1
自夫有天地焉，有人物焉，樹司牧以君臨，懸政教而成務，莫不擬乾坤之大象，稟中和以建極，揆影響之幽賾，成律呂之精微。 是用範圍百度，財成萬品。 昔者淳古葦籥，創睹人籟之源，女媧笙簧，仍昭鳳律之首。 後聖廣業，稽古彌崇，伶倫含少，乃擅比竹之工，虞舜昭華，方傳刻玉之美。 是以《書》稱：「葉時月正日，同律度量衡。」 又曰：「予欲聞六律、五聲、八音、七始詠，以出納五言。」 此皆候金常而列管，憑璿璣以運鈞，統三極之元，紀七衡之響，可以作樂崇德，殷薦上帝。 故能動天地，感鬼神，和人心，移風俗，考得失，徵成敗者也。 粵在夏、商，無聞改作。 其于《周禮》，曲同則「掌六律六同之和，以辨天地四方陰陽之聲，以為樂器。」 景王鑄鐘，問律於泠州鳩，對曰：「夫律者，所以立鈞出度。」 鈞有五，則權衡規矩準繩鹹備。 故《詩》曰：「尹氏太師，執國之鈞，天子是裨，俾眾不迷」是也。 太史公《律書》云：「王者制事立物，法度軌則，一稟於六律，為萬事之本。 其于兵械，尤所重焉。 故云：'望敵知吉凶，聞聲效勝負。」 百王不易之道也。」
From the moment Heaven and Earth existed and humanity arose, every ruler who governed and every state that taught its people modeled itself on the cosmos, drew on cosmic balance to set standards, read nature's hidden signs, and perfected the science of pitch and measure. Thus they regulated all standards and shaped the ten thousand kinds of things. In deepest antiquity, reed flutes first disclosed the origin of human music; Nüwa's reed pipes still marked the first phoenix-toned pitch. Later sages enlarged the tradition and revered the past: Ling Lun's "Containing the Lesser" perfected the art of calibrated bamboo pipes; Yu Shun's Bright Splendor preserved the craft of jade pitch pipes. Hence the Documents states: "Align the seasons, months, and corrected day with unified pitch pipes, measures, and weights. It also says: "I desire to hear the six pitch standards, five tones, eight timbres, and seven beginnings sung, to produce and receive the five-word verses." These all depend on metal bells to set the pipes, on the armillary instrument to drive the steelyard, to unify the three cosmic poles and mark the seven celestial harmonies—making music to ennoble virtue and richly offering worship to Heaven. Music thus moves Heaven and Earth, stirs spirits, harmonizes hearts, changes customs, and reveals success or failure. Under Xia and Shang, no alterations to the system are recorded. The Rites of Zhou's section on pitch concordance says: "He oversees the harmony of the six pitch standards and six concordances, distinguishing the sounds of Heaven, Earth, the four directions, and yin and yang, for use in instruments. When King Jing of Zhou cast bells, he asked Leng Zhoujiu about pitch; the reply was: "Pitch standards establish the steelyard and derive all measures." With five parts to the steelyard, scales, weights, compasses, squares, plumb lines, and measuring cords all follow. As the Odes put it: "Grand Master Yin holds the nation's steelyard, assists the Son of Heaven, and keeps the people from losing their way." Sima Qian's Treatise on Pitch Standards states: "The king, in ordering affairs and setting standards, derives all laws and measures from the six pitch standards—the foundation of everything. They are held in particular esteem for military equipment. Hence the saying: "Look at the enemy and know fortune or misfortune; listen to sounds and foretell victory or defeat." This is the unchanging principle of all dynasties. End of quotation.
2
及秦氏滅學，其道浸微。 漢室初興，丞相張蒼，首言音律，未能審備。 孝武帝創置協律之官，司馬遷言律呂相生之次詳矣。 及王莽之際，考論音律，劉歆條奏，班固因志之。 蔡邕又記建武以後言律呂者，司馬紹統采而續之。 炎曆將終，而天下大亂，樂工散亡，器法湮滅。 魏武始獲杜夔，使定音律，夔依當時尺度，權備典章。 及晉武受命，遵而不革。 至泰始十年，光祿大夫荀勖，奏造新度，更鑄律呂。 元康中，勖子籓複嗣其事。 未及成功，屬永嘉之亂，中朝典章，咸沒于石勒。 及帝南遷，皇度草昧，禮容樂器，掃地皆盡。 雖稍加采掇，而多所淪胥，終於恭、安，竟不能備。 宋錢樂之衍京房六十律，更增為三百六十，梁博士沈重，述其名數。 後魏、周、齊，時有論者。 今依班志，編錄五代聲律度量，以志於篇雲。
After Qin suppressed scholarship, the tradition faded. At Han's founding, Chancellor Zhang Cang first addressed pitch standards but could not complete a thorough review. Emperor Wu created the office of pitch harmonizer; Sima Qian gave a full account of how pitch pipes and bell tones generate one another. Under Wang Mang, pitch standards were re-examined; Liu Xin submitted a detailed report, which Ban Gu incorporated into his Treatise. Cai Yong recorded post-Jianwu discussions of pitch and bell tones; Sima Shao collected and continued them. When Han neared collapse, the empire descended into chaos; musicians fled, and instruments and methods vanished. Wei's Cao Cao first acquired Du Kui and charged him with fixing pitch standards, using contemporary measures to restore the canonical system as best he could. Jin's Emperor Wu kept the system unchanged. In Taishi 10, Palace Attendant Xun Xu proposed new standard measures and a recasting of the pitch pipes. During Yuankang, Xu's son Fan took up the work again. Before the project finished, the Yongjia upheaval struck; the central court's standards were lost to Shi Le. After the court fled south, institutions were still primitive; ritual and musical equipment were utterly destroyed. Some materials were recovered, but much was lost forever; through the Gong and An reigns, the system remained incomplete. Song's Qian Yuezhi expanded Jing Fang's sixty pitch standards to three hundred sixty; Liang scholar Shen Chong recorded their names and values. Northern Wei, Northern Zhou, and Northern Qi all produced their own theorists. Following Ban Gu's Treatise, this chapter records the pitch standards, measures, and weights of five dynasties.
3
《漢志》言律，一曰備數，二曰和聲，三曰審度，四曰嘉量，五曰衡權。 自魏、晉已降，代有沿革。 今列其增損之要雲。 備數五數者，一、十、百、千、萬也。 《傳》曰：「物生而後有象，滋而後有數。」 是以言律者，雲數起於建子，黃鐘之律，始一，而每辰三之，曆九辰至酉，得一萬九千六百八十三，而五數備成，以為律法。 又參之，終亥，凡曆十二辰，得十有七萬七千一百四十七，而辰數該矣，以為律積。 以成法除該積，得九寸，即黃鐘宮律之長也。 此則數因律起，律以數成，故可曆管萬事，綜核氣象。 其算用竹，廣二分，長三寸，正策三廉，積二百一十六枚，成六觚，乾之策也。 負策四廉，積一百四十四枚，成方，坤之策也。 觚方皆經十二，天地之大數也。 是故探賾索隱，鉤深致遠，莫不用焉。 一、十、百、千、萬，所同由也。 律、度、量、衡、曆、率，其別用也。 故體有長短，檢之以度，則不失毫釐； 物有多少，受之以器，則不失圭撮； 量有輕重，平之以權衡，則不失黍絲； 聲有清濁，協之以律呂，則不失宮商； 三光運行，紀以歷數，則不差晷刻； 事物糅見，禦之以率，則不乖其本。 故幽隱之情，精微之變，可得而綜也。
The Han Treatise lists five aspects of pitch standards: complete numbers, harmonizing sounds, examining measures, commended capacity, and steelyard weights. From Wei and Jin onward, each dynasty revised the system. The key changes are summarized here. The five complete numbers are one, ten, hundred, thousand, and ten thousand. The Commentary states: "Things first exist, then images form; as they proliferate, numbers emerge. Pitch theorists hold that counting begins at the jianzi month: the Yellow Bell pitch starts at one, triples each two-hour period, and after nine periods reaches 19,683—completing the five numbers and forming the pitch law. Continuing through all twelve periods to hai yields 177,147—the full period accumulation. Dividing that accumulation by the completed law gives nine inches—the length of the Yellow Bell palace pipe. Numbers derive from pitch, and pitch is fixed by numbers—so they can regulate all affairs and verify cosmic patterns. Counting rods are bamboo strips two fen wide and three cun long; positive rods with three edges, 216 in all, form a hexagonal prism—the Qian rods. Negative rods with four edges, 144 in all, form a square—the Kun rods. Hexagon and square both use twelve as their measure—the great numbers of Heaven and Earth. In probing mysteries and reaching into the profound, nothing is done without them. One through ten thousand are the shared foundation. Pitch, length, capacity, weight, calendar, and proportional calculation are the separate applications. Bodies vary in length; measured by the ruler, not a hair's breadth is missed; quantities vary in amount; held in vessels, not a grain or spoonful is lost; mass varies in weight; balanced on scales, not a millet seed or silk thread is missed; sounds vary in pitch; harmonized by pitch pipes, not a note of gong or shang is missed; the sun, moon, and stars move; tracked by calendrical reckoning, not a moment is missed; complex mixed quantities are handled by proportional calculation without losing their basis. Hidden truths and subtle changes can thus be fully comprehended.
4
夫所謂率者，有九流焉：一曰方田，以禦田疇界域。 二曰栗米，以禦交質變易。 三曰衰分，以禦貴賤廩稅。 四曰少廣，以禦積冪方圓。 五曰商功，以禦功程積實。 六曰均輸，以禦遠近勞費。 七曰盈肭，以禦隱雜互見。 八曰方程，以禦錯糅正負。 九曰句股，以禦高深廣遠。 皆乘以散之，除以聚之，齊同以通之，今有以貫之。 則算數之方，盡於斯矣。
Proportional calculation has nine branches: first, rectangular fields, for land boundaries and areas. Second, millet and rice, for commodity exchange and conversion. Third, proportional distribution, for rank-based grain levies and taxes. Fourth, lesser breadth, for volumes and areas of squares and circles. Fifth, construction works, for engineering projects and solid volumes. Sixth, fair transportation, for labor and cost over varying distances. Seventh, excess and deficit, for hidden quantities appearing in mixed problems. Eighth, rectangular arrays, for systems of positive and negative quantities. Ninth, right triangles and legs, for height, depth, width, and distance. All are multiplied to expand, divided to consolidate, equalized to connect, and unified by the present quantity. The full scope of calculation is contained in these.
5
古之九數，圓周率三，圓徑率一，其術疏舛。 自劉歆、張衡、劉徽、王蕃、皮延宗之徒，各設新率，未臻折衷。 宋末，南徐州從事史祖沖之，更開密法，以圓徑一億為一丈，圓周盈數三丈一尺四寸一分五厘九毫二秒七忽，朒數三丈一尺四寸一分五厘九毫二秒六忽，正數在盈朒二限之間。 密率，圓徑一百一十三，圓周三百五十五。 約率，圓徑七，週二十二。 又設開差冪，開差立，兼以正圓參之。 指要精密，算氏之最者也。 所著之書，名為《綴術》，學官莫能究其深奧，是故廢而不理。
The ancient Nine Chapters used a circumference-to-diameter ratio of three to one—a crude approximation. Liu Xin, Zhang Heng, Liu Hui, Wang Fan, Pi Yanzong, and others each proposed new ratios, but none achieved a definitive value. Late in Song, Zu Chongzhi of Southern Xuzhou developed a precise method: with a diameter of one hundred million as one zhang, the excess circumference was 3.1415927 zhang and the deficit 3.1415926 zhang—the true value falling between. Zu's precise ratio was 113 to 355 for diameter and circumference. His rough ratio was 7 to 22. He also devised root extraction for differences and powers, cross-checked against regular circles. His methods were precise and subtle—the finest achievement in mathematics. His book, the Method of Interpolation, was too profound for the academicians to master, and it fell into neglect.
6
○和聲
○ On Harmonizing Sounds
7
傳稱黃帝命伶倫斷竹，長三寸九分，而吹以為黃鐘之宮，曰含少。 次制十二管，以聽鳳鳴，以別十二律，此雌雄之聲，以分律呂。 上下相生，因黃鐘為始。 《虞書》云：「葉時月正日，同律度量衡。」 夏禹受命，以聲為律，以身為度。 《周禮》，樂器以十二律為之度數。 司馬遷《律書》云：「黃鐘長八寸七分之一，太簇長七寸七分二，林鐘長五寸七分三，應鐘長四寸三分二。」 此樂之三始，十二律之本末也。 班固、司馬彪《律志》：「黃鐘長九寸，聲最濁； 太簇長八寸； 林鐘長六寸； 應鐘長四寸七分四厘強，聲最清。」 鄭玄《禮·月令注》、蔡邕《月令章句》及杜夔、荀勖等所論，雖尺有增損，而十二律之寸數並同。 《漢志》京房又以隔八相生，一始自黃鐘，終於中呂，十二律畢矣。 中呂上生黃鐘，不滿九寸，謂之執始，下生去滅。 上下相生，終於南事，更增四十八律，以為六十。 其依行在辰，上生包育，隔九編於冬至之後。 分焉、遲內，其數遂減應鐘之清。 宋元嘉中，太史錢樂之因京房南事之餘，引而伸之，更為三百律，終於安運，長四寸四分有奇。 總合舊為三百六十律。 日當一管，宮徵旋韻，各以次從。 何承天《立法制議》云：「上下相生，三分損益其一，蓋是古人簡易之法。 猶如古曆周天三百六十五度四分之一，後人改制，皆不同焉。 而京房不悟，謬為六十。」 承天更設新率，則從中呂還得黃鐘，十二旋宮，聲韻無失。 黃鐘長九寸，太簇長八寸二厘，林鐘長六寸一厘，應鐘長四寸七分九厘強。 其中呂上生所益之分，還得十七萬七千一百四十七，複十二辰參之數。
Tradition holds that the Yellow Emperor ordered Ling Lun to cut a bamboo tube three cun nine fen long and blow it to produce the Yellow Bell palace pitch, called "Containing the Lesser." He then made twelve pipes to listen for the phoenix's call, distinguishing the twelve pitch standards—the male and female tones that divide the pitch pipes. Upward and downward generation begins from Yellow Bell. The Book of Yu states: "Align the seasons, months, and corrected day with unified pitch pipes, measures, and weights. When Yu of Xia received the Mandate, he used sound for pitch and his body for measure. The Rites of Zhou specifies that instruments are sized by the twelve pitch standards. Sima Qian's Treatise gives: Yellow Bell eight cun and one-seventh; Great Cluster seven cun and seven-sevenths and two; Forest Bell five cun and seven-sevenths and three; Responding Bell four cun and three-sevenths and two. These are the three origins of music and the foundation of the twelve pitch standards. Ban Gu and Sima Biao's Treatise: "Yellow Bell is nine cun long, the lowest pitch; Great Cluster measures eight cun; Forest Bell measures six cun; Responding Bell is four cun seven fen four li and a fraction, the highest pitch. Zheng Xuan, Cai Yong, Du Kui, and Xun Xu debated the measures, but all agreed on the cun lengths of the twelve pitch standards. The Han Treatise adds: Jing Fang used generation across eight steps—from Yellow Bell through Middle Bell Female, completing the twelve standards. Middle Bell Female generates Yellow Bell upward but falls short of nine cun—called "Holding the Beginning"; downward generation subtracts the remainder. Upward and downward generation, ending at Southern Affair, added forty-eight standards to make sixty. Those generating from the chen period produce Bao Yu upward, nine steps after the winter solstice. Fen Yan and Chi Nei reduce the clarity of Responding Bell. In Liu Song's Yuanjia era, Grand Astrologer Qian Yuezhi extended Jing Fang's Southern Affair to three hundred pitch standards, ending at An Yun at four cun four fen and a fraction. Combined with the earlier standards, the total reached three hundred sixty pitch pipes. One pipe per day; palace and zhi modes cycled in sequence. He Chengtian's Discourse on Establishing Laws states: "Upward and downward generation by adding or subtracting one-third was the ancients' simple method. Like the ancient calendar's 365¼-day year—later reformers all produced different values. Jing Fang failed to grasp this and wrongly devised sixty pitch standards. He Chengtian's new ratio returns from Middle Bell Female to Yellow Bell; the twelve rotating modes preserve pitch without error. Yellow Bell nine cun; Great Cluster eight cun two li; Forest Bell six cun one li; Responding Bell four cun seven fen nine li and a fraction. The increment from Middle Bell Female's upward generation again yields 177,147—the full twelve-period product.
8
梁初，因晉、宋及齊，無所改制。 其後武帝作《鐘律緯》，論前代得失。 其略云：
Early Liang retained the systems of Jin, Song, and Qi without change. Later Emperor Wu of Liang wrote the Treatise on Bell Standards and Pitch Pipes, reviewing earlier successes and failures. In summary:
9
案律呂，京、馬、鄭、蔡，至蕤賓，並上生大呂； 而班固《律曆志》，至蕤賓，仍以次下生。 若從班義，夾鐘唯長三寸七分有奇。 律若過促，則夾鐘之聲成一調，中呂複去調半，是過於無調。 仲春孟夏，正相長養，其氣舒緩，不容短促。 求聲索實，班義為乖。 鄭玄又以陰陽六位，次第相生。 若如玄義，陰陽相逐生者，止是升陽，其降陽複將何寄？ 就筮數而論，乾主甲壬而左行，坤主乙癸而右行，故陰陽得有升降之義。 陰陽從行者，真性也，六位升降者，象數也。 今鄭乃執象數以配真性，故言比而理窮。 雲九六相生，了不釋十二氣所以相通，鄭之不思，亦已明矣。
On pitch pipes: Jing Fang, Ma Rong, Zheng Xuan, and Cai Yong all generate Great Bell upward through Luxuriant Guest; Ban Gu's Treatise, however, generates downward in sequence through Luxuriant Guest. Following Ban's view, Pinched Bell would measure only three cun seven fen and a fraction. Overly short pipes make Pinched Bell a single mode and Middle Bell Female lose half a mode—leaving the system without proper tuning. Mid-spring and early summer nurture growth; the qi flows gently and cannot be compressed into overly short pipes. Measured against acoustic reality, Ban's interpretation fails. Zheng Xuan also arranged generation by the six yin-yang positions in sequence. On Zheng's view, mutual yin-yang generation accounts only for ascending yang—leaving nowhere for descending yang. In divination terms, Qian governs jia and ren moving left, Kun governs yi and gui moving right—giving yin and yang their ascending and descending roles. Yin-yang in motion is true nature; the six positions rising and falling are symbolic numbers. Zheng forced symbolic numbers onto true nature—his analogy collapses under scrutiny. His talk of nine and six generating each other never explains how the twelve qi connect—Zheng simply did not think it through.
10
案京房六十，准依法推，乃自無差。 但律呂所得，或五或六，此一不例也。 而分焉上生，乃複遲內上生盛變，盛變仍複上生分居，此二不例也。 房妙盡陰陽，其當有以，若非深理難求，便是傳者不習。
Jing Fang's sixty standards, properly calculated, are internally consistent. Yet the resulting pitch values are sometimes five, sometimes six—the first irregularity. Fen Yan generates upward, then Chi Nei generates Sheng Bian, which generates Fen Ju—this is the second irregularity. Fang mastered yin-yang theory; either the deep principle is elusive or later transmitters did not understand his method.
11
比敕詳求，莫能辨正。 聊以餘日，試推其旨，參校舊器，及古夾鐘玉律，更制新尺，以證分毫，制為四器，名之為通。 四器弦間九尺，臨岳高一寸二分。 黃鐘之弦二百七十絲，長九尺，以次三分損益其一，以生十二律之弦絲數及弦長。 各以律本所建之月，五行生王，終始之音，相次之理，為其名義，名之為通。 通施三弦，傳推月氣，悉無差舛。 即以夾鐘玉律命之，則還相中。
An imperial order demanded clarification, but no one could resolve the discrepancies. In spare time I deduced the theory, compared old instruments with the ancient Pinched Bell jade pipe, made a new ruler to verify measurements, and created four instruments called the Tong. The four instruments span nine chi between strings, with bridge height of one cun two fen. The Yellow Bell string uses 270 silk threads nine chi long; tripling or dividing by three in sequence yields the twelve pitch strings. Each was named by the month of its pitch root, the five phases' waxing and waning, and the logic of successive tones—the Tong instruments. Applied to three strings, the monthly qi calculations matched without error. Tuned against the Pinched Bell jade pipe, they matched perfectly.
12
又制為十二笛，以寫通聲。 其夾鐘笛十二調，以飲玉律，又不差異。 山謙之《記》云：「殿前三鐘，悉是周景王所鑄無射也。」 遣樂官以今無射新笛飲，不相中。 以夷則笛飲，則聲韻合和。 端門外鐘，亦案其銘題，定皆夷則。 其西廂一鐘，天監中移度東。 以今笛飲，乃中南呂。 驗其鐫刻，乃是太簇，則下今笛二調。 重敕太樂丞斯宣達，令更推校，鐘定有鑿處，表裡皆然。 借訪舊識，乃是宋泰始中，使張永鑿之，去銅既多，故其調嘽下。 以推求鐘律，便可得而見也。 宋武平中原，使將軍陳傾致三鐘，小大中各一。 則今之太極殿前二鐘，端門外一鐘是也。 案西鐘銘則雲「清廟撞鐘」，秦無清廟，此周制明矣。 又一銘雲「太簇鐘徵」，則林鐘宮所施也。 京房推用，似有由也。 檢題既無秦、漢年代，直雲夷則、太簇，則非秦、漢明矣。 古人性質，故作僮僕字，則題而言，彌驗非近。 且夫驗聲改政，則五音六律，非可差舛。 工守其音，儒執其文，歷年永久，隔而不通。 無論樂奏，求之多缺，假使具存，亦不可用。 周頌漢歌，各敘功德，豈容複施後王，以濫名實？ 今率詳論，以言所見，並詔百司，以求厥中。
Twelve flutes were also made to replicate the Tong sounds. The Pinched Bell flute's twelve modes matched the jade pitch standard without deviation. Shan Qianzhi's Record states: "The three hall bells are all Pitchless bells cast by King Jing of Zhou. Musicians tested them with the current Pitchless flute—they did not match. With the Luxuriant Guest flute, the tones harmonized. The bell outside the Duan Gate, its inscription confirms it as Luxuriant Guest. One west-wing bell was moved east in the Tianjian era. Tested with the current flute, it matched Southern Bell Female. Its inscription reads Great Cluster—two modes lower than the current flute. Si Xuanda was ordered to re-examine the bell; chisel marks at the tuning point appeared on both sides. Old records show Zhang Yong chiseled it in Song's Taishi era, removing so much copper that its pitch dropped. Thus investigating bell and pitch standards reveals the truth. When Liu Song's Emperor Wu pacified the north, General Chen Qing delivered three bells—small, medium, and large. These are the two Supreme Ultimate Hall bells and the Duan Gate bell of today. The west bell's inscription reads "Pure Temple Strike Bell"; Qin had no Pure Temple—clearly a Zhou bell. Another reads "Great Cluster Bell Zhi"—used in Forest Bell palace mode. Jing Fang's method appears to have sound reasoning. The inscriptions bear no Qin or Han dates, only Luxuriant Guest and Great Cluster—not Qin or Han work. Ancient craftsmen used servant-boy script in inscriptions—confirming these are not recent pieces. Sound must be verified to govern properly—the five notes and six standards cannot be mistaken. Craftsmen preserved the sounds while scholars held the texts—over centuries they lost contact. Musical performance itself is largely lost; even if texts survived intact, they could not be applied. Zhou hymns and Han songs celebrate specific achievements—how could they be reused for later rulers? I now present my findings and order the hundred offices to seek the balanced standard.
13
未及改制，遇侯景亂。 陳氏制度，亦無改作。
Reform was interrupted by the Hou Jing rebellion. Chen made no reforms either.
14
西魏廢帝元年，周文攝政。 又詔尚書蘇綽詳正音律。 綽時得宋尺，以定諸管，草創未就會閔帝受禪，政由塚宰，方有齊寇，事竟不行。 後掘太倉，得古玉鬥，按以造律及衡，其事又多湮沒。
In Western Wei's first year of the Deposed Emperor, Yuwen Tai held regency. An edict ordered Minister Su Chuo to examine and correct pitch standards. Su Chuo obtained a Song foot measure to calibrate the pipes, but the project was unfinished when Emperor Min ascended; with Qi invading, the work never proceeded. Later an ancient jade dipper was found in the Grand Granary; used to make pitch pipes and weights, but much was again lost.
15
至開皇初，詔太常牛弘議定律呂。 於是博征學者，序論其法，又未能決。 遇平江右，得陳氏律管十有二枚，並以付弘。 遣曉音律者陳山陽太守毛爽及太樂令蔡子元、於普明等，以候節氣，作《律譜》。 時爽年老，以白衣見高祖，授淮州刺史，辭不赴官。 因遣協律郎祖孝孫就其受法。 弘又取此管，吹而定聲。 既天下一統，異代器物，皆集樂府，曉音律者，頗議考核，以定鐘律。 更造樂器，以被《皇夏》十四曲，高祖與朝賢聽之，曰：「此聲滔滔和雅，令人舒緩。」
At Kaihuang's opening, Grand Master Niu Hong was ordered to fix pitch and bell standards. Scholars were summoned to debate the method, but no consensus emerged. After pacifying the south, twelve Chen pitch pipes were delivered to Niu Hong. Pitch experts including Mao Shuang of Shanyang and Grand Music Director Cai Ziyuan were sent to observe seasonal nodes and write the Treatise on Pitch Standards. Mao Shuang, though elderly, was received by Emperor Wen as a commoner and offered Huai Province; he declined. Pitch-Harmonizing Official Zu Xiaosun was sent to learn the method from him. Niu Hong also used these pipes to establish the pitch. With unification, instruments from all eras gathered at the Music Office; pitch experts debated to fix bell and pitch standards. New instruments accompanied the fourteen "August Sovereign" movements; Emperor Wen listened with his court and said: "This music flows harmoniously and puts one at ease. End of quotation.
16
然萬物人事，非五行不生，非五行不成，非五行不滅。 故五音用火尺，其事火重。 用金尺則兵，用木尺則喪，用土尺則亂，用水尺則律呂合調，天下和平。 魏及周、齊，貪布帛長度，故用土尺。 今此樂聲，是用水尺。 江東尺短於土，長於水。 俗間不知者，見玉作，名為玉尺，見鐵作，名為鐵尺。 詔施用水尺律樂，其前代金石，並鑄毀之，以息物議。
All things and human affairs depend on the five phases for birth, completion, and extinction. The five notes therefore use the fire foot measure—fire being the dominant element. The metal measure brings war, wood brings mourning, earth brings disorder—but the water measure harmonizes pitch and brings peace. Wei, Zhou, and Qi, seeking longer cloth measures, used the earth foot measure. The current music uses the water foot measure. The Jiangdong measure is shorter than the earth measure but longer than the water measure. Common people, seeing jade instruments call them jade measures, seeing iron ones call them iron measures. An edict mandated water-measure pitch music; older metal and stone instruments were recast to silence debate.
17
至仁壽四年，劉焯上啟於東宮，論張胄玄曆，兼論律呂。 其大旨曰：「樂主於音，音定於律，音不以律，不可克諧，度律均鐘，於是乎在。 但律終小呂，數複黃鐘，舊計未精，終不復始。 故漢代京房，妄為六十，而宋代錢樂之更為三百六十。 考禮詮次，豈有得然，化未移風，將恐由此。 匪直長短失於其差，亦自管圍乖於其數。 又尺寸意定，莫能詳考，既亂管弦，亦舛度量。 焯皆校定，庶有明發。」 其黃鐘管六十三為實，以次每律減三分，以七為寸法。 約之，得黃鐘長九寸，太簇長八寸一分四厘，林鐘長六寸，應鐘長四寸二分八厘七分之四。 其年，高祖崩，煬帝初登，未遑改作，事遂寢廢。 其書亦亡。 大業二年，乃詔改用梁表律調鐘磬八音之器，比之前代，最為合古。 其制度文議，並毛爽舊律，並在江都淪喪。
In Renshou 4, Liu Zhuo memorialized the crown prince on Zhang Zhouxuan's calendar and pitch standards. His main argument: "Music depends on notes, notes on pitch standards—without standards, harmony is impossible; balancing standards and bells is essential. Standards end at Lesser Bell and return to Yellow Bell, but old calculations were imprecise and never truly cycled back. Hence Han's Jing Fang arbitrarily devised sixty standards, and Song's Qian Yuezhi three hundred sixty. Examined against ritual order, this is untenable—and customs may suffer accordingly. Not only are lengths wrong—the pipe bore circumferences are also incorrect. The intended dimensions cannot be verified in detail; strings, pipes, and all measures are confused. Liu Zhuo corrected all of these, seeking clarity. His Yellow Bell pipe used 63 as the base; each subsequent standard subtracted three parts, with seven as the cun divisor. This yielded Yellow Bell nine cun, Great Cluster eight cun one fen four li, Forest Bell six cun, Responding Bell four cun two fen eight li and seven-fourths. That year Emperor Wen died; Emperor Yang had no time for reform and the project lapsed. His treatise was lost as well. Daye 2 ordered adoption of Liang's external pitch standard for bells, chimes, and the eight timbres—the most antiquity-conforming system yet. The institutional records and Mao Shuang's old standards were all lost at Jiangdu.
18
○律管圍容黍
○ On Pipe Bore Circumference and Millet Capacity
19
《漢志》云：「黃鐘圍九分，林鐘圍六分，太簇圍八分。」 《續志》及鄭玄並云：「十二律空，皆徑三分，圍九分。」 後魏安豐王依班固《志》，林鐘空圍六分，及太簇空圍八分，作律吹之，不合黃鐘商徵之聲。 皆空圍九分，乃與均鐘器合。 開皇九年平陳後，牛弘、辛彥之、鄭譯、何妥等，參考古律度，各依時代，制其黃鐘之管，俱徑三分，長九寸。 度有損益，故聲有高下； 圓徑長短，與度而差，故容黍不同。 今列其數雲。
The Han Treatise gives: Yellow Bell bore nine fen, Forest Bell six fen, Great Cluster eight fen. The Continuation Treatise and Zheng Xuan both state: all twelve pipes have diameter three fen, circumference nine fen. Northern Wei's Prince of Anfeng, following Ban Gu, made Forest Bell six fen and Great Cluster eight fen bore—but they failed to produce Yellow Bell's shang and zhi tones. Only nine-fen bore circumferences matched the balanced bell instrument. After pacifying Chen in Kaihuang 9, Niu Hong, Xin Yanzhi, Zheng Yi, and He Tuo made Yellow Bell pipes of each era—all three fen diameter, nine cun long. Measure variations produced pitch differences; bore size and length varied with the measure, so millet capacity differed. Their values are listed below.
20
晉前尺黃鐘容黍八百八粒。
Pre-Jin measure: Yellow Bell bore held 808 millet grains.
21
梁法尺黃鐘容八百二十八。
Liang legal measure: Yellow Bell held 828 grains.
22
梁表尺黃鐘三：其一容九百二十五，其一容九百一十，其一容一千一百二十。
Liang shadow-table measure had three Yellow Bell pipes: holding 925, 910, and 1,120 grains respectively.
23
漢官尺黃鐘容九百三十九。
Han official measure: Yellow Bell held 939 grains.
24
古銀錯題黃鐘籥容一千二百。
Ancient silver-inscribed Yellow Bell key held 1,200 grains.
25
宋氏尺，即鐵尺，黃鐘凡二：其一容一千二百，其一容一千四十七。
Song iron measure had two Yellow Bell pipes: one holding 1,200, one 1,047 grains.
26
後魏前尺黃鐘容一千一百一十五。
Northern Wei early measure: Yellow Bell held 1,115 grains.
27
後周玉尺黃鐘容一千二百六十七。
Northern Zhou jade measure: Yellow Bell held 1,267 grains.
28
後魏中尺黃鐘容一千五百五十五。
Northern Wei middle measure: Yellow Bell held 1,555 grains.
29
後魏後尺黃鐘容一千八百一十九。
Northern Wei later measure: Yellow Bell held 1,819 grains.
30
東魏尺黃鐘容二千八百六十九。
Eastern Wei measure: Yellow Bell held 2,869 grains.
31
萬寶常水尺律母黃鐘容黍一千三百二十。
Wan Baochang's water-measure Yellow Bell mother pipe held 1,320 grains.
32
梁表、鐵尺律黃鐘副別者，其長短及口空之圍徑並同，而容黍或多或少，皆是作者旁庣其腹，使有盈虛。
Liang shadow-table and iron measure Yellow Bell variants shared length and bore but differed in capacity—makers had hollowed the pipe walls unevenly.
33
○侯氣
○ On Observing Seasonal Qi by Pitch Pipes
34
後齊神武霸府田曹參軍信都芳，深有巧思，能以管候氣，仰觀雲色。 嘗與人對語，即指天曰：「孟春之氣至矣。」 人往驗管，而飛灰已應。 每月所候，言皆無爽。 又為輪扇二十四，埋地中，以測二十四氣。 每一氣感，則一扇自動，他扇並住，與管灰相應，若符契焉。
Northern Qi clerk Xin Dufang, serving Shenwu's regent office, ingeniously used pipes to observe qi and read cloud colors. Once in conversation he pointed skyward: "Early spring qi has arrived. Inspectors found the pipe ash already risen in response. His monthly observations never missed. He also built twenty-four buried wheel-fans to measure the twenty-four qi periods. Each qi period activated one fan while the others stopped—matching the pipe ash like a seal and tally.
35
開皇九年平陳後，高祖遣毛爽及蔡子元、於普明等，以候節氣。 依古，於三重密屋之內，以木為案，十有二具。 每取律呂之管，隨十二辰位，置於案上，而以土埋之，上平於地，中實葭莩之灰，以輕緹素覆律口。 每其月氣至，與律冥符，則灰飛沖素，蔂出於外。 而氣應有早晚，灰飛有多少，或初入月其氣即應； 或至中下旬間，氣始應者； 或灰飛出，三五夜而盡； 或終一月，才飛少許者。 高祖異之，以問牛弘。 弘對曰：「灰飛半出為和氣，吹灰全出為猛氣，吹灰不能出為衰氣。 和氣應者其政平，猛氣應者其臣縱，衰氣應者其君暴。」 高祖駁之曰：「臣縱君暴，其政不平，非月別而有異也。 今十二月律，於一歲內應並不同。 安得暴君縱臣，若斯之甚也？」 弘不能對。 令爽等草定其法。 爽因稽諸故實，以著於篇，名曰《律譜》。 其略云：
After pacifying Chen in Kaihuang 9, Emperor Wen sent Mao Shuang, Cai Ziyuan, and Yu Puming to observe seasonal nodes. Following ancient practice, twelve wooden tables were set inside a triple-walled chamber. Each pitch pipe was placed on a table at its double-hour position, buried level with the ground, filled with reed-pith ash, and covered with silk gauze at the mouth. When monthly qi matched the pipe, ash flew through the gauze cover. Qi responses varied in timing; ash flight varied in amount—sometimes responding at month's start, sometimes not until mid or late month, sometimes exhausting in three to five nights, or through a whole month barely rising at all. Emperor Wen was puzzled and asked Niu Hong. Niu Hong replied: "Half-rising ash means harmonious qi; full rising means fierce qi; no rising means declining qi. Harmonious qi means balanced government; fierce qi means unruly ministers; declining qi means a tyrannical ruler. Emperor Wen objected: "Unruly ministers and tyrannical rulers mean bad government—it cannot vary month by month. The twelve monthly pipes should not all imply different political conditions within one year. How could every month signal tyranny or unruliness?" Niu Hong had no answer. Mao Shuang and others were ordered to draft a proper method. Mao Shuang researched old records and wrote the Treatise on Pitch Standards. In summary:
36
臣爽按，黃帝遣伶倫氏取竹于嶰穀，聽鳳阿閣之下，始造十二律焉。 乃致天地氣應，是則數之始也。 陽管為律，陰管為呂，其氣以候四時，其數以紀萬物。 雲隸首作數，蓋律之本也。 夫一、十、百、千、萬、億、兆者，引而申焉，曆度量衡，出其中矣。 故有虞氏用律和聲，鄒衍改之，以定五始。 正朔服色，亦由斯而別也。 夏正則人，殷正則地，周正則天。 孔子曰：「吾得夏時焉。」 謂得氣數之要矣。
Mao Shuang reports: the Yellow Emperor sent Ling Lun to Xie Valley for bamboo; listening at Phoenix Pavilion, he created the twelve pitch standards. Heaven and Earth qi responded—this was the origin of number. Yang pipes are pitch standards, yin pipes bell tones; their qi marks the four seasons, their numbers record all things. Li Shou invented number—the foundation of pitch standards. One through trillion—extended further, calendars, measures, and weights all derive from them. Yu Shun harmonized sounds with pitch standards; Zou Yan modified this to establish the five beginnings. Calendar, dress, and color all followed from this. Xia prioritized man, Shang earth, Zhou Heaven. Confucius said: "I have recovered the Xia calendar. Meaning he grasped the essentials of qi and number.
37
漢初興也，而張蒼定律，乃推五勝之法，以為水德。 實因戰國官失其守，後秦滅學，其道浸微，蒼補綴之，未獲詳究。 及孝武創制，乃置協律之官，用李延年以為都尉，頗解新聲變曲，未達音律之源，故其服色不得而定也。 至於元帝，自曉音律，郎官京房，亦達其妙，因使韋玄成等雜試問房。 房自敘云：「學焦延壽，用六十律相生之法。 以上生下，皆三生二，以下生上，皆三生四。 陽下生陰，陰上生陽，乃還相為宮之正法也。」 于後劉歆典領條奏，著其始末，理漸研精。 班氏《漢志》，盡歆所出也，司馬彪《志》，並房所出也。
At Han's founding, Zhang Cang fixed pitch standards by the five-conquest method, declaring water the dominant element. Warring States disorder and Qin's suppression of learning had degraded the tradition—Zhang Cang patched it without full understanding. Emperor Wu created the pitch-harmonizing office under Li Yannian, who knew new music but not pitch theory—so dress and color remained unsettled. Emperor Yuan understood pitch himself; Jing Fang mastered its subtleties; Wei Xuancheng and others were sent to test him. Jing Fang wrote: "I studied under Jiao Yanshou, using the sixty-standard generation method. Upward generation: three produces two; downward generation: three produces four. Yang generates yin downward, yin generates yang upward—the proper rotating-palace method. Liu Xin later submitted a detailed memorial refining the theory. Ban Gu's Treatise came entirely from Liu Xin; Sima Biao's from Jing Fang.
38
至於後漢，尺度稍長。 魏代杜夔，亦制律呂，以之候氣，灰悉不飛。 晉光祿大夫荀勖，得古銅管，校夔所制，長古四分，方知不調，事由其誤。 乃依《周禮》，更造古尺，用之定管，聲韻始調。
Later Han foot measures grew somewhat longer. Wei's Du Kui made pitch pipes to observe qi—but the ash never rose. Jin's Xun Xu obtained ancient bronze pipes four fen longer than Du Kui's—revealing the error. Following the Rites of Zhou, he remade the ancient foot measure and fixed the pipes—restoring harmony.
39
左晉之後，漸又訛謬。 至梁武帝時，猶有汲塚玉律，宋蒼梧時，鑽為橫吹，然其長短厚薄，大體具存。 臣先入棲誠，學算于祖暅，問律於何承天，沈研三紀，頗達其妙。 後為太常丞，典司樂職，乃取玉管及宋太史尺，並以聞奏。 詔付大匠，依樣制管。 自斯以後，律又飛灰。 侯景之亂，臣兄喜于太樂得之。 後陳宣帝詣荊州為質，俄遇梁元帝敗，喜沒于周。 適欲上聞，陳武帝立，遂又以十二管衍為六十律，私侯氣序，並有徵應。 至太建時，喜為吏部尚書，欲以聞奏。 會宣帝崩，後主嗣立，出喜為永嘉內史，遂留家內，貽諸子孫。 陳亡之際，竟並遺失。
After Eastern Jin, errors accumulated again. Liang still had the Ji-tomb jade pitch pipe; Song drilled it for flutes but its dimensions largely survived. I studied calculation under Zu Geng and pitch under He Chengtian for three cycles, reaching considerable mastery. As Grand Ceremonies assistant, I reported the jade pipe and Song astrologer's foot measure. The Master Craftsman was ordered to replicate the pipes. From then on, the pipes again produced flying ash. During Hou Jing's rebellion, my brother Xi recovered them from the Music Office. Chen's Emperor Xuan was hostage at Jingzhou; when Yuan of Liang fell, Xi was captured by Zhou. Before reporting, Chen Wu ascended; Xi extended twelve pipes to sixty standards, privately observing qi—all confirmed. In Taichang, Xi as Minister of Personnel sought to report his findings. Emperor Xuan died; the Later Lord sent Xi to Yongjia; he left the pipes with his family. At Chen's fall, they were lost entirely.
40
今正十二管在太樂者，陽下生陰，始于黃鐘，陰上生陽，終於中呂，而一歲之氣，畢於此矣。 中呂上生執始，執始下生去滅，終於南事。 六十律候，畢於此矣。 仲冬之月，律中黃鐘。 黃鐘者，首于冬至，陽之始也。 應天之數而長九寸，十一月氣至，則黃鐘之律應，所以宣養六氣，緝和九德也。 自此之後，並用京房律准，長短宮徵，次日而用。 凡十二律，各有所攝，引而申之，至於六十。 亦由八卦衍而重之，以為六十四也。 相生者相變。 始黃鐘之管，下生林鐘，以陽生陰，故變也。 相攝者相通。 如中呂之管，攝于物應，以母權子。 故相變者，異時而各應，相通者，同月而繼應。 應有早晚者，非正律氣，乃子律相感，寄母中應也。
The twelve pipes at Grand Music: yang generates yin from Yellow Bell, yin generates yang to Middle Bell Female—completing the year's qi. Middle Bell Female generates Holding the Beginning upward; downward to Removing the Excess, ending at Southern Affair. The sixty-standard qi observations end here. Mid-winter: the pitch standard is Yellow Bell. At the winter solstice, yang begins with Yellow Bell. Nine cun long, matching Heaven's number—when eleventh-month qi arrives, Yellow Bell responds, nourishing the six qi and harmonizing the nine virtues. Thereafter all use Jing Fang's ratios; modes rotate day by day. Each of the twelve standards governs a domain; extended, they reach sixty. Like the eight trigrams doubled to sixty-four. Generation means transformation. Yellow Bell generates Forest Bell downward—yang producing yin, hence transformation. Domain means connection. Middle Bell Female's pipe connects at Material Response—mother holding child. Transformations respond at different times; connections respond in succession within one month. Early or late responses come not from main standard qi but from child standards responding within the mother.
41
其律，大業末于江都淪喪。
These standards were lost at Jiangdu at Daye's end.
42
○律直日
○ On Pitch Standards Corresponding to Days
43
宋錢樂之因京房南事之余，更生三百律。 至梁博士沈重鐘《律議》曰：「《易》以三百六十策當期之日，此律曆之數也。 《淮南子》云：'一律而生五音，十二律而為六十音，因而六之，故三百六十音，以當一歲之日。 律曆之數，天地之道也。 '此則自古而然矣。」 重乃依《淮南》本數，用京房之術求之，得三百六十律。 各因月之本律，以為一部。 以一部律數為母，以一中氣所有日為子，以母命子，隨所多少，各一律所建日辰分數也。 以之分配七音，則建日冬至之聲，黃鐘為宮，太簇為商，林鐘為徵，南呂為羽，姑洗為角，應鐘為變宮，蕤賓為變徵。 五音七聲，於斯和備。 其次日建律，皆依次類運行。 當日者各自為宮，而商徵亦以次從。 以考聲徵氣，辨識時序，萬類所宜，各順其節。 自黃鐘終於壯進，一百五十律，皆三分損一以下生。 自依行終於億兆，二百九律，皆三分益一以上生。 唯安運一律為終，不生。 其數皆取黃鐘之實十七萬七千一百四十七為本，以九三為法，各除其實，得寸分及小分，餘皆委之。 即各其律之長也。 修其律部，則上生下生宮徵之次也。 今略其名次雲。
Song's Qian Yuezhi extended Jing Fang's Southern Affair to three hundred pitch standards. Liang's Shen Chong wrote: "The Changes uses 360 rods for the days of a year—the number of pitch and calendar. The Huainanzi states: "One standard generates five notes; twelve standards make sixty; times six yields 360 notes for the year's days." Pitch and calendar numbers are the Way of Heaven and Earth. This has been true since antiquity. Shen Chong used the Huainanzi's base number with Jing Fang's method to derive 360 standards. Each month's root pitch standard formed one section. Each section's pitch number was mother, mid-qi days child—yielding each standard's governing day and fraction. Distributed to seven notes: winter solstice day—Yellow Bell gong, Great Cluster shang, Forest Bell zhi, Southern Bell yu, Maiden Wash jue, Responding Bell altered gong, Luxuriant Guest altered zhi. The five notes and seven sounds were thus complete. Each subsequent governing day follows the same pattern in sequence. Each day takes its own pitch as gong, with shang and zhi following in order. Sound verifies qi and marks the seasons—each thing follows its proper period. From Yellow Bell through Zhuang Jin, 150 standards all generate downward by subtracting one-third. From Yi Xing through Yi Zhao, 209 standards all generate upward by adding one-third. Only the final standard An Yun does not generate further. All calculations use Yellow Bell's base value 177,147, divided by nine-cubed, yielding cun and fen fractions—the remainder discarded. These give each pitch standard's length. Arranging the pitch sections yields the order of generation and modal succession. The names and order are listed below.
44
黃鐘：
Yellow Bell section:
45
包育含微帝德廣運下濟克終執始握鑒持樞黃中通聖潛升
Bao Yu, Han Wei, Di De, Guang Yun, Xia Ji, Ke Zhong, Zhi Shi, Wo Jian, Chi Shu, Huang Zhong, Tong Sheng, Qian Sheng, and others
46
殷普景盛滋萌光被咸亨乃文乃聖微陽分動生氣雲繁鬱湮
Yin Pu, Jing Sheng, Zi Meng, Guang Bei, Xian Heng, Nai Wen, Nai Sheng, Wei Yang, Fen Dong, Sheng Qi, Yun Fan, Yu, and others
47
升引屯結開元質未僾昧逋建玄中玉燭調風
Sheng Yin, Tun Jie, Kai Yuan, Zhi Wei, Qian Mei, Yu Jian, Xuan Zhong, Yu Zhu, and Diao Feng
48
右黃鐘一部，三十四律。 每律直三十四分日之三十一
Yellow Bell section: thirty-four pitch standards. Each standard governs thirty-four thirty-firsts of a day.
49
大呂：
Great Bell section:
50
荄動始贊大有坤元輔時匡弼分否又繁唯微棄望庶幾執義秉強陵陰侶陽識沈緝熙知道適時權變少出阿衡同雲承明善述休光
Gai Dong, Shi Zan, Da You, Kun Yuan, Fu Shi, Kuang Bi, Fen Fou, You Fan, Wei Wei, Qi Wang, Shu Yi, Bing Qiang, and twenty-one others
51
右大呂一部，二十七律。 每律直一日及二十七分日之三
Great Bell section: twenty-seven pitch standards. Each standard governs one day plus three twenty-sevenths of a day.
52
太簇：
Great Cluster section:
53
未知其己義建亭毒條風湊始時息達生匏奏初角少陽柔橈商音屈齊扶弱承齊動植鹹擢兼山止速隨期龍躍勾芒調序青要結萼延敷刑晉辨秩東作讚揚顯滯俶落
Wei Zhi, Qi Yi, Jian Ting, Du, Tiao Feng, Cou Shi, Shi Xi, Da Sheng, and twenty-six others
54
右太簇一部，三十四律。
Great Cluster section: thirty-four pitch standards.
55
○夾鐘
○ Pinched Bell section
56
明庶協侶陰贊風從布政萬化開時震德乘條芬芳散朗淑氣風馳佚喜幹黨四隙種生恣性逍遙仁威爭南旭旦晨朝生遂群分潔新
Ming Shu, Xie Lu, Yin Zan, Feng Cong, Bu Zheng, Wan Hua, Kai Shi, and twenty others
57
右夾鐘一部，二十七律。
Pinched Bell section: twenty-seven pitch standards.
58
姑洗：
Maiden Wash section:
59
南授懷來考神方顯攜角洗陳變虞擢穎嘉氣始升卿雲媚嶺疏道路時日旅實沈炎風首節柔條方結刑始方齊物華革荑茂實登明壯進下生安運依行上生包育少選道從硃黻揚庭含貞
Nan Shou, Huai Lai, Kao Shen, Fang Xian, and twenty-nine others ending with Zhuang Jin, then An Yun and Bao Yu
60
右姑洗一部，三十四律。
Maiden Wash section: thirty-four pitch standards.
61
中呂：
Middle Bell Female section:
62
硃明啟運景風初緩羽物斯奮南中離春率農有程南訛敬致相趣內貞硃草含輝屈軼曜疇巳氣清和物應戒Ｑ荒落貞軫天庭祚周
Zhu Ming, Qi Yun, Jing Feng, Chu Huan, Yu Wu, and twenty others
63
右中呂一部，二十七律。
Middle Bell Female section: twenty-seven pitch standards.
64
蕤賓：
Luxuriant Guest section:
65
南事京房終律謐靜則選布萼滿羸潛動盛變賓安懷遠聲暨軌同海水息沴離躬安壯崇明遠眺升中鳳翥朝陽制時瑞通鶉火乂次高焰其煌。
Nan Shi, Jing Fang's terminal standard, Mi Jing, Ze Xuan, Bu E, and twenty-one others ending with Qi Huang.
66
右蕤賓一部，二十七律。
Luxuriant Guest section: twenty-seven pitch standards.
67
林鐘：
Forest Bell section:
68
謙侍崇德循道方壯陰升靡慝去滅華銷朋慶雲布均任仰成寬中安度德均無蹇禮溢智深任肅純恪歸嘉美音溫風候節蓂華繡嶺物無否與景口曜井日煥重輪財華
Qian Shi, Chong De, Xun Dao, Fang Zhuang, Yin Sheng, and twenty-six others
69
右林鐘一部，三十四律。
Forest Bell section: thirty-four pitch standards.
70
夷則：
Luxuriant Guest Mode section:
71
升商清爽氣精陰德白藏禦敘鮮刑貞克金天劉獮會道歸仁陰侶去南陽消柔辛延乙和庚靡卉荑晉分積孔修九德鹹藎僉惟俾乂
Sheng Shang, Qing Shuang, Qi Jing, Yin De, Bai Cang, and eighteen others
72
右夷則一部，二十七律。
Luxuriant Guest Mode section: twenty-seven pitch standards.
73
南呂：
Southern Bell section:
74
白呂捐秀敦實素風勁物酋稔結躬肥遁羸中晟陰抗節威遠有截歸期中德王猷允塞蓐收撙轡搖落未印質隨分滿道心貞堅蓄止歸藏夷汗均義悅使亡勞九有光賁
Bai Lu, Juan Xiu, Dun Shi, Su Feng, Jin Wu, and twenty-eight others
75
右南呂一部，三十四律。
Southern Bell section: thirty-four pitch standards.
76
無射：
Pitchless section:
77
思沖懷謙恭儉休老恤農銷祥閉奄降婁藏邃日在旋春閹藏明奎鄰齊軌眾大蓄嗇斂下濟息肩無邊期保延年秋深野色玄月澄天
Si Chong, Huai Qian, Gong Jian, Xiu Lao, Xu Nong, and twenty others
78
右無射一部，二十七律。
Pitchless section: twenty-seven pitch standards.
79
應鐘：
Responding Bell section:
80
分焉祖微據始功成乂定靜謐遲內無為而乂姑射凝晦動寂應徵未育萬機萬壽無疆地久天長修復遲時方制無休九野八荒億兆安運
Fen Yan, Zu Wei, Ju Shi, Gong Cheng, Yi Ding, and twenty-two others ending with An Yun
81
右應鐘一部，二十八律。
Responding Bell section: twenty-eight pitch standards.
82
○審度
○ On Examining Measures
83
《史記》曰：「夏禹以身為度，以聲為律。」 《禮記》曰：「丈夫布手為尺。」 《周官》云：「璧羨起度。」 鄭司農云：「羨，長也。 此璧徑尺，以起度量。」 《易緯通卦驗》：「十馬尾為一分。」 《淮南子》云：「秋分而禾緌定，緌定而禾熟。 律數十二而當一粟，十二粟而當一寸。」 緌者，禾穗芒也。 《說苑》云：「度量權衡以粟生，一粟為一分。」 《孫子算術》云：「蠶所生吐絲為忽，十忽為秒，十秒為毫，十毫為厘，十厘為分。」 此皆起度之源，其文舛互。 唯《漢志》：「度者，所以度長短也，本起黃鐘之長。 以子穀秬黍中者，一黍之廣度之，九十黍為黃鐘之長。 一黍為一分，十分為一寸，十寸為一尺，十尺為一丈，十丈為一引，而五度審矣。」 後之作者，又憑此說，以律度量衡，並因秬黍散為諸法，其率可通故也。 黍有大小之差，年有豐耗之異，前代量校，每有不同，又俗傳訛替，漸致增損。 今略諸代尺度一十五等，並異同之說如左。
Sima Qian records: "Yu of Xia used his body for measure and sound for pitch. The Record of Rites states: "A man's outstretched hand defines the foot measure." The Offices of Zhou says: "The jade surplus initiates measure." Zheng Sizhong explains: "Surplus means length. This one-chi-diameter jade disk establishes all measures." The Changes Weft states: "Ten horse-tail widths make one fen." The Huainanzi says: "At the autumn equinox grain awns set; when awns set, grain ripens. Twelve pitch numbers equal one millet grain; twelve grains equal one cun." Awn refers to the grain ear's bristle. The Garden of Persuasions states: "Weights and measures derive from millet—one grain equals one fen. The Sunzi Calculation Methods defines: silkworm thread is a hu; ten hu a miao; ten miao a hao; ten hao a li; ten li a fen. These are all origins of measure—but the texts conflict. Only the Han Treatise is authoritative: "Measure gauges length, originating from Yellow Bell's length. Using medium black millet grains, one grain's width measured—ninety grains equal Yellow Bell's length. One grain one fen; ten fen one cun; ten cun one chi; ten chi one zhang; ten zhang one yin—the five measures verified. Later makers followed this theory—pitch, measure, and weight all derived from black millet with commensurable ratios. Millet varies in size, harvests vary in yield, and each age's calibrations differ—popular error gradually altered the standards. Fifteen grades of historical foot measures are listed below with their differences.
84
一、周尺
I. Zhou foot measure
85
《漢志》王莽時劉歆銅斛尺。
Han Treatise: Liu Xin's copper hu measure from Wang Mang's era.
86
後漢建武銅尺。
The Later Han Jianwu copper measure.
87
晉泰始十年荀勖律尺，為晉前尺。
Jin Taishi 10 Xun Xu pitch measure—the pre-Jin standard.
88
祖沖之所傳銅尺。
Zu Chongzhi's transmitted copper foot measure.
89
徐廣、徐爰、王隱等《晉書》云：「武帝泰始九年，中書監荀勖校太樂八音，不和，始知為後漢至魏，尺長於古四分有餘。 勖乃部著作郎劉恭，依《周禮》制尺，所謂古尺也。 依古尺更鑄銅律呂，以調聲韻。 以尺量古器，與本銘尺寸無差。 又汲郡盜發魏襄王塚，得古周時玉律及鐘磬，與新律聲韻暗同。 于時郡國或得漢時故鐘，吹新律命之，皆應。」 梁武《鐘律緯》云：「祖沖之所傳銅尺，其銘曰：'晉泰始十年，中書考古器，揆校今尺，長四分半。 所校古法有七品：一曰姑洗玉律，二曰小呂玉律，三曰西京銅望臬，四曰金錯望臬，五曰銅斛，六曰古錢，七曰建武銅尺。 姑洗微強，西京望臬微弱，其餘與此尺同。 '銘八十二字。 此尺者，勖新尺也。 今尺者，杜夔尺也。 雷次宗、何胤之二人作《鐘律圖》，所載荀勖校量古尺文，與此銘同。 而蕭吉樂譜，謂為梁朝所考七品，謬也。 今以此尺為本，以校諸代尺」雲。
Jin History records: in Taishi 9, Xun Xu found the eight timbres discordant—the Wei measure exceeded antiquity by four fen. Xu ordered Liu Gong to make a Rites of Zhou foot measure—the ancient standard. Using the ancient measure, bronze pitch pipes were recast to restore harmony. Ancient vessels measured against it matched their inscriptions exactly. Ji commandery tomb robbers found Zhou jade pitch pipes and bells matching the new standards. Han-era bells found in the provinces all matched when tested against the new pipes. Liang Wu's Treatise cites Zu Chongzhi's copper measure: "Jin Taishi 10—four fen and a half longer than the present measure. Seven ancient reference standards were tested: Maiden Wash jade pipe, Lesser Bell jade pipe, Western Capital bronze gnomon, gold-inlaid gnomon, copper hu, ancient coins, and Jianwu copper measure. Maiden Wash ran slightly high; the Western Capital gnomon slightly low—the rest matched. The inscription contains eighty-two characters. This is Xu's new measure. The contemporary measure is Du Kui's. Lei Cizong and He Yin's Diagram records the same Xun Xu examination text. Xiao Ji wrongly attributes these to Liang-era examination. This measure serves as the base for comparing all dynastic foot measures."
90
二、晉田父玉尺
II. Jin farmer's jade foot measure
91
梁法尺，實比晉前尺一尺七厘。
Liang legal measure exceeds pre-Jin by one chi seven li.
92
《世說》稱，有田父于野地中得周時玉尺，便是天下正尺。 荀勖試以校尺，所造金石絲竹，皆短校一米。 梁武帝《鐘律緯稱》，主衣從上相承，有周時銅尺一枚，古玉律八枚。 檢主衣周尺，東昏用為章信，尺不復存。 玉律一囗蕭，餘定七枚夾鐘，有昔題刻。 乃制為尺，以相參驗。 取細毫中黍，積次詶定，今之最為詳密，長祖沖之尺校半分。 以新尺制為四器，名為通。 又依新尺為笛，以命古鐘，按刻夷則，以笛命飲和韻，夷則定合。 案此兩尺長短近同。
Tales of the World tells of a farmer finding a Zhou jade measure—the realm's true standard. Xun Xu tested it—all metal, stone, silk, and bamboo instruments proved one meter short. Liang Wu's Treatise records one Zhou copper measure and eight jade pitch pipes from the Master of Robes. The Master of Robes' Zhou measure was used as Emperor Donghun's seal credential—it no longer survives. One jade pipe was damaged; seven Pinched Bell pipes with old inscriptions remain. A foot measure was made for cross-verification. Fine-haired medium millet was accumulated for precise calibration—half a fen longer than Zu Chongzhi's measure. Four Tong instruments were made from the new measure. Flutes from the new measure tuned ancient bells inscribed Luxuriant Guest—confirming the match. These two measures are nearly identical in length.
93
三、梁表尺實比晉前尺一尺二分二厘一毫有奇。
III. Liang shadow-table measure exceeds pre-Jin by one chi two fen two li one hao and a fraction.
94
蕭吉云：「出於《司馬法》。 梁朝刻其度於影表，以測影。」 案此即奉朝請祖暅所算造銅主影表者也。 經陳滅入朝。 大業中，議以合古，乃用之調律，以制鐘磬等八音樂器。
Xiao Ji attributes it to the Sima Methods. The Liang court carved its measure on a gnomon table for shadow measurement. This is Court Gentleman Zu Geng's calculated bronze gnomon table. It entered the court after Chen's fall. In Daye, it was deemed most antiquity-conforming and used to tune bells, chimes, and the eight timbres.
95
四、漢官尺實比晉前尺一尺三分七毫。
IV. Han official measure exceeds pre-Jin by one chi three fen seven hao.
96
晉時始平掘地得古銅尺。
At Shiping during Jin, excavations yielded an ancient copper foot measure.
97
蕭吉《樂譜》云：「漢章帝時，零陵文學史奚景於泠道縣舜廟下得玉律，度為此尺。」 傅暢《晉諸公贊》云：「葛勖造鐘律，時人並稱其精密，唯陳留阮鹹，譏其聲高。 後始平掘地，得古銅尺，歲久欲腐，以校荀勖今尺，短校四分。 時人以咸為解。」 此兩尺長短近同。
Xiao Ji records: Han Zhangdi's scholar Xi Jing found a jade pipe at Shun's temple in Lengdao and derived this measure. Fu Chang records: Ge Xun's standards were praised for precision—only Ruan Xian of Chenliu criticized the pitch as too high. Later at Shiping, a decayed ancient copper measure proved four fen shorter than Xun Xu's—vindicating Ruan Xian. Contemporaries acknowledged Ruan Xian was correct. These two measures are nearly identical.
98
五、魏尺杜夔所用調律，比晉前尺一尺四分七厘。
V. Du Kui's Wei tuning measure exceeds pre-Jin by one chi four fen seven li.
99
魏陳留王景元四年，劉徽注《九章》雲，王莽時劉歆斛尺，弱於今尺四分五厘，比魏尺，其斛深九寸五分五厘。 即晉荀勖所雲「杜夔尺長於今尺四分半」是也。
Liu Hui noted Wang Mang's hu measure was four fen five li shorter; Wei's hu depth was nine cun five fen five li. This confirms Xun Xu's statement that Du Kui's measure exceeded the contemporary by four fen and a half.
100
六、晉後尺實比晉前尺一尺六分二厘。
VI. Post-Jin measure exceeds pre-Jin by one chi six fen two li.
101
蕭吉雲，晉氏江東所用。
Xiao Ji says Eastern Jin used this measure in Jiangdong.
102
七、後魏前尺實比晉前尺一尺二寸七厘。
VII. Northern Wei early measure exceeds pre-Jin by one chi two cun seven li.
103
八、中尺實比晉前尺一尺二寸一分一厘。
VIII. Middle measure exceeds pre-Jin by one chi two cun one fen one li.
104
九、後尺實比晉前尺一尺二寸八分一厘。 即開皇官尺及後周市尺
IX. Later measure exceeds pre-Jin by one chi two cun eight fen one li. These are the Kaihuang official and Northern Zhou market measures.
105
後周市尺，比玉尺一尺九分三厘。
Northern Zhou market measure exceeds the jade measure by one chi nine fen three li.
106
開皇官尺，即鐵尺，一尺二寸。
Kaihuang official measure—the iron measure—is one chi two cun.
107
此後魏初及東西分國，後周未用玉尺之前，雜用此等尺。
These were used during early Northern Wei and before Northern Zhou adopted the jade measure.
108
甄鸞《算術》云：「周朝市尺，得玉尺九分二厘。」 或傳梁時有志公道人作此尺，寄入周朝； 雲與多須老翁。 周太祖及隋高祖，各自以為謂己。 周朝人間行用。 及開皇初，著令以為官尺，百司用之，終於仁壽。 大業中，人間或私用之。
Zhen Luan records: Northern Zhou market measure equaled nine fen two li of the jade measure. Tradition holds a Liang Daoist Zhi Gongdao made this measure and sent it to Zhou; claiming it matched the elder Duoxu. Northern Zhou's Taizu and Sui's Gaozu each thought it referred to himself. Northern Zhou commoners used it in daily life. Kaihuang made it the official measure, used by all offices until Renshou. Daye saw occasional private use.
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十、東後魏尺實比晉前尺一尺五寸八毫。
X. Eastern Northern Wei measure exceeds pre-Jin by one chi five cun eight hao.
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此是魏中尉元延明累黍用半周之廣為尺，齊朝因而用之。 魏收《魏史·律曆志》云：「公孫崇永平中更造新尺，以一黍之長，累為寸法。 尋太常卿劉芳受詔修樂，以秬黍中者一黍之廣，即為一分。 而中尉元匡，以一黍之廣度黍二縫，以取一分。 三家紛競，久不能決。 大和十九年高祖詔，以一黍之廣，用成分體，九十之黍，黃鐘之長，以定銅尺。 有司奏從前詔，而芳尺同高祖所制，故遂典修金石。 迄武定未有論律者。」
Wei Commandant Yuan Yanming made this by accumulating millet at half Zhou breadth—adopted by Qi. Wei Shou records: Gongsun Chong remade the measure in Yongping, accumulating cun from one millet grain's length. Grand Master Liu Fang used medium black millet—one grain's width as one fen. Commandant Yuan Kuang measured two grain seams for one fen. Three factions disputed without resolution. Taihe 19, the emperor ordered: one grain's width as fen, ninety grains for Yellow Bell's length, fixing the copper measure. Fang's measure matched the imperial standard—he was charged with metal and stone instruments. No pitch discussion occurred until Wuding. End of quotation.
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十一、蔡邕銅籥尺
XI. Cai Yong's copper pitch key measure
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後周玉尺，實比晉前尺一尺一寸五分八厘。
Northern Zhou jade measure exceeds pre-Jin by one chi one cun five fen eight li.
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從上相承，有銅籥一，以銀錯題，其銘曰：「籥，黃鐘之宮，長九寸，空圍九分，容秬黍一千二百粒，稱重十二銖，兩之為一合。 三分損益，轉生十二律。」 祖孝孫云：「相承傳是蔡邕銅籥。」
A transmitted copper pitch key bears silver inscription: "Yellow Bell palace pitch, nine cun, bore nine fen circumference, 1,200 black millet grains, twelve zhu weight, two he per pair. Tripling or dividing by three generates the twelve standards. Zu Xiaosun identifies it as Cai Yong's transmitted copper pitch key. End of inscription.
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後周武帝保定中，詔遣大宗伯盧景宣、上党公長孫紹遠、岐國公斛斯徵等，累黍造尺，從橫不定。 後因修倉掘地，得古玉鬥，以為正器，據鬥造律度量衡。 因用此尺，大赦，改元天和，百司行用，終於大象之末。 其律黃鐘，與蔡邕古籥同。
Baoding era, Lu Jingxuan, Changsun Shaoyuan, and Husizheng were ordered to accumulate millet for a new measure—but dimensions remained unsettled. Repairing a granary yielded an ancient jade dipper used to make pitch pipes, measures, and weights. This measure was adopted with a Tianhe era amnesty, used until Daxiang's end. Its Yellow Bell matched Cai Yong's ancient pitch key.
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十二、宋氏尺實比晉前尺一尺六分四厘。
XII. Song measure exceeds pre-Jin by one chi six fen four li.
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錢樂之渾天儀尺。
Qian Yuezhi's armillary sphere measure.
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後周鐵尺。
Northern Zhou iron measure.
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開皇初調鐘律尺及平陳後調鐘律水尺。
Kaihuang bell-tuning measure and post-Chen water measure.
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此宋代人間所用尺，傳入齊、梁、陳，以制樂律。 與晉後尺及梁時俗尺、劉曜渾天儀尺，略相依近。 當由人間恆用，增損訛替之所致也。 周建德六年平齊後，即以此同律度量，頒於天下。 其後宣帝時，達奚震及牛弘等議曰：
Song's popular measure passed through Qi, Liang, and Chen for musical standards. It closely resembles post-Jin, Liang popular, and Liu Yao armillary measures. Constant popular use caused gradual distortion. After Jiande 6 pacified Qi, this standard was promulgated empire-wide. Later under Emperor Xuan, Daxi Zhen and Niu Hong submitted:
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竊惟權衡度量，經邦懋軌，誠須詳求故實，考校得衷。 謹尋今之鐵尺，是太祖遣尚書故蘇綽所造，當時檢勘，用為前周之尺。 驗其長短，與宋尺符同，即以調鐘律，並用均田度地。 今以上黨羊頭山黍，依《漢書·律曆志》度之。 若以大者稠累，依數滿尺，實于黃鐘之律，須撼乃容。 若以中者累尺，雖複小稀，實于黃鐘之律，不動而滿。 計此二事之殊，良由消息未善，其於鐵尺，終有一會。 且上黨之黍，有異他鄉，其色至烏，其形圓重，用之為量，定不徒然。 正以時有水旱之差，地有肥瘠之異，取黍大小，未必得中。 案許慎解，秬黍體大，本異于常。 疑今之大者，正是其中，累百滿尺，即是會古。 賓籥之外，才剩十餘，此恐圍徑或差，造律未妙。 就如撼動取滿，論理亦通。 今勘周漢古錢，大小有合，宋氏渾儀，尺度無舛。 又依《淮南》，累粟十二成寸。 明先王制法，索隱鉤深，以律計分，義無差異。 《漢書·食貨志》云：「黃金方寸，其重一斤。」 今鑄金校驗，鐵尺為近。 依文據理，符會處多。 且平齊之始，已用宣佈，今因而為定，彌合時宜。 至於玉尺累黍，以廣為長，累既有剩，實複不滿。 尋訪古今，恐不可用。 其晉、梁尺量，過為短小，以黍實管，彌複不容，據律調聲，必致高急。 且八音克諧，明王盛範，同律度量，哲後通規。 臣等詳校前經，斟量時事，謂用鐵尺，於理為便。
We hold that weights and measures are foundational to governance—requiring thorough examination of historical evidence. Today's iron measure was made by the late Su Chuo for Taizu, verified as Former Zhou's standard. It matches the Song measure—used for pitch tuning and equal-field land measurement. We now measure using Shangdang Yangtou Mountain millet per the Han Treatise. Large grains densely packed require shaking to fill Yellow Bell's pipe. Medium grains fill Yellow Bell's pipe without shaking. This discrepancy suggests imperfect calibration—but the iron measure will ultimately prove correct. Shangdang millet differs from other regions—black, round, and heavy—making a reliable standard. Harvest and soil variations mean medium-sized grains may not always be obtainable. Xu Shen notes black millet is inherently larger than ordinary grain. Today's large grains may be the true medium—one hundred filling the measure matches antiquity. Beyond the guest key, only ten-odd grains remain—perhaps bore circumference is slightly off. Even requiring shaking to fill, the principle still holds. Zhou and Han coins confirm the measure; Song's armillary measure shows no error. The Huainanzi also specifies twelve millet grains per cun. Ancient law-making probed deeply—calculating fen from pitch standards without discrepancy. The Han Treatise on Food and Money states: "One square cun of gold weighs one jin. Casting gold for verification, the iron measure proves closest. Text and principle align in many respects. Already promulgated at Qi's pacification—confirming it now best suits the times. The jade measure uses grain width as length—accumulation leaves gaps, never truly full. Historical review suggests the jade measure is unusable. Jin and Liang measures are too short—millet cannot fill the pipes, producing excessively high pitch. Harmonious eight timbres mark enlightened rule; unified pitch and measure is the wise ruler's standard. We have examined the classics and present circumstances—the iron measure is most practical.
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未及詳定，高祖受終，牛弘、辛彥之、鄭譯、何妥等，久議不決。 既平陳，上以江東樂為善，曰：「此華夏舊聲，雖隨俗改變，大體猶是古法。」 祖孝孫云：「平陳後，廢周玉尺律，便用此鐵尺律，以一尺二寸即為市尺。」
Before resolution, Emperor Wen died; Niu Hong, Xin Yanzhi, Zheng Yi, and He Tuo debated without conclusion. After pacifying Chen, the emperor praised Jiangdong music: "This is Huaxia's ancient sound—though changed by custom, its essence remains old method. Zu Xiaosun records: after Chen's fall, Zhou's jade measure was abandoned; the iron measure at one chi two cun became the market standard. End of Zu Xiaosun's account.
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十三、開皇十年萬寶常所造律呂水尺實比晉前尺一尺一寸八分六厘。
XIII. Kaihuang 10 Wan Baochang's water measure exceeds pre-Jin by one chi one cun eight fen six li.
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今太樂庫及內出銅律一部，是萬寶常所造，名水尺律。 說稱其黃鐘律當鐵尺南呂倍聲。 南呂，黃鐘羽也，故謂之水尺律。
The Grand Music storehouse holds Wan Baochang's copper pitch set—the water-measure standards. Its Yellow Bell corresponds to the iron measure's Southern Bell at double pitch. Southern Bell is Yellow Bell's yu mode—hence the water-measure name.
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十四、雜尺趙劉曜渾天儀土圭尺，長於梁法尺四分三厘，實比晉前尺一尺五分。
XIV. Liu Yao's armillary earthen gnomon measure exceeds Liang legal by four fen three li, pre-Jin by one chi five fen.
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十五、梁朝俗間尺長於梁法尺六分三厘、于劉曜渾儀尺二分，實比晉前尺一尺七分一厘。 梁武《鐘律緯》云：「宋武平中原，送渾天儀土圭，雲是張衡所作。 驗渾儀銘題，是光初四年鑄，土圭是光初八年作。 並是劉曜所制，非張衡也。 制以為尺，長今新尺四分三厘，短俗間尺二分。」 新尺謂梁法尺也。 ○嘉量《周禮》，蠙氏「為量，鬴深尺，內方尺而圓其外，其實一鬴； 其臀一寸，其實一豆； 其耳三寸，其實一升。 重一鈞。 其聲中黃鐘。 概而不稅。 其銘曰：時文思索，允臻其極。 嘉量既成，以觀四國。 永啟厥後，茲器維則。」 《春秋左氏傳》曰：「齊舊四量，豆、區、鬴、鐘。 四升曰豆，各自其四，以登於鬴。」 六斗四升也。 「鬴十則鐘」，六十四斗也。 鄭玄以為方尺積千寸，比九章粟米法少二升八十一分升之二十二。 祖沖之以算術考之，積凡一千五百六十二寸半。 方尺而圓其外，減傍一厘八毫，共徑一尺四寸一分四毫七秒二忽有奇而深尺，即古斛之制也。 《九章商功法》程粟一斛，積二千七百寸。 米一斛，積一千六百二十寸。 菽荅麻麥一斛，積二千四百三十寸。 此據精粗為率，使價齊而不等。 其器之積寸也，以米斛為正，則同於《漢志》。 《孫子算術》曰：六粟為圭，十圭為秒，十秒為撮，十撮為勺，十勺為合。」 應勳曰：「圭者自然之形，陰陽之始。 四圭為撮。」 孟康曰：「六十四黍為圭。」 《漢志》曰：「量者，籥、合、升、鬥、斛也，所以量多少也。 本起于黃鐘之龠。 用度數審其容，以子穀秬黍中者千有二百實其龠，以井水準其概。 十龠為合，十合為升，十升為鬥，十斗為斛，而五量嘉矣。 其法用銅方尺而圓其外，旁有庣焉。 其上為斛，其下為鬥，左耳為升，右耳為合、龠。 其狀似爵，以縻爵祿。 上三下二，參天兩地。 圓而函方，左一右二，陰陽之象也。 圓象規，其重二鈞，備氣物之數，各萬有一千五百二十也。 聲中黃鐘，始于黃鐘而反覆焉。」 其斛銘曰：「律嘉量斛，方尺而圓其外，庣旁九厘五毫，冪百六十二寸，深尺，積一千六百二十寸，容十斗。」 祖沖之以圓率考之，此斛當徑一尺四寸三分六厘一毫九秒二忽，庣旁一分九毫有奇。 劉歆庣旁少一厘四毫有奇，歆數術不精之所致也。
XV. Liang popular measure exceeds Liang legal by six fen three li, Liu Yao's by two fen, pre-Jin by one chi seven fen one li. Liang Wu's Treatise records: Song Wu sent an armillary earthen gnomon attributed to Zhang Heng. The armillary inscription reads Guangchu 4; the gnomon Guangchu 8. Both were Liu Yao's work—not Zhang Heng's. Made into a measure—four fen three li longer than the new measure, two fen shorter than the popular one. The new measure means the Liang legal measure. ○ Commended Capacity. The Rites of Zhou's Bin clan makes measures: a cauldron one chi deep, one chi square inside with rounded exterior, holding one cauldron; its base one cun deep, holding one dou; its ears three cun, holding one sheng. Weight: one jun. Its tone matches Middle Bell Female. Leveled without scraping the overflow. Inscription: "In this era of cultural reflection, truly reaching the utmost." Once completed, this commended measure observes the four quarters. Forever establishing the standard for posterity. The Zuo Commentary records: "Qi's four old measures—dou, qu, cauldron, and bell. Four sheng make a dou; four of each ascending to the cauldron." That equals six dou and four sheng. Ten cauldrons make a bell—sixty-four dou. Zheng Xuan calculated one square chi as one thousand cun—two sheng eighty-one twenty-second parts short of the Nine Chapters method. Zu Chongzhi calculated the total volume at 1,562.5 cun. Square one chi, rounded exterior, side reduced one li eight hao—diameter one chi four cun one fen four hao seven miao two hu odd, depth one chi—the ancient hu. Nine Chapters: one hu husked millet equals 2,700 cun volume. One hu rice: 1,620 cun. One hu beans, hemp, wheat: 2,430 cun. Fine and coarse grains use different ratios to equalize prices. Using rice hu as the vessel standard matches the Han Treatise. Sunzi Methods: six grains a gui; ten gui a miao; ten miao a cuo; ten cuo a shao; ten shao a he. Ying Shao: "Gui is nature's form—the origin of yin and yang. Four gui constitute one cuo." Meng Kang: sixty-four grains make a gui. Han Treatise: "Capacity measures are pitch key, he, sheng, dou, hu—for measuring quantity. It originates from Yellow Bell's pitch key. Medium black millet—1,200 grains fill the pitch key; well water levels the overflow strip. Ten keys a he; ten he a sheng; ten sheng a dou; ten dou a hu—the five capacities commended. Made of copper, square one chi with rounded exterior and slanted side. Hu above, dou below, sheng left ear, he and pitch key right ear. Shaped like a wine vessel—symbolizing rank and salary. Three parts above and two below—reflecting Heaven and Earth. Round containing square, one left two right—the yin-yang image. Round as the compass; weight two jun—each ten thousand one thousand five hundred twenty qi-things. Tone matching Middle Bell Female—beginning at Yellow Bell and returning." Hu inscription: "Commended capacity hu, square one chi rounded, slanted side nine li five hao, area 162 cun, depth one chi, volume 1,620 cun, ten dou capacity." Zu Chongzhi calculated: diameter one chi four cun three fen six li one hao nine miao two hu, slanted side one fen nine hao odd. Liu Xin's slanted side was one li four hao short—inaccurate calculation.
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魏陳留王景元四年，劉徽注《九章商功》曰：「當今大司農斛圓徑一尺三寸五分五厘，深一尺，積一千四百四十一寸十分之三。 王莽銅斛於今尺為深九寸五分五厘，徑一尺三寸六分八厘七毫。 以徽術計之，於今斛為容九斗七升四合有奇。」 此魏斛大而尺長，王莽斛小而尺短也。
Liu Hui noted: contemporary Grand Granary hu diameter one chi three cun five fen five li, depth one chi, volume 1,441.3 cun. Wang Mang's copper hu: depth nine cun five fen five li, diameter one chi three cun six fen eight li seven hao by contemporary measure. By Hui's calculation: 9 dou 7 sheng 4 he and a fraction in contemporary hu. Wei's hu was large with a long measure; Wang Mang's hu small with a short measure.
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梁、陳依古。 齊以古升五升為一斗。
Liang and Chen adhered to the ancient standard. Qi used five ancient sheng per dou.
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後周武帝「保定元年辛巳五月，晉國造倉，獲古玉鬥。 暨五年乙酉冬十月，詔改制銅律度，遂致中和。 累黍積龠，同茲玉量，與衡度無差。 准為銅升，用頒天下。 內徑七寸一分，深二寸八分，重七斤八兩。 天和二年丁亥，正月癸酉朔，十五日戊子校定，移地官府為式。」 此銅升之銘也。 其玉升銘曰：「維大周保定元年，歲在重光，月旅蕤賓，晉國之有司，修繕倉廩，獲古玉升，形制典正，若古之嘉量。 太師晉國公以聞，敕納於天府。 暨五年歲在協洽，皇帝乃詔稽準繩，考灰律，不失圭撮，不差累黍。 遂熔金寫之，用頒天下，以合太平權衡度量。」 今若以數計之，玉升積玉尺一百一十寸八分有奇，斛積一千一百八五分七厘三毫九秒。 又甄鸞《算術》云：「玉升一升，得官斗一升三合四勺。 「此玉升大而官斗小也。 以數計之，甄鸞所據後周官斗，積玉尺九十七寸有奇，斛積九百七十七寸有奇。 後周玉鬥並副金錯銅斗及建德六年金錯題銅斗，實同以秬黍定量。 以玉稱權之，一升之實，皆重六斤十三兩。
Northern Zhou Wu: "Baoding 1, fifth month, Jin state granary construction yielded an ancient jade dipper. Baoding 5, tenth month, edict to reform copper pitch measures, achieving harmony. Millet and pitch keys accumulated—matching the jade measure, consistent with weights and lengths. Fixed as copper sheng, promulgated empire-wide. Inner diameter seven cun one fen, depth two cun eight fen, weight seven jin eight liang. Tianhe 2, first month new moon, fifteenth day verified and issued as government standard. This is the copper sheng inscription. Jade sheng inscription: "Great Zhou Baoding 1, month Luxuriant Guest—Jin granary repair yielded an ancient jade sheng, canonical like antiquity's commended measure. Grand Preceptor Duke of Jin reported; edict received it into the Heavenly Storehouse. Baoding 5, the emperor ordered examination of plumb lines and pitch ash—without losing a gui or cuo, without millet error. Gold was melted to cast copies, promulgated empire-wide for Taiping weights and measures. By calculation: jade sheng volume 110.8+ jade-measure cun; hu volume 1,108.57+ cun. Zhen Luan records: one jade sheng equals one official dou three he four shao. The jade sheng is large; the official dou is small. Zhen Luan's Northern Zhou official dou: 97+ jade-measure cun; hu 977+ cun. Northern Zhou jade dipper, gold-inlaid copper dou, and Jiande 6 dou all used black millet for capacity. Weighed on the jade steelyard, one sheng solid content weighed six jin thirteen liang.
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開皇以古斗三升為一升。 大業初，依復古鬥。 ○衡權衡者，平也； 權者，重也。 衡所以任權而鈞物平輕重也。 其道如底，以見准之正，繩之直。 左旋見規，右折見矩。 其在天也，佐助璿璣，斟酌建指，以齊七政，故曰玉衡。 權者，銖、兩、斤、鈞、石也，以秤物平施，知輕重也。 古有黍、Ｒ、錘、錙、鐶、鉤、鋝、鎰之目，歷代差變，其詳未聞。 《前志》曰：權本起于黃鐘之重。 一龠容千二百黍，重十二銖。 兩之為兩，二十四銖為兩。 十六兩為斤。 三十斤為鈞。 四鈞為石。 五權謹矣。 其制以義立之，以物鈞之。 其餘大小之差，以輕重為宜。 圜而環之，令之肉倍好者，周旋亡端，終而複始，亡窮已也。 權與物鈞而生衡，衡運生規，規圓生矩，矩方生繩，繩直生准。 准正則衡平而鈞權矣。 是為五則，備於鈞器，以為大範。 案《趙書》，石勒十八年七月，造建德殿，得圓石，狀如水碓。 其銘曰：「律權石，重四鈞，同律度量衡。 有辛氏造。」 續咸議是王莽時物。 後魏景明中，并州人王顯達獻古銅權一枚，上銘八十一字。 其銘云：律權石，重四鈞。」 又云：「黃帝初祖，德匝于虞。 虞帝始祖，德匝於新。 歲在大樑，龍集戊辰。 戊辰直定，天命有人。 據土德受，正號即真。 改正建醜，長壽隆崇。 同律度量衡，稽當前人。 龍在己巳，歲次實沈，初班天下，萬國永遵。 子子孫孫，享傳億年。」 此亦王莽所制也。 其時太樂令公孫崇依《漢志》先修稱尺，及見此權，以新稱稱之，重一百二十斤。 新稱與權，合若符契。 於是付崇調樂。 孝文時，一依《漢志》作鬥尺。
Kaihuang used three ancient dou per sheng. Daye initially restored the ancient dou. ○ Steelyard and Weights. The steelyard denotes balance; while weight denotes heaviness. The steelyard bears weights and balances light and heavy. Its principle is like a base—showing the level's correctness and the cord's straightness. Turn left to reveal the compass; turn right the square. In Heaven it assists the armillary sphere, adjusting the pointer to align the seven regulators—the jade steelyard. Weights are zhu, liang, jin, jun, shi—using scales to know light and heavy. Antiquity had millet, R, chui, zi, huan, gou, lue, and yi weight units—dynastic variations unrecorded. The Former Treatise: weights originate from Yellow Bell's weight. One pitch key holds 1,200 grains, weighing twelve zhu. Two keys make a liang; twenty-four zhu a liang. Sixteen liang equal one jin. Thirty jin equal one jun. Four jun equal one shi. Thus the five weight units are verified. Established by principle, balanced by things. Other size differences follow light and heavy as appropriate. Round and looped with flesh double the hole—turning endlessly, never exhausted. Weights balance things and generate the steelyard; steelyard motion the compass; compass roundness the square; square the cord; cord the leveling base. Correct leveling base means balanced steelyard and equalized weights. These five standards, complete in the steelyard, form the great model. Zhao History records: Shi Le's eighteenth year, seventh month, building Jiande Hall, a round stone like a water pestle was found. Inscription: "Pitch-standard weight shi, four jun weight, unified pitch, measure, and steelyard. It was made by the Xin clan. Xu Xian identified it as Wang Mang-era. Northern Wei Jingming—a Bingzhou man Wang Xianda presented an ancient copper weight with eighty-one-character inscription. Inscription: "Pitch-standard weight shi, four jun." Also: "Yellow Emperor's first ancestor, virtue extending to Yu. The Yu Emperor's first ancestor, whose virtue extended to Xin. In the year Great Beam, the dragon gathered at wuchen. At wuchen directly fixed, Heaven's Mandate found its bearer. Receiving earth virtue, correct title then true. Correcting the calendar and establishing chou, long life lofty and grand. Unified pitch, measure, and steelyard, examining predecessors. Dragon at jisi, year Shi Shen, first promulgated empire-wide, ten thousand states forever following. Sons and grandsons, enjoying transmission for a hundred million years." This was also Wang Mang's work. Grand Music Director Gongsun Chong first repaired the steelyard measure per the Han Treatise; weighing this object on the new steelyard—it weighed 120 jin. The new steelyard and weight matched like seal and tally. Chong was then charged with tuning music. Under Emperor Xiaowen, dou and foot measure were made per the Han Treatise.
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梁、陳依古稱。 齊以古稱一斤八兩為一斤。 周玉稱四兩，當古稱四兩半。 開皇以古稱三斤為一斤，大業中，依復古秤。
Liang and Chen used the ancient steelyard. Qi counted eight ancient liang as one jin. Zhou jade steelyard four liang equaled ancient steelyard four and a half liang. Kaihuang counted three ancient jin as one jin; Daye restored the ancient steelyard.