is strong; the standard measurement is 5.6 plus 16,422.
Then is Yi Ze, with a numerical value of 115,092. Shang Sheng takes the form of Jia Zhong; Yi Ze should be in Gong tuning, Wu She (No Shooting) is in Shang tuning, and Jia Zhong is in Zhi tuning. This lasted for eight days. The tuning is 5.6 plus a small increment of 0.2, which is weak; the standard measurement is 5.6 plus 3,672.
Next is Jie Xing, with a numerical value of 109,103. Shang Sheng takes the form of Kai Shi; Jie Xing should be in Gong tuning, Bi Yan is in Shang tuning, and Kai Shi is in Zhi tuning. This lasted for eight days. The tuning is 5.5 plus a small increment of 0.4, which is strong; the standard measurement is 5.5 plus 8,465.
Finally, it is Go South, with a numerical value of 107,635. Shang Sheng takes the form of Zu Jia; Go South should be in Gong tuning, Lin Qi is in Shang tuning, and Zu Jia is in Zhi tuning. On the eighth day, the tuning is 5.4 plus a little bit, which is relatively long. The standard length is 5.4, with the specific value being 13,468. The calculated value is 106,187. The Shang Sheng's sound is Nan Yin; the Gong sound calculated from this value is Shang Yin, and the Zhi sound is Nan Yin.
On the seventh day, the tuning is 5.3 plus 0.5, which is quite long. The standard length is 5.3, with the specific value being 18,671. The value for Nan Lu is 104,976. Shang Sheng's sound is Gu Xi; Nan Lu serves as the Gong sound, the Shang sound is Zhong Yin, and the Zhi sound is Gu Xi.
On the first day, the tuning is 5.3 plus a little bit. The standard length is 5.3, with the specific value being 6,561. The value for Bai Lu is 104,756. Shang Sheng's sound is Nan Shou; Bai Lu serves as the Gong sound, the Shang sound is Wu Yin, and the Zhi sound is Nan Shou.
On the fifth day, the pitch length is five inches and three tenths, plus a tiny bit. The specific figure is 4361. The total accumulation is 103563. The upper tone is Bianyu, the total accumulation is Gongyin, the Shang note is Chiyin, and the Zheng note is Bianyu.
On the sixth day, the pitch length is five feet two inches, plus a tiny bit. The specific figure is 12114. The total accumulation is 102169. The upper tone is Lushi, the total accumulation is Gongyin, the Shang note is Weiyuyin, and the Zheng note is Lushi.
On the sixth day, the pitch length is five feet one inch, plus a tiny bit. The specific figure is 17857. The total accumulation is 10794. The upper tone is Xingshi, the total accumulation is Gongyin, the Shang note is Chishiyin, and the Zheng note is Xingshi.
On the sixth day, the pitch length is five feet one inch, plus a tiny bit. The specific figure is 4117. The total accumulation is 99437. The upper tone is Yixing, the total accumulation is Gongyin, the Shang note is Seyeuyin, and the Zheng note is Yixing.
On the seventh day, the pitch length is five feet, plus a tiny bit. The specific figure is 12220. The total accumulation is 9834. The upper tone is Zhonglv, the total accumulation is Gongyin, the Shang note is Zhishiyin, and the Zheng note is Zhonglv.
On the eighth day, the pitch length is four feet nine inches, plus a tiny bit. The specific figure is 18573. The total accumulation is 96980. The upper tone is Nanzhong, the total accumulation is Gongyin, the Shang note is Bingshengyin, and the Zheng note is Nanzhong.
On the eighth day, the pitch length is four feet nine inches, slightly shorter than the standard. The specific figure is 5333. The total accumulation is 95675.
Initially, it was referred to as "the upper birth is negative." The neighbor's house constructed a palace, with the Shang diao moving, the negative is the Zheng diao.
After seven days, the pitch length of the tube is four feet eight inches, plus a tiny bit. The standard length is four feet eight inches, eleven thousand nine hundred and sixty-six. The corresponding pitch frequency is ninety-four thousand three hundred and eighty-eight.
Next is "the upper birth of living beings is." This time, the Qibao is the Gong diao, the Zhimo is the Shang diao, and the living beings should be the Zheng diao.
After eight days, the pitch length of the tube is four feet seven inches, plus nine and a half tenths. The standard length is four feet seven inches, eighteen thousand seven hundred and seventy-nine. The corresponding pitch frequency is ninety-three thousand three hundred and twelve.
Then we have "Shangsheng Ruibin." Using Yingzhong as the gong scale, Dalü as the shang scale, and Ruibin as the zhi scale.
Only one day. The length of the tube is four inches and seven tenths, plus a little bit. The standard length is four feet seven inches, or eight thousand nineteen units. The corresponding pitch is 93,116.
Next is "Shangsheng Nanshi." Using Fenwu as the base, without the zhi mode, so it is not considered the gong scale.
After seven hundred days. The length of the tube is four inches and seven tenths, plus a little bit. The standard length is four feet seven inches, or six thousand fifty-nine units. The corresponding pitch is 92,056.
Next is "Shangsheng Shengbian." Using Chinei as the gong scale, Fenfou as the shang scale, and Shengbian as the zhi scale.
After eight days. The length of the tube is four inches and six tenths, slightly reduced. The standard length is four feet six inches, or ten thousand one hundred forty-two units. The corresponding pitch is 98,117.
Then we have "Shangsheng Ligong." Using Weiyu as the gong scale, Lingyin as the shang scale, and Ligong as the zhi scale.
After eight days. The length of the tube is four inches and six tenths, plus a little bit. The standard length is four feet six inches, or two thousand seven hundred fifty-two units. The corresponding pitch is 89,595.
Finally, we have "Shangsheng Zhishi." Using Chishi as the gong scale, Shaochu as the shang scale, and Zhishi as the zhi scale.
After six days. The length of the tube is four inches and five tenths, plus a little bit. The standard length is four feet five inches, or twelve thousand one hundred fifteen units.
The tube is crafted for sound testing, used to measure the vibrational frequency of objects; this is the fundamental principle of music. Musicians, because the sound of the tube is subtle and difficult to grasp, and the notes are not clear, use the standard length instead. The sound of the standard length is clear and easy to spread, and the size is relatively large. However, the pitch of string instruments is determined by the tension and thickness of the strings and cannot be corrected without a tube. Adjust the pitch of the string instrument to harmonize with the Huangzhong, and then calculate other musical tones based on the standard length; all musical tones align with the calculated results.
The sound is very subtle; only those who understand can comprehend it. In the year 806 AD, the official Yin Yong of the Hou Zhonglu submitted a memorial to the emperor, saying: "There is no one in the court who understands the sixty laws, so they cannot be used to calibrate the tones of musical instruments. Therefore, I request that Yan Xuan, the son of Yan Chong, be appointed to take charge of this matter. Yan Xuan has studied under his father and has mastered this knowledge. I hope to summon Yan Xuan and appoint him as a teacher to be in charge of calibrating the musical instruments." The emperor ordered: "Carefully examine whether Yan Chong's son truly understands the laws, can distinguish different tones and harmonize various musical sounds. He must not rely solely on his father's knowledge, pretending to understand while actually lacking comprehension. The sound is very subtle; not everyone can understand it, and it is not enough to understand it on one's own. He must be able to accurately distinguish the twelve pitches by playing the reed pipe before he can be considered to have inherited his father's knowledge." Then the Grand Historian Cheng Hong examined Yan Xuan's ability to distinguish the twelve pitches, and the result was that he only got two pitches right, four pitches wrong, and did not even know what the other six pitches were, so Yan Xuan was eliminated. Since then, there has been no way for those who understand the laws to calibrate the strings of musical instruments, and there has been no one in charge of musical laws. In the year 143 AD, the Dongguan summoned the Prince's attendants Zhang Guang and others in charge of the laws, inquiring about the specific methods of calibrating musical instruments. Zhang Guang and the others did not know either, so they had to return to consult ancient texts to find related instruments, which resembled the Fangshu (a type of musical instrument), but still could not ascertain the tension of the strings. The sound cannot be recorded in words for people to understand; those who understand wish to teach others but struggle to find a means to do so. Those who can experience it in their hearts do not need a teacher, thus, those historians capable of distinguishing between clear and muddled musical tones have vanished entirely. Those that have been passed down are only the constant values of Dage and the knowledge of Houqi.
It is said that the five sounds arise from the changes of yin and yang, then divided into twelve pitches, which then develop into sixty pitches, used to record solar term changes and reflect the laws of nature. The celestial phenomena and earthly sounds correspond to these pitches. When yin and yang are harmonized, the scenery becomes beautiful; when the pitches are in harmony, disasters are eliminated. Therefore, the emperor will gather eight talented individuals in the palace every winter solstice and summer solstice, set up the eight sounds, listen to music, measure the length of the sun's shadow, observe the rhythm of the bells, weigh the soil and charcoal, to observe the changes of yin and yang.
During the winter solstice, yang energy begins to grow, and the music sounds bright and clear; the sun's shadow is longest, the Huangzhong pitch resonates clearly, the soil and charcoal are light, and the balance tips upward. During the summer solstice, yin energy begins to grow, and the music sounds deep and murky; the sun's shadow is shortest, the Ruibin pitch resonates clearly, the soil and charcoal are heavy, and the balance tips downward. In the five days before and after, the eight talented individuals will report the observed situation to the emperor, and the court historian will record these reports. During the heavenly worship ceremony, if yin and yang are in harmony, everything will go smoothly; if not, divination must be conducted based on these observations.
The method for observing solar terms is as follows: first, construct a three-story house, sealing the doors and windows tightly, coating the walls and doors with mud, and hanging thick silk fabric to seal the house tightly. Place a wooden table inside the house, with wooden blocks representing the twelve pitches arranged on top, one for each pitch, with the inside lower than the outside, arranged according to the directions. Then place reed ash on each wooden block (a light grass and wood ash) to detect the energy. When the energy arrives, the ash will move; if the energy causes the ash to move, it will scatter; if it is moved by a person or the wind, it will gather together. During palace observations, twelve jade pitch pipes are used; only during the winter solstice and summer solstice, sixty bamboo pitch pipes are used to observe in the Lingtai, to track the sun's movement, much like a calendar.
In ancient times, when discussing numbers, it was said: "Things must be produced to have a shape, a shape must exist for growth to occur, and with growth comes quantity." Therefore, with the formation of heaven and earth, and the appearance of humans and all things, the act of calculation emerged. It is recorded in books that Da Rao (大桡) invented the method of recording days in cycles of sixty years, while Li Shou (隶首) established a method of counting. Once these two methods were established, they became tools for recording days and managing various affairs.
Look, everyone uses numbers such as one, ten, hundred, thousand, and ten thousand; while measurements such as length, volume, weight, and time each serve specific purposes. Use a ruler to measure length, a container to measure quantity, a scale to weigh items, musical intervals to harmonize sounds, and a calendar to record the movements of the sun, moon, and stars. This way, hidden aspects and subtle changes can be grasped.
After the establishment of the Han Dynasty, Marquis Zhang Cang of Beiping was the first to formulate musical scales and calendars. During the reign of Emperor Wu of Han, music was highly valued, and a Music Bureau was established to manage music. In the era of Wang Mang's Xin Dynasty, experts in musical scales were widely recruited to study the significance of these scales. The officials responsible for recording and submitting reports at that time were Xi He and Liu Xin, while the historian Ban Gu documented these events in his historical records.
During the reign of Emperor Huan of Han, there was an official named Jing Fang (styled Junming), who was especially knowledgeable about the five-note scale and the six pitches. The emperor instructed the Grand Preceptor of the Crown Prince, Wei Xuan Cheng (styled Shaoweng), and Adviser Zhang to question Jing Fang about music theory in the Imperial Music Bureau. Jing Fang replied, "I learned about music theory from a minor eunuch named Jiao Yanshou. The principles behind the generation of the sixty pitches are: the upper note produces the lower note, with a ratio of three to two; the lower note produces the upper note, with a ratio of three to four. The yang note produces the yin note downward, and the yin note produces the yang note upward, until reaching the central note, completing the twelve pitches. The central note produces the starting note upward, and the starting note produces the ending note downward, mutually generating, until reaching the southern note, completing the sixty pitches. The transition from the twelve pitches to the sixty pitches is akin to the transition from the eight trigrams to the sixty-four hexagrams. Fuxi created the I Ching, recording the beginning of yang energy and establishing music theory based on this. Taking the musical tones of the winter solstice as the standard: Huangzhong is designated as the tonic, Taicu as the supertonic, Guxi as the mediant, Linzhong as the subdominant, Nanlu as the dominant, Yingzhong as the submediant, and Ruibin as the subdominant. These are the foundations of music theory, which serve as the standards for the five tones, so each tone corresponds to a day. The other musical tones operate in sequence, with the tone corresponding to that day acting as the tonic, and the supertonic, mediant, and so on following suit. The Book of Rites says 'The five tones, six pitches, and twelve pipes are all related to the tonic,' which illustrates this principle. By using it to regulate various sounds and assess their pitches, aside from the sounds of plants, all other sounds can correspond to musical tones. The Book of Documents says 'Tune and harmonize,' which illustrates this principle."
Jing Fang also said: "Bamboo pipe sounds cannot be used to determine the pitch, so standardized instruments must be made to determine the numerical values of the pitches. This kind of instrument is shaped like a se instrument, one zhang long, with thirteen strings, each string being nine chi long, corresponding to the nine cun of the Huangzhong pitch; the middle string has markings in cun below it, used to indicate the clarity and turbidity of the sixty pitches." Jing Fang's discussion of pitch was more comprehensive than Liu Xin's report, and his method was adopted by historians and the Ministry of Rites and Ceremonies. Due to the extensive content, not all of it could be recorded, so only the main points were documented to supplement the deficiencies of the "History of the Former Han Dynasty."
In "The Art of Pitch," it is said that yang qi is like a circle, moving back and forth; yin qi is like a square, quiet and still. The number of movements for yang is three, while for yin it is two. To use yang to generate yin, multiply by two; to use yin to generate yang, multiply by four: finally, divide by three and then take one. The generation of yin by yang is called "descending birth," and the generation of yang by yin is called "ascending birth." Ascending birth cannot exceed the turbid sound of Huangzhong, and descending birth cannot fall below the clear and bright sound of Huangzhong. All of this follows the rules of the circular nature of heaven and the square nature of earth, the principle of yin and yang mutually generating each other, the principle of six yin matching one yang. Huangzhong is the foundation of the pitches, from which the other eleven pitches are generated. The rules governing their mutual generation involve adding or subtracting one-third. Therefore, the total numerical value of the twelve pitches equals 177,147, which is the actual numerical value of Huangzhong. Multiply this by two and then divide by three to obtain the numerical value of Linzhong derived from descending birth; multiply by four, then divide by three to get the numerical value of Taicu from ascending birth. By following this pattern, the numerical values of the sixty pitches can be determined. Multiply by nine, then by three, to get 19,683 as the calculation base. In pitch, it is cun; in tuning, it is chi. If it's not a whole number, multiply by ten to get fen; if still not a whole number, multiply by ten to get li. Use the remaining values to adjust the pitch strength.
Huangzhong, 177,147.
Descending birth of Linzhong. Huangzhong serves as the tonic, Taicu as the subdominant, and Linzhong as the mediant.
One day, the pitch is nine cun, the tuning is nine chi.
Color Huang, 176,776.
Descending birth of Qiandai. Color Huang serves as the tonic, Weizhi as the subdominant, and Qiandai as the mediant.
On the sixth day, the pitch is eight inches and nine minutes, strong in eight microns, and the standard is eight feet nine inches, fifteen thousand nine hundred and seventy-three. The initial value is one hundred seventy-four thousand seven hundred sixty-two. Birth, flourishing, decline. Starting from the palace, resting in the time of commerce, declining to the note.
On the sixth day, the pitch is eight inches and eight minutes, strong in seven microns, and the standard is eight feet eight inches, fifteen thousand five hundred and sixteen. Bing Sheng represents the palace, aligned with commerce, and stable in the note.
On the sixth day, the pitch is eight inches and seven minutes, weak in six microns, and the standard is eight feet seven inches, eleven thousand six hundred and seventy-nine. Division, one hundred seventy-eight thousand and eighty-nine. Birth, return to good. Division as the palace, following the commerce, returning to good in the note.
On the sixth day, the pitch is eight inches and six minutes, strong in four microns, and the standard is eight feet six inches, eight thousand one hundred and fifty-two. Quality conclusion, one hundred sixty-seven thousand eight hundred. Birth, disagreement. Quality conclusion as the palace, forming Jin in the commerce, disagreement in the note.
On the sixth day, the pitch measures eight inches and five minutes, plus a slight increment. The standard length is eight feet five inches, and the corresponding frequency is 4945 Hz. The frequency of Da Lu is 165888 Hz. Next is Yi Ze, where Da Lu serves as the palace tone, Jia Zhong as the commerce tone, and Yi Ze as the note tone.
On the eighth day, the pitch measures eight inches and four minutes, plus a slight increment. The standard length is eight feet four inches, and the corresponding frequency is 5580 Hz. The frequency of Fen Fou is 163654 Hz. Next is Jie Xing, where Fen Fou serves as the palace tone, Kai Shi as the commerce tone, and Jie Xing as the note tone.
On the eighth day, the pitch measures eight inches and three minutes, plus a slight increment. The standard length is eight feet three inches, and the corresponding frequency is 2851 Hz. The frequency of Ling Yin is 161452 Hz. Next is Qu Nan, where Ling Yin serves as the palace tone, Zu Jia as the commerce tone, and Qu Nan as the note tone.
On the eighth day, the pitch measures eight inches and two minutes, slightly reduced. The standard length is eight feet two inches, and the corresponding frequency is 514 Hz. The frequency of Shao Chu is 159280 Hz. Next is Fen Ji, where Shao Chu serves as the palace tone, Zheng Nan as the commerce tone, and Fen Ji as the note tone.
On the sixth day, the pitch measures eight inches, plus a slight increment. The standard length is eight feet, and the corresponding frequency is 18160 Hz. The frequency of Tai Cu is 157464 Hz. Finally, for Nan Lu, Tai Cu serves as the palace tone, Gu Xi as the commerce tone, and Nan Lu as the note tone.
On the first day, the tuning length is eight inches. The standard length is eight feet. The unknown frequency is 157134. Then comes Bai Lu, serving as the tonic, Nan Shou as the dominant, and Bai Lu as the mediant.
On the sixth day, the tuning length is seven inches and nine points, adding just a bit more. The standard length is seven feet and nine inches, with a frequency of 16383. The frequency of Shi Xi is 155344. Then comes Jie Gong, with Shi Xi as the tonic, Bian Yu as the dominant, and Jie Gong as the mediant.
On the sixth day, the tuning length is seven inches and eight points, adding a little more, but not quite as much. The standard length is seven feet and eight inches, with a frequency of 18166. The frequency of Qu Qi is 153253. Then comes Gui Qi, with Qu Qi as the tonic, Lu Shi as the dominant, and Gui Qi as the mediant.
On the sixth day, the tuning length is seven inches and seven points, just a tad less. The standard length is seven feet and seven inches, with a frequency of 16939. The frequency of Sui Qi is 151190. Then comes Wei Mao, with Sui Qi as the tonic, Xing Shi as the dominant, and Wei Mao as the mediant.
On the sixth day, the tuning length is seven inches and six points, adding just a bit more. The standard length is seven feet and six inches, with a frequency of 15992. The frequency of Xing Jin is 149156.
Let's talk about this musical tuning, starting with "Yi Han". This uses "Yi Han" as the tonic, "Xing Shang" as the dominant, and "Yi Han Zhi" as the mediant. This spans a total of six days. The tuning length is seven inches and five points, subdivided into eight weak parts; the standard length is seven feet and five inches, 15335; the Jia Zhong is 147456.
Next is "Wu She". It uses "Jia Zhong" as the tonic, "Zhong Lu" as the dominant, and "Wu She" as the mediant. This also spans six days. The tuning length is seven inches and four points, subdivided into nine strong parts; the standard length is seven feet and four inches, 18118; the Kai Shi is 145470.
Then comes "Bi Yan". "Kai Shi" is the tonic, "Nan Zhong" is the dominant, and "Bi Yan" is the mediant. This one spans eight days. The tuning length is seven inches and three points, subdivided into nine slightly stronger parts; the standard length is seven feet and three inches, 77841; the Zu Jia is 143513.
Now let's examine "Linqi". "Zuxi" is the palace, "Neifu" is the commerce, and "Linqi" is the note. It also spans eight days. The length of the pitch is seven inches two fen, with nine minor tones; the standard length is seven feet two inches, seventeen thousand nine hundred and fifty-four; the southern value is one hundred and forty-one thousand five hundred and eighty-two.
Next is "Qibao". "Competition in the south" is the palace, "Wuying" is the commerce, and "Qibao" is the note. This one also spans eight days. The length of the pitch is seven inches one fen, with nine strong tones; the standard length is seven feet one inch, eighteen thousand three hundred and twenty-seven; Guxi is one hundred and thirty-nine thousand nine hundred and sixty-eight.
Then it is "Yingzhong". "Guxi" is the palace, "Ruibin" is the commerce, and "Yingzhong" is the note. This time it lasts only one day. The length of the pitch is seven inches one fen, with one minor tone; the standard length is seven feet one inch, two thousand one hundred and eighty-seven; Nanshou is one hundred and thirty-nine thousand six hundred and seventy-four.
Take a look at "Fenwu". "Nanshou" is the palace, "Nanshi" is the commerce, and "Fenwu" is the note. This one spans six days. The length of the pitch is seven inches, with nine major tones; the standard length is seven feet, eighteen thousand nine hundred and thirty; Bianyu is one hundred and thirty-eight thousand eighty-four.
Next is "Chinei". "Bianyu" is the palace, "Shengbian" is the commerce, and "Chinei" is the note. It also spans six days. The length of the pitch is seven inches, with half a tone; the standard length is seven feet, three thousand thirty; Lushi is one hundred and thirty-six thousand two hundred and twenty-five.
Lastly, we have "Weiyu". "Lushi" is the palace, "Ligong" is the commerce, and "Weiyu" is the note. This one also spans six days. The length of the pitch is six inches nine fen, with two minor tones; the standard length is six feet nine inches, four thousand one hundred and twenty-three; Xingshi is one hundred and thirty-four thousand three hundred and ninety-two.
Finally, it is "Chishi". "Xingshi" is the palace, "Zhishi" is the commerce, and "Chishi" is the note.
This passage provides a detailed account of the palace, commerce, and note pitches of different music laws and their corresponding lengths, standard lengths, and some numerical values. The calculation methods and lengths of each music law are different.
On the fifth day, the length of the pitch is six inches eight fen, with a slight weakness of three fen; the standard sound length is six feet eight inches, with a frequency of five thousand four hundred and seventy-six. The calculation result is one hundred and thirty-two thousand five hundred and eighty-two. This time it is the essence of color, using the essence of color as the palace sound, approaching the commerce sound with humility, and using the essence of color as the note sound.
On the seventh day, the tuning pipe measures six inches and seven tenths, with a slight deviation of half a tenth; the standard pitch is six feet and seven inches, with a frequency of seven thousand fifty-nine. The calculated result for the Zhonglü pitch is 131,072. This event marks the beginning of Shangsheng, using Zhonglü as the tonic pitch, eliminating the Shang pitch, and Shizhi as the leading pitch.
On the eighth day, the tuning pipe measures six inches and six tenths, with a slight deviation of six tenths; the standard pitch is six feet and six inches, with a frequency of eleven thousand six hundred forty-two. The calculated result for the Nanzhong pitch is 129,308. This event represents the peak of Bingsheng, using Nanzhong as the tonic pitch, maintaining a steady approach to the Shang pitch, and Bingsheng as the leading pitch.
On the seventh day, the tuning pipe measures six inches and five tenths, with a slight deviation of seven tenths; the standard pitch is six feet and five inches, with a frequency of thirteen thousand six hundred eighty-five. The calculated result for the Neifu pitch is 127,567. This event signifies the movement of Fendong, using Neifu as the tonic pitch, obediently treating the Shang pitch, and Fendong as the leading pitch.
On the eighth day, the tuning pipe measures six inches and four tenths, with a slight deviation of eight tenths; the standard pitch is six feet and four inches, with a frequency of fifteen thousand nine hundred fifty-eight. The calculated result for the Wuying pitch is 125,850. This event signifies the end of Zhimo, using Wuying as the tonic pitch, rejecting the Shang pitch, and Zhimo as the leading pitch.
On the seventh day, the tuning pipe measures six inches and three tenths, with a slight deviation of nine tenths; the standard pitch is six feet and three inches, with a frequency of eighteen thousand four hundred seventy-one. The calculated result for the Ruibin pitch is 124,416. This event represents the Dalue of Shangsheng, using Ruibin as the tonic pitch, Yize as the Shang pitch, and Dalue as the leading pitch.
On the first day, the tuning pipe measures six inches and three tenths, with a slight deviation of two tenths; the standard pitch is six feet and three inches, with a frequency of four thousand one hundred thirty-one. The calculated result for the Nanshi pitch is 124,154. This event signifies that there is no Shangsheng; the Nanshi pitch is exhausted, with neither Shang nor leading pitch, so it cannot be used as the tonic pitch.
On the seventh day, the tuning pipe measures six inches and three tenths, with a slight deviation of one tenth; the standard pitch is six feet and three inches, with a frequency of one thousand five hundred eleven. The calculated result for the Shengbian pitch is 122,741. This event signifies the denial of Fenfou, using Shengbian as the tonic pitch, resolving the Shang pitch, and Fenfou as the leading pitch.
On the seventh day, the pipe measures six inches and two tenths, with the minor third being half a tenth strong; the standard pitch is six feet two inches, with a frequency of seven thousand sixty-four. The calculation result for the Liyuan mode is one hundred and twenty-one thousand eighty-nine. This refers to the Shangsheng Lingyin, using the Liyuan mode as the pitch, excluding the Shang pitch from the Southern mode, and using Lingyin as the Zhi pitch.
On the seventh day, the pipe measures six inches and one tenth, with the minor third being five tenths strong; the standard pitch is six feet one inch, with a frequency of twelve thousand two hundred twenty-seven.
Wow, these numbers are really dizzying! The first sentence says that this refers to something with a numerical value of one hundred and nineteen thousand four hundred and sixty.
Next, it says this is referred to as "Zhishi," its corresponding mode is "Zhishi," the Shang mode is "Fenji Shang," and the Zhi mode is "Shaochu Zhi." It lasted for eight days, with a pipe length of six inches, seven weak, and an accurate length of six feet three hundred and sixty.
Another thing called "Linzong," with a numerical value of one hundred and eighteen thousand nine hundred and ninety-eight. Its mode is "Linzong," the Shang mode is "Nanlu Shang," and the Zhi mode is "Tai Cu Zhi." This only lasted for one day, with a pipe length of six inches and an accurate length of six feet.
Then there is "Qiandai," with a numerical value of one hundred and seventeen thousand eight hundred and fifty-one. Its mode is "Qiandai," the Shang mode is "Bailu Shang," and the Zhi mode is "Weizhi Zhi." It lasted for five days, with a pipe length of five inches and nine tenths, nine weak in minor thirds, and an accurate length of five feet nine inches, seventeen thousand two hundred and thirteen.
Next up is "Qu Mie," with a numerical value of one hundred and sixteen thousand five hundred and eight. The mode is "Qu Mie," the Shang mode is "Jiegong Shang," and the Zhi mode is "Shixi Zhi." It lasted for seven days, with a pipe length of five inches and nine tenths, two weak in minor thirds, and an accurate length of five feet nine inches, three thousand seven hundred and eighty-three.
"An Du," with a numerical value of one hundred and fourteen thousand nine hundred and forty. The mode is "An Du," the Shang mode is "Guiqi Shang," and the Zhi mode is "Quqi Zhi." It lasted for six days, with a pipe length of five inches and eight tenths, four weak in minor thirds, and an accurate length of five feet eight inches, seven hundred and eighty-six.
"Gui Jia," the numerical value is one hundred thirteen thousand three hundred ninety-three. The palace tone is "Gui Jia," the commercial tone is "Wei Mao Commercial," and the zhi tone is "Sui Qi Zhi." Lasted for six days, the lu measures five inches and seven tenths, with a strength of six, and the standard measures five feet seven inches, specifically one thousand nine hundred ninety-nine.
"Fou Yu," the numerical value is one hundred eighteen thousand six hundred eighty-seven. The palace tone is "Fou Yu," the commercial tone is "Yi Han Commercial," and the zhi tone is "Xing Jin Zhi." Lasted for five days, the lu measures five inches and six tenths, with a strength of eight, and the standard measures five feet six inches, specifically one thousand six hundred twenty-two.
"Yi Ze," the numerical value is one hundred fifteen thousand nine hundred two. The palace tone is "Yi Ze," the commercial tone is "Wu She Commercial," and the zhi tone is "Jia Zhong Zhi." Lasted for eight days, the lu measures five inches and six tenths, with a strength of two, and the standard measures five feet six inches, specifically three thousand six hundred seventy-two.
Finally, "Jie Xing," the numerical value is one hundred thousand one hundred three. The palace tone is "Jie Xing," the commercial tone is "Bi Yan Commercial," and the zhi tone is "Kai Shi Zhi." Lasted for eight days, the lu measures five inches and five tenths, with a strength of four, and the standard measures five feet five inches, specifically eight thousand four hundred sixty-five.
The last one is "Qu Nan," the numerical value is one hundred seventy-six thousand three hundred thirty-five. The palace tone is "Qu Nan," the commercial tone is "Lin Qi Commercial," and the zhi tone is "Zu Jia Zhi." I feel like this string of numbers and names represents a record of some ancient musical scales, doesn't it?
On the eighth day, the lu measures five inches and four tenths, plus a little bit, counted as a strong sound. The standard measures five feet four inches, specifically five feet four inches, one thousand three hundred sixty-eight. The total area is one hundred sixty thousand one hundred eighty-seven. The upper string corresponds to the southern sound, using this area to calculate the palace tone; the commercial sound uses Qi Bao, which refers to a particular musical scale, and the zhi sound uses Zheng Nan.
On the seventh day, the lu measures five inches and three tenths, plus a little bit, counted as a strong sound. The standard measures five feet three inches, specifically five feet three inches, one thousand eight hundred seventy-one. The Nan Lyu area is one hundred four thousand nine hundred seventy-six. The upper string corresponds to Gu Xi. Nan Lyu serves as the palace tone, Ying Zhong represents the commercial tone, and Gu Xi corresponds to the zhi tone.
On the first day, the pitch length is five inches and three tenths, plus a little bit more, considered a strong sound. The standard length is five feet and three inches, specifically five feet three inches six thousand five hundred and sixty-one. The area of the white lü note is one hundred and four thousand seven hundred and fifty-six. The upper string corresponds to the south imparted. White lü is the tonic, divided wu is the subdominant, and the south imparted is the leading tone.
On the fifth day, the pitch length is five inches and three tenths, plus a little bit more, considered a strong sound. The standard length is five feet and three inches, specifically five feet three inches four thousand three hundred and sixty-one. The area of the binding note is one hundred and three thousand five hundred and sixty-three. The upper string corresponds to the changing yu. The binding is the tonic, the late inner is the subdominant, and the changing yu is the leading tone.
On the sixth day, the pitch length is five inches and two tenths, plus a little bit more, considered a strong sound. The standard length is five feet and two inches, specifically five feet two inches ten thousand two hundred and fourteen. The area of the return note is one hundred and two thousand one hundred and sixty-nine. The upper string corresponds to the road time. The return is the tonic, the unborn is the subdominant, and the road time is the leading tone.
On the sixth day, the pitch length is five inches and one tenth, plus a little bit more, considered a weak strong sound. The standard length is five feet and one inch, specifically five feet one inch seventeen thousand eight hundred and fifty-seven. The area of the unhatched note is one hundred and seventy-nine thousand four hundred. The upper string corresponds to the form beginning. The unhatched is the tonic, the late time is the subdominant, and the form beginning is the leading tone.
On the sixth day, the pitch length is five inches and one tenth, plus a little bit more, considered a weak strong sound. The standard length is five feet and one inch, specifically five feet one inch four thousand one hundred and seven. The area of the Yi Han note is ninety-nine thousand four hundred and thirty-seven. The upper string corresponds to the following line. The Yi Han is the tonic, the color is the subdominant, and the following line is the leading tone.
On the seventh day, the pitch length is five inches, plus a little bit more, considered a strong sound. The standard length is five feet, specifically five feet ten thousand and twenty. The area of the no-shoot note is ninety-eight thousand three hundred and four. The upper string corresponds to the middle lü. The no-shoot is the tonic, the beginning is the subdominant, and the middle lü is the leading tone.
On the eighth day, the pitch length is four inches and nine tenths, plus a little bit more, considered a strong sound. The standard length is four feet and nine inches, specifically four feet nine inches ten thousand eight hundred and fifty-seven. The area of the closed cover note is ninety-six thousand nine hundred and eighty. The upper string corresponds to the south middle. The closed cover is the tonic, the third is the subdominant, and the south middle is the leading tone.
On the eighth day, the length is four inches and nine tenths, plus a little bit more, considered as a weak sound. The standard length is four feet and nine inches, specifically four feet nine inches five thousand three hundred thirty-three. The area of the neighboring land is ninety-five thousand six hundred seventy-five.
At the beginning, it was "Shang Sheng Nei Fu." The neighbor built a palace, using the Shang Diao, and the internal Fu was the Zhi Diao. This took seven days. The tuning pipe measures four inches and eight tenths, plus a little more; the standard length is four feet and eight inches, eleven thousand nine hundred sixty-six. The final count was ninety-four thousand three hundred eighty-eight.
Next, it was "Shang Sheng Sheng Wu Ying." Using Qi Bao to make the Gong Diao, the Zhi Mo is the Shang Diao, and the Sheng Wu Ying is the Zhi Diao. This took eight days. The tuning pipe measures four inches and seven tenths, plus a little more than half; the standard length is four feet and seven inches, eighteen thousand seven hundred seventy-nine. The final count was ninety-three thousand three hundred twelve.
Then it was "Shang Sheng Rui Bin." Using Ying Zhong to make the Gong Diao, the Da Lu is the Shang Diao, and the Rui Bin is the Zhi Diao. This took seven days. The tuning pipe measures four inches and seven tenths, plus a little bit more; the standard length is four feet and seven inches, eight thousand nineteen. The final count was ninety-three thousand one hundred sixteen.
After that, it was "Shang Sheng Nan Shi." Using Fen Wu Qiong Ci, without Zhi Diao, so it was not used as the Gong Diao. This process took an astonishing seven hundred days. The tuning pipe measures four inches and seven tenths, plus a little bit more; the standard length is four feet and seven inches, six thousand fifty-nine. The final count was ninety-two thousand fifty-six.
Next was "Shang Sheng Sheng Bian." Using Chi Nei to make the Gong Diao, the Fen Fou is the Shang Diao, and the Sheng Bian is the Zhi Diao. This took eight days. The tuning pipe measures four inches and six tenths, slightly reduced; the standard length is four feet and six inches, fifteen thousand one hundred forty-two. The final count was ninety-eight thousand one hundred seventeen.
Then it was "Shang Sheng Li Gong." Using Wei Yu to make the Gong Diao, the Ling Yin is the Shang Diao, and the Li Gong is the Zhi Diao. This took eight days. The tuning pipe measures four inches and six tenths, plus a little bit more; the standard length is four feet and six inches, two thousand seven hundred fifty-two. The final count was eighty-nine thousand five hundred ninety-five.
Finally, it is "the establishment of the upper octave." Using late timing for the gong tone, a lesser output corresponds to the commercial tone, and making the timing is the zhi tone. This took six days. The length of the lu pipe is four inches and five tenths, and a tiny bit more; the length of the tuning string is four feet and five inches, totaling twelve thousand one hundred and fifteen. Cutting the tube into a lu, blowing to test the sound, and arranging to observe physical phenomena, this embodies the fundamental principles of music. However, because the sound of the lu pipe is delicate and hard to discern, and the divisions are rather broad, a tuning string is used as a substitute. The sound of the tuning string is clear and easy to understand, and the divisions are relatively coarse. However, the pitch of string instruments is determined by the tension of the strings, and without the lu pipe, it cannot be corrected. By tuning the strings to align with the Huangzhong (yellow bell), and then adjusting the other lu pipes according to the standard, every tone can be accurate. The sound is extremely subtle, and only those with expertise can truly grasp it. In the year 806 AD, the official Yin Yougong submitted a report to the emperor, saying: "Currently, there is no one in the court who truly understands the sixty lu, and they cannot be used to calibrate the tones of musical instruments. Therefore, I request that Yan Xuan, the son of Yan Chong, who has mastered this knowledge, be summoned for study. I hope you can summon Yan Xuan and appoint him as a teacher to be responsible for calibrating the tones of musical instruments." The emperor decreed: "Carefully assess whether Yan Chong's son genuinely comprehends the lu, whether he can distinguish different tones, and harmonize various sounds. He cannot rely solely on his father's teachings, nor can he pretend to understand. The sound is very subtle and not everyone can understand it; only those who truly understand can teach it, not just by rote memorization. He must play the lu pipe and accurately identify the twelve tones in order to truly inherit his father's knowledge."
Then, Cheng Hong came to test Yan Xuan's mastery of the twelve tones. As a result, he only answered two correctly, four were wrong, and he had no idea what the other six were. Therefore, Yan Xuan was eliminated. Since then, no one who understood the tones could calibrate the strings of musical instruments, and no one in the Department of Houzhong Tones understood them either. In the year 153 AD, the Dongguan court summoned officials knowledgeable about musical tones, including Zhang Guang, a court official and son of the crown prince, to inquire about the method of calibrating musical instruments. Zhang Guang and the others did not know, so they had to go back and consult old classics to find relevant instruments, which resembled those described in the Fang Shu, but they still could not determine the tightness of the strings. The musical tones could not be clearly expressed in words; those who understood wanted to teach but could not find a way, and those who understood in their hearts could experience it without needing a teacher, so those in historiography who could distinguish between clear and turbid tones disappeared completely. What has been passed down are only the principles of Daqu music and the knowledge of Houqi.
We all know that the five musical tones originate from the interplay of yin and yang, and further subdivided into twelve tones, which then give rise to sixty tones, all of which are used to record the changes of the solar terms and reflect the laws of all things. The celestial phenomena and earthly sounds are closely related to these tones. When yin and yang are harmonized, favorable phenomena emerge; when the tones and qi are in harmony, adverse effects are dispelled.
Therefore, every winter solstice and summer solstice, the emperor would summon eight experts in musical theory to the Imperial Palace, set up eight musical instruments, play music, observe the length of the sun's shadow, calibrate the tones of the bells, weigh the charcoal, and observe the changes of yin and yang. At the winter solstice, yang qi begins to grow, and the music played at this time is relatively clear and bright; the sun's shadow is longest, the Huangzhong tone is the most precise, the charcoal is lighter, and the balance scale tips upward. At the summer solstice, yin qi begins to grow, and the music played at this time is relatively low and turbid; the sun's shadow is shortest, the tone of the Ruibinlu is most accurate, the charcoal is heavier, and the balance scale tips downward.
During the five days before and after the winter solstice and summer solstice, these eight experts will observe and report daily, and the Court Astrologer will present these records to the emperor. If the yin and yang are harmonious during the ritual sacrifices to the heavens, all will be well; if not, divination will be carried out based on these observations.
The method of observing the weather is as follows: a sturdy three-layered room must be built, with doors and windows tightly shut and walls securely painted, and thick silk hung up. Inside the room, a wooden case is made, with each bamboo tube corresponding to a position, the case lower on the inside and higher on the outside, arranged according to the positions of the bamboo tubes. The bamboo tubes are placed in the case, with reed ash placed inside the bamboo tubes, and then the movement of the ash is observed. If the ash disperses, it suggests changes in the weather; if it gathers, it indicates movement caused by people or the wind.
In the palace, observations are conducted using twelve jade tubes; only during the winter solstice and summer solstice, sixty bamboo tubes are used at the spiritual platform for observation, with daily records kept according to the calendar.
