1
左史記言，右史記事，事則春秋是也，言則尚書是也。 至於楚書、鄭志、晉乘、楚杌之篇，皆所以昭述前史，俾不泯於後。
The left historiographer kept the record of speeches; the right historiographer kept the record of events. Events became the Spring and Autumn Annals; speeches became the Documents. Works such as the Chu Annals, the Zheng Records, the Jin History, and the Chu Chronicles all served to set forth earlier histories in full light, lest they be lost to posterity.
2
司馬遷制一家之言，始區別名題，至乎禮儀刑政，有所不盡，乃於紀傳之外，創立八書，片文隻事，鴻纖備舉。 班氏因之，靡違前式，網羅一代，條流遂廣。 律曆禮樂，其名不變，以天官為天文，改封禪為郊祀，易貨殖、平準之稱，革河渠、溝洫之名； 綴孫卿之辭，以述刑法，采孟軻之書，用序食貨。 劉向鴻範，始自春秋，劉歆七略，儒墨異部，朱贛博采風謠，尤為詳洽，固並因仍，以為三志。 而禮樂疏簡，所漏者多，典章事數，百不記一。 天文雖為該舉，而不言天形，致使三天之說，紛然莫辨。 是故蔡邕於朔方上書，謂宜載述者也。
When Sima Qian shaped his independent historical vision, he was the first to sort material under distinct topical headings. Where ritual, penal law, and administration still eluded full treatment, he went beyond annals and biographies to create the Eight Treatises, gathering every scrap of evidence, large or small. Ban Gu took up his model without breaking from the earlier form, sweeping an entire dynasty into his net until the topical branches spread wide. Pitch pipes, calendars, ritual, and music kept their old titles; he renamed the Heavenly Offices section Astronomy, turned Feng and Shan into Suburban Sacrifice, retitled Goods and Wealth and Equalization, and renamed the River Works and Ditches and Channels sections. He drew on Xunzi to compose the treatise on penal law and on Mencius to order the section on food and wealth. Liu Xiang's Great Plan reached back to the Spring and Autumn era; Liu Xin's Seven Summaries separated Confucian and Mohist writings into different categories; Zhu Gan's wide gathering of folk songs was especially comprehensive. Ban Gu followed these lines as well, treating them as three treatises. Yet ritual and music were treated thinly, with much left out, and of institutional records and numerical data scarcely one item in a hundred was preserved. Astronomy was surveyed at length, yet the shape of Heaven itself went unaddressed, so the competing doctrines of the Three Heavens fell into dispute with no way to settle them. That is why Cai Yong, writing from Shuofang, urged that such matters be fully recorded in the history.
3
漢興，接秦阬儒之後，典墳殘缺，耆生碩老，常以亡逸為慮。 劉歆七略，固之藝文，蓋為此也。 河自龍門東注，橫被中國，每漂決所漸，寄重災深，堤築之功，勞役天下。 且關、洛高塏，地少川源，是故鎬、酆、潦、潏，咸入禮典。 漳、滏、鄭、白之饒，溝渠沾溉之利，皆民命所祖，國以為天，溝洫立志，亦其宜也。 世殊事改，於今可得而略。
When the Han dynasty rose, it came after Qin's suppression of classical learning. The canonical libraries lay in ruins, and veteran scholars lived in constant fear that the tradition would be lost. Liu Xin's Seven Summaries and Ban Gu's Bibliographic Treatise were created above all for that reason. East of Longmen the Yellow River poured across the heartland of China. Each burst and shift brought disaster in its wake, and the endless labor of dike-building wore out the realm. The Guanzhong and Luoyang regions moreover stood on high ground with few natural waterways, which is why the Hao, Feng, Liao, and Ju were all enshrined in ritual texts. The wealth of the Zhang, Fu, Zheng, and Bai waterways and the bounty brought by irrigation ditches were matters on which the people's lives depended and the state founded its very survival. A treatise on ditches and channels was only fitting. Times change and institutions shift; what can be set down today must be treated in outline.
4
竊以班氏律曆，前事已詳，自楊偉改創景初，而魏書闕志。 及元嘉重造新法，大明博議回改，自魏至宋，宜入今書。
Ban Gu's sections on pitch pipes and the calendar already cover earlier matters in detail. From Yang Wei's Jingchu reform onward, however, the Wei history left no corresponding treatise. When the Yuanjia reign created a new calendar and the Daming reign debated further revisions, the calendrical work from Wei through Song belongs in this history.
5
班固禮樂、郊祀，馬彪祭祀、禮儀，蔡邕朝會，董巴輿服，並各立志。 夫禮之所苞，其用非一，郊祭朝饗，匪云別事，旗章服物，非禮而何？ 今總而裁之，同謂禮志。 刑法、食貨，前說已該，隨流派別，附之紀傳。 樂經殘缺，其來已遠，班氏所述，政抄舉樂記，馬彪後書，又不備續。 至於八音眾器，並不見書，雖略見世本，所闕猶眾。 爰及雅鄭，謳謠之節，一皆屏落，曾無概見。 郊廟樂章，每隨世改，雅聲舊典，咸有遺文。 又案今鼓吹鐃歌，雖有章曲，樂人傳習，口相師祖，所務者聲，不先訓以義。 今樂府鐃歌，校漢、魏舊曲，曲名時同，文字永異，尋文求義，無一可了。 不知今之鐃章，何代曲也。 今志自郊廟以下，凡諸樂章，非淫哇之辭，並皆詳載。
Ban Gu wrote treatises on ritual, music, and suburban sacrifice; Ma Biao on sacrificial rites and ceremonial protocol; Cai Yong on court assemblies; and Dong Ba on chariots and garments—each as its own section. Ritual embraces many functions at once. Suburban sacrifice, court audiences, and ceremonial feasts are not separate subjects, and banners, regalia, and vestments belong to ritual by their very nature. I have therefore gathered these topics together under a single Treatise on Ritual. Penal law and food and wealth were already treated in the earlier account; following their separate lines of development, they are attached to the annals and biographies. The Music Classic had long lain damaged and incomplete. Ban Gu's account largely copied from the Record of Music, and Ma Biao's Later History failed to carry the subject forward. The eight categories of tone and the full range of instruments scarcely appear in the histories at all. Even the World Roots offers only glimpses, and much remains unrecorded. Elegant court music and popular songs alike were cast aside, until not even a general account survived. Temple and suburban hymns changed from reign to reign, yet the old refined repertory still left texts behind. Today's Music Office drum-and-bugle songs, though they retain their melodies, are handed down mouth to ear. Musicians care for the sound alone and are not first taught what the words mean. When one compares present Music Office drum songs with Han and Wei originals, the titles sometimes match but the words never do. Search the texts for meaning and nothing can be made out. No one can even say which age produced the drum songs in use today. In this treatise, every hymn from suburban rites downward that is not licentious or vulgar is recorded in full.
6
天文、五行，自馬彪以後，無復記錄。 何書自黃初之始，徐志肇義熙之元。 今以魏接漢，式遵何氏。 然則自漢高帝五年之首冬，暨宋順帝昇明二年之孟夏，二辰六沴，甲子無差。 聖帝哲王，咸有瑞命之紀，蓋所以神明寶位，幽贊禎符，欲使逐鹿弭謀，窺覬不作，握河括地，綠文赤字之書，言之詳矣。 爰逮道至天而甘露下，德洞地而醴泉出，金芝玄秬之祥，朱草白烏之瑞，斯固不可誣也。 若夫衰世德爽，而嘉應不息，斯固天道茫昧，難以數推。 亦由明主居上，而震蝕之災不弭； 百靈咸順，而懸象之應獨違。 今立符瑞志，以補前史之闕。
From Ma Biao onward, astronomy and the Five Phases received no further historical record. He Chen's account began with the Huangchu era; Xu Yi's with the founding of the Yixi reign. Treating Wei as the continuation of Han, I follow He's model. From the first month of winter in Han Gaozu's fifth year to the first month of summer in Song Shundi's second Shengming year, the two chronologies and six portents align through the sexagenary cycle without discrepancy. Sage rulers all possessed records of auspicious mandates by which they illuminated the throne and confirmed heaven's favor, hoping to still the ambitions of rival claimants. Texts that 'grasped the river,' 'enclosed the earth,' and bore green characters on red ground spoke of such things at length. When the Way touched Heaven, sweet dew fell; when virtue penetrated the earth, sweet springs welled up. Omens such as golden fungus, black millet, vermilion grass, and the white crow cannot simply be dismissed. Yet when virtue faded in a declining age while auspicious signs still multiplied, that too shows how obscure Heaven's way is and how poorly it yields to reckoning. It may also happen that a worthy ruler reigns above while earthquakes and eclipses continue unabated; or that all spirits appear obedient while celestial signs alone refuse to accord. I therefore establish a Treatise on Tokens and Omens to fill the gaps left by earlier histories.
7
地理參差，事難該辨，魏晉以來，遷徙百計，一郡分為四五，一縣割成兩三，或昨屬荊、豫，今隸司、兗，朝為零、桂之士，夕為廬、九之民，去來紛擾，無暫止息，版籍為之渾淆，職方所不能記。 自戎狄內侮，有晉東遷，中土遺氓，播徙江外，幽、并、冀、雍、兗、豫、青、徐之境，幽淪寇逆。 自扶莫而裹足奉首，免身於荊、越者，百郡千城，流寓比室。 人佇鴻雁之歌，士蓄懷本之念，莫不各樹邦邑，思復舊井。 既而民單戶約，不可獨建，故魏邦而有韓邑，齊縣而有趙民。 且省置交加，日回月徙，寄寓遷流，迄無定託，邦名邑號，難或詳書。 大宋受命，重啟邊隙，淮北五州，翦為寇境，其或奔亡播遷，復立郡縣，斯則元嘉、泰始，同名異實。 今以班固、馬彪二志，晉、宋起居，凡諸記註，悉加推討，隨條辨析，使悉該詳。
Geography is uneven, and no account can fully compass it. From Wei and Jin onward territories were carved and re-carved countless times: one commandery became four or five, one county split in two or three. Lands that yesterday belonged to Jing or Yu might today answer to Si or Yan; people who at dawn were subjects of Ling or Gui by dusk were counted among the households of Lu or Jiu. Movement never ceased, registers fell into chaos, and even the office charged with mapping the realm could not keep pace. After the northern peoples invaded and Jin fled east, the remnant population of the central plains was driven beyond the rivers. You, Bing, Ji, Yong, Yan, Yu, Qing, and Xu were lost to the invaders. Those who bound their feet, bowed their heads, and fled south to Jing and Yue filled a hundred commanderies and a thousand cities, until exiles outnumbered natives in house after house. The people sang songs of longing like the wild geese's cry; scholars cherished the hope of returning home. Everywhere they founded new settlements in memory of the old. But households were few and could not stand alone, so Han communities appeared inside Wei territory and Zhao families inside Qi counties. Provinces and districts were added and abolished month by month; migrants wandered without fixed abode, and the names of states and towns could scarcely be written down in full. When the Song dynasty arose, the northern frontier was reopened, yet the five Huai-north provinces became enemy ground. Refugees who fled south re-established old commanderies and counties in name only—so under Yuanjia and Taishi, the same names concealed different realities. Drawing on Ban Gu and Ma Biao, on Jin and Song court records, and on every relevant commentary, I have traced each entry so that the account may be as complete as possible.
8
百官置省，備有前說，尋源討流，於事為易。
The creation and abolition of the hundred offices already have earlier accounts; tracing origins and following their course is the easier part.
9
元嘉中，東海何承天受詔纂宋書，其志十五篇，以續馬彪漢志，其證引該博者，即而因之，亦由班固、馬遷共為一家者也。 其有漏闕，及何氏後事，備加搜采，隨就補綴焉。 淵流浩漫，非孤學所盡； 足蹇途遙，豈短策能運。 雖斟酌前史，備覩妍嗤，而愛嗜異情，取捨殊意，每含毫握簡，杼軸忘飡，終亦不足與班、左並馳，董、南齊轡。 庶為後之君子削藳而已焉。
In the Yuanjia era He Chengtian of Donghai received orders to compile the History of Song. His fifteen treatises continued Ma Biao's Han Treatises; where his evidence is sound I follow it, for Ban Gu and Sima Qian belong to one continuous tradition. Where he left gaps, and for events after his day, I have searched widely and filled in what was missing. The stream of learning is vast, far beyond what one scholar can master; with lame feet on a long road, no short whip can carry one through. Though I have studied earlier histories and seen their strengths and flaws, personal taste shapes every choice. Again and again I take up brush and slip and forget to eat at the loom—yet I still cannot keep pace with Ban Gu and Sima Qian, or run even with Dong and Nan. I can only offer later readers something to cut and reshape for themselves.
10
黃帝使伶倫自大夏之西，阮隃之陰，取竹之嶰谷生，其竅厚均者，斷兩節間而吹之，以為黃鍾之宮。 制十二管，以聽鳳鳴，以定律呂。 夫聲有清濁，故協以宮商； 形有長短，故檢以丈尺； 器有大小，故定以斛斗； 質有輕重，故平以鈞石。 故虞書曰：「乃同律、度、量、衡。」 然則律呂，宮商之所由生也。
The Yellow Emperor sent Ling Lun west beyond Great Xia, to the northern side of Mount Wanqu, to take bamboo from Xie Valley with even bore and wall, cut between two nodes, and blow it to establish the Yellow Bell as the fundamental pitch. He then made twelve pipes, listened to the phoenixes' cries, and fixed the standards of pitch. Because sound has clear and murky tones, it is harmonized through gong and shang. Because form has length and brevity, it is measured by foot and yard. Because vessels differ in size, they are fixed by the hu and the dou. Because mass differs in weight, it is balanced by the jun and the stone. Hence the Documents of Yu says: 'Thus unify pitch pipes, length measures, capacity measures, and balances.' Pitch pipes, then, are what give rise to the modes of gong and shang.
11
夫樂有器有文，有情有官。 鍾鼓干戚，樂之器也； 屈伸舒疾，樂之文也； 「論倫無患，樂之情也； 欣喜歡愛，樂之官也。」 「是以君子反情以和志，廣樂以成教，故能情深而文明，氣盛而化神，和順積中，而英華發外。」 故曰：「樂者，心之動也； 聲者，樂之象也。」 周禮曰：「乃奏黃鍾，歌大呂，舞雲門，以祀天神。 乃奏太蔟，歌應鍾，舞咸池，以祭地祇。」 四望山川先祖，各有其樂。 又曰：「圜鍾為宮，黃鍾為角，太蔟為徵，[1]姑洗為羽，雷鼓雷鼗，孤竹之管，雲和之琴瑟，雲門之舞，冬日至，於地上之圜丘奏之。 若樂六變，則天神皆降，可得而禮矣。」 地祇人鬼，禮亦如之。 其可以感物興化，若此之深也。
Music possesses instruments and pattern, feeling and function. Bells, drums, shields, and axes are music's instruments; bending, stretching, hastening, and slowing are its pattern; 'to discuss harmony without injury is music's inner feeling; joy, delight, and affection are its offices.' Therefore the gentleman turns feeling back upon itself to harmonize the will, extends music to complete instruction, makes feeling deep and pattern bright, breath strong and transformation numinous; harmony gathers within, and splendor shines without.' Hence it is said: 'Music is the movement of the heart; sound is the image of music.' The Rites of Zhou says: 'Then play the Yellow Bell, sing the Great Lu, and dance the Cloud Gate to sacrifice to the Heavenly Spirit. Then play the Great Cu, sing the Responding Bell, and dance the Xian Pool to sacrifice to the Earthly Spirits.' Sacrifices to the four outlooks, mountains, rivers, and ancestors each had its proper music. It also says: 'The round bell serves as gong, the Yellow Bell as jue, the Great Cu as zhi, [1] the Gu Xian as yu; with thunder drums and thunder tambourines, pipes of solitary bamboo, Yunhe qin and se, and the Cloud Gate dance—at the winter solstice these are performed at the round altar on earth. When the six musical changes are performed, the heavenly spirits descend and may be received in sacrifice.' Earthly spirits and human ghosts were honored by the same ritual logic. That music can move things and transform customs to such depth is evident.
12
「道始於一，一生二，二生三，三三而九。 [2]故黃鍾之數六，分而為雌雄十二鍾。 鍾以三成，故置一而三之，凡積分十七萬七千一百四十七，為黃鍾之實。 故黃鍾位子，主十一月，下生林鍾。 林鍾之數五十四，主六月，上生太蔟。 太蔟之數七十二，主正月，下生南呂。 南呂之數四十八，主八月，上生姑洗。 姑洗之數六十四，主三月，下生應鍾。 應鍾之數四十三，主十月，上生蕤賓。 蕤賓之數五十七，主五月，上生大呂。 大呂之數七十六，主十二月，下生夷則。 夷則之數五十一，[3]主七月，上生夾鍾。 夾鍾之數六十七，主二月，下生無射。 無射之數四十五，主九月，上生中呂。 中呂之數六十，主四月，極不生。 〈極不生，鍾律不能復相生。〉 宮生徵，徵生商，商生羽，羽生角，角生姑洗，姑洗生應鍾，比於正音，故為和。 [4] 〈姑洗三月，應鍾十月，與正音比，故為和。 和，從聲也。〉 [5]應鍾生蕤賓，蕤賓不比於正音，故為繆。 〈繆，音相干也。 周律故有繆、和，為武王伐紂七音也。〉 日冬至，音比林鍾浸以濁； 日夏至，音比黃鍾浸以清。 以十二月律應二十四時。 甲子，中呂之徵也； 丙子，夾鍾之羽也； 戊子，黃鍾之宮也； 庚子，無射之商也； 壬子，夷則之角也。」
'The Way begins in One; One engenders Two, Two engenders Three, and three threes make nine. [2] The number of the Yellow Bell is six; divided, it yields the twelve male and female pitch pipes. Each pipe is built by tripling; set one and triple it repeatedly until the accumulated fraction reaches 177,147 as the full measure of the Yellow Bell. The Yellow Bell stands in the zi position and governs the eleventh month; from it the Lin Bell is generated downward. The Lin Bell's number is fifty-four; it governs the sixth month; upward from it comes the Great Cu. The Great Cu's number is seventy-two; it governs the first month; downward from it comes the Southern Lu. The Southern Lu's number is forty-eight; it governs the eighth month; upward from it comes the Gu Xian. The Gu Xian's number is sixty-four; it governs the third month; downward from it comes the Responding Bell. The Responding Bell's number is forty-three; it governs the tenth month; upward from it comes the Flaccid Guest. The Flaccid Guest's number is fifty-seven; it governs the fifth month; upward from it comes the Great Lu. The Great Lu's number is seventy-six; it governs the twelfth month; downward from it comes the Leveling Ze. The Leveling Ze's number is fifty-one, [3] governing the seventh month; upward from it comes the Pinched Bell. The Pinched Bell's number is sixty-seven; it governs the second month; downward from it comes the Untempered Pitch. The Untempered Pitch's number is forty-five; it governs the ninth month; upward from it comes the Middle Lu. The Middle Lu's number is sixty; it governs the fourth month; at the extreme, no further generation occurs. 〈At the extreme no further generation occurs; the pitch pipes cannot generate one another again.〉 Gong generates zhi, zhi generates shang, shang generates yu, yu generates jue; jue generates Gu Xian, and Gu Xian generates Responding Bell. Compared with the correct pitches, these form harmony. [4] (Editorial note.) 〈Gu Xian corresponds to the third month and Responding Bell to the tenth month; compared with the correct pitches, they form harmony. Harmony is a following tone.〉 [5] Responding Bell generates Flaccid Guest; Flaccid Guest does not match the correct pitch, and therefore is dissonant. 〈Dissonance means the tones interfere with one another. The Zhou pitch standards thus included dissonant and harmonious tones—the seven tones used when King Wu campaigned against the Tyrant of Shang.〉 At the winter solstice the tone aligns with the Lin Bell and gradually grows murky; at the summer solstice it aligns with the Yellow Bell and gradually grows clear. The twelve monthly pitch pipes correspond to the twenty-four seasonal nodes. The jiazi day is the zhi-tone of Middle Lu; the bingzi day is the yu-tone of the Pinched Bell; the wuzi day is the gong-tone of the Yellow Bell; the gengzi day is the shang-tone of the Untempered Pitch; the renzi day is the jue-tone of the Leveling Ze.」'
13
「古人為度量輕重，皆生乎天道。 黃鍾之律長九寸，物以三生，三三九，三九二十七，故幅廣二尺七寸，古之制也。 音以八相生，故人長八尺，尋自倍，故八尺而為尋。 有形即有聲，音之數五，以五乘八，五八四十尺為匹。 匹者，中人之度也，一匹為制。 秋分而禾䅺定， 〈䅺，禾穗芒也。〉 䅺定而禾孰。 律之數十二，故十二䅺而當一粟，十二粟而當一寸。 [6]律以當辰，音以當日。 日之數十，故十寸而為尺，十尺為丈。 其以為重，十二粟而當一分，十二分而當一銖，十二銖而當半兩。 衡有左右，因而倍之，故二十四銖而當一兩。 天有四時，以成一歲，因而四之，四四十六，故十六兩而一斤。 三月而一時，三十日一月，故三十斤而為一鈞。 四時而一歲，故四鈞而一石。」 「其為音也，一律而生五音，十二律而為六十音； 因而六之，六六三十六，故三百六十音以當一歲之日。 故律曆之數，天地之道也。 下生者倍，以三除之； 上生者四，以三除之。」
「In establishing measures of weight, the ancients all derived them from Heaven's way. The Yellow Bell pipe is nine inches long. Things are born by threes: three threes make nine, three nines twenty-seven—hence cloth was two feet seven inches wide in the ancient system. Because tones are generated by eights, a man's height is eight feet. The xun doubles upon itself, so eight feet make one xun. Form gives rise to sound. Tones number five; five times eight is forty feet, which makes one bolt of cloth. A bolt was the measure of an ordinary man and served as the standard length. At the autumn equinox the grain awns are fixed, 〈The awn is the bristle of the grain ear.〉 and when the awns are set the grain ripens. Pitch standards number twelve, so twelve awns equal one grain and twelve grains equal one inch. [6] Pitch standards correspond to the chronograms; tones correspond to days. Days number ten, so ten inches make a foot and ten feet a zhang. For weight, twelve grains make one fen, twelve fen one zhu, and twelve zhu half a liang. The balance has left and right pans; doubled, twenty-four zhu make one liang. Heaven has four seasons to complete a year; multiply by four and four fours make sixteen, so sixteen liang make one jin. Three months make a season and thirty days a month, so thirty jin make one jun. Four seasons make a year, so four jun make one shi. 」「In sound, one pitch standard generates five tones; twelve standards yield sixty tones; multiply by six and six sixes make thirty-six, so three hundred sixty tones match the days of a year. Thus the numbers of pitch pipes and the calendar embody the way of Heaven and Earth. In downward generation, double and divide by three; in upward generation, multiply by four and divide by three.」
14
揚子雲曰：「聲生於日， 〈謂甲己為角，乙庚為商，丙辛為徵，丁壬為羽，戊癸為宮。〉 律生於辰， 〈謂子為黃鍾，丑為大呂之屬。〉 聲以情質， 〈質，正也。 各以其行本情為正也。〉 律以和聲， 〈當以律管鍾均，和其清濁之聲。〉 聲律相協，而八音生。 〈協，和。〉 宮、商、角、徵、羽，謂之五聲。 金、石、匏、革、絲、竹、土、木，謂之八音。 聲和音諧，是謂五樂。」
Yang Xiong said: 「Sound is born from the day, 〈That is, jia-ji days produce jue, yi-geng shang, bing-xin zhi, ding-ren yu, and wu-gui gong.〉 pitch standards are born from the chronograms, 〈That is, zi is the Yellow Bell, chou the Great Lu, and so forth.〉 sound takes feeling as its substance, 〈Substance means correctness. Each mode takes the native character of its phase as the standard.〉 pitch standards harmonize sound, 〈One matches clear and murky tones with pitch pipes and bell standards.〉 When sound and pitch standards accord, the eight classes of tone arise. 〈Accord means harmony.〉 Gong, shang, jue, zhi, and yu are called the five tones. Metal, stone, gourd, hide, silk, bamboo, earth, and wood are called the eight materials of sound. When sound and tone are in harmony, this is called the five kinds of music.」
15
夫陰陽和則景至，律氣應則灰除。 是故天子常以冬夏至御前殿，合八能之士，陳八音，聽樂均，度晷景，候鍾律，權土炭，効陰陽。 冬至陽氣應，則樂均清，景長極，黃鍾通，土炭輕而衡仰。 [7]夏至陰氣應，則樂均濁，景短極，蕤賓通，土炭重而衡低。 進退於先後五日之中，八能各以候狀聞。 太史令封上。 効則和，否則占。 候氣之法，為室三重，戶閉，塗釁周密，布緹幔。 室中以木為案，每律各一，內庳外高，從其方位，加律其上。 以葭莩灰布其內端，案曆而候之。 氣至者灰動。 其為氣動者其灰散，人及風所動者，其灰聚。 [8]殿中候，用玉律十二。 唯二至乃候靈臺，用竹律六十。 [9]取弘農宜陽縣金門山竹為管，河內葭莩為灰。 [10]
When yin and yang are in harmony the shadow is cast; when pitch-breath responds the ash is expelled. Therefore at the winter and summer solstices the Son of Heaven would attend the front hall, gather masters of the eight skills, array the eight tones, listen to the musical balance, measure the gnomon shadow, observe pitch standards, weigh charcoal and earth, and test yin and yang. At the winter solstice yang-breath responds: the balance sounds clear, the shadow reaches its maximum, the Yellow Bell pipe is active, and the charcoal and earth are light while the balance arm rises. [7] At the summer solstice yin-breath responds: the balance sounds murky, the shadow is shortest, the Flaccid Guest pipe is active, and the charcoal and earth are heavy while the balance arm falls. Within the five days before and after each solstice, each of the eight skills reports what it has observed. The Grand Astrologer seals and submits the reports. When the signs accord, all is harmonious; when they do not, divination follows. The method for observing qi: construct a triple chamber, close the doors, seal the walls tightly, and hang fine silk curtains. Inside, set a wooden stand for each pitch standard—lower within, higher without—placed according to its direction with the standard pipe set on top. Pack reed-fluff ash at the inner end and observe according to the calendar. When qi arrives, the ash stirs. If qi moves it the ash scatters; if people or wind move it the ash clumps. [8] Observations within the palace used twelve jade pitch standards. Only at the two solstices was the Spirit Terrace used, with sixty bamboo pitch standards. [9] Bamboo tubes came from Golden Gate Mountain in Yiyang county, Hongnong; ash came from reed-fluff of the interior marshes. [10] (Editorial note.)
16
三代陵遲，音律失度。 漢興，北平侯張蒼始定律曆。 孝武之世，置協律之官。 元帝時，郎中京房知五音六十律之數，受學於小黃令焦延壽。 其下生、上生，終於中呂，而十二律畢矣。 中呂上生執始，執始下生去滅，終於南事，而六十律畢矣。 夫十二律之變至於六十，猶八卦之變至於六十四也。 宓羲作易，紀陽氣之初，以為律法。 建日冬至之聲，以黃鍾為宮，太蔟為商，姑洗為角，林鍾為徵，南呂為羽，應鍾為變宮，蕤賓為變徵。 此聲氣之元，五音之正也。 故各統一日。 其餘以次運行，當日者各自為宮，而商角徵羽以類從焉。 禮運篇曰：「五聲、六律、十二管還相為宮。」 此之謂也。 以六十律分一朞之日，黃鍾自冬至始，及冬至而復，陰陽寒煖風雨之占於是生焉。 房又曰：「竹聲不可以度調，故作準以定數。 準之狀如瑟，長丈而十三弦，隱間九尺，以應黃鍾之律九寸； 中央一弦，下有畫分寸，以為六十律清濁之節。」 房言律詳於歆所奏，[11]其術施行於史官，候部用之。 續漢志具載其律準度數。
After the three dynasties declined, pitch pipes and measures lost their proper standards. When the Han arose, Marquis Zhang of Beiping first established pitch pipes and the calendar. Under Emperor Wu offices were created to harmonize pitch standards. Under Emperor Yuan the palace gentleman Jing Fang mastered the five tones and sixty pitch standards, studying under Director Jiao Yanshou of the Yellow Gate. His downward and upward generation ended at Middle Lu, completing the twelve pitch standards. From Middle Lu upward came Zhi Shi; from Zhi Shi downward Qu Mie; ending at Southern Affairs—and the sixty pitch standards were complete. The extension of twelve pitch standards to sixty parallels the extension of the eight trigrams to sixty-four. Fu Xi created the Changes, marking the beginning of yang-breath, and made it the basis of pitch law. Taking the winter-solstice tone as foundation, he set Yellow Bell as gong, Great Cu as shang, Gu Xian as jue, Lin Bell as zhi, Southern Lu as yu, Responding Bell as altered gong, and Flaccid Guest as altered zhi. This is the root of breath-sound and the true foundation of the five tones. Each therefore governs one day. The rest follow in sequence: whichever day is current serves as gong, with shang, jue, zhi, and yu arranged by kind. The Record of Rites says: 「The five tones, six pitch standards, and twelve pipes rotate to serve as one another's gong. 」This is what is meant. Dividing the days of a cycle among sixty pitch standards, the Yellow Bell begins at the winter solstice and returns at winter solstice; from this arise forecasts of yin and yang, cold and warmth, wind and rain. Fang also said: 「Bamboo sound cannot fix tuning by itself, so he made the pitch-standard instrument to establish the numbers. The instrument resembles a se, one zhang long with thirteen strings; the hidden interval is nine feet, matching the Yellow Bell's nine inches; beneath the central string are marked inches and fen as gradations for the clear and murky levels of the sixty pitch standards. 」Fang held that pitch theory was more detailed than Liu Xin's presentation; [11] his method was practiced by historiographers and used in the observation offices. The Continued Han Treatises record his pitch-standard measurements in full.
17
漢章帝元和元年，待詔候鍾律殷肜上言：「官無曉六十律以準調音者，故待詔嚴嵩具以準法教子男宣，願召宣補學官，主調樂器。」 詔曰：「嵩子學審曉律，別其族，協其聲者，審試。 不得依託父學，以聾為聰。 聲微妙，獨非莫知，獨是莫曉，以律錯吹，能知命十二律不失一，乃為能傳嵩學耳。」 試宣十二律，其二中，其四不中，其六不知何律，宣遂罷。 自此律家莫能為準。 靈帝熹平六年，東觀召典律者太子舍人張光等問準意。 光等不知。 歸閱舊藏，乃得其器，形制如房書，猶不能定其絃緩急。 音不可書以曉人，[12]知之者欲教而無從，心達者體知而無師，故史官能辨清濁者遂絕。 其可以相傳者，唯候氣而已。
In the first year of Yuanhe under Emperor Zhang, awaiting-edict pitch observer Yin Hong submitted: 「No one in office understands the sixty pitch standards for tuning instruments. Awaiting-edict Yan Song has fully taught his son Nan Xuan the standard method; I ask that Xuan be summoned to the learning office to take charge of tuning instruments. 」The edict replied: 「If Song's son has truly mastered pitch standards, distinguishing their families and harmonizing their sounds, test him carefully. He must not rely on his father's learning and pass off deafness as hearing. Sound is subtle: only the tone-deaf cannot know it, only the untrained cannot grasp it. If, when pitch standards are used to test him by blowing, he can identify all twelve without missing one, only then may he transmit Song's art. 」They tested Xuan on the twelve standards: two correct, four wrong, and six he could not identify at all—so Xuan was dismissed. From that time onward no master of pitch standards could make the standard instrument. In the sixth year of Xiping under Emperor Ling, the Eastern Pavilion summoned pitch specialists including Zhang Guang, household attendant to the heir apparent, to inquire about the standard instrument. Guang and the others did not know. On returning to the old repository they found the instrument; its form matched Fang's description, yet they still could not determine how tight or slack the strings should be. Sound cannot be written down for others to understand; [12] those who know it wish to teach but find no pupils, those who grasp it inwardly have no master—so among historiographers the ability to distinguish clear from murky died out. What could still be handed down was only the method of observing qi.
18
舊律度新律度舊律分新律分 〈新律小分母三十六〉 [13]
Old pipe length New pipe length Old pitch fraction New pitch fraction 〈The new pitch standard uses thirty-six as the denominator for small fractions〉 [13] (Editorial note.)
19
黃鍾九寸九寸十七萬七千一百四十七十七萬七千一百四十七
Yellow Bell: nine inches (old), nine inches (new); fraction 177,147 (old and new).
20
林鍾六寸六寸一釐十一萬八千九十八十一萬八千二百九十六 〈二十五〉
Lin Bell: six inches (old), six inches one fen (new); fraction 118,098 (old), 118,296 (new). 〈Twenty-five〉
21
太蔟八寸八寸二釐十五萬七千四百六十四十五萬七千八百六十一 〈十四〉
Great Cu: eight inches (old), eight inches two fen (new); fraction 157,464 (old), 157,861 (new). 〈Fourteen〉
22
南呂五寸三分三釐 〈少強〉 [14]五寸三分六釐 〈少強〉 十萬四千九百七十六十萬五千五百七十二 〈三〉
Southern Lu: five inches, three fen, three li (old measure). 〈Slightly sharp〉 [14] Five inches, three fen, six li (new measure). 〈Slightly sharp〉 Fraction 104,976 (old), 105,572 (new). 〈Three〉
23
姑洗七寸一分一釐 〈強〉 七寸一分五釐 〈強〉 [15]十三萬九千九百六十八十四萬七百六十二 〈二十八〉
Gu Xian: seven inches, one fen, one li (old measure). 〈Sharp〉 Seven inches, one fen, five li (new measure). 〈Sharp〉 [15] Fraction 139,968 (old), 140,762 (new). 〈Twenty-eight〉
24
應鍾四寸七分四釐 〈強〉 [16]四寸七分九釐 〈強〉 九萬三千三百一十二九萬四千三百五 〈十七〉
Responding Bell: four inches, seven fen, four li (old measure). 〈Sharp〉 [16] Four inches, seven fen, nine li (new measure). 〈Sharp〉 Fraction 93,312 (old), 94,305 (new). 〈Seventeen〉
25
蕤賓六寸三分二釐 〈強〉 六寸三分八釐 〈強〉 [17]十二萬四千四百一十六[18]十二萬五千六百八 〈六〉 [19]
Flaccid Guest: six inches, three fen, two li (old measure). 〈Sharp〉 Six inches, three fen, eight li (new measure). 〈Sharp〉 [17] Fraction 124,416 (old) [18], 125,608 (new). 〈Six〉 [19] (Editorial note.)
26
大呂八寸四分二釐 〈大強〉 八寸四分九釐 〈大強〉 十六萬五千八百八十八十六萬七千二百七十八 〈三十一〉
Great Lu: eight inches, four fen, two li (old measure). 〈Very sharp〉 Eight inches, four fen, nine li (new measure). 〈Very sharp〉 Fraction 165,888 (old), 167,278 (new). 〈Thirty-one〉
27
夷則五寸六分一釐 〈大強〉 五寸七分 〈弱〉 十一萬五百九十二十一萬二千一百八十一 〈二十〉
Leveling Ze: five inches, six fen, one li (old measure). 〈Very sharp〉 Five inches, seven fen (new measure). 〈Flat〉 Fraction 110,592 (old), 112,181 (new). 〈Twenty〉
28
夾鍾七寸四分九釐 〈少弱〉 [20]七寸五分八釐 〈少弱〉 [21]十四萬七千四百五十六十四萬九千二百四十四 〈九〉
Pinched Bell: seven inches, four fen, nine li (old measure). 〈Slightly flat〉 [20] Seven inches, five fen, eight li (new measure). 〈Slightly flat〉 [21] Fraction 147,456 (old), 149,244 (new). 〈Nine〉
29
無射四寸九分九釐 〈半弱〉 [22]五寸九釐 〈半〉 九萬八千三百四十萬二百九十 〈三十四〉
Untempered Pitch: four inches, nine fen, nine li (old measure). 〈Half flat〉 [22] Five inches, nine li (new measure). 〈Half〉 Fraction 98,304 (old), 100,290 (new). 〈Thirty-four〉
30
中呂六寸六分六釐 〈弱〉 六寸七分七釐十三萬一千七十二十三萬三千二百五十七 〈二十五〉 [23]
Middle Lu: six inches, six fen, six li (old measure). 〈Flat〉 Six inches, seven fen, seven li (new); fraction 131,072 (old), 133,257 (new). 〈Twenty-five〉 [23] (Editorial note.)
31
黃鍾八寸八分八釐 〈弱〉 九寸十七萬四千七百六十二 〈三分之二，不足二千三百八十四，三分之一〉 [24]十七萬七千一百四十七
Yellow Bell: eight inches, eight fen, eight li (adjusted measure). 〈Flat〉 Nine inches; fraction 174,762. 〈Two-thirds of the remainder; short by 2,384, plus one-third〉 [24] 177,147 (full Yellow Bell fraction).
32
論曰：律呂相生，皆三分而損益之。 先儒推十二律，從子至亥，每三之，凡十七萬七千一百四十七，而三約之，是為上生。 故漢志云：三分損一，下生林鍾，三分益一，上生太蔟。 無射既上生中呂，則中呂又當上生黃鍾，然後五聲、六律、十二管還相為宮。 今上生不及黃鍾實二千三百八十四，九約實一千九百六十八為一分，此則不周九寸之律一分有奇，豈得還為宮乎？ 凡三分益一為上生，三分損一為下生，此其大略，猶周天斗分四分之一耳。 京房不思此意，比十二律微有所增，方引而伸之，中呂上生執始，執始下生去滅，至于南事，為六十律，竟復不合，彌益其疏。 班氏所志，未能通律呂本源，徒訓角為觸，徵為祉，陽氣施種於黃鍾，如斯之屬，空煩其文，而為辭費。 又推九六，欲符劉歆三統之數，假託非類，以飾其說，皆孟堅之妄矣。
The discussion states: pitch pipes generate one another by adding or subtracting one-third each time. Earlier scholars derived the twelve standards from zi to hai by tripling until they reached 177,147, then dividing by three for upward generation. Hence the Han Treatises: subtract one-third downward to get Lin Bell; add one-third upward to get Great Cu. Once Untempered Pitch generates Middle Lu upward, Middle Lu should generate Yellow Bell upward—only then can the five tones, six standards, and twelve pipes rotate as one another's gong. Yet upward generation now falls 2,384 short of the Yellow Bell's full measure—more than one fen shy of nine inches. How can the cycle return to gong? Increasing by one-third is upward generation; decreasing by one-third is downward generation—the broad principle, comparable to the quarter-day fraction in a full celestial circuit. Jing Fang missed this point. Slightly enlarging each of the twelve standards and extending the series—Middle Lu to Zhi Shi, Zhi Shi to Qu Mie, down to Southern Affairs for sixty standards—he still could not close the cycle, only widening the error. Ban Gu's account never reached the root of pitch theory; he merely glossed jue as 'touch' and zhi as 'blessing,' or said yang-breath sows in the Yellow Bell—empty verbiage that burdens the text. He also forced the numbers nine and six to fit Liu Xin's Three Systems, borrowing unrelated categories to dress up his doctrine—all Ban Gu's mistakes.
33
蔡邕從朔方上書，云前漢志但載十二律，[25]不及六十。 六律尺寸相生，司馬彪皆已志之。 漢末，亡失雅樂，黃初中，鑄工柴玉巧有意思，形器之中，多所造作。 協律都尉杜夔令玉鑄鍾，其聲清濁，多不如法。 數毀改作，玉甚厭之，謂夔清濁任意。 更相訴白於魏王。 魏王取玉所鑄鍾，雜錯更試，然後知夔為精，於是罪玉及諸子，皆為養馬士。 [26]
Cai Yong wrote from Shuofang that the Former Han Treatises recorded only twelve pitch standards, [25] not sixty. Sima Biao had already recorded how the six standards generate one another by pipe length. By the end of Han refined music was lost. In the Huangchu era the bell-caster Chai Yu was ingenious and produced many new instruments. Director of Harmonizing Pitch Standards Du Kui had Yu cast bells, but their clear and murky tones mostly failed to match the standard. Yu remade them again and again until he grew weary, accusing Kui of adjusting clear and murky arbitrarily. They repeatedly brought accusations against each other before the King of Wei. The King of Wei mixed and retested Yu's bells, then recognized Kui's mastery and punished Yu and his sons, reducing them all to horse-keepers. [26] (Editorial note.)
34
晉泰始十年，中書監荀勗、中書令張華，出御府銅竹律二十五具，部太樂郎劉秀等校試，其三具與杜夔及左延年律法同，其二十二具，視其銘題尺寸，是笛律也。 問協律中郎將列和，辭：「昔魏明帝時，令和承受笛聲，以作此律，欲使學者別居一坊，歌詠講習，依此律調。 至於都合樂時，但識其尺寸之名，則絲竹歌詠，皆得均合。 歌聲濁者，用長笛長律； 歌聲清者，用短笛短律。 凡絃歌調張清濁之制，不依笛尺寸名之，則不可知也。」
In Jin Taishi year ten, Xun Xu and Zhang Hua brought out twenty-five bronze and bamboo standards from the imperial treasury for testing by Director of Music Liu Xiu and others. Three matched Du Kui's and Zuo Yanian's pitch law; the other twenty-two, by their inscriptions and dimensions, were flute standards. They questioned Lie He, Director of Harmonizing Pitch Standards, who replied: 「Under Emperor Ming of Wei I was ordered to take flute sound as the basis for these standards, so students might practice in a separate ward tuned to them. When music was assembled at court, knowing the dimension names alone allowed strings, bamboo, and voices to blend evenly. Murky voices used the long flute and long standard; clear voices the short flute and short standard. The system for adjusting clear and murky in string-song tuning depends on those flute dimension names—without them it cannot be known.」
35
勗等奏：「昔先王之作樂也，以振風蕩俗，饗神佑賢，[27]必協律呂之和，以節八音之中。 [28]是故郊祀朝宴，用之有制，歌奏分敍，清濁有宜。 故曰『五聲十二律，還相為宮』。 此經傳記籍可得而知者也。 如和對辭，笛之長短，無所象則，率意而作，不由曲度。 考以正律，皆不相應，吹其聲均，多不諧合。 又辭：『先師傳笛，別其清濁，直以長短，工人裁制，舊不依律。』 是為作笛無法。 而和寫笛造律，[29]又令琴瑟歌詠，從之為正，非所以稽古先哲，垂憲于後者也。 謹條牒諸律，問和意狀如左。 及依典制，用十二律造笛像十二枚，聲均調和，器用便利。 講肄彈擊，必合律呂，況乎宴饗萬國，奏之廟堂者哉！ 雖伶、夔曠遠，至音難精，猶宜儀刑古昔，[30]以求厥衷，合于經禮，於制為詳。 若可施用，請更部笛工，選竹造作，下太樂、樂府施行。 [31]平議諸杜夔、左延年律可皆留。 其御府笛正聲下徵各一具，皆銘題作者姓名。 其餘無所施用，還付御府毀。」 奏可。
Xu and his colleagues memorialized: 「When the former kings made music, they stirred the wind and moved custom, feasted spirits and aided the worthy, [27] always harmonizing pitch pipes and tones to regulate the eight sounds. [28] Hence suburban sacrifice and court feast followed fixed rules; song and performance were ordered, clear and murky properly placed. Thus the saying: 'The five tones and twelve standards revolve to serve as one another's gong.' This is known from the classics, transmissions, and historical records. He's reply shows that flute length had no model; he made them by inclination, not by musical degree. Tested against correct pitch standards they do not correspond; blown evenly, most fail to harmonize. He also said: 『The master transmitted flutes by distinguishing clear and murky through length alone; craftsmen cut them by habit, never following pitch standards. 』That is making flutes without method. Yet He wrote flutes into pitch law [29] and made zithers, se, and songs follow them as the standard—not the way to examine antiquity and hand down law to posterity. We respectfully list the pitch standards and question He's intent as follows. By canonical system, twelve pitch standards should yield twelve flutes, one hole per standard, evenly tuned and convenient in use. In instruction and performance they must match pitch pipes and tones—how much more when feasting the myriad states in the ancestral hall! Though Ling Lun and Kui are far away and perfect tone hard to attain, one should still model the ancients [30], seek the central meaning, and conform to the classic rites. If approved, assign flute craftsmen to select bamboo and make them, and order the Director of Music and Music Office to implement them. [31] The court discussion held that Du Kui's and Zuo Yanian's pitch standards should all be retained. Of the imperial flutes, one each for correct sound and lower zhi bore the maker's inscribed name. The rest were useless and were returned to the imperial store for destruction. 」The memorial was approved.
36
勗又問和：「作笛為可依十二律作十二笛，令一孔依一律，然後乃以為樂不？」 和辭：「太樂東廂長笛正聲已長四尺二寸，今當復取其下徵之聲； 於法，聲濁者笛當長，計其尺寸，乃五尺有餘，和昔日作之，不可吹也。 又笛諸孔，雖不校試，意謂不能得一孔輒應一律也。」 案太樂，四尺二寸笛正聲均應蕤賓，以十二律還相為宮，推法下徵之孔，當應律大呂。 大呂笛長二尺六寸有奇，不得長五尺餘。 令太樂郎劉秀、鄧昊等依律作大呂笛以示和。 又吹七律，一孔一校，聲皆相應。 然後令郝生鼓箏，宋同吹笛，以為雜引、相和諸曲。 和乃辭曰：「自和父祖漢世以來，笛家相傳，不知此法，而今調均與律相應，實非所及也。」 郝生、魯基、种整、朱夏，皆與和同。
Xu questioned He again: 「Can flutes be made according to the twelve pitch standards, twelve flutes with one hole per standard—and only then serve as the basis of music? 」He replied: 「The eastern-wing long flute in correct sound is already four feet two inches; we must now take the lower-zhi tone as well; by rule murky sound requires a longer pipe; by calculation it would exceed five feet—the flute He made before cannot be blown. Moreover, though the flute holes were never tested, it seems impossible that each hole could match one pitch standard. 」The Grand Music Office found that a four-foot-two-inch flute in correct sound matches Flaccid Guest; by the twelve-standard cycle the lower-zhi hole should match Great Lu. A Great Lu flute is only a little over two feet six inches and cannot be five feet long. They ordered Liu Xiu, Deng Hao, and other music officers to make a Great Lu flute by the standards and show it to He. When each of the seven standards was tested at one hole, every sound corresponded. Then Master Hao played the zheng and Song Tong the flute on miscellaneous preludes and harmony pieces. He then said: 「Flute masters in my family since Han times never knew this method; that tuning now matches the standards is truly beyond me. 」Hao, Lu Ji, Chong Zheng, and Zhu Xia all agreed with He.
37
又問和：「笛有六孔，及其體中之空為七。 和為能盡名其宮商角徵不？ 孔調與不調，以何檢知？」 和辭：「先師相傳，吹笛但以作曲相語，為某曲當舉某指，[32]初不知七孔盡應何聲也。 若當作笛，其仰尚方笛工，依案舊像訖，但吹取鳴者，初不復校其諸孔調與不調也。」 案周禮調樂金石，有一定之聲，是故造鍾磬者，先依律調之，然後施於廂懸。 作樂之時，諸音皆受鍾磬之均，即為悉應律也。 至於饗宴殿堂之上，無廂懸鍾磬，以笛有一定調，故諸絃歌皆從笛為正。 是為笛猶鍾磬，宜必合於律呂。 如和所對，直以意造，率短一寸，七孔聲均，不知其皆應何律。 調與不調，無以檢正。 唯取竹之鳴者，為無法制。 輒令部郎劉秀、鄧昊、王豔、魏邵等與笛工參共作笛，[33]工人造其形，律者定其聲，然後器象有制，音均和協。
They asked He again: 「A flute has six holes, and the hollow within makes seven. Can you name every gong, shang, jue, and zhi? How can one test whether each hole is in tune? 」He replied: 「Masters taught only by pieces—'for this melody use this finger' [32]—without knowing what the seven holes should sound. When making a flute one copied the imperial craftsmen's old models and merely blew until it sounded, never calibrating the holes. 」The Rites of Zhou require fixed tones for bells and stones; casters first tune by pitch standards, then hang them in the frame. In performance all tones take their evenness from bells and chimes and thus match the standards. At hall feasts without frame bells and chimes, the flute's fixed tuning makes all string songs follow it. The flute, like bells and chimes, must accord with pitch pipes and tones. He's method was mere inclination, usually shortening by an inch; seven even holes with no knowledge of which standard each matched. There was no way to test or correct tuning. Taking whatever bamboo happens to sound was lawless. They ordered Liu Xiu, Deng Hao, Wang Yan, Wei Shao, and flute craftsmen to make flutes together; [33] craftsmen shaped them, specialists fixed the tones—so instruments had system and sounds harmonized.
38
又問和：「若不知律呂之義，作樂音均高下清濁之調，當以何名之？」 和辭：「每合樂時，隨歌者聲之清濁，用笛有長短。 假令聲濁者用三尺二笛，因名曰此三尺二調也。 聲清者用二尺九笛，因名曰此二尺九調也。 漢、魏相傳，施行皆然。」 案周禮奏六樂，乃奏黃鍾，歌大呂； 乃奏太蔟，歌應鍾。 皆以律呂之義，紀歌奏清濁。 而和所稱以二尺三尺為名，雖漢、魏用之，俗而不典。 部郎劉秀、鄧昊等以律作笛，三尺二寸者，應無射之律，若宜用長笛，執樂者曰「請奏無射」。 周語曰：「無射所以宣布哲人之令德，示民軌儀也。」 二尺八寸四分四釐應黃鍾之律，若宜用短笛，執樂者曰「請奏黃鍾」。 周語曰：「黃鍾所以宣養六氣九德也。」 是則歌奏之義，當合經禮，考之古典，於制為雅。
They asked: 「Without knowing pitch theory, what names should high-low and clear-murky tuning bear? 」He replied: 「When assembling music we followed the singer's voice, using long or short flutes. A murky voice might use a three-foot-two flute, hence the 'three-foot-two tuning.' A clear voice used a two-foot-nine flute, hence the 'two-foot-nine tuning.' Han and Wei transmitted this practice throughout. 」The Rites of Zhou on the six musics: play Yellow Bell, sing Great Lu; play Great Cu, sing Responding Bell. All record song and performance in terms of pitch standards, clear and murky. Naming tunings by two or three feet, though Han and Wei used it, is vulgar and uncanonical. Liu Xiu and Deng Hao made flutes by standard: three feet two inches matches Untempered Pitch—the director would say, 'Perform Untempered Pitch.' The Discourses of Zhou: 「Untempered Pitch proclaims the sage's command and shows the people their measure. 」Two feet eight inches four fen four li matches Yellow Bell—the director would say, 'Perform Yellow Bell.' The Discourses of Zhou: 「Yellow Bell nourishes the six breaths and nine virtues. 」Song and performance should follow the classic rites; by ancient canon this is refined.
39
書曰：「予欲聞六律五聲八音，在治忽。」 [34]周禮載六律六同。 禮記又曰：「五聲十二律，還相為宮。」 劉歆、班固纂律曆志，亦紀十二律。 唯京房始創六十律，至章帝時，其法已亡； 蔡邕雖追紀其言，[35]亦曰「今無能為者」。 依案古典及今音家所用六十律者，無施於樂。 謹依典記，以五聲十二律還相為宮之法，制十二笛象，記注圖側，如別。 省圖，不如視笛之了，故復重作蕤賓伏孔笛。 其制云：
The Documents: 「I wish to hear the six standards, five tones, and eight sounds—in order and disorder. 」[34] The Rites of Zhou record six standards and six unisons. The Record of Rites: 「The five tones and twelve standards revolve as one another's gong. 」Liu Xin and Ban Gu recorded the twelve standards in their treatises. Only Jing Fang created sixty standards; by Emperor Zhang's time the method was lost; though Cai Yong recorded his words, [35] he said, 'Today no one can do it.' Ancient canon and modern practice show the sixty standards have no use in music. Following canonical records, we made twelve flute models by the five-tone twelve-standard cycle, with diagrams appended separately. Diagrams are less clear than the flute itself; we therefore remade a Flaccid Guest stopped-hole flute. Its specifications read:
40
黃鍾之笛，正聲應黃鍾，下徵應林鍾，長二尺八寸四分四釐有奇。 〈周語曰：「黃鍾所以宣養六氣九德也。」 正聲調法，[36]以黃鍾為宮，則姑洗為角。 翕笛之聲應姑洗，故以四角之長為黃鍾之笛也。 其宮聲正而不倍，故曰正聲。〉 正聲調法，黃鍾為宮， 〈第一孔。〉 應鍾為變宮， 〈第二孔。〉 南呂為羽， 〈第三孔。〉 林鍾為徵， 〈第四孔。〉 蕤賓為變徵， 〈第五附孔。〉 姑洗為角， 〈笛體中聲。〉 太蔟為商。 〈笛後出孔也。 商聲濁於角，當在角下，而角聲以在體中，故上其商孔，令在宮上，清於宮也。 然則宮商正也，餘聲皆倍也。 是故從宮以下，孔轉下轉濁也。 此章說笛孔上下次第之名也。 [37]下章說律呂相生，笛之制也。〉 正聲調法，黃鍾為宮， 〈作黃鍾之笛，將求宮孔，以姑洗及黃鍾律從笛首下度之，盡二律之長而為孔，則得宮聲也。〉 宮生徵，黃鍾生林鍾也。 〈以林鍾之律從宮孔下度之，盡律作孔，則得徵聲也。〉 徵生商，林鍾生太蔟也。 〈以太蔟律從徵孔上度之，盡律以為孔，則得商聲也。〉 商生羽，太蔟生南呂也。 〈以南呂律從商孔下度之，[38]盡律為孔，則得羽聲也。〉 羽生角，南呂生姑洗也。 〈以姑洗律從羽孔上行度之，盡律而為孔，則得角聲也。 然則出於商孔之上，吹笛者左手所不及也。 從羽孔下行度之，盡律而為孔，亦得角聲，出於變徵附孔之下，[39]則吹者右手所不逮也，故不作角孔。 推而下之，復倍其均，是以角聲在笛體中，古之制也。 音家舊法，雖一倍再倍，[40]但令均同。 適足為唱和之聲，無害於曲均故也。 周語曰，匏竹利制，議宜，謂便於事用從宜者也。〉 角生變宮，姑洗生應鍾也。 〈上句所謂當為角孔而出商上者，[41]墨點識之，以應律也。 從此點下行度之，盡律為孔，[42]則得變宮之聲也。〉 變宮生變徵，應鍾生蕤賓也。 〈以蕤賓律從變宮下度之，盡律為孔，則得變徵之聲。 十二笛之制，各以其宮為主。 [43]相生之法，或倍或半，其便事用，[44]例皆一者也。〉 下徵調法，林鍾為宮， 〈第四孔也。 本正聲黃鍾之徵。 徵清當在宮上，用笛之宜，倍令濁下，故曰下徵。 下徵更為宮者，記所謂「五聲十二律還相為宮」也。 [45]然則正聲調清，下徵調濁也。〉 南呂為商， 〈第三孔也。 [46]本正聲黃鍾之羽，今為下徵之商。〉 應鍾為角， 〈第二孔也。 本正聲黃鍾之變宮，今為下徵之角也。〉 黃鍾為變徵， 〈下徵之調，林鍾為宮，大呂當變徵。 而黃鍾笛本無大呂之聲，故假用黃鍾以為變徵也。 假用之法：當變徵之聲，則俱發黃鍾及太蔟、應鍾三孔。 黃鍾濁而太蔟清，[47]大呂律在二律之間，俱發三孔而微磑𥖪之，[48]則得大呂變徵之聲矣。 諸笛下徵調求變徵之法，皆如此。〉 太蔟為徵， 〈笛後出孔，本正聲之商，今為下徵之徵。〉 姑洗為羽， 〈笛體中翕聲也。 本正聲之角，今為下徵之羽也。〉 蕤賓為變宮， 〈附孔是也。 本正聲之變徵也，今為下徵之變宮也。 然則正聲之調，孔轉下轉濁； 下徵之調，孔轉上轉清也。〉 清角之調：以姑洗為宮， 〈即是笛體中翕聲也，於正聲為角，於下徵為羽。 清角之調，乃以為宮，而哨吹令清，故曰清角。 唯得為宛詩謠俗之曲，不合雅樂也。〉 蕤賓為商， 〈正也。〉 林鍾為角， 〈非正也。〉 南呂為變徵， 〈非正也。〉 應鍾為徵， 〈正也。〉 黃鍾為羽， 〈非正也。 太蔟為變宮。 非正也。 清角之調，唯宮商及徵，與律相應，餘四聲非正者皆濁，一律哨吹令清，假而用之，其例一也。〉
Yellow Bell flute: correct sound on Yellow Bell, lower zhi on Lin Bell, length two feet eight inches four fen four li and a fraction. 〈Discourses of Zhou: 「Yellow Bell nourishes the six breaths and nine virtues. 」Correct-sound method: [36] with Yellow Bell as gong, Gu Xian is jue. The closed sound matches Gu Xian; hence the Yellow Bell flute length equals four corner measures. Its gong tone is correct, not doubled; hence 'correct sound.'〉 Correct-sound method, Yellow Bell as gong, 〈First hole.〉 Responding Bell as altered gong, 〈Second hole.〉 Southern Lu as yu, 〈Third hole.〉 Lin Bell as zhi, 〈Fourth hole.〉 Flaccid Guest as altered zhi, 〈Fifth auxiliary hole.〉 Gu Xian as jue, 〈Tone within the flute body.〉 Great Cu as shang. 〈Rear hole of the flute. Shang is murkier than jue and should lie below jue, but because jue is in the body the shang hole is placed above gong, clearer than gong. Gong and shang are correct; other tones are doubled. Below gong, holes descend and grow murkier. This section names the flute holes in order from top to bottom. [37] The next section treats pitch generation and flute construction.〉 Correct-sound method, Yellow Bell as gong, 〈To find the gong hole on a Yellow Bell flute, measure two standards down from the head with Gu Xian and Yellow Bell—then gong is obtained.〉 Gong generates zhi; Yellow Bell generates Lin Bell. 〈Measure down from the gong hole by Lin Bell standard to obtain zhi.〉 Zhi generates shang; Lin Bell generates Great Cu. 〈Measure up from the zhi hole by Great Cu standard to obtain shang.〉 Shang generates yu; Great Cu generates Southern Lu. 〈Measure down from the shang hole by Southern Lu standard [38] to obtain yu.〉 Yu generates jue; Southern Lu generates Gu Xian. 〈Measure up from the yu hole by Gu Xian standard to obtain jue. That would lie above the shang hole, beyond the player's left hand. Measuring down from the yu hole also yields jue below the altered-zhi hole [39], beyond the right hand—so no jue hole is cut. Doubling downward places jue in the flute body—the ancient system. Old specialists, though doubling once or twice, [40] only equalized the blend. That sufficed for harmony without harming melodic balance. Discourses of Zhou: gourd and bamboo are regulated for convenience—suited to practical use.〉 Jue generates altered gong; Gu Xian generates Responding Bell. 〈Where jue should be but appears above shang [41], mark in ink to match the standard. Measure down from that mark [42] to obtain altered gong.〉 Altered gong generates altered zhi; Responding Bell generates Flaccid Guest. 〈Measure down from altered gong by Flaccid Guest standard to obtain altered zhi. Each of the twelve flutes takes its own gong as master. [43] Generation may double or halve for convenience; [44] the pattern is always one.〉 Lower-zhi method, Lin Bell as gong, 〈Fourth hole. Originally correct-sound Yellow Bell's zhi. Zhi should lie above gong; for the flute, doubling lowers it—hence 'lower zhi.' Lower zhi becoming gong is the 'five tones and twelve standards revolving as gong' of the records. [45] Correct sound is clear; lower zhi murky.〉 Southern Lu serves as shang, 〈The third hole. [46] In correct sound this was Yellow Bell's yu; in lower zhi it is shang.〉 Responding Bell serves as jue, 〈The second hole. Originally Yellow Bell's altered gong in correct sound; now lower zhi's jue.〉 Yellow Bell serves as altered zhi, 〈In lower-zhi tuning Lin Bell is gong and Great Lu should be altered zhi. The Yellow Bell flute lacks a Great Lu tone, so Yellow Bell stands in for altered zhi. To borrow it: for altered zhi, sound Yellow Bell, Great Cu, and Responding Bell together. Yellow Bell is murky, Great Cu clear; [47] Great Lu falls between them—open all three holes and fine-tune [48] to get Great Lu altered zhi. Every flute follows this method for altered zhi in lower-zhi tuning.〉 Great Cu serves as zhi, 〈The flute's rear hole was originally the correct-sound shang, but now serves as the zhi of the lower zhi mode.〉 Gu Xian serves as yu, 〈The stopped tone inside the flute. Correct-sound jue in the old tuning; lower-zhi yu in the new.〉 Flaccid Guest serves as altered gong, 〈This is the auxiliary hole. It was correct-sound altered zhi; now it is lower-zhi altered gong. In correct-sound tuning holes descend and grow murkier; in lower-zhi tuning they rise and grow clearer.〉 Clear-jue tuning takes Gu Xian as gong, 〈The body's stopped tone—jue in correct sound, yu in lower zhi. Clear-jue makes it gong and whistles it clear—hence the name clear jue. It suits only rustic songs and popular airs, not canonical ritual music.〉 Flaccid Guest serves as shang, 〈In tune.〉 Lin Bell serves as jue, 〈Out of tune.〉 Southern Lu serves as altered zhi, 〈Out of tune.〉 Responding Bell serves as zhi, 〈In tune.〉 Yellow Bell serves as yu, 〈Out of tune. Great Cu as altered gong. Out of tune. In clear-jue tuning only gong, shang, and zhi match the standards; the other four improper tones are murky—one standard is whistled clear and borrowed by the same rule.〉
41
凡笛體用角律，其長者八之， 〈蕤賓、林鍾也。〉 短者四之， 〈其餘十笛，皆四角也。〉 空中實容，長者十六， 〈短笛竹宜受八律之黍也。 [49]若長短大小不合於此，或器用不便聲均法度之齊等也。 然笛竹率上大下小，不能均齊，必不得已，取其聲均合。〉 三宮 〈一曰正聲，二曰下徵，三曰清角。〉 二十一變也。 〈宮有七聲，錯綜用之，故二十一變也。 諸笛例皆一也。〉 伏孔四，所以便事用也。 〈一曰正角，出於商上者也。 二曰倍角，近笛下者也。 三曰變宮，近於宮孔，倍令下者也。 四曰變徵，遠於徵孔，倍令高者也。 [50]或倍或半，或四分一，取則於琴徽也。 四者皆不作其孔而取其度，以應進退上下之法，所以協聲均，便事用也。 其本孔隱而不見，故曰伏孔。〉
Flutes built on jue standards: the longer pipes use an eighth measure, 〈Flaccid Guest and Lin Bell.〉 the shorter by a quarter, 〈the remaining ten flutes all use four corner measures.〉 The bore's capacity: sixteen for the longer, 〈Short-flute bamboo should receive millet of eight pitch standards. [49] If dimensions fall short of this, or the instrument is awkward to use, tonal evenness and standard alignment are lost. Flute bamboo is usually thick above and thin below and cannot be perfectly even—when there is no choice, choose what sounds balanced.〉 Three gong modes 〈Correct sound, lower zhi, and clear jue.〉 Twenty-one permutations. 〈Seven tones interwoven under gong yield twenty-one permutations. All flutes follow the same rule.〉 There are four hidden holes for practical convenience. 〈First is correct jue, placed above shang. Second is doubled jue, near the flute's lower end. Third is altered gong, beside the gong hole, doubled downward. Fourth is altered zhi, farther from the zhi hole, doubled upward. [50] Doubling, halving, or quartering follows the frets of the zheng. None of the four is bored open; their distances are taken to match rising, falling, advancing, and retreating—harmonizing tone and easing performance. The base holes stay concealed—hence the name hidden holes.〉
42
大呂之笛：正聲應大呂，下徵應夷則，長二尺六寸六分三釐有奇。 〈周語曰：「元間大呂，助宣物也。」〉
Great Lu flute: correct sound matches Great Lu, lower zhi matches Leveling Pitch, length two feet six inches six fen three li odd. 〈Discourses of Zhou: 「The primal interval Great Lu helps spread creation abroad.」〉
43
太蔟之笛：正聲應太蔟，下徵應南呂，長二尺五寸二分八釐有奇。 [51] 〈周語曰：「太蔟所以金奏，贊陽出滯也。」〉
Great Cu flute: correct sound matches Great Cu, lower zhi matches Southern Lu, length two feet five inches two fen eight li odd. [51] (Editorial note.) 〈Discourses of Zhou: 「Great Cu serves metal music, helping yang drive out stagnation.」〉
44
夾鍾之笛：正聲應夾鍾，下徵應無射，長二尺四寸。 周語曰：「二間夾鍾，出四隙之細也。」
Pressed Bell flute: correct sound matches Pressed Bell, lower zhi matches Untempered Pitch, length two feet four inches. Discourses of Zhou: 「The second interval Pressed Bell draws out the subtle within the four gaps.」
45
姑洗之笛：正聲應姑洗，下徵應應鍾，長二尺二〔寸四分七釐有奇。 〈周語曰：「姑洗所以修潔百物，考神納賓也。」〉〕
Gu Xian flute: correct sound matches Gu Xian, lower zhi matches Responding Bell, length two feet two [inches four fen seven li odd. 〈Discourses of Zhou: 「Gu Xian cleanses the myriad things and welcomes spirits and guests.」〉
46
〔中呂之笛：正聲應中呂，下徵應黃鍾，長二尺一〕寸三分三釐有奇。 [52] 〈周語曰：「三間中呂，宣中氣也。」〉 [53]
[Inner Lu flute: correct sound matches Inner Lu, lower zhi matches Yellow Bell, length two feet one] inch three fen three li odd. [52] (Editorial note.) 〈Discourses of Zhou: 「The third interval Inner Lu spreads the central qi.」〉 [53] (Editorial note.)
47
蕤賓之笛：正聲應蕤賓，下徵應大呂，長三尺九寸九分五釐有奇。 〈周語曰：「蕤賓所以安靜神人，獻酬交酢。」 變宮近宮孔，故倍半令下，[54]便於用也。 林鍾亦如之。〉
Flaccid Guest flute: correct sound matches Flaccid Guest, lower zhi matches Great Lu, length three feet nine inches nine fen five li odd. 〈Discourses of Zhou: 「Flaccid Guest calms spirits and people in the exchange of toasts. 」Altered gong lies near the gong hole, so halving downward [54] makes it easier to play. Lin Bell follows the same rule.〉
48
林鍾之笛：正聲應林鍾，下徵應太蔟，長三尺七寸九分二釐有奇。 [55] 〈周語曰：「四間林鍾，和展百事，俾莫不任肅純恪。」〉
Lin Bell flute: correct sound matches Lin Bell, lower zhi matches Great Cu, length three feet seven inches nine fen two li odd. [55] (Editorial note.) 〈Discourses of Zhou: 「The fourth interval Lin Bell harmonizes and unfolds the hundred tasks, so all may keep solemn purity.」〉
49
夷則之笛：正聲應夷則，下徵應夾鍾，長三尺六寸。 〈周語曰：「夷則所以詠歌九則，平民無貳也。」 [56]變宮之法，亦如蕤賓，體用四角，故四分益一也。〉
Leveling Pitch flute: correct sound matches Leveling Pitch, lower zhi matches Pressed Bell, length three feet six inches. 〈Discourses of Zhou: 「Leveling Pitch chants the nine principles; the common folk have no second heart. 」[56] Altered gong follows Flaccid Guest's method; the body uses four corner measures, so one quarter is added.〉
50
南呂之笛：正聲應南呂，下徵應姑洗，長三尺三寸七分一釐有奇。 [57] 〈周語曰：「五間南呂，贊陽秀也。」〉
Southern Lu flute: correct sound matches Southern Lu, lower zhi matches Gu Xian, length three feet three inches seven fen one li odd. [57] (Editorial note.) 〈Discourses of Zhou: 「The fifth interval Southern Lu nurtures yang's flowering.」〉
51
無射之笛：正聲應無射，下徵應中呂，長三尺二寸。 〈周語曰：「無射所以宣布哲人之令德，示民軌儀也。」〉
Untempered Pitch flute: correct sound matches Untempered Pitch, lower zhi matches Inner Lu, length three feet two inches. 〈Discourses of Zhou: 「Untempered Pitch announces the wise man's commanding virtue and sets the people's standard.」〉
52
應鍾之笛：正聲應應鍾，下徵應蕤賓，長二尺九寸九分六釐有奇。 [58] 〈周語曰：「六間應鍾，均利器用，俾應復也。」〉
Responding Bell flute: correct sound matches Responding Bell, lower zhi matches Flaccid Guest, length two feet nine inches nine fen six li odd. [58] (Editorial note.) 〈Discourses of Zhou: 「The sixth interval Responding Bell evens keen instruments for use, that things may answer in turn.」〉
53
勗又以魏杜夔所制律呂，檢校太樂、總章、鼓吹八音，與律乖錯。 始知後漢至魏，尺度漸長於古四分有餘。 夔依為律呂，故致失韻。 乃部佐著作郎劉恭依周禮更積黍起度，[59]以鑄新律。 既成，募求古器，[60]得周時玉律，比之不差毫釐。 又漢世故鍾，以律命之，不叩而自應。 初勗行道，逢趙郡商人縣鐸於牛，其聲甚韻。 至是搜得此鐸，以調律呂焉。
Xun also tested the pitch pipes Du Kui had made in Wei against the Grand Music Office, General Statement, and military-revel ensemble—and found them out of tune with the standards. He realized that from Later Han through Wei the standard foot had grown more than four tenths longer than the ancient measure. Kui had built his pitch pipes on that longer measure, which caused the loss of true pitch. He then ordered assistant editorial director Liu Gong, following the Rites of Zhou, to reestablish measure by accumulated millet [59] and cast new pitch pipes. When they were finished he searched for ancient objects [60] and found jade pitch pipes from Zhou; comparison showed not a hair's breadth of difference. He also found an old Han bell assigned to a pitch standard that resonated without being struck. Long before, traveling on the road, Xun had met a Zhao merchant with a bell hung on an ox whose tone was unusually true. Now he recovered that very bell and used it to tune the pitch pipes.
54
晉武帝以勗律與周、漢器合，乃施用之。 散騎侍郎阮咸譏其聲高，非興國之音。 咸亡後，掘地得古銅尺，果長勗尺四分，時人咸服其妙。
Emperor Wu of Jin, seeing that Xun's pitch pipes matched Zhou and Han instruments, adopted them. Palace Attendant Ruan Xian ridiculed them as too sharp—not the pitch by which a state flourishes. After Xian's death an ancient bronze foot-rule was unearthed; it was exactly four tenths longer than Xun's measure, and everyone then marveled at his precision.
55
元康中，裴頠以為醫方民命之急，而稱兩不與古同，為害特重，宜因此改治權衡。 不見省。
During Yuankang, Pei Ji argued that medicine touches the people's lives directly, yet the ounce-weight no longer matched antiquity—a serious harm—and weights and measures ought to be corrected on this basis. The court did not act on it.
56
黃鍾箱笛，晉時三尺八寸，元嘉九年，太樂令鍾宗之減為三尺七寸。 十四年，治書令史奚縱又減五分，為三尺六寸五分。 〈列和云：「東箱長笛四尺二寸也。」〉 太蔟箱笛，晉時三尺七寸，宗之減為三尺三寸七分，縱又減一寸一分，為三尺二寸六分。 姑洗箱笛，晉時三尺五寸，宗之減為二尺九寸七分，縱又減五分，為二尺九寸二分。 蕤賓箱笛，晉時二尺九寸，宗之減為二尺六寸，縱又減二分，為二尺五寸八分。
The Yellow Bell chest flute was three feet eight inches in Jin; in the ninth year of Yuanjia Grand Music Director Zhong Zongzhi shortened it to three feet seven inches. In the fourteenth year of Yuanjia Editorial Secretary Xi Zong cut it another five fen, to three feet six inches five fen. 〈Lie He said: 「The eastern-wing long flute measures four feet two inches.」〉 The Great Cu chest flute was three feet seven inches in Jin; Zongzhi shortened it to three feet three inches seven fen, and Zong cut another inch one fen, to three feet two inches six fen. The Gu Xian chest flute was three feet five inches in Jin; Zongzhi shortened it to two feet nine inches seven fen, and Zong cut another five fen, to two feet nine inches two fen. The Flaccid Guest chest flute was two feet nine inches in Jin; Zongzhi shortened it to two feet six inches, and Zong cut another two fen, to two feet five inches eight fen.
57
校勘記
Collation notes
58
黃鍾為角太蔟為徵各本脫「為角太蔟」四字，據周禮春官大司樂職文補。
'Yellow Bell as jue, Great Cu as zhi': all editions omit 'as jue, Great Cu'; restored from the Rites of Zhou, Spring Officials, Grand Music Master.
59
三三而九各本並作「三而九」，據淮南子天文訓原文補正。
'Three threes make nine': all editions have 'three make nine'; corrected from the Huainanzi, Astronomical Treatise.
60
夷則之數五十一「五十一」宋書各本並作「五十」，據淮南子天文訓及晉書律曆志 (以下簡稱晉志) 補。 錢寶琮宋書律志校勘記云：「夷則之數為五０。 五七，若舉成數言之，當作五十一。」
'The number of Leveling Pitch is fifty-one': all Song Shu editions read 'fifty'; restored from the Huainanzi Astronomical Treatise and the Jin Shu Treatise on Pitch and Calendar (hereafter Jin Treatise) Restored. Qian Baozong's collation note on the Song Shu Treatise on Pitch says: 「The number of Leveling Pitch is 50. 57; expressed as a whole number it should read fifty-one.」
61
比於正音故為和各本「比」字上並有「不」字，據淮南子天文訓原文刪。 小注「與正音比」上各本亦有「不」字，今並刪去。
'Compared with the correct pitch, therefore it is harmony': all editions insert 'not' before 'compared'; removed per the Huainanzi Astronomical Treatise. The small gloss 'compared with the correct pitch' likewise had 'not' in all editions; both instances are now removed.
62
故為和和從聲也「故」各本作「效」，「從」各本作「徙」，並據淮南子天文訓原文改正。
'Therefore harmony, harmony follows sound': all editions have 'effect' for 'therefore' and 'migrate' for 'follow'; both corrected from the Huainanzi Astronomical Treatise.
63
十二粟而當一寸各本並作「一粟而當一寸」，據淮南子天文訓原文改正。
'Twelve grains equal one inch': all editions read 'one grain equals one inch'; corrected from the Huainanzi Astronomical Treatise.
64
土炭輕而衡仰「仰」，各本譌卭，當由卬之形似而譌。 卬仰古今字，續漢志、晉志作仰，今改正。
'Earth and charcoal are light and the balance tilts upward': all editions miswrite 'upward' as qiong, probably through confusion with the similar graph ang. The graphs ang and yang are old and new variants of the same word; the Continued Han Treatise and Jin Treatise use yang; corrected here.
65
氣至者灰動其為氣動者其灰散人及風所動者其灰聚三朝本、北監本、毛本、局本原作「氣至者次去散人及風所動者其灰聚」，殿本但「次」字作「吹」字，其餘文字並同。 字句奪譌，義不可通。 今據續漢志、晉志改正。
'When qi arrives the ash moves; when qi moves the ash scatters; when people or wind move it the ash gathers': Three Dynasties, Beijian, Mao, and Bureau editions originally had 'when qi arrives, next departs and scatters; when people or wind move it the ash gathers'; the Palace edition changes only 'next' to 'blow,' otherwise identical. Words are missing or corrupt and the passage will not parse. Corrected from the Continuation of the Han Treatise and Jin Treatise.
66
唯二至乃候靈臺用竹律六十「靈臺用竹律六十」七字，各本並脫，據續漢志、御覽一六引京房傳補。
'Only at the two solstices does one observe at the Spirit Terrace with sixty bamboo pitch pipes': all editions omit these seven characters; restored from the Continuation of the Han Treatise and Imperial Readings 160 citing Jing Fang's biography.
67
取弘農宜陽縣金門山竹為管河內葭莩為灰各本並脫「為管河內葭莩」六字，據晉志補。
'Take bamboo from Jinyang Gate Mountain in Yiyang, Hongnong, for pipes and reed foam from Henei for ash': all editions omit 'for pipes and reed foam from Henei'; restored from the Jin Treatise.
68
房言律詳於歆所奏各本並脫「於歆所奏」四字，據晉志補。
'Fang's account of pitch is more detailed than what Xin presented': all editions omit 'than what Xin presented'; restored from the Jin Treatise.
69
音不可書以曉人「書以」各本作「以書」，據晉志乙正。
'Pitch cannot be written to instruct people': all editions read 'write by' for 'by write'; transposed per the Jin Treatise.
70
新律小分母三十六「母」各本並作「十」，據錢寶琮校勘記改。
'The new pitch pipes' small fractional denominator is thirty-six': all editions read 'ten' for 'denominator'; corrected per Qian Baozong's collation note.
71
南呂五寸三分三釐 〈少強〉 「三分」各本並作「二分」，張文虎舒藝室隨筆云：「當作南呂五寸三分三釐少強。」 錢寶琮校勘記云：「太蔟正律度八寸，二乘而三除之，正得五寸三分三釐少強也。」 今據張、錢二家說改正。
Southern Lu: five inches three fen three li 〈Slightly sharp〉 'Three fen' appears as 'two fen' in all editions; Zhang Wenhu's Shuyi Studio Miscellany says: 「It should read Southern Lu five inches three fen three li, slightly sharp. 」Qian Baozong's collation note says: 「Great Cu's standard length is eight inches; doubled and divided by three gives exactly five inches three fen three li, slightly sharp. 」Corrected here following Zhang and Qian.
72
七寸一分五釐 〈強〉 「強」各本並作「少強」，據律理校算改正。
Seven inches one fen five li 〈Sharp〉 'Sharp' appears as 'slightly sharp' in all editions; corrected by pitch calculation.
73
應鍾四寸七分四釐 〈強〉 百衲本、北監本、毛本作「應鍾四寸七」。 殿本、局本作「應鍾四寸七分」。 據錢寶琮校勘記訂正。
Responding Bell: four inches seven fen four li 〈Sharp〉 Hundred-Patch, Beijian, and Mao editions read 'Responding Bell four inches seven.' Palace and Bureau editions read 'Responding Bell four inches seven fen.' Emended per Qian Baozong's collation note.
74
六寸三分八釐 〈強〉 「強」各本並作「少強」，據律理校算改正。
Six inches three fen eight li 〈Sharp〉 'Sharp' appears as 'slightly sharp' in all editions; corrected by pitch calculation.
75
十二萬四千四百一十六各本並作「十二萬四千四百三十六」。 據續漢志改。
124,416: all editions have 124,436. Corrected from the Continuation of the Han Treatise.
76
十二萬五千六百八 〈六〉 各本並作「十二萬五千六八 〈六〉」。 錢寶琮校勘記云：「據術當作十二萬五千六百八。 六。」 今改正。
125,608 〈Six〉 All editions read '125,6 〈Six〉' Qian Baozong's collation note says: 「By calculation it should be 125,608. Six. 」Corrected here.
77
夾鍾七寸四分九釐 〈少弱〉 「少弱」各本並作「少強」，據錢寶琮校勘記改。
Pressed Bell: seven inches four fen nine li 〈Slightly flat〉 'Slightly flat' appears as 'slightly sharp' in all editions; corrected per Qian Baozong's collation note.
78
七寸五分八釐 〈少弱〉 「少」字，各本並脫，據律理校算補正。
Seven inches five fen eight li 〈Slightly flat〉 The word 'slightly' is missing in all editions; restored by pitch calculation.
79
無射四寸九分九釐 〈半弱〉 「半弱」各本並作「半強」，據錢寶琮校勘記改。
Untempered Pitch: four inches nine fen nine li 〈Half flat〉 'Half flat' appears as 'half sharp' in all editions; corrected per Qian Baozong's collation note.
80
十三萬三千二百五十七 〈二十五〉 「二十五」各本並作「二十三」，據錢寶琮校勘記改正。
133,257 〈Twenty-five〉 'Twenty-five' appears as 'twenty-three' in all editions; corrected per Qian Baozong's collation note.
81
三分之二不足二千三百八十四三分之一各本並作「三分之二分二千四百八十四三分之一」，據錢寶琮校勘記改正。
'Two-thirds lacking 2,384 one-third': all editions have 'two-thirds divide 2,484 one-third'; corrected per Qian Baozong's collation note.
82
云前漢志但載十二律「十二律」各本皆脫「二」字。 今據前漢志補。
'It says the Former Han Treatise records only the twelve pitch pipes': all editions drop 'two' from 'twelve pitch pipes.' Restored from the Former Han Treatise.
83
於是罪玉及諸子皆為養馬士「士」各本並作「主」，據三國志魏志杜夔傳改。
'Thereupon Yu and all the disciples were made horse-keepers': all editions read 'master' for 'keeper'; corrected from Du Kui's biography in the Records of the Three Kingdoms, Wei.
84
饗神佑賢「佑」各本並作「佐」，據晉志改。
'Feasting spirits and aiding the worthy': all editions read 'assisting' for 'aiding'; corrected per the Jin Treatise.
85
以節八音之中「中」各本並作「用」，據晉志改。
'To regulate among the eight materials of sound': all editions read 'use' for 'among'; corrected per the Jin Treatise.
86
而和寫笛造律「和」各本並作「知」，據晉志改。 按和指協律中郎將列和。
'And harmonizing and writing flutes to make pitch pipes': all editions read 'know' for 'harmonize'; corrected per the Jin Treatise. Note: 'He' refers to Harmonizing-Pitch Gentleman Lie He.
87
猶宜儀刑古昔各本並奪「儀」字，據晉志補。
'One should still take ancient models as law': all editions omit 'take'; restored from the Jin Treatise.
88
下太樂樂府施行「下」字各本並奪去，據晉志補。
'Issue to the Grand Music Office and Music Bureau for implementation': all editions omit 'issue'; restored from the Jin Treatise.
89
為某曲當舉某指「舉」各本並作「與」，據晉志改。
'For such a piece raise such a finger': all editions read 'give' for 'raise'; corrected per the Jin Treatise.
90
輒令部郎劉秀鄧昊王豔魏邵等與笛工參共作笛「輒」晉志作「趣」，嚴可均全晉文「趣」下有「令」字，今不改「輒」字，補「令」字。 「王豔」二字各本皆空白，據晉志補。
'Then ordered department officer Liu Xiu, Deng Hao, Wang Yan, Wei Shao, and others together with flute craftsmen to make flutes': the Jin Treatise has 'hasten' for 'then'; Yan Kejun's Complete Jin Writings adds 'order' after 'hasten'—'then' is kept, but 'order' is supplied. 'Wang Yan' is blank in all editions; restored from the Jin Treatise.
91
在治忽三朝本作「在治七始」，北監、毛本、殿本、局本作「在治忽始」。 按尚書益稷篇作「在治忽」，今據改。
'In governance and disorder': the Three Dynasties edition reads 'in governance seven beginnings'; Beijian, Mao, Palace, and Bureau editions read 'in governance disorder beginnings.' Note: the Documents, Yiji chapter has 'in governance and disorder'; corrected here accordingly.
92
蔡邕雖追紀其言「紀」字，百衲本空格一字。 北監、毛本、殿本、局本作「古作」二字。 今據晉志補。
'Although Cai Yong traced and recorded his words': the character 'record' is blank in the Hundred-Patch edition. Beijian, Mao, Palace, and Bureau editions read 'ancient made.' Restored from the Jin Treatise.
93
正聲調法「正聲」各本並作「主聲」，據晉志改。
'Correct-sound tuning method': all editions read 'master sound' for 'correct sound'; corrected per the Jin Treatise.
94
此章說笛孔上下次第之名也「次第」百衲本作「太律」，北監、毛本、殿本、局本作「大律」，今據晉志改。
'This section explains the names of flute holes in order above and below': Hundred-Patch has 'great pitch standard' for 'in order'; Beijian, Mao, Palace, and Bureau have 'large pitch standard'; corrected per the Jin Treatise.
95
以南呂律從商孔下度之「南呂律」下各本有「度」字，據晉志刪。 「商孔」各本作「角孔」，據晉志改。
'Measure down from the Southern Lu standard at the shang hole': all editions add 'measure' after 'Southern Lu standard'; removed per the Jin Treatise. 'Shang hole' appears as 'jue hole' in all editions; corrected per the Jin Treatise.
96
出於變徵附孔之下「變徵附孔」各本並作「附商孔」，晉志作「商附空」。 錢寶琮校勘記云：「晉志亦誤。 當云出於變徵附孔之下。 變徵附孔，即上文所謂第五孔也。」 今據錢說改。
'Issuing below the altered-zhi auxiliary hole': all editions have 'below the shang auxiliary hole'; the Jin Treatise has 'shang auxiliary empty.' Qian Baozong's collation note says: 「The Jin Treatise is likewise in error. It should say 'issuing below the altered-zhi auxiliary hole.' The altered-zhi auxiliary hole is the fifth hole described above. 」Corrected here following Qian.
97
雖一倍再倍「一倍」各本並作「一部」，據晉志改。
'Although doubled once or again': all editions read 'one section' for 'doubled once'; corrected per the Jin Treatise.
98
上句所謂當為角孔而出商上者「商上」各本及晉志並作「商下」。 張文虎舒藝室隨筆及錢寶琮校勘記並云商下當作商上。 今據改。
'What the preceding sentence calls what should be the jue hole but issues above shang': all editions and the Jin Treatise read 'below shang' for 'above shang.' Zhang Wenhu's Shuyi Studio Miscellany and Qian Baozong's collation note both hold that 'below shang' should read 'above shang.' Corrected here accordingly.
99
盡律為孔各本只有「為孔」二字，奪去上二字。 晉志作「應律為孔」。 張文虎舒藝室隨筆云：「應律為孔，當作盡律為孔。」 今據張氏說補。
'Exhaust the pitch standard to make the hole': all editions retain only 'make hole,' omitting the first two characters. The Jin Treatise reads 'respond to pitch standard to make hole.' Zhang Wenhu's Shuyi Studio Miscellany says: 「'Respond to pitch standard to make hole' should be 'exhaust pitch standard to make hole.' 」Restored here following Zhang.
100
各以其宮為主「各」各本並作「名」，據晉志改。
'Each takes its own gong as master': all editions read 'name' for 'each'; corrected per the Jin Treatise.
101
其便事用「便」各本並作「使」，據晉志改。
'For convenience in use': all editions read 'make' for 'convenience'; corrected per the Jin Treatise.
102
記所謂五聲十二律還相為宮也「也」各本並作「者」，據晉志改。
'What the record calls the five tones and twelve pitch standards revolving as gong': all editions read 'one who' for 'also'; corrected per the Jin Treatise.
103
第三孔也各本奪「也」字，依前後文例，據晉志補。
'Third hole': all editions omit the final particle; supplied from the Jin Treatise by parallel with surrounding glosses.
104
黃鍾濁而太蔟清「濁」字上，各本並有「應」字，錢寶琮校勘記云：「應字是衍文。」 今刪去。
'Yellow Bell is murky and Great Cu clear': all editions insert 'responding' before 'murky'; Qian Baozong's collation note says: 「'Responding' is an interpolation. 」Removed here.
105
俱發三孔而微磑𥖪之「微」各本並作「徵」。 晉書斠注改作「微」。 張文虎舒藝室隨筆云：「徵當作微，晉志亦誤。」 按斠注蓋據張氏說改。 今改正。
'Blow all three holes and slightly adjust': all editions read 'zhi' for 'slightly.' The collated Jin Shu changes this to 'slightly.' Zhang Wenhu's Shuyi Studio Miscellany says: 「'Zhi' should read 'slightly'; the Jin Treatise is wrong too. 」The collated emendation probably follows Zhang. Corrected here.
106
長者十六 〈短笛竹宜受八律之黍也〉 錢寶琮校勘記云：「注文與正文不相屬，疑有脫誤。」
The longer ones: sixteen 〈Short-flute bamboo should receive millet of eight pitch standards〉 Qian Baozong's collation note says: 「The gloss does not belong with the main text; text is probably missing or corrupt.」
107
四曰變徵遠於徵孔倍令高者也據錢寶琮校勘記云：「當云四曰變徵，近於徵孔，半令高者也。」
'Fourth, altered zhi, distant from the zhi hole, doubled upward': Qian Baozong's collation note says it should read 'Fourth, altered zhi, near the zhi hole, half raised upward.'
108
長二尺五寸二分八釐有奇各本並作「長二尺五寸三分一釐有奇」。 據張文虎舒藝室隨筆說改正。
'Length two feet five inches two fen eight li and a fraction': all editions have 'length two feet five inches three fen one li and a fraction'; corrected per Zhang Wenhu's Shuyi Studio Miscellany. Corrected following Zhang Wenhu's Shuyi Studio Miscellany.
109
長二尺二寸四分七釐有奇 〈至〉 長二尺一寸三分三釐有奇各本均奪去「寸四分 〈至〉 二尺一」，據張文虎舒藝室隨筆說補。
Length: two feet two inches four fen seven li odd 〈To〉 'Length two feet one inch three fen three li and a fraction': all editions uniformly omit 'inches four fen 〈To〉 two feet one'; restored per Zhang Wenhu's Shuyi Studio Miscellany.
110
三間中呂宣中氣也「宣」各本譌「宮」，據晉志改。
'The third interval Inner Lu diffuses the middle breath': all editions corruptly read 'palace' for 'diffuse'; corrected per the Jin Treatise.
111
變宮近宮孔故倍半令下各本並脫去「近宮孔」之宮字，今據晉志補。 「倍」，各本作「陪」，今據晉志改正。
'Altered gong near the gong hole, therefore halved downward': all editions drop 'gong' from 'near the gong hole'; restored from the Jin Treatise. 'Doubled' appears as 'accompany' in all editions; corrected per the Jin Treatise.
112
長三尺七寸九分二釐有奇「二釐」各本並作「七釐」。 據錢寶琮校勘記改。
'Length three feet seven inches nine fen two li and a fraction': 'two li' appears as 'seven li' in all editions. Corrected per Qian Baozong's collation note.
113
夷則所以詠歌九則平民無貳也「九則」各本並作「九州」，據國語原文改正。
'Leveling Pitch sings the nine rules; common people have no duplicity': 'nine rules' appears as 'nine regions' in all editions; corrected from the Discourses.
114
長三尺三寸七分一釐有奇「一釐有奇」四字，各本並脫，據錢寶琮校勘記補。
'Length three feet three inches seven fen one li and a fraction': all editions omit 'one li and a fraction'; restored per Qian Baozong's collation note.
115
長二尺九寸九分六釐有奇「二尺」各本作「三尺」，殿本作「五尺」。 張文虎舒藝室隨筆、錢寶琮校勘記並云：「三尺當作二尺。」 今據張、錢二家說改。
'Length two feet nine inches nine fen six li and a fraction': all editions read 'three feet' for 'two feet'; the Palace edition reads 'five feet.' Zhang Wenhu's Shuyi Studio Miscellany and Qian Baozong's collation note both say: 「'Three feet' should read 'two feet.' 」Corrected here following Zhang and Qian.
116
乃部佐著作郎劉恭依周禮更積黍起度「乃」各本並作「及」，據晉志改。
'Then had assistant editorial director Liu Gong according to the Rites of Zhou again accumulate millet to establish measure': all editions read 'and' for 'then'; corrected per the Jin Treatise.
117
募求古器「募」各本並作「慕」，今改正。
'Sought ancient objects': all editions read 'admire' for 'seek'; corrected here.