1
光宗受禪，崇上壽皇聖帝、壽成皇后暨壽聖皇太后尊號，壽皇樂用《乾安》，壽聖、壽成樂用《坤安》，三殿慶禮，在當時侈為盛儀。 尋以禮部、太常寺言：“國朝歲饗上帝，太祖肇造王業，則配冬饗於圜丘； 太宗混一區宇，則春祈穀、夏大雩、秋明堂俱配焉。 高宗身濟大業，功德茂盛，所宜奉侑，仰繼祖宗，以協先儒嚴祖之議，以彰文祖配天之烈。 ”乃季秋升侑於明堂，奠幣用《宗安之樂》，酌獻用《德安之樂》，並登歌作大呂宮。 及加上高宗徽號，奉冊、寶以告，用《顯安之樂》。
After Emperor Guangzong took the throne, he bestowed honorific titles upon the Retired Emperor Shouhuang, Empress Shoucheng, and Empress Dowager Shousheng. "Qian'an" was played for Shouhuang, and "Kun'an" for Shousheng and Shoucheng. The celebration rites held in all three halls were regarded at the time as the most magnificent ceremonies ever staged. Shortly afterward the Ministry of Rites and the Court of Imperial Sacrifices submitted a memorial: "In our dynasty's annual sacrifice to Heaven, Taizu, who founded the imperial enterprise, is associated at the winter offering at the Round Mound; Taizong, who unified the realm, is associated at the spring grain prayer, the summer great rain sacrifice, and the autumn Bright Hall ceremony alike. Gaozong personally brought the great enterprise to completion, and his merit and virtue were abundant. He ought therefore to be received as an associated sacrifice, following the precedent of our forebears, in keeping with the ancient scholars' insistence on revering the founding ancestor, and to manifest the martial founder's glory in sharing Heaven's sacrifice. " Accordingly, in late autumn he was elevated as an associated sacrifice in the Bright Hall. "Zong'an" was used when presenting the silks, "De'an" for the libation offering, and the ascension songs were all composed in the palace mode of great Lü. When Gaozong's honorific title was conferred, the register and seal were presented in announcement with the music "Xian'an."
2
紹熙元年，始行中宮冊禮，發冊於文德殿：皇帝升降御坐用《乾安之樂》，持節展禮官出入殿門用《正安之樂》。 受冊於穆清殿：皇后出就褥位用《坤安》，至位用《承安》，受冊寶，用《成安》，受內外命婦賀就坐，用《和安》，內命婦進行賀禮，用《惠安》，外命婦進行賀禮用《鹹安》，皇后降坐用《徽安》，歸閣用《泰安》冊、寶入殿門用《宜安》。 宋初立後，自景祐始行冊命之禮。 元祐納後，典章彌盛，而六禮發制書日，樂備不作，惟皇后入宣德門，朝臣班迎，鳴鍾鼓而已。 崇寧中，乃陳宮架，用女工，皇后升降行止，並以樂為節。 至紹興復製樂，以重禕翟，詔執色勿用女工，令太常止於門外設樂。 隆興冊禮時，則國樂未舉，淳熙始遵用之，而紹熙敷賁舊典，於此特加詳備。 紹興樂奏仲呂宮，仲呂為陰； 紹熙樂奏太簇宮，太簇為陽：用樂同而揆律異焉。
In the first year of Shaoxi (1190), the inner-palace investiture ceremony was performed for the first time. The register was issued at Wende Hall: "Qian'an" accompanied the emperor's ascent and descent of the imperial seat, and "Zheng'an" when credential-bearing ritual officers entered and left the hall gates. The register was received at Muqing Hall: "Kun'an" when the empress came out to the cushion seat, "Cheng'an" on reaching her position, "Cheng'an" when receiving the register and seal, "He'an" when she took her seat after receiving congratulations from titled ladies within and without the palace, "Hui'an" when inner titled ladies performed their congratulatory rites, "Xian'an" when outer titled ladies did the same, "Hui'an" when the empress descended, "Tai'an" on her return to the inner quarters, and "Yi'an" when the register and seal were brought through the hall gates. In the early Song, when an empress was first installed, the formal investiture ceremony was not performed until the Jingyou era (1034–1038). By the Yuanyou period (1086–1094), when an empress was welcomed, the ritual code had grown ever more elaborate; yet on the day the six rites issued the imperial commission, though the full musical apparatus was ready, no music was actually performed. Only when the empress entered Xuande Gate did the court officials form ranks to receive her, with bells and drums sounded—and nothing more. During the Chongning era (1102–1106), the palace musical frame was arrayed and female performers employed; the empress's every ascent, descent, step, and pause was timed to the music. By the Shaoxing period (1131–1162) music was restored. To honor the sacred ceremonial headdress, an edict forbade female performers among the color-bearing musicians and directed the Court of Imperial Sacrifices to station the musicians outside the gate only. At the Longxing investiture (1163–1164) state music had not yet been performed; only in Chunxi (1174–1189) was it first adopted in full. Shaoxi then revived the old canon and added an especially detailed completeness to the ceremony. Shaoxing music was performed in the zhonglü palace mode, and zhonglü belongs to the yin register; Shaoxi music was performed in the taicu palace mode, and taicu belongs to the yang register: the pieces employed were the same, but the pitch standards differed.
3
明年郊祀，太常耿秉奏：“致敬鬼神，以禮樂為本，樂欲其備，音欲其和。 今所用雷鼓之屬，正所以祀天致神，而皮革虛緩，聲不能振應； 登歌、大樂樂器及樂舞工人冠服，有積歲久而損弊者，宜葺新之。 太常在籍樂工，不給於役，召募百姓，罕能習熟。 郊祀事重，其樂工親扈乘輿，和樂雅奏，期以接天地、享祖宗，請優其日廩，以籍田司錢給之，樂藝稍精，仍加賞勸。 其緣托權要、送名充數者，嚴戢絕之。 ”又言：“大禮前期，皇帝朝饗太廟，別廟內安穆、安恭皇后二室，前此係大臣分詣行事。 今既親詣室祼，其酌獻、升殿所奏樂曲，恐不相協，宜命有司更製。 ”皆從之。
The following year, at the suburban sacrifice, Geng Bing of the Court of Imperial Sacrifices memorialized: "In paying homage to spirits and ghosts, ritual and music are the foundation. Music should be complete, and the tones harmonious. The thunder drums and their kind, now in use, are precisely what serve to sacrifice to Heaven and summon the spirits; yet their hides are slack and loose, and the sound cannot ring out in response; The ascension-song instruments, the great ceremonial music apparatus, and the caps and robes of the musicians and dancers—some of which have deteriorated over many years—should be restored. The Court's registered musicians were too few to meet demand, and commoners recruited to fill the gap rarely mastered their parts. The suburban sacrifice is a weighty affair: its musicians attend the imperial carriage in person and perform the elegant harmonies, expected to link Heaven and earth and honor the ancestors. I beg that their daily provisions be increased, paid from the memorial-field office treasury, so that their skill may gradually improve, with rewards and encouragement added besides. Those who used connections with the powerful merely to submit names and fill quotas should be strictly suppressed and barred. " He added: "Before the great ceremony, the emperor performs the morning sacrifice at the Imperial Ancestral Temple. Within the subsidiary temples are the chambers of Empresses Anmu and Angong; previously high ministers went separately to conduct the rites. Now that he goes in person to pour the libation at the chambers, the music performed at the libation offering and the hall ascent may not be properly coordinated. The responsible offices should be ordered to compose new pieces. " All of this was approved.
4
寧宗即位，孝宗升祔，祧僖祖，立別廟，禮官言：“僖祖既仿唐興聖立為別廟，遇祫則即廟以饗，孟冬祫饗日，合先詣僖祖廟室行禮。 其樂舞欲依每歲別廟五饗設樂禮例，於僖祖添設登歌樂。 如僖廟行禮，就廟殿依次作登歌樂，其宮架樂則於太廟殿上通作。 ”詔從之。
When Ningzong ascended the throne, Xiaozong was enshrined in the main temple line, Xizu was moved to a separate temple, and a dedicated shrine was established. The ritual officers submitted: "Xizu, having been established as a separate temple on the Tang model of Xingsheng, is sacrificed at his own shrine when the collapse rite is performed. On the mid-winter day of the collapse sacrifice, rites should first be conducted at Xizu's temple chamber. The music and dance should follow the precedent for the five annual sacrifices at separate temples, with ascension-song music added for Xizu. When rites are performed at the Xi temple, the ascension songs should be played in sequence within the temple hall, while the palace-frame music is performed continuously in the main hall of the Imperial Ancestral Temple. " The edict approved this.
5
既而臣僚言：“皇帝因重明聖節，詣壽康宮上壽舉樂，仰體聖主事親盡孝之誌，俯遂臣子尊君親上之忱，此國家典禮之大者也。 檢照典故，天申節賜禦筵，在上壽次日。 今乃於前一日賜文武百僚宴，重明上壽，用樂攸始，而臣下聽樂乃在君父之先，義有未安。 ”遂命改用次日。 凡奉上冊寶於慈福、壽康宮者，再備樂行禮，一用乾道舊制。 尋禦文德殿製冊皇后，有司請設宮架之樂，依儀施行。 慶元六年瑞慶節，金使至，以執光宗、慈懿皇后喪，詔就驛賜禦筵，並不作樂。
Then the officials submitted: "On the Double Ninth holy day the emperor went to Shoukang Palace to offer longevity wishes and perform music—embodying the retired sovereign's utmost filial devotion to his parent, and fulfilling his subjects' reverence toward ruler and parent alike. This is among the greatest ceremonial norms of the state. According to precedent, on the Heavenly Application festival the imperial banquet was granted on the day following the longevity offering. Yet now the feast for civil and military officials is granted on the day before. Music for the Chongming longevity offering has only just begun, while the subjects hear music before their ruler and father—this is improper in principle. " The court accordingly ordered that the banquet be moved to the following day. Whenever registers and seals were presented to Cifu and Shoukang palaces, music and ceremonial rites were again fully provided, all according to the old Qiandao (1165–1173) regulations. Soon afterward, at Wende Hall, the empress's register was composed. The responsible offices requested the palace musical frame be set up and the ceremony performed according to protocol. In the sixth year of Qingyuan (1200), on the Auspicious Celebration festival, Jin envoys arrived. Because the court was in mourning for Guangzong and Empress Ciyi, an edict directed that the imperial banquet be granted at the post station, with no music performed.
6
嘉定二年，明堂大饗，禮部尚書章穎奏：“太常工籍闕少，率差借執役。 當親行薦饗，或容不根遊手出入殿庭，非所以肅儀衛、嚴禁防也。 乞申紹興、開禧已行禁令，不許用市井替名，顯示懲戒，庶俾駿奔之人小大嚴潔，以稱精禋。 ”臣僚又奏：“郊祀登歌列於壇上，簉於上龕，蓋在天地祖宗之側也。 宮架列於午階下，則百神所同聽也。 夫樂音莫尚於和，今絲、竹、管、弦類有闕斷，拊搏、佾舞，賤工、窶人往往垢玩猱雜，宜申嚴以肅祀事。 ”皆俞其請。 至十四年，詔：“山東、河北連城慕義，殊俗郊順，奉玉寶來獻，其文曰‘皇帝恭膺天命之寶’，實惟我祖宗之舊。 ”乃明年元日，上御大慶殿受寶，用鼓吹導引，備陳宮架大樂，奏詩三章：一曰《恭膺天命》，二曰《舊疆來歸》，三曰《永清四海》，並奏以太簇宮。
In the second year of Jiading (1209), at the Bright Hall great sacrifice, Zhang Ying, Minister of Rites, memorialized: "The Court of Imperial Sacrifices has too few registered craftsmen and mostly impresses borrowed laborers for service. When the emperor personally performs the recommendation sacrifice, idle persons with no grounding in the craft may be allowed into the hall precincts—hardly the way to maintain dignified protocol and strict security. I beg that the bans already enforced in Shaoxing and Kaixi be reissued, forbidding marketplace substitutes registered under false names, with punishments made visible, so that all who serve at the sacrifice, high and low alike, may be scrupulously proper and worthy of so refined a ceremony. " The officials added: "At the suburban sacrifice the ascension songs are arrayed on the altar, beside the upper niche—they stand in the presence of Heaven and earth and the ancestors. The palace frame is arrayed below the south steps, where all the spirits listen alike. Nothing in music surpasses harmony; yet now the silk, bamboo, pipe, and string instruments are broken and incomplete, and the clappers and dancers—often lowly workers and paupers—foul their instruments with careless handling. Strict enforcement is needed to dignify the sacrificial rites. " All their requests were approved. By the fourteenth year (1222), an edict proclaimed: "Cities of Shandong and Hebei, moved by our righteousness, and foreign peoples submitting at the suburban sacrifice, have presented jade and treasure as tribute. The inscription reads 'The Emperor Respectfully Receives the Mandate of Heaven Treasure'—truly an heirloom of our ancestors. " The following New Year's Day the emperor received the treasure at Daqing Hall, escorted by drums and pipes, with the full palace-frame great music arrayed. Three odes were performed: "Respectfully Receives Heaven's Mandate," "Former Territories Return," and "Forever Clear the Four Seas," all in the taicu palace mode.
7
理宗享國四十餘年，凡禮樂之事，式遵舊章，未嚐有所改作。 先是，孝宗廟用《大倫之樂》，光宗廟用《大和之樂》； 至是，寧宗祔廟，用《大安之樂》。 紹定三年，行中宮冊禮，並用紹熙元年之典。 及奉上壽明仁福慈睿皇太后冊寶，始新製樂曲行事。 當時中興六七十載之間，士多歎樂典之久墜，類欲蒐講古製，以補遺軼。 於是，薑夔乃進《大樂議》於朝。 夔言：
Emperor Lizong reigned for more than forty years; in all matters of ritual and music he followed the established regulations and never altered or newly composed anything. Previously, the Xiaozong temple used the music "Great Human Relations," and the Guangzong temple used "Great Harmony;" at this point, when Ningzong was enshrined, the music "Great Peace" was used. In the third year of Shaoding (1230), the inner-palace investiture ceremony was performed, entirely according to the canon of Shaoxi's first year. Only when presenting the register and seal to Empress Dowager Shou Mingren Fuci Ruishou were new musical pieces composed for the ceremony. During the sixty or seventy years of the restoration, scholar-officials frequently lamented how long the music canon had lain in ruins, and many wished to gather and expound ancient systems to restore what had been lost. Thereupon Jiang Kui presented his "Treatise on Great Music" to the court. Kui wrote:
8
紹興大樂，多用大晟所造，有編鍾、鎛鍾、景鍾，有特磬、玉磬、編磬，三鍾三磬未必相應。 塤有大小，簫、篪、笛有長短，笙、竽之簧有厚薄，未必能合度，琴、瑟弦有緩急燥濕，軫有旋復，柱有進退，未必能合調。 總眾音而言之，金欲應石，石欲應絲，絲欲應竹，竹欲應匏，匏欲應土，而四金之音又欲應黃鍾，不知其果應否。 樂曲知以七律為一調，而未知度曲之義； 知以一律配一字，而未知永言之旨。 黃鍾奏而聲或林鍾，林鍾奏而聲或太簇。 七音之協四聲，各有自然之理。 今以平、入配重濁，以上、去配輕清，奏之多不諧協。
The Shaoxing great music relied largely on instruments made under the Dasheng Bureau. There were serial bells, bo bells, and jing bells; special stone chimes, jade chimes, and serial stone chimes—but the three bells and three chimes did not necessarily correspond with one another. The xun come in large and small sizes; the xiao, chi, and di in long and short; the reeds of the sheng and yu in thick and thin—they did not necessarily conform to the standard measures. The qin and se strings varied in tension, dryness, and moisture; the pegs turned and the bridges shifted—they did not necessarily achieve proper tuning. Considering all the sounds together: metal should respond to stone, stone to silk, silk to bamboo, bamboo to gourd, gourd to earth—and the four metal tones should also respond to yellow bell. Whether they truly did so was unknown. Composers knew to take the seven tones as one mode, but did not understand what it meant to set a tune properly; they knew to assign one tone to each character, but did not grasp the principle of sustained melodic phrasing. When yellow bell was played, the sound produced might be forest bell; when forest bell was played, it might come out as great cluster. The coordination of the seven tones with the four tones of Chinese phonology each follows a natural principle. Now level and entering tones are paired with heavy, thick notes, and rising and departing tones with light, clear ones—yet in performance much of this coordination fails.
9
八音之中，琴、瑟尤難。 琴必每調而改弦，瑟必每調而退柱，上下相生，其理至妙，知之者鮮。 又琴、瑟聲微，常見蔽於鍾、磬、鼓、簫之聲； 匏、竹、土聲長，而金石常不能以相待，往往考擊失宜，消息未盡。 至於歌詩，則一句而鍾四擊，一字而竽一吹，未協古人槁木貫珠之意。 況樂工苟焉占籍，擊鍾磬者不知聲，吹匏竹者不知穴，操琴瑟者不知弦。 同奏則動手不均，迭奏則發聲不屬。 比年人事不和，天時多忒，由大樂未有以格神人、召和氣也。
Among the eight categories of sound, the qin and se are especially difficult. The qin must have its strings changed for each mode, the se its bridges repositioned; upper and lower tones generate one another by a principle of utmost subtlety, and few understand it. Moreover, the qin and se are faint in sound and are often drowned out by bells, chimes, drums, and xiao; Gourd, bamboo, and earth instruments sustain their tones, while metal and stone often cannot accommodate them; the striking is frequently mistimed and the resonance left incomplete. As for sung poetry, four bell strikes accompany a single line and one yu breath per character—far from the ancients' ideal of pearls strung on withered wood. Moreover, musicians merely hold places on the registry: bell and chime players do not understand tone, gourd and bamboo players do not understand their instruments' holes, and qin and se players do not understand their strings. When playing together their movements are uneven; when playing in alternation their sounds fail to connect. In recent years human affairs have fallen into discord and the seasons have often gone awry—because great music has not yet been able to reach spirits and men and summon harmonious qi.
10
宮為君、為父，商為臣、為子，宮商和則君臣父子和。 徵為火，羽為水，南方火之位，北方水之宅，常使水聲衰、火聲盛，則可助南而抑北。 宮為夫，徵為婦，商雖父宮，實徵之子，常以婦助夫、子助母，而後聲成文。 徵盛則宮唱而有和，商盛則徵有子而生生不窮，休祥不召而自至，災害不祓而自消。 聖主方將講禮郊見，願詔求知音之士，考正太常之器，取所用樂曲，條理五音，隱括四聲，而使協和。 然後品擇樂工，其上者教以金、石、絲、竹、匏、土、歌詩之事，其次者教以戛、擊、幹、羽、四金之事，其下不可教者汰之。 雖古樂未易遽復，而追還祖宗盛典，實在茲舉。
Gong represents the ruler and the father, shang the minister and the son; when gong and shang are in harmony, ruler and minister, father and son are in harmony. Zhi is fire and yu is water; the south is fire's domain and the north water's home. By consistently weakening the water tone and strengthening the fire tone, one can support the south and restrain the north. Gong is the husband and zhi the wife; though shang is gong's parent tone, it is in fact zhi's child—by having the wife assist the husband and the son assist the mother, the tones then form a coherent pattern. When zhi flourishes, gong leads the song and harmony follows; when shang flourishes, zhi has its child and generation succeeds generation without end. Auspicious omens arrive unbidden, and disasters dissipate without need of exorcism. The sage ruler is about to perform the suburban sacrifice and audience rites. I beg that an edict be issued to seek those who understand music, to examine and correct the Court of Imperial Sacrifices' instruments, to take the pieces now in use, arrange the five tones, encompass the four phonetic tones, and bring them into harmony. Then grade and select the musicians: the best should be taught metal, stone, silk, bamboo, gourd, earth, and sung poetry; the next rank taught striking, beating, shields, feathers, and the four metal instruments; those at the bottom who cannot be taught should be dismissed. Though ancient music cannot easily be restored at once, to recover the great ceremonies of our ancestors truly depends on this effort.
11
其議雅俗樂高下不一，宜正權衡度量：
On the question that elegant and vulgar music differ in pitch and are not uniform, he argued that weights, measures, and pitch standards should be corrected:
12
自尺律之法亡於漢、魏，而十五等尺雜出於隋、唐正律之外，有所謂倍四之器，銀字、中管之號。 今大樂外有所謂下宮調，下宮調又有中管倍五者。 有曰羌笛、孤笛，曰雙韻、十四弦以意裁聲，不合正律，繁數悲哀，棄其本根，失之太清； 有曰夏笛、鷓鴣，曰胡盧琴、渤海琴，沉滯抑鬱。 腔調含糊，失之太濁。 故聞其聲者，性情蕩於內，手足亂於外，《禮》所謂“慢易以犯節，流湎以忘本，廣則容奸，狹則思欲”者也。 家自為權衡，鄉自為尺度，乃至於此。 謂宜在上明示以好惡。 凡作樂製器者，一以太常所用及文思所頒為準。 其他私為高下多寡者悉禁之，則斯民“順帝之則”，而風俗可正。
Since the method of foot-and-pitch standards was lost in Han and Wei, fifteen grades of measuring foot emerged outside the proper pitch standards of Sui and Tang, along with so-called double-four instruments and designations such as silver character and middle pipe. Outside the great ceremonial music there is now the so-called lower palace mode, and within lower palace mode there is also the middle-pipe double-five variant. There are the Qiang flute and solitary flute, the double rhyme and fourteen-string instruments—shaping sound at whim, not conforming to proper pitch, elaborate and mournful, abandoning their musical roots, erring toward excessive clarity; There are the summer flute and partridge call, the gourd lute and Bohai lute—heavy, stagnant, and oppressive in tone. Their melodic patterns are indistinct, erring toward excessive thickness. Those who hear such sounds find their inner natures unsettled and their limbs in disorder—precisely what the Rites describes as "careless and easy in violating propriety, dissolute in forgetting one's roots; when broad, harboring treachery; when narrow, given to desire." Each household sets its own weights, each village its own measures—and matters have come to this pass. He argued that the ruler above should make his preferences clearly known. All who compose music and manufacture instruments should take as their sole standard what the Court of Imperial Sacrifices uses and what the Wensi Bureau promulgates. All other private variations in pitch or quantity should be forbidden; then the people will "follow the emperor's standard," and customs may be set right.
13
其議古樂止用十二宮：
On the question that ancient music used only the twelve palace modes, he argued:
14
周六樂奏六律、歌六呂，惟十二宮也。 “王大食，三侑。 ”注云：“朔日、月半。 ”隨月用律，亦十二宮也。 十二管各備五聲，合六十聲； 五聲成一調，故十二調。 古人於十二宮又特重黃鍾一宮而已。 齊景公作《徵招》、《角招》之樂，師涓、師曠有清商、清角、清徵之操。 漢、魏以來，燕樂或用之，雅樂未聞有以商、角、徵、羽為調者，惟迎氣有五引而已，《隋書》雲“梁、陳雅樂，並用宮聲”是也。 若鄭譯之八十四調，出於蘇祗婆之琵琶。 大食、小食、般涉者，胡語； 《伊州》、《石州》、《甘州》、《婆羅門》者，胡曲； 《綠腰》、《誕黃龍》、《新水調》者，華聲而用胡樂之節奏。 惟《瀛府》、《獻仙音》謂之法曲，即唐之法部也。 凡有催袞者，皆胡曲耳，法曲無是也。 且其名八十四調者，其實則有黃鍾、太簇、夾鍾、仲呂、林鍾、夷則、無射七律之宮、商、羽而已，於其中又闕太簇之商、羽焉。 國朝大樂諸曲，多襲唐舊。 竊謂以十二宮為雅樂，周製可舉； 以八十四調為宴樂，胡部不可雜。 郊廟用樂，鹹當以宮為曲，其間皇帝升降、盥洗之類，用黃鍾者，群臣以太簇易之，此周人王用《王夏》、公用《驁夏》之義也。
The Zhou six great ceremonial musics played the six lü and sang the six lü complement—nothing but the twelve palace modes. "The king's great feasts, with three libations." " The commentary explains: "The first day of the month and the month's midpoint." Using the pitch standard appropriate to each month is likewise a matter of the twelve palace modes. The twelve pipes each carry the five tones, making sixty tones in all; five tones forming one mode, hence twelve modes. Among the twelve palace modes, the ancients especially valued only the yellow bell mode. Duke Jing of Qi composed "Zhi Summons" and "Jue Summons"; the masters Shi Juan and Shi Kuang had pieces in Clear Shang, Clear Jue, and Clear Zhi. From Han and Wei onward, banquet music sometimes employed them, but elegant music was never known to use shang, jue, zhi, or yu as modes—only the five introductions for welcoming the seasons. The Book of Sui states that "Liang and Chen elegant music both used the gong tone," and this is correct. Zheng Yi's eighty-four modes, for instance, derived from Su Zhiba's pipa. Dashi, xiaoshi, and banshe are foreign terms; "Yizhou," "Shizhou," "Ganzhou," and "Brahmana" are foreign melodies; "Green Waist," "Birth of the Yellow Dragon," and "New Water Mode" are Chinese melodies set to foreign rhythmic patterns. Only the pieces "Yingfu" and "Offering Immortal Music" are termed courtly pieces (fayue); these are the Tang dynasty's courtly music department. Whatever pieces employ accelerated ornamentation are foreign tunes; courtly pieces have no such feature. Moreover, although they are called the eighty-four modes, in practice there are only the gong, shang, and yu modes for the seven tones Huangzhong, Taicu, Jiazhong, Zhonglü, Linzhong, Yize, and Wushe—and even among these, the shang and yu of Taicu are missing. Most of the great ceremonial music pieces of our dynasty largely follow Tang models. I would suggest that the twelve gong modes be adopted as elegant music, following the Zhou system; and that the eighty-four modes serve as banquet music, without mixing in foreign music. For suburban and temple rites, all music should be set in the gong mode; where the emperor's ascent, descent, or ablutions would use Huangzhong, the ministers substitute Taicu—just as in Zhou times the king performed to "Royal Summer" and a duke to "Piebald Summer."
15
其議登歌當與奏樂相合：
His proposal on ascending song and instrumental performance:
16
《周官》歌奏，取陰陽相合之義。 歌者，登歌、徹歌是也； 奏者，金奏、下管是也。 奏六律主乎陽，歌六呂主乎陰，聲不同而德相合也，自唐以來始失之。 故趙慎言云：祭祀有下奏太簇、上歌黃鍾，俱是陽律，既違禮經，抑乖會合。 ”今太常樂曲，奏夾鍾者奏陰歌陽，其合宜歌無射，乃或歌大呂； 奏函鍾者奏陰歌陽，其合宜歌蕤賓，乃或歌應鍾； 奏黃鍾者奏陽歌陰，其合宜歌大呂，乃雜歌夷則、夾鍾、仲呂、無射矣。 苟欲合天人之和，此所當改。
In the Offices of Zhou, singing and instrumental performance embody the principle of yin and yang in harmony. "Song" refers to ascending song and withdrawal song; "Performance" refers to metal percussion and lower wind instruments. The six lü in performance are yang-dominant; the six lü in song are yin-dominant—the timbres differ yet their virtue harmonizes. This principle has been lost since the Tang. Hence Zhao Shenyan remarked: in sacrifice, performing Taicu below while singing Huangzhong above—both yang modes—violates the ritual classics and defeats their intended harmony. "In the Court of Imperial Sacrifices' repertoire today: where Jiazhong is performed (yin), yang is sung—the proper pairing should be Wushe, yet sometimes Dalü is sung instead; where Hanzhong is performed (yin), yang is sung—the proper pairing should be Ruibin, yet sometimes Yingzhong is sung; where Huangzhong is performed (yang), yin should be sung—the proper pairing is Dalü, yet Yize, Jiazhong, Zhonglü, and Wushe are sung indiscriminately. If one seeks harmony between Heaven and humanity, these are the points that must be corrected.
17
其議祀享惟登歌、徹豆當歌詩：
His proposal on sacrificial music and when to sing odes:
18
古之樂，或奏以金，或吹以管，或吹以笙，不必皆歌詩。 周有《九夏》，鍾師以鍾鼓奏之，此所謂奏以金也。 大祭祀登歌既畢，下管《象》、《武》。 管者，簫、篪、笛之屬。 《象》、《武》皆詩而吹其聲，此所謂吹以管者也。 周六笙詩，自《南陔》皆有聲而無其詩，笙師掌之以供祀饗，此所謂吹以笙者也。 周升歌《清廟》，徹而歌《雍》詩，一大祀惟兩歌詩。 漢初，此製未改，迎神曰《嘉至》，皇帝入曰《永至》：皆有聲無詩。 至晉始失古製，既登歌有詩，夕牲有詩，饗神有詩，迎神、送神又有詩。 隋、唐至今，詩歌愈富，樂無虛作。 謂宜仿周製，除登歌、徹歌外，繁文當刪，以合於古。
In ancient music, pieces were sometimes performed on metal percussion, sometimes on pipes, sometimes on the sheng—not every piece required singing an ode. The Zhou had the Nine Summers, performed by the bell master on bells and drums—this is what is meant by performing with metal. After the ascending song of a great sacrifice concluded, the lower pipes performed "Xiang" and "Wu." Pipes comprise the xiao, chi, di, and related instruments. "Xiang" and "Wu" are odes whose melodies were blown on pipes—this is what is meant by blowing on pipes. The Zhou's six sheng pieces, from "Southern Hills" onward, had melodies but no surviving texts; the sheng master performed them for sacrifices and feasts—this is what is meant by blowing on the sheng. The Zhou ascended with "Clear Temple" and withdrew singing "Yong"—a great sacrifice employed only two sung odes. In early Han this system remained: welcoming the spirit used "Fine Arrival," the emperor's entrance used "Eternal Arrival"—both had melodies but no texts. By the Jin the ancient system was lost: ascending song, evening sacrifice, spirit feasting, and welcoming and sending the spirit—all had sung odes. From Sui and Tang to the present, sung odes have proliferated until no musical moment lacks a text. He proposed imitating the Zhou system: apart from ascending and withdrawal songs, superfluous texts should be removed to restore ancient practice.
19
其議作鼓吹曲以歌祖宗功德：
His proposal on composing drum-and-blow pieces to celebrate ancestral merit:
20
古者，祖宗有功德，必有詩歌，《七月》之陳王業是也。 歌於軍中，周之愷樂、愷歌是也。 漢有短簫鐃歌之曲凡二十二篇，軍中謂之騎吹，其曲曰《戰城南》、《聖人出》之類是也。 魏因其聲，製為《克官渡》等曲十有二篇； 晉亦製為《征遼東》等曲二十篇； 唐柳宗元亦嚐作為鐃歌十有二篇，述高祖、太宗功烈。 我朝太祖、太宗平僭偽，一區宇； 真宗一戎衣而卻契丹； 仁宗海涵春育，德如堯、舜； 高宗再造大功，上儷祖宗。 願詔文學之臣，追述功業之盛，作為歌詩，使知樂者協以音律，領之太常，以播於天下。
In antiquity, when ancestors achieved merit and virtue, odes inevitably followed—"Seventh Month," presenting the royal enterprise, is an example. Singing in the army—the Zhou's triumphant music and songs are examples. The Han possessed twenty-two short xiao and nao song pieces, termed cavalry blow in the army—pieces such as "Battle South of the City" and "The Sage Appears." Wei adapted these melodies into twelve pieces, including "Conquering Guandu"; Jin likewise composed twenty pieces, including "Campaigning in Liaodong"; Tang's Liu Zongyuan likewise once composed twelve nao songs recounting the achievements of Gaozu and Taizong. Our dynasty's Taizu and Taizong suppressed usurpers and reunified the realm; Zhenzong repelled the Khitan at a single stroke; Renzong's virtue encompassed all as the sea and nourished as spring, rivaling Yao and Shun; Gaozong restored the dynasty in grand achievement, equaling his forebears. May literary officials be commissioned to recount these splendid achievements in song and ode, have musicians set them to proper pitch, and entrust the Court of Imperial Sacrifices to disseminate them throughout the realm.
21
夔乃自作《聖宋鐃歌曲》：宋受命曰《上帝命》，平上黨曰《河之表》，定維揚曰《淮海濁》，取湖南曰《沅之上》，得荊州曰《皇威暢》，取蜀曰《蜀山邃》，取廣南曰《時雨霈》，下江南曰《望鍾山》，吳越獻國曰《大哉仁》，漳、泉獻土曰《謳歌歸》，克河東曰《伐功繼》，征澶淵曰《帝臨墉》，美仁治曰《維四葉》，歌中興曰《炎精復》，凡十有四篇，上於尚書省。 書奏，詔付太常。 然夔言為樂必定黃鍾，迄無成說。 其議今之樂極為詳明，而終謂古樂難復，則於樂律之原有未及講。
Kui then composed the "Holy Song Nao Songs" himself: "Heaven's Command" for the Song receiving the Mandate, "Beyond the River" for pacifying Shangdang, "Huaihai Turbid" for securing Weiyang, "Above the Yuan" for taking Hunan, "Imperial Might Unfettered" for obtaining Jingzhou, "Shu Mountains Deep" for conquering Shu, "Seasonal Rain Abundant" for taking Guangnan, "Gazing at Zhong Mountain" for subduing Jiangnan, "How Great the Benevolence" for Wu and Yue's submission, "Songs of Praise Return" for Zhang and Quan's offering of territory, "Merit of Campaign Continued" for conquering Hedong, "The Emperor Approaches the Rampart" for the Chanyuan campaign, "Sustaining Four Generations" praising benevolent rule, and "Blazing Essence Restored" celebrating the restoration—fourteen pieces in all, submitted to the Ministry of Personnel. When the memorial was submitted, an edict entrusted it to the Court of Imperial Sacrifices. Yet Kui insisted that establishing music required fixing Huangzhong as the standard—and no settled theory was ever reached. His analysis of contemporary music was remarkably thorough, yet he ultimately held that ancient music could not be restored—leaving the origins of pitch standards insufficiently explored.
22
其後，朱熹深悼先王製作之湮泯，與其友武夷蔡元定相與講明，反覆參訂，以究其歸極。 熹在慶元經筵，嚐草奏曰：“自秦滅學，禮樂先壞，而樂之為教，絕無師授。 律尺短長，聲音清濁，學士大夫莫知其說，而不知其為闕也。 望明詔許臣招致學徒，聚禮樂諸書，編輯別為一書，以補六藝之闕。 ”後修禮書，定為《鍾律》、《樂製》等篇，垂憲言以貽後人。
Thereafter Zhu Xi deeply lamented the obliteration of the former kings' musical creations. With his friend Cai Yuanding of Wuyi he engaged in sustained study, repeatedly collating and revising their work to reach its fundamental principles. At the Qingyuan Classics Lectures, Xi once drafted a memorial stating: "Since the Qin extinguished learning, ritual and music were the first to collapse, and music as a discipline has lacked any transmission from masters. The length of pitch measures, the clarity and murkiness of tones—scholar-officials know nothing of these matters, unaware even that this constitutes a grave deficiency. I humbly request a clear edict permitting me to gather students, collect works on ritual and music, and compile them into a separate volume to fill the gap in the Six Arts. "Later, while compiling his Book of Rites, he established chapters on "Bell Standards" and "Music Institutions," leaving authoritative teachings for posterity.
23
蓋宋之樂議，因時迭出，其樂律高下不齊，俱有原委。 建隆初用王樸樂，藝祖一聽，嫌其太高，近於哀思，詔和峴考西京表尺，令下一律，比舊樂始和暢。 至景祐、皇祐間，訪樂、議樂之詔屢頒，於是命李照改定雅樂，比樸下三律。 照以縱黍累尺，雖律應古樂，而所造鍾磬，才中太簇，樂與器自相矛盾。 阮逸、胡瑗復定議，止下一律，以尺生律，而黃鍾律短，所奏樂聲復高。 元豐中，以楊傑條樂之疵，召範鎮、劉幾參定。 幾、傑所奏，下舊樂三律，範鎮以為聲雜鄭、衛，且律有四厘六毫之差，太簇為黃鍾，宮商易位，欲求真黍以正尺律，造樂來獻，復下李照一律。 至元祐廷奏，而詔獎之。 初，鎮以房庶所得《漢書》，其言黍律異於他本，以大府尺為黃帝時尺，司馬光力辨其不然。 鎮以周鬴、漢斛為據，光謂鬴本《考工》所記，斛本劉歆所作，非經不足法。 鎮以所收開元中笛及方響合於仲呂，校太常樂下五律，教坊樂下三律。 光謂此特開元之仲呂，未必合於後夔，力止鎮勿奏所為樂。 光與鎮平生大節不謀而同，惟鍾律之論往返爭議，凡三十餘年，終不能以相一。
Broadly speaking, Song debates on music emerged successively over time; their pitch standards varied in height, each with its own history and rationale. At the beginning of Jianlong, Wang Pu's music was adopted. The Founding Emperor, upon hearing it once, found it too high and uncomfortably mournful. He ordered He Ning to examine the Western Capital pitch measure and lower the pitch by one degree; compared with the previous music, it first became harmonious. By the Jingyou and Huangyou reigns, edicts commissioning music research and debate were issued repeatedly. Li Zhao was then ordered to revise elegant music, three pitches lower than Pu's standard. Zhao used the method of stacking millet grains to determine the foot. Although his pitch standards accorded with ancient music in theory, the bells and chime stones he cast only matched Taicu—music and instruments contradicted one another. Ruan Yi and Hu Yuan revised the standard again, lowering only one pitch and deriving pitch standards from the foot measure—but the Huangzhong standard proved too short, and the performed music sounded high once more. During the Yuanfeng reign, Yang Jie enumerated defects in the music system, and Fan Zhen and Liu Ji were summoned to assist in revising it. Ji and Jie proposed lowering the old music by three pitches. Fan Zhen objected that the sound resembled vulgar Zheng and Wei music, and that the pitch standards were off by four li and six hao—Taicu was mistaken for Huangzhong, gong and shang reversed. Seeking true millet to correct the foot and pitch measures, he composed new music and presented it, yet the court lowered it one pitch from Li Zhao's standard. When it was performed at court during Yuanyou, an edict commended the achievement. Initially Fan Zhen relied on a Book of Han obtained by Fang Shu, whose account of millet and pitch standards differed from other versions, and took the Grand Storehouse foot as the Yellow Emperor's measure—Sima Guang vigorously disputed this. Fan Zhen cited the Zhou cauldron and Han hu as evidence. Guang replied that the cauldron was recorded only in the Artificers' Standards and the hu was devised by Liu Xin—neither being canonical texts, neither could serve as authoritative precedent. Fan Zhen argued that a Kaiyuan-period flute and square sounding stone in his collection matched Zhonglü, and proposed lowering the Court of Imperial Sacrifices' music by five pitches and the Music Bureau's by three. Guang countered that this was merely the Kaiyuan period's Zhonglü, not necessarily matching Hou Kui's standard, and vigorously prevented Fan Zhen from presenting his newly composed music. Guang and Fan Zhen shared the same moral integrity throughout their lives, yet on bell standards they debated back and forth for over thirty years without ever reaching agreement.
24
是時，濂、洛、關輔諸儒繼起，遠溯聖傳，義理精究。 周惇頤之言樂，有曰：“古者聖王製禮法、修教化，三綱正，九疇敘，百姓大和，萬物鹹若，乃作樂以宣八風之氣。 樂聲淡而不傷，和而不淫。 淡則欲心平，和則躁心釋。 德盛治至，道配天地，古之極也。 後世禮法不修，刑政苛紊，代變新聲，導欲增悲，故有輕生敗倫不可禁者矣。 樂者，古以平心，今以助欲； 古以宣化，今以長怨。 不復古禮，不變今樂，而欲至治者，遠哉！”
At this time, scholars of the Lian, Luo, and Guanfu traditions arose in succession, tracing the sage transmission to its roots and pursuing principle with rigorous precision. Zhou Dunyi wrote on music: "In antiquity the sage kings established ritual law and cultivated moral transformation. When the three bonds were rectified and the nine categories ordered, when the people lived in great harmony and all things flourished, they then composed music to disseminate the qi of the eight winds. Its sound was plain yet not harsh, harmonious yet not licentious. Plainness calmed the mind of desire; harmony released the restless mind. When virtue flourished and governance reached perfection, when the Way matched Heaven and Earth—this was the pinnacle of antiquity. In later ages ritual law fell into neglect, punishments and governance grew harsh and chaotic, and each generation produced new sounds that stirred desire and deepened sorrow—giving rise to those who lightly abandoned life and violated human relations beyond all prohibition. Music—in antiquity served to calm the mind; today it serves to inflame desire; in antiquity it disseminated moral transformation; today it deepens resentment. Without restoring ancient ritual or reforming present music, yet hoping to achieve perfect governance—how remote that prospect!
25
程頤有曰：“律者，自然之數。 先王之樂，必須律以考其聲。 尺度權衡之正，皆起於律。 律管定尺，以天地之氣為準，非黍之比也。 律取黃鍾，黃鍾之聲亦不難定，有知音者，參上下聲考之，自得其正。”
Cheng Yi remarked: "Pitch standards are numbers inherent in Nature. The music of the former kings must be tested against pitch standards. The correctness of measures, weights, and balances all derives from pitch standards. The pitch-standard tube determines the foot measure, taking the qi of Heaven and Earth as the standard—not the proportions of millet grains. The standard takes Huangzhong; Huangzhong's pitch is not difficult to determine—one who understands music, comparing higher and lower tones, will naturally arrive at the correct pitch.
26
張載有曰：“聲音之道與天地通，蠶吐絲而商弦絕，木氣盛則金氣衰，乃此理自相應。 今人求古樂太深，始以古樂為不可知，律呂有可求之理，惟德性深厚者能知之。 ”此三臣之學，可謂窮本知變，達樂之要者矣。
Zhang Zai remarked: "The way of sound connects with Heaven and Earth. When silkworms spin silk, the shang string breaks; when wood qi flourishes, metal qi declines—such is the mutual correspondence of this principle. People today pursue ancient music so obsessively that they conclude it is unknowable. Yet pitch standards have principles that can be discovered—only those of profound moral cultivation can grasp them. "The learning of these three masters may be said to have penetrated fundamentals, understood transformation, and grasped the essentials of music.
27
熹與元定蓋深講於其學者，而研覃真積，述為成書。 元定先究律呂本原，分其篇目，又從而證辨之。 其黃鍾篇曰：
Xi and Yuanding engaged deeply with this tradition, pursuing sustained study until they composed a definitive work. Yuanding first investigated the origins of pitch standards, organized them into chapters, and then provided detailed verification and analysis. His chapter on Huangzhong states:
28
天地之數始於一，終於十：其一、三、五、七、九為陽，九者，陽之成也； 其二、四、六、八、十為陰，十者，陰之成也。 黃鍾者，陽聲之始，陽氣之動也，故其數九。 分寸之數，具於聲氣之先，不可得而見。 及斷竹為管，吹之而聲和，候之而氣應，而後數始形焉。 均其長，得九寸； 審其圍，得九分； 積其實，得八百一十分。 長九寸，圍九分，積八百一十分，是為律本，度量權衡於是而受法，十一律由是損益焉。 〈（其《證辨》曰：古者考聲候氣，皆以聲之清濁、氣之先後求黃鍾也。 夫律長則聲濁而氣先至，律短則聲清而氣後至，極長極短則不成聲而氣不應。 今欲求聲氣之中，而莫適為準，莫若且多截竹以擬黃鍾之管，或極其短，或極其長，長短之內，每差一分而為一管，皆即以其長權為九寸，而度圍徑如黃鍾之法焉。 更迭以吹，則中聲可得； 淺深以列，則中氣可驗。 苟聲和氣應，則黃鍾之為黃鍾者信矣。 黃鍾信，則十一律與度量權衡者得矣。 後世不知出此，而惟尺之求。 晉氏而下，多求之金石； 梁、隋以來，又參之黍； 至王樸專恃累黍，金石亦不復考。 夫金石真偽固難盡信，而黍長短小大不同，尤不可恃。 古人謂‘子穀黍，中者實其籥’，是先得黃鍾而後度之以黍，以見周徑之度，以生度量權衡之數而已，非律生於黍也。 百世之下，欲求百世之前之律者，亦求之聲氣之元而毋必之於黍，斯得之矣。”）〉
The numbers of Heaven and Earth begin at one and end at ten: one, three, five, seven, and nine are yang—nine being the completion of yang; two, four, six, eight, and ten are yin—ten being the completion of yin. Huangzhong is the beginning of yang sound, the movement of yang qi—hence its number is nine. The numerical proportions of length exist prior to sound and qi, and cannot be perceived directly. Only when bamboo is cut into a tube, blown until the sound harmonizes, and observed until the qi responds do the numbers first take visible form. Balancing its length yields nine inches; measuring its circumference yields nine tenths of an inch; and calculating its volume yields eight hundred and ten cubic tenths of an inch. Nine inches in length, nine tenths in circumference, eight hundred and ten tenths in volume—this is the fundamental pitch standard. Measures, weights, and balances derive their standards from it, and the eleven pitch standards are adjusted accordingly. (His "Verification and Distinction" states: In antiquity, examining sound and observing qi both relied on the clarity or murkiness of sound and the precedence or succession of qi to determine Huangzhong. When the pitch tube is too long, the sound is murky and qi arrives early; when too short, the sound is clear and qi arrives late. At extremes of length, no proper sound forms and qi fails to respond. To find the mean between sound and qi when no suitable standard exists, one should cut many bamboo tubes approximating the Huangzhong standard—some extremely short, some extremely long. Within this range, make one tube for each fen of difference, proportioning each length to nine inches and measuring circumference and diameter by the Huangzhong method. Blowing them in succession, the correct middle pitch can be found; By arranging them according to depth of tone, the correct middle qi can be verified. If sound and qi accord, one can be confident that the tube is truly Huangzhong. Once Huangzhong is established, the eleven pitch standards and the systems of measure, weight, and balance can all be derived. Later generations, ignorant of this method, sought pitch standards solely through physical measurements. From the Jin dynasty onward, scholars relied chiefly on metal and stone bells; from the Liang and Sui dynasties onward, they also incorporated millet grains; by the time of Wang Pu, scholars relied exclusively on stacked millet measures and ceased even to test metal and stone standards. Metal and stone artifacts are difficult to authenticate, and millet grains vary greatly in size; neither can be trusted. The ancients said, 'Use millet grains; the medium-sized grain fills the pitch tube.' They first established Huangzhong and only then used millet to measure it, thereby deriving circumference and diameter and producing the numbers for measures, weights, and balances—not deriving pitch standards from millet itself. A hundred generations later, anyone seeking to recover the pitch standards of antiquity should likewise seek the origin of sound and qi rather than insisting on millet; in that way the true standards may be found.
29
《黃鍾生十一律篇》曰：
The chapter "Huangzhong Generates the Eleven Pitch Standards" states:
30
子、寅、辰、午、申、戌六陽辰皆下生，醜、卯、巳、未、酉、亥六陰辰皆上生。 陽數以倍者，三分本律而損其一也； 陰數以四者，三分本律而增其一也。 六陽辰當位，自得六陰位以居其衝。 其林鍾、南呂、應鍾三呂在陰，無所增損； 其大呂、夾鍾、仲呂三呂在陽，則用倍數，方與十二月之氣相應，蓋陰陽自然之理也。 〈（其《證辨》曰：“按《呂氏》、《淮南子》，上下相生，與司馬氏《律書》、《漢前志》不同，雖大呂、夾鍾、仲呂用倍數則一，然《呂氏》、《淮南》不過以數之多寡為生之上下，律呂陰陽錯亂而無倫，非其本法也。”）〉
The six yang branches—zi, yin, chen, wu, shen, and xu—all generate pitch standards by downward progression; the six yin branches—chou, mao, si, wei, you, and hai—all generate by upward progression. For yang numbers, the method is doubling: take one-third of the fundamental pitch and subtract one part; for yin numbers, the method is fourfold progression: take one-third of the fundamental pitch and add one part. Each of the six yang branches occupies its proper position, paired with a yin branch in direct opposition. Linzhong, Nanlü, and Yingzhong—the three yin pitch standards—undergo no augmentation or diminution; whereas Dàlǚ, Jiazhong, and Zhonglü—the three yang pitch standards—employ doubling, thereby corresponding to the qi of the twelve months. This reflects the natural principle of yin and yang. (His "Verification and Distinction" states: "The Lüshi Chunqiu and Huainanzi describe upward and downward generation differently from Sima Qian's Treatise on Pitch Standards and the Former Han Annals. Although they agree that Dàlǚ, Jiazhong, and Zhonglü use doubling, the Lüshi and Huainan merely treat numerical abundance or scarcity as the basis for upward or downward generation, disordering the yin-yang arrangement of the pitch standards. This is not the correct original method."
31
《十二律篇》曰：
The chapter "The Twelve Pitch Standards" states:
32
按十二律之實，約以寸法，則黃鍾、林鍾、太簇得全寸； 約以分法，則南呂、姑洗得全分； 約以厘法，則應鍾、蕤賓得全厘； 約以毫法，則大呂、夷則得全毫； 約以絲法，則夾鍾、無射得全絲。 約至仲呂之實十三萬一千七十二，以三分之，不盡二算，其數不行，此律之所以止於十二也。 〈（其《證辨》曰：“黃鍾為十二律之首，他律無大於黃鍾，故其正聲不為他律役。 至於大呂之變宮、夾鍾之羽、仲呂之徵、蕤賓之變征、夷則之角、無射之商，自用變律半聲，非復黃鍾矣。 此其所以最尊而為君之象，然亦非人所能為，乃數之自然，他律雖欲役之而不可得也。 此一節最為律呂旋宮用聲之綱領也。”）〉
Calculating the volumes of the twelve pitch standards: by the inch method, Huangzhong, Linzhong, and Taicu yield whole inches; by the fen method, Nanlü and Guxian yield whole fen; by the li method, Yingzhong and Ruibin yield whole li; by the hao method, Dalü and Yize yield whole hao; by the si method, Jiazhong and Wushe yield whole si. Zhonglü's volume approximates to 131,072; divided by three, two counts remain undivided and the progression cannot continue. This is why the pitch standards end at twelve. (His "Verification and Distinction" states: "Huangzhong stands first among the twelve pitch standards; no other standard surpasses it, and therefore its proper tone is not subordinate to any other standard." Dalü's altered gong, Jiazhong's yu, Zhonglü's zhi, Ruibin's altered zhi, Yize's jue, and Wushe's shang all employ altered pitch standards and half-tones; they are no longer Huangzhong tones. This is why Huangzhong is supreme and symbolizes the sovereign—yet it is not a human contrivance but a necessity of number itself; other pitch standards cannot subordinate it even if they try. This passage is the essential principle governing the circular arrangement of pitch standards and the deployment of tones.
33
《變律篇》曰：
The chapter "Altered Pitch Standards" states:
34
十二律各自為宮，以生五聲二變。 其黃鍾、林鍾、太簇、南呂、姑洗、應鍾六律，則能具足。 至蕤賓、大呂、夷則、夾鍾、無射、仲呂六律，則取黃鍾、林鍾、太簇、南呂、姑洗、應鍾六律之聲，少下，不和，故有變律。 律之當變者有六：黃鍾、林鍾、太簇、南呂、姑洗、應鍾。 變律者，其聲近正律而少高於正律，然後洪纖、高下不相奪倫。 變律非正律，故不為宮。 〈（其《證辨》曰：“十二律循環相生，而世俗不知三分損益之數，往而不返。 仲呂再生黃鍾，止得八寸七分有奇，不成黃鍾正聲。 京房覺其如此，故仲呂再生，別名執始，轉生四十八律。 不知變律之數止於六者，出於自然，不可復加。 雖強加之，亦無所用也。 房之所傳出於焦氏，焦氏卦氣之學，亦去四而為六十，故其推律必求合此數。 不知數之自然，在律不可增，於卦不可減也。 何承天、劉焯譏房之病，乃欲增林鍾已下十一律之分，使至仲呂反生黃鍾，還得十七萬七千一百四十七之數，則是惟黃鍾一律成律，他十一律皆不應三分損益之數，其失又甚於房。）〉
Each of the twelve pitch standards serves in turn as the tonal center, generating the five primary tones and the two altered tones. Huangzhong, Linzhong, Taicu, Nanlü, Guxian, and Yingzhong—the six standards—can produce the full set of tones. For Ruibin, Dalü, Yize, Jiazhong, Wushe, and Zhonglü, borrowing tones from the first six standards produces pitches slightly too low and out of harmony; hence altered pitch standards are required. Six pitch standards require alteration: Huangzhong, Linzhong, Taicu, Nanlü, Guxian, and Yingzhong. Altered pitch standards produce tones close to the proper standards but slightly higher, so that loud and soft, high and low, do not violate their proper hierarchy. Altered pitch standards are not proper standards and therefore cannot serve as the tonal center. (His "Verification and Distinction" states: "The twelve pitch standards generate one another in a cycle, but common scholars do not understand the mathematics of three-part diminish-and-augment progression, which advances without returning." Regenerating Huangzhong from Zhonglü yields only eight and seven-tenths odd inches, not the proper Huangzhong tone. Jing Fang recognized this problem and, when regenerating from Zhonglü, named the new standard Zhishi and proceeded to generate forty-eight pitch standards in succession. He failed to see that the six altered pitch standards arise from natural necessity and cannot be increased. Even if more were forcibly added, they would serve no purpose. Fang's doctrine derived from the Jiao clan, whose hexagram-qi theory also reduces the cycle to sixty by removing four; hence his pitch calculations were compelled to conform to that number. He did not understand that these numbers follow natural law: pitch standards cannot be augmented, nor can hexagram cycles be arbitrarily reduced. He Chengtian and Liu Chuo criticized Fang's error yet proposed increasing the fractional divisions of the eleven standards below Linzhong so that regenerating Huangzhong from Zhonglü would restore the number 177,147—leaving only Huangzhong as a true standard while the other eleven failed to conform to three-part diminish-and-augment mathematics. Their error was even graver than Fang's.) [End of editorial commentary.]
35
《律生五聲篇》曰：
The chapter "Pitch Standards Generate the Five Sounds" states:
36
宮聲八十一，商聲七十二，角聲六十四，徵聲五十四，羽聲四十八。 按黃鍾之數九九八十一，是為五聲之原，三分損一以下生徵，徵三分益一以上生商，商三分損一以下生羽，羽三分益一以上生角。 至角聲之數六十四，以三分之，不盡一算，數不可行，此聲之數所以止於五也。 〈（其《證辨》曰：“《通典》曰：‘黃鍾為均，用五聲之法以下十一辰，辰各有五聲，其為宮商之法亦如之。 辰各有五聲，合為六十聲，是十二律之正聲也。 ’夫黃鍾一均之數，而十一律於此取法焉。 以十二律之宮長短不同，而其臣、民、事、物、尊卑，莫不有序而不相亂，良以是耳。 沈括不知此理，乃以為五十四在黃鍾為徵、在夾鍾為角、在仲呂為商者，其亦誤矣。 俗樂之有清聲，略知此意。 但不知仲呂反生黃鍾，黃鍾又自林鍾再生太簇，皆為變律，已非黃鍾、太簇之清聲耳。 胡瑗於四清聲皆小其圍徑，則黃鍾、太簇二聲雖合，而大呂、夾鍾二聲又非本律之半。 且自夷則至應鍾四律，皆以次而小其徑圍以就之，遂使十二律、五聲皆有不得其正者。 李照、範鎮止用十二律，則又未知此理。 蓋樂之和者，在於三分損益； 樂之辨者，在於上下相生。 若李照、範鎮之法，其合於三分損益者則和矣，自夷則已降，其臣、民、事、物，豈能尊卑有辨而不相淩犯乎？ 晉荀勖之笛，梁武帝之通，皆不知而作者也。”）〉
The gong tone is 81, the shang tone 72, the jue tone 64, the zhi tone 54, and the yu tone 48. Huangzhong's number is 9 × 9 = 81, the origin of the five tones. Diminishing by one-third generates the zhi tone downward; augmenting zhi by one-third generates shang upward; diminishing shang by one-third generates yu downward; augmenting yu by one-third generates jue upward. The jue tone's number is 64; divided by three, one count remains undivided and the progression cannot continue. This is why there are only five primary tones. (His "Verification and Distinction" states: "The Tongdian says: 'With Huangzhong as the standard pitch, apply the method of the five tones to the eleven branches below; each branch has five tones, and the methods for gong and shang follow the same principle.'" Each branch has five tones, totaling sixty tones—the proper sounds of the twelve pitch standards. Huangzhong provides the single standard number from which the eleven other pitch standards derive their proportions. Because the tonal centers of the twelve pitch standards differ in length, the hierarchical relationships among minister, commoner, affair, and object—high and low—remain ordered and distinct. This is precisely why. Shen Kuo failed to understand this principle and mistakenly held that the number 54 represents zhi in Huangzhong, jue in Jiazhong, and shang in Zhonglü. Popular music's use of clear tones reflects a partial grasp of this principle. Yet they do not realize that regenerating Huangzhong from Zhonglü or Taicu from Linzhong via Huangzhong produces altered pitch standards, not the clear tones of Huangzhong and Taicu proper. Hu Yuan reduced the circumference of all four clear-tone pipes; although Huangzhong and Taicu then matched, Dalü and Jiazhong no longer represented true half-lengths of their fundamental standards. Furthermore, from Yize through Yingzhong he progressively reduced the circumference of four standards to make them fit, so that none of the twelve pitch standards or five tones remained properly tuned. Li Zhao and Fan Zhen, who used only the twelve pitch standards, were equally ignorant of this principle. Harmony in music depends on three-part diminish-and-augment; while distinction in music depends on upward and downward generation among the standards. Under the methods of Li Zhao and Fan Zhen, tones conforming to three-part diminish-and-augment may be harmonious, but from Yize downward, how could the hierarchical relationships of minister, commoner, affair, and object retain proper distinction without mutual violation? The flutes of Jin's Xun Xu and the pitch pipes of Liang's Emperor Wu were likewise devised in ignorance of this principle.
37
《變聲篇》曰：
The chapter "Altered Sounds" states:
38
變宮聲四十二，變徵聲五十六。 五聲宮與商、商與角、徵與羽相去各一律，至角與徵、羽與宮相去乃二律。 相去一律則音節和，相去二律則音節遠。 故角、徽之間，近徵收一聲，比徵少下，故謂之變徵； 羽、宮之間，近宮收一聲，少高於宮，故謂之變宮。 角聲之實六十有四，以三分之，不盡一算，既不可行，當有以通之。 聲之變者二，故置一而兩，三之得九，以九因角聲之實六十有四，得五百七十六。 三分損益，再生變徵、變宮二聲，以九歸之，以從五聲之數，存其餘數，以為強弱。 至變徵之數五百一十二，以三分之，又不盡二算，其數又不行，此變聲所以止於二也。 變宮、變徵，宮不成宮，徵不成徵，《淮南子》謂之“和謬”，所以濟五聲之不及也。 變聲非正聲，故不為調。 〈（其《證辨》曰：“宮、羽之間有變宮，角、徵之間有變徵，此亦出於自然，《左氏》所謂‘七音’，《漢前志》所謂“七始”是也。 然五聲者，正聲，故以起調、畢曲，為諸聲之綱。 至二變聲，則不比於正音，但可濟其所不及而已。 然有五聲而無二變，亦不可以成樂也。”）〉
The altered gong tone is 42; the altered zhi tone is 56. Among the five tones, gong and shang, shang and jue, and zhi and yu are each one pitch standard apart; but jue and zhi, and yu and gong, are two standards apart. A separation of one standard produces harmonious intervals; a separation of two standards produces distant intervals. Therefore between jue and zhi, a tone is drawn toward zhi but placed slightly below it; this is called the altered zhi; between yu and gong, a tone is drawn toward gong but placed slightly above it; this is called the altered gong. The jue tone's volume is 64; divided by three, one count remains undivided and the progression cannot continue. A method must be found to resolve this. There are two altered tones; therefore one is doubled to make two, and tripling yields nine. Multiplying the jue volume of 64 by 9 gives 576. By three-part diminish-and-augment, the two altered tones—altered zhi and altered gong—are generated; dividing by 9 aligns them with the five-tone system, and the remainders indicate relative strength. The altered zhi tone's number is 512; divided by three, two counts remain undivided and the progression again cannot continue. This is why there are only two altered tones. Altered gong and altered zhi are neither true gong nor true zhi; the Huainanzi calls them "harmonic dissonance," bridging the gaps that the five primary tones cannot fill. Altered tones are not proper tones and therefore cannot serve as modal centers. (His "Verification and Distinction" states: "Between gong and yu stands altered gong; between jue and zhi stands altered zhi. These too arise from natural law—the 'seven sounds' of the Zuo Commentary and the 'seven origins' of the Former Han Annals refer to this." The five primary tones are proper tones; they open and close musical modes and serve as the governing framework for all sounds. The two altered tones are not ranked with proper tones; they merely supplement what the primary tones cannot achieve. Yet music cannot be complete with only the five primary tones and without the two altered tones.
39
《八十四聲篇》曰：
The chapter "Eighty-Four Sounds" states:
40
黃鍾不為他律役，所用七聲皆正律，無空、積、忽、微。 自林鍾而下，則有半聲：大呂、太簇一半聲，夾鍾、姑洗二半聲，蕤賓、林鍾四半聲，夷則、南呂五半聲，無射、應鍾為六半聲。 中呂為十二律之窮，三半聲也。 自蕤賓而下則有變律：蕤賓一變律，大呂二變律，夷則三變律，夾鍾四變律，無射五變律，中呂六變律也。 皆有空、積、忽、微，不得其正，故黃鍾獨為聲氣之元。 雖十二律八十四聲皆黃鍾所生，然黃鍾一均，所謂純粹中之純粹者也。 八十四聲：正律六十三，變律二十一。 六十三者，九七之數也； 二十一者，三七之數也。
Huangzhong is not subordinate to other standards; all seven tones it employs are proper standards, free of void, accumulated, neglected, or minute discrepancies. From Linzhong downward, half-tones appear: Dalü and Taicu require one half-tone; Jiazhong and Guxian require two; Ruibin and Linzhong require four; Yize and Nanlü require five; Wushe and Yingzhong require six. Zhonglü marks the limit of the twelve pitch standards, requiring three half-tones. From Ruibin downward come altered pitch standards: Ruibin requires one; Dalü requires two; Yize requires three; Jiazhong requires four; Wushe requires five; Zhonglü requires six. All suffer void, accumulated, neglected, and minute errors and fail to achieve proper pitch; therefore Huangzhong alone remains the origin of sound and qi. Although all eighty-four sounds of the twelve pitch standards derive from Huangzhong, Huangzhong's single standard pitch is the purest among the pure. Of the eighty-four sounds, sixty-three belong to proper standards and twenty-one to altered standards. Sixty-three is the product of 9 and 7; twenty-one is the product of 3 and 7.
41
《六十調篇》曰：
The chapter "Sixty Modes" states:
42
十二律旋相為宮，各有七聲，合八十四聲。 宮聲十二，商聲十二，角聲十二，徵聲十二，羽聲十二，凡六十聲，為六十調，其變宮十二，在羽聲之後、宮聲之前； 變徵十二，在角聲之後、徵聲之前：宮徵皆不成，凡二十四聲，不可為調。 黃鍾宮至夾鍾羽，並用黃鍾起調、黃鍾畢曲； 大呂宮至姑洗羽，並用大呂起調、大呂畢曲； 太簇宮至仲呂，並用太簇起調、太簇畢曲； 夾鍾宮至蕤賓羽，並用夾鍾起調、夾鍾畢曲； 姑洗宮至林鍾羽，並用姑洗起調、姑洗畢曲； 仲呂宮至夷則羽，並用仲呂起調、仲呂畢曲； 蕤賓宮至南呂羽，並用蕤賓起調、蕤賓畢曲； 林鍾宮至無射羽，並用林鍾起調、林鍾畢曲； 夷則宮至應鍾羽，並用夷則起調、夷則畢曲； 南呂宮至黃鍾羽，並用南呂起調、南呂畢曲； 無射宮至大呂羽，並用無射起調、無射畢曲； 應鍾宮至太簇羽，並用應鍾起調、應鍾畢曲，是為六十調。 六十調即十二律也，十二律即一黃鍾也。 黃鍾生十二律，十二律生五聲二變。 五聲各有紀綱，以成六十調，六十調皆黃鍾損益之變也。 宮、商、角三十六調，老陽也； 其徵、羽二十四調，老陰也。 調成而陰陽備也。
The twelve pitch standards rotate as tonal centers; each produces seven tones, totaling eighty-four sounds. There are twelve gong tones, twelve shang, twelve jue, twelve zhi, and twelve yu—sixty tones in all, constituting the sixty modes. The twelve altered gong tones fall after the yu tones and before the gong tones; There are twelve altered-zhi tones, set after the jiao tone and before the zhi tone: neither gong nor zhi can be fully established; all twenty-four such tones cannot serve as modes. From Yellow Bell gong through Compressed Bell yu, every mode takes Yellow Bell to open the tune and Yellow Bell to close it; From Great Clay gong through Maiden Wash yu, each relies on Great Clay both to begin the mode and to finish the melody; From Great Cluster gong through Mid Bell, the mode is raised with Great Cluster and concluded with Great Cluster; Compressed Bell gong through Luxuriant Guest yu likewise open and close upon Compressed Bell alone; For Maiden Wash gong down to Forest Bell yu, Maiden Wash alone sets the opening key and seals the cadence; Mid Bell gong through Level Rule yu are governed throughout by Mid Bell for both the opening and the final stroke; Luxuriant Guest gong to Southern Bell yu share one rule: Luxuriant Guest raises the mode and Luxuriant Guest ends the piece; Between Forest Bell gong and Untempered yu, Forest Bell alone marks where the tune begins and where it ends; Level Rule gong through Responding Bell yu keep Level Rule as the tone that lifts the mode and the tone that closes the song; Southern Bell gong down to Yellow Bell yu still begin and end on Southern Bell for mode and cadence; Untempered gong through Great Clay yu are bound to Untempered at the opening of the mode and at the piece's close; Responding Bell gong through Great Cluster yu likewise take Responding Bell to raise the mode and Responding Bell to finish the piece—thus are constituted the sixty modes. The sixty modes are none other than the twelve pitches, and the twelve pitches are ultimately one Yellow Bell. Yellow Bell gives rise to the twelve pitches; the twelve pitches give rise to the five tones and the two alterations. Each of the five tones has its own governing principle, and through them the sixty modes are completed; every mode is but a transformation wrought by diminishing and increasing Yellow Bell. The thirty-six modes of gong, shang, and jiao belong to old yang; the twenty-four modes of zhi and yu belong to old yin. When the modes are complete, yin and yang are fully in place.
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或曰：“日辰之數由天五、地六錯綜而生，律呂之數由黃鍾九寸損益而生，二者不同。 至數之成，則日有六甲、辰有五子為六十日； 律呂有六律、五聲為六十調，若合符節，何也？ ”曰：“即所謂調成而陰陽備也。 ”夫理必有對待，數之自然也。 以天五、地六合陰與陽言之，則六甲、五子究於六十，其三十六為陽，二十四為陰。 以黃鍾九寸紀陽不紀陰言之，則六律、五聲究於六十，亦三十六為陽，二十四為陰。 蓋一陽之中，又自有陰陽也。 非知天地之化育者，不能與於此。 〈（其《證辨》曰：“《禮運》：‘五聲、六律、十二管還相為宮。 ’孔氏疏曰：‘黃鍾為第一宮，至中呂為第十二宮，各有五聲，凡六十聲。 ’聲者，所以起調、畢曲，為諸聲之綱領，正《禮運》所謂‘還相為宮’也。 《周禮·大司樂》，祭祀不用商，惟宮、角、徵、羽四聲。 古人變宮、變徵不為調，《左氏傳》曰：‘中聲以降，五降之後，不容彈矣。 ’以二變聲之不可為調也。 後世以變宮、變徵參而為八十四調，其亦不考矣。”）〉
Someone asked: "The numbers of days and branches arise from the interweaving of Heaven's five and Earth's six, while the numbers of pitches and lü arise from diminishing and increasing the nine inches of Yellow Bell—these two origins are not the same. Yet when the reckoning is complete, the six jia of the days and the five zi of the branches together make sixty days; and among pitches and lü the six pitches and five tones likewise yield sixty modes. If they accord so neatly, how is that?" The answer came: "It is precisely what is meant by 'when the modes are complete, yin and yang are fully in place.'" " In principle there must always be counterparts; such is the nature of number. Speaking in terms of Heaven's five and Earth's six joining yin and yang, the six jia and five zi together amount to sixty, of which thirty-six are yang and twenty-four are yin. Speaking in terms of the nine inches of Yellow Bell, which record yang but not yin, the six pitches and five tones likewise total sixty, again with thirty-six yang and twenty-four yin. For within a single yang there is yin and yang of its own once more. Only those who understand how Heaven and Earth transform and nurture all things can share in such understanding. (In his Evidential Discrimination he writes: "The Record of Rites, 'Evolution of Rites,' states: 'The five tones, the six pitches, and the twelve tubes each in turn serve as gong.'" ' Kong Yingda's commentary explains: 'Yellow Bell is the first gong, and Mid Bell the twelfth; each has five tones, making sixty tones in all.'" ' The tone is what raises the mode and closes the piece; it is the head-thread of all tones—exactly what the Evolution of Rites means by 'each in turn serving as gong.'" The Rites of Zhou, "Grand Director of Music," records that in sacrifice shang is not used; only the four tones gong, jiao, zhi, and yu are employed. The ancients did not treat altered gong and altered zhi as modes. The Zuo Tradition says: 'Below the central tone, after five descents there is no room left to play.'" '—because the two alteration tones cannot constitute modes. Later generations mixed altered gong and altered zhi into eighty-four modes; they too failed to investigate the matter properly."
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《候氣篇》曰：
The chapter "Awaiting the Qi" states:
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以十二律分配節氣，按曆而俟之。 其氣之升，分、毫、絲、忽，隨節各異。 夫陽生於《復》，陰生於《後》，如環無端。 今律呂之數，三分損益，終不復始，何也？ 曰：“陽之升始於子，午雖陰生，而陽之升於上者未已，至亥而後窮上反下； 陰之升始於午，子雖陽生，而陰升於上亦未已，至巳而後窮上反下。 律於陰則不書，故終不復始也。 是以升，陽之數，自子至巳差強，在律為尤強，在呂為差弱； 自午至亥漸弱，在律為尤弱，在呂為差強。 分數多寡，雖若不齊，然而絲分毫別，各有條理，此氣之所以飛灰，聲之所以中律也。”
The twelve pitches are assigned to the solar terms, and one waits for them according to the calendar. The rising of the qi differs by fen, hao, si, and hu with each solar term. Yang is born in the hexagram Return; yin is born in the hexagram After; like a ring, they have no beginning or end. Yet the numbers of pitches and lü follow the method of diminishing and increasing by one-third, and in the end never return to the beginning—why is that? The answer runs: "Yang's ascent begins at zi. At wuyin may be born, yet yang still continues rising above; only at hai does it exhaust the upper reach and turn back downward; yin's ascent begins at wu. At zi yang may be born, yet yin likewise continues rising above; only at si does it exhaust the upper reach and turn back downward. The pitches do not record yin, and therefore in the end they never return to the beginning." Thus in the rising phase, yang's numbers from zi to si are comparatively strong—strongest in the pitches (lü), somewhat weaker in the secondary tubes (lü in the yin sense); from wu to hai they gradually weaken—weakest in the pitches, somewhat stronger in the secondary tubes. The fractional measures may seem uneven in quantity, yet divided to the finest si and hao each has its own pattern; this is why the qi makes the ash fly and why sound strikes the pitch true.
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或曰：“《易》以道陰陽，而律不書陰，何也？ ”曰：“《易》盡天下之變，善惡無不備，律致中和之用，止於至善者也，以聲言之，大而至於雷霆，細而至於蠛蠓，無非聲也。 《易》則無不備也，律則寫其所謂黃鍾一聲而已。 雖有十二律六十調，然實一黃鍾也。 是理也，在聲為中聲，在氣為中氣，在人則喜怒哀樂未發與發而中節，此聖人所以一天人、讚化育之道也。” 〈（其《證辨》曰：“律者，陽氣之動，陽聲之始，必聲和氣應，然後可以見天地之心。 今不此之務，乃區區於黍之縱橫、古錢之大小，其亦難矣。 然非精於曆數，則氣節亦未易正。”）〉
Someone asked: "The Changes expounds yin and yang, yet the pitches do not record yin—why is that?" The reply came: "The Changes embraces every transformation under Heaven; good and evil alike are all included. The pitches aim at the function of central harmony and rest at utmost goodness. Considered as sound, they range from the thunderclap above to the gnat below—nothing is not sound." The Changes leaves nothing out; the pitches inscribe only what is called the single tone of Yellow Bell. Though there are twelve pitches and sixty modes, in substance there is but one Yellow Bell. Such is the principle: in sound it is the central tone; in qi the central qi; in the person, the joy, anger, sorrow, and delight neither yet expressed nor expressed but hitting the measure. This is how the sage unifies Heaven and humanity and assists the Way of transformation and nurture. (In his Evidential Discrimination he writes: "The pitches are the movement of yang qi and the beginning of yang sound; sound and qi must answer each other—only then can one discern the heart of Heaven and Earth." Yet if one does not pursue this but fusses instead over the length and breadth of millet grains or the size of ancient coins, how difficult the task becomes!" Yet unless one is skilled in calendrical reckoning, the qi and solar terms are not easily set right either."
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至於審度量、謹權衡，會粹古今，辨析尤詳，皆所以參伍而定黃鍾為中聲之符驗也。 朱熹深好其書，謂國家行且平定，中原必將審音協律，以諧神人。 受詔典領之臣，宜得此書奏之，以備東都郊廟之樂。
As for examining measures and weights with care, gathering ancient and modern learning, and discriminating with exceptional detail—all serve to cross-check and establish Yellow Bell as the proof-token of the central tone. Zhu Xi greatly admired his book, declaring that as the state was about to be pacified, the Central Plain would surely examine tones and harmonize pitches to bring spirits and humanity into accord. The ministers charged by imperial mandate to oversee such matters ought to obtain this book and present it to the throne, that it might supply music for the suburban sacrifices and ancestral temples of the Eastern Capital.
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熹定《鍾律》、《詩樂》、《樂製》、《樂舞》等篇，彙分於所修禮書中，皆聚古樂之根源，簡約可觀。 而《鍾律》分前後篇，其前篇為條凡七：一曰十二律陰陽、辰位相生次第之圖，二曰十二律寸、分、厘、毫、絲、忽之數，三曰五聲五行之象、清濁高下之次，四曰五聲相生、損益、先後之次，五曰變宮、變徽二變相生之法，六曰十二律正變、倍半之法，七曰旋宮八十四聲、六十調之圖。 其後篇為條凡六：一曰明五聲之義，二曰明十二律之義，三曰律寸舊法，四曰律寸新法，五曰黃鍾分寸數法，六曰黃鍾生十一律數。 大率采元定所著，更互演繹，尤為明邃。 其《樂製》彙於王朝禮，其《樂舞》彙於祭禮，上下千載，旁搜遠紹，昭示前聖禮樂之非迂，而將期古樂之復見於今，熹蓋深致意焉。 其《詩樂篇》別係於後。
Xi compiled the chapters "Bell Pitches," "Ode Music," "Music Institutions," and "Music Dance," among others, and distributed them through the ritual book he was editing; all gather the roots of ancient music in a concise form well worth reading. "Bell Pitches" is divided into two parts. The first part comprises seven sections: (1) a chart of the yin and yang of the twelve pitches, their branch positions, and the order of mutual generation; (2) the numbers of the twelve pitches in inches, fen, li, hao, si, and hu; (3) the images of the five tones within the five phases and the order of clear, murky, high, and low; (4) the order of mutual generation, diminishment and increase, and precedence among the five tones; (5) the method by which altered gong and altered zhi—the two alterations—generate one another; (6) the methods of standard and altered pitches and of doubling and halving; (7) a chart of the eighty-four tones of rotating gong and the sixty modes. The second part comprises six sections: (1) explaining the meaning of the five tones; (2) explaining the meaning of the twelve pitches; (3) the old method of pitch inches; (4) the new method of pitch inches; (5) the method of counting Yellow Bell in fen and cun; (6) the numbers by which Yellow Bell generates the eleven other pitches. For the most part it draws on what Cai Yuanding wrote and develops it further through mutual elaboration, achieving a clarity and depth that is especially penetrating. "Music Institutions" is gathered under the rites of the royal court, and "Music Dance" under the rites of sacrifice. Spanning a thousand years, searching widely and transmitting from afar, it shows that the ritual music of the former sages was not impractical, and looks forward to ancient music appearing again in the present—toward which Xi surely directed his deepest intent. The chapter "Ode Music" is appended separately at the end.