¹ I. M. Pina, ‘From Lisbon to Beijing’, in Tomás Pereira, S.J. 1646–1708: Life, Work and World, ed. L. F. Barreto (Lisbon, 2010), pp. 185–201, at pp. 185–99.

² N. Golvers, The Astronomia Europaea of Ferdinand Verbiest, S.J. (Dillingen, 1687): Text, Translation, Notes, and Commentaries, Monumenta Serica Monograph Series, 28 (Nettetal, 1993), pp. 125–6.

³ All translations in this essay are mine unless otherwise specified. Thomas Pereira, ‘Relação da jornada que o Padre Tomás Pereira fez â Tartária [Manchúria], no ano de 1685, com o Imperador Kangxi, Peguim, 1685’, in Tomás Pereira: Obras, vol. 2 (Lisbon, 2011), pp. 19–40, at p. 20.

⁴ L. Hostetler, ‘Contending Cartographic Claims?: The Qing Empire in Manchu, Chinese, and European Maps’, in J. R. Akerman (ed.), The Imperial Map: Cartography and the Mastery of Empire (Chicago, 2009), pp. 93–132, at pp. 100–15.

⁵ D. De Lucca, Jesuits and Fortifications: The Contribution of the Jesuits to Military Architecture in the Baroque Age (Leiden, 2012), pp. 174–83.

⁶ B. A. Elman, On their Own Terms: Science in China, 1550–1900 (Cambridge, MA, 2005), pp. 63–105.

⁷ Kangxi, Shengzu renhuangdi yuzhiwen di si ji 聖祖仁皇帝御製文第四集 [Writings of the Kangxi Emperor, vol. 4], Jingyin wenyuange Siku quanshu 1299 (Taipei, 1984), pp. 566–603. The essay on resonance is on pp. 582–3.

⁸ C. Jami, The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662–1722) (New York and Oxford, 2011), pp. 139–40.

⁹ N. Sivin, ‘Copernicus in China’, in Science in Ancient China: Researches and Reflections (Aldershot, 1995), p. 3.

¹⁰ Under the support of the general-governor of Zhejiang province, opponents of Christianity attacked the Church of the Saviour in Hangzhou and abused its members. Woodblocks used for printing Christian books were destroyed. The Jesuit Prospero Intorcetta (1626–96) was exiled. D. E. Mungello, The Forgotten Christians of Hangzhou (Honolulu, 1994), pp. 61–5.

¹¹ Italics mine. ‘Depois disto se compuzerão dentro em Palacio pellos nossos Padres por espaço de mais de vinte annos muitos liuros de algumas sciencias Europeas como Astronomia, Aritmetica, Geometria, Philosophia, e outros semelhantes, entre os quaes foi hum de Muzica composto pello Padre Thomas Pereyra, reduzindo a praxi, o que ensinaua na espiculação com não pequena admiração de todos.’ Tomás Pereira and Antoine Thomas, ‘Memorial Apresentado por Tomás Pereira e Antoine Thomas ao Imperador Kangxi, Pequim, 2/2/1692’, Rellação em que se contem o felis sucesso, e inestimavel beneficio da liberdade da rellegião christã; microfilm, Biblioteca Nacional de Portugal, num 23.

In response to the Jesuits’ petition, Kangxi issued an edict of toleration, which addressed the Europeans’ contributions and promulgated to the provincial governments that since the Europeans had not violated the law, they should be allowed to practise their religion just as the Buddhists were allowed to offer incense in their temples. For the Chinese versions of Thomas and Pereira’s memorial and Kangxi’s edict and different interpretations of the edict, see N. Standaert, ‘The “Edict of Tolerance” (1692): A Textual History and Reading’, in A. K. Wardega and A. Vasconcelos de Saldanha (eds.), In the Light and Shadow of an Emperor: Tomás Pereira, SJ (1645–1708), the Kangxi Emperor and the Jesuit Mission in China (Newcastle, 2012), pp. 307–58.

¹² Zhongguo guji shanben shumu: jing bu 中國古籍善本書目：經部 [Catalogue of Chinese Rare Books: Classics], juan 2 (Shanghai, 1985), fol. 53^r. While manuscript copies of A Compilation are held in the National Library of China, A Summary is kept in the National Palace Museum in Beijing and had not been accessible to the public until its facsimile was published together with that of A Compilation in the National Palace Museum Rare Book Collection (gugong zhenben congkan 故宮珍本叢刊) by the Hainan Publishing Company (Hainan chubanshe 海南出版社) in 2000. Lülü jieyao 律呂節要 [A Summary of the Essentials of Music] Gugong zhenben congkan 故宮珍本叢刊 23 (Haikou, 2000), pp. 37–80; Lülü zuanyao 律呂纂要 [A Compilation of the Essentials of Music] Gugong zhenben congkan 故宮珍本叢刊 24 (Haikou, 2000), pp. 339–79. For research on different editions of A Compilation of the Essentials of Music, see W. Bing, ‘Lülü zuanyao zhi yanjiu《律呂纂要》之研究 [A Study of A Compilation of the Essentials of Music]’, Palace Museum Journal 故宮博物院院刊, no. 4 (2002), pp. 68–81.

¹³ Wai-Yee Chiu and Wang Bing 王冰 hesitate to attribute A Summary to Pereira because they find its content too different from that of A Compilation. Yoko Arai 新居洋子 and Weng Panfeng 翁攀峰 take it for granted that Pereira is the author of the treatise without providing any proof. Y. Arai, ‘Shinchou kyuutei ni okeru seiyou ongaku riron no juyou 清朝宮廷における西洋音楽理論の受容 [The Import of Western Muisc Theory into the Qing Court]’, in H. Kawahara (ed.), Chuugoku no ongaku bunka: sanzen nen no rekishi to riron 中国の音楽文化 ：三千年の歴史と理論 [Musical Cultures of China: Three Thousand Years of History and Theory] (Tokyo, 2016), pp. 124–44; W. Y. L. Chiu, ‘The Function of Western Music in the Eighteenth-Century Chinese Court’ (Ph.D. thesis, The Chinese University of Hong Kong, 2007), pp. 37–8; B. Wang and M. Serrano Pinto, ‘Thomas Pereira and the Knowledge of Western Music in the 17th and 18th Centuries in China’, in L. Saraiva (ed.), Europe and China: Science and Arts in the 17th and 18th Centuries (Singapore, 2012), pp. 135–51, at pp. 145–6; P. Weng, ‘Xiyue yu chuantong lüxue jiehe zhi zuo—Kangxi shusi lü sixiang laiyuan xinjie 西樂與傳統律學結合之作——康熙十四律思想來源新解 [A Product of Synthesising Western Music and Traditional Harmonics—A New Theory about the Intellectual Origin of Kangxi’s Fourteen-Tone Temperament]’, Music Research 音樂研究, no. 5 (2014), pp. 30–43.

¹⁴ Ethnomusicologists have found polyphonic songs in musical cultures of some minority nationalities, such as the Miao and Dong ethnic groups. These would be exceptions to my general statement if such musical styles were already developed in early Qing. S. Yin-kuan, ‘The Polyphonic Songs of the Miao People in China – A Structural Analysis’, Chinese Music, 12, no. 1 (1989), pp. 5–13; S. Yin-kuan, ‘The Polyphonic Songs of the Miao People in China – A Structural Analysis II’, Chinese Music, 12, no. 2 (1989), pp. 27–31.

¹⁵ B. Wang, ‘Lülü zuanyao neirong laiyuan chutan《律呂纂要》內容來源初探 [A Preliminary Study on the Sources of A Compilation of the Essentials of Music]’, Studies in the History of Natural Sciences 自然科學史研究, 33, no. 4 (2014), pp. 411–26; G. Gild, ‘Mission by Music: The Challenge of Translating European Music into Chinese in the Lülü Zuanyao’, in In the Light and Shadow of an Emperor: Tomás Pereira, SJ (1645–1708), the Kangxi Emperor and the Jesuit Mission in China (Newcastle, 2012), pp. 532–45; J. Lindorff, ‘Tomás Pereira and 17th-Century Western Music Theory’, in L. F. Barreto (ed.), Europe–China: Intercultural Encounters, 16th–18th Centuries (Lisbon, 2012), pp. 241–8; H. Fang, Zhong Xi jiaotong shi 中西交通史 [History of Sino-Foreign Communications] (Shanghai, 2008), pp. 627–9; Y. Tao, Ming Qing jian de Zhong Xi yinyue jiaoliu 明清間的中西音樂交流 [Musical Exchange between China and the West during the Ming and Qing Dynasties] (Beijing, 2001), pp. 47–59; G. Gild, Das Lü Lü Zheng Yi Xubian: Ein Jesuitentraktat über die europäische Notation in China 1713 (Göttingen, 1991).

¹⁶ S. L. Montgomery, Science in Translation: Movements of Knowledge through Cultures and Time (Chicago, 2000), p. 4.

¹⁷ M. Lackner, I. Amelung and J. Kurtz (eds.), New Terms for New Ideas: Western Knowledge and Lexical Change in Late Imperial China (Leiden, 2001); D. Wright, Translating Science: The Transmission of Western Chemistry into Late Imperial China, 1840–1900 (Leiden, 2000), pp. 183–226; D. Wright, ‘The Translation of Modern Western Science in Nineteenth-Century China, 1840–1895’, Isis, 89 (1998), pp. 667–71.

¹⁸ K.-w. Chow, The Rise of Confucian Ritualism in Late Imperial China: Ethics, Classics, and Lineage Discourse (Stanford, 1994), p. 165.

¹⁹ O.-c. Ng, Cheng-Zhu Confucianism in the Early Qing: Li Guangdi (1642–1718) and Qing Learning (New York, 2001), p. 185; G. Li, Guyue jingzhuan 古樂經傳 [Annotations to Ancient Writings on Music], Jingyin wenyuange Siku quanshu 景印文淵閣四庫全書, vol. 220 (Taipei, 1983).

²⁰ M. Callon and J. Law, ‘On Interests and their Transformation: Enrolment and Counter-Enrolment’, Social Studies of Science, 12 (1982), pp. 615–25; B. Latour, Science in Action: How to Follow Scientists and Engineers through Society (Cambridge, MA, 1987), pp. 103–76; S. L. Star and J. R. Griesemer, ‘Institutional Ecology, “Translations” and Boundary Objects: Amateurs and Professionals in Berkeley’s Museum of Vertebrate Zoology, 1907–39’, Social Studies of Science, 19 (1989), pp. 387–420. Thomas Irvine has used the concept of boundary object to study the role of the harpsichord in China. T. Irvine, ‘Western Technoscience and Western Musicking in the Sinosphere (and Beyond)’ (paper presented at the the American Musicological Society Annual Meeting, San Antonio, TX, Nov. 2018).

²¹ Star and Griesemer, ‘Institutional Ecology, “Translations” and Boundary Objects’, pp. 396–9, 401.

²² Ibid., p. 393.

²³ S. L. Star, ‘This is Not a Boundary Object: Reflections on the Origin of a Concept’, Science, Technology, & Human Values, 35 (2010), pp. 601–13, at pp. 602–3.

²⁴ A. Rehding, ‘Music-Historical Egyptomania, 1650–1950’, Journal of the History of Ideas, 75 (2014), pp. 545–80, at pp. 550–66; J. Levy, ‘Joseph Amiot and Enlightenment Speculation on the Origin of Pythagorean Tuning in China’, Theoria, 4 (1989), pp. 63–81.

²⁵ E.g. S. Pederson, ‘A. B. Marx, Berlin Concert Life, and German National Identity’, 19th-Century Music, 18 (1994), pp. 87–107.

²⁶ For the music instruments built by Pereira in China and their cultural meanings, see D. F. Urrows, ‘The Pipe Organ of the Baroque Era in China’, in China and the West: Music, Representation, and Reception (Ann Arbor, 2017), pp. 21–48, at pp. 29–35; Wang and Serrano Pinto, ‘Thomas Pereira and the Knowledge of Western Music’, pp. 135–9.

²⁷ D. R. M. Irving, ‘The Dissemination and Use of European Music Books in Early Modern Asia’, Early Music History, 28 (2009), pp. 39–59, at pp. 39, 54, 57.

²⁸ On Western music as hegemony, see N. Cook, ‘Western Music as World Music’, in P. V. Bohlman (ed.), The Cambridge History of World Music (Cambridge, 2013), p. 75–100.

²⁹ Besides using the Jesuits’ European knowledge to produce calendars, maps and cannons, Kangxi also utilised the Jesuits’ language skills to deal with diplomatic matters. Pereira was sent to Nerchinsk in 1689 as a translator for the Sino-Russian meeting that led to the Treaty of Nerchinsk signed on 27 August 1689, whose official version was in Latin with translations into Russian and Manchu. See J. Sebes, The Jesuits and the Sino-Russian Treaty of Nerchinsk (1689); The Diary of Thomas Pereira (Rome, 1961).

³⁰ C. Jami, ‘Tome Pereira (1645–1708), Clockmaker, Musician and Interpreter at the Kangxi Court: Portuguese Interests and the Transmission of Science’, in L. Saraiva and C. Jami (eds.), The Jesuits, the Padroado and East Asian Science (1552–1773) (Singapore, 2008), pp. 187–204.

³¹ For instance, Xiao Youmei 蕭友梅 (1884–1940), the founder of the Shanghai National Conservatory of Music (nowadays Shanghai Conservatory of Music), proposed that traditional Chinese music instruments should be completely replaced with Western music instruments so as to keep up with the pace of progress because traditional Chinese instruments were inferior to Western instruments in pitch range and pitch accuracy. Y. Xiao, Xiao Youmei Yinyue wenji 蕭友梅音樂文集 [Xiao Youmei’s Essays on Music] (Shanghai, 1990), pp. 539–42. On conflicting views among different classes on the role of Western music in reforming Chinese music in twentieth-century China, see R. C. Kraus, Pianos and Politics in China: Middle-Class Ambitions and the Struggle over Western Music (New York and Oxford, 1989), pp. 100–27.

³² H. F. Cohen, Quantifying Music: The Science of Music at the First Stage of Scientific Revolution 1580–1650 (Dordrecht, 1984); S. Dostrovsky, ‘Early Vibration Theory: Physics and Music in the Seventeenth Century’, Archive for History of Exact Sciences, 14, no. 3 (1975), pp. 169–218. The relationship between frequency and pitch was discussed in Europe as early as the sixth century by Boethius (c. 480–524), but vibrational frequency was not quantified, be it absolutely or relatively, until the sixteenth century. C. Burnett and H. F. Cohen, ‘Boethius on Vibrational Frequency and Pitch’, Annals of Science 52, no. 3 (1995), pp. 303–5.

³³ Sivin, ‘Copernicus in China’, pp. 1, 2–53.

³⁴ N. Sivin, ‘Why the Scientific Revolution Did Not Take Place in China—Or Didn’t It’, Chinese Science, 5 (1982), pp. 45–66, at p. 53.

³⁵ B. Francesca, Technology, Gender and History in Imperial China: Great Transformations Reconsidered (New York, 2013), pp. 182–3.

³⁶ According to Needham, ‘bureaucratic feudalism’ is a social system ‘operated by a non-hereditary elite upon the basis of a large number of relatively self-governing peasant communities, still retaining much tribal character and with little or no labour division as between agriculture and industry’. Needham argues that the bureaucratic elite prevented the merchant class from rising to power. The lack of mercantile mentality in the society in turn impeded the incorporation of mathematical and logical reasoning in artisanal techniques, observation of nature and experiment, which is the basis of modern science. J. Needham etal., Science and Civilisation in China, vii, Part 2, General Conclusions and Reflections (Cambridge, 2004), pp. 1, 5, 9, 17.

³⁷ M. Elvin, ‘Vale Atque Ave’, ibid., pp. xxiv–xliii, at p. xxv. See also J. Goody, The Theft of History (Cambridge, 2006), pp. 137–65.

³⁸ J. Law, ‘Technology and Heterogeneous Engineering: The Case of Portuguese Expansion’, in W. E. Bijker, T. P. Hughes and T. Pinch (eds.), The Social Construction of Technological Systems (Cambridge, MA, 2012), pp. 105–28; B. Latour, Reassembling the Social: An Introduction to Actor-Network-Theory (New York and Oxford, 2005).

³⁹ Latour, Reassembling the Social, pp. 5, 71. See also E. Sayes, ‘Actor-Network Theory and Methodology: Just What Does It Mean to Say that Nonhumans Have Agency?’, Social Studies of Science, 44, no. 1 (2014), pp. 134–49.

⁴⁰ B. Piekut, ‘Actor-Networks in Music History: Clarifications and Critiques’, Twentieth-Century Music, 11 (2014), pp. 191–215, at p. 193.

⁴¹ P. Gouk, ‘The Role of Harmonics in the Scientific Revolution’, in T. Christensen (ed.), The Cambridge History of Western Music Theory (Cambridge, 2002), pp. 223–45, at pp. 228–9; T. Christensen, Rameau and Musical Thought in the Enlightenment (Cambridge, 1993), pp. 29–31; Dostrovsky, ‘Early Vibration Theory: Physics and Music in the Seventeenth Century’. See also T. Christensen, ‘The Sound World of Father Mersenne’, in S. McClary (ed.), Structures of Feeling in Seventeenth-Century Cultural Expression (Toronto, 2013), pp. 60–89.

⁴² Yunzhi etal., Kangxi neifu ben Lülü zhengyi 康熙內府本律呂正義 [Kangxi Imperial Household’s Edition of The True Doctrine of Music], 2 vols. (Beijing, 2016), ii, pp. 626–7.

⁴³ Lülü jieyao, pp. 37, 62. Tao Yabing 陶亞兵 associates ‘the cause of consonance and dissonance’ in the first theme with a chapter in A Compilation entitled ‘Consonances and Dissonances of Musical Tones’ (yueyin he yu buhe 樂音合與不合), concluding that A Compilation is the treatise to which the passage is referring. Yet this chapter in A Compilation deals with the ways of using different consonant and dissonant intervals in contrapuntal composition rather than the physical cause of the perceptual qualities of consonance and dissonance, which is only discussed in A Summary. Y. Tao, ‘Lülü zuanyao ji qi yu Lülü zhengyi xubian de guanxi《律呂纂要》及其與《律呂正義．續編》的關係 [A Compilation of the Essentials of Music and Its Relation to the supplementary volume of The True Doctrine of Music]’, Journal of the Central Conservatory of Music 中央音樂學院學報, no. 4 (1991), p. 49.

⁴⁴ Lülü jieyao, p. 42.

⁴⁵ Cohen, Quantifying Music; Dostrovsky, ‘Early Vibration Theory: Physics and Music in the Seventeenth Century’; C. V. Palisca, ‘Scientific Empiricism in Musical Thought’, in C. V. Palisca etal. (eds.), Seventeenth-Century Science and the Arts (Princeton, 1961), pp. 91–137, at pp. 104–13.

⁴⁶ Gild, Das Lü Lü Zheng Yi Xubian, pp. 114–18.

⁴⁷ ‘Quod si itaque motus tardi & veloces simul fuerint proportionati, & facile inter se misceantur, orietur consonantia; Si verò fuerint improportionati & nullam mixturam, seu coitionem admittant, nascetur dissonantia.’ A. Kircher, Musurgia universalis, sive ars magna consoni et dissoni, vol. 2 (Rome, 1650), p. 209.

⁴⁸ R. J. Raphael, Reading Galileo: Scribal Technologies and the Two New Sciences (Baltimore, MD, 2017), pp. 82–92.

⁴⁹ Ibid., pp. 164–88.

⁵⁰ For Pereira’s education, see I. M. Pina, ‘Some Data on Tomás Pereira’s (Xu Risheng 徐日昇) Biography and Manuscripts’, in Saraiva (ed.), Europe and China, pp. 98, 103; J. P. Janeiro, ‘The Organist and Organ Builder Tomás Pereira: Some New Data on his Activity’, in Wardega and Saldanha (eds.), In the Light and Shadow of an Emperor, pp. 546–67, at pp. 547–9; L. M. Brockey, Journey to the East: The Jesuit Mission to China, 1579–1724 (Cambridge, MA, 2007), pp. 211–15.

⁵¹ G. Galilei, Dialogues Concerning Two New Sciences, trans. H. Crew and A. de Salvio (New York, 1933), pp. 104–5.

⁵² Lülü jieyao, pp. 47–55.

⁵³ T. Hobbes, Elements of Philosophy: The First Section, Concerning Body (London, 1656), pp. 371–2; Kircher, Musurgia universalis, ii, pp. 206–9. For Galileo’s influence on Hobbes, see D. Garber, ‘Natural Philosophy in Seventeenth-Century Context’, in A. P. Martinich and K. Hoekstra (eds.), The Oxford Handbook of Hobbes (New York and Oxford, 2016), pp. 106–30, at pp. 107–14.

⁵⁴ Lülü jieyao, p. 42.

⁵⁵ Galilei, Dialogues Concerning Two New Sciences, pp. 100–1.

⁵⁶ Ibid., p. 107.

⁵⁷ M. Mersenne, Harmonie universelle, Livre premier des consonances, prop. 32, coroll. 2, 82, translated in Cohen, Quantifying Music, p. 105.

⁵⁸ ‘quand de deux lignes proposées l’une surpasse l’autre d’un quart, que quand elle la surpasse de deux tiers. Et puis la Tierce majeure est produite par la troisiesme bisection, ce qui n’arriue pas à la Sexte majeure; de là vient que la Trompette fait cette Tierce immediatement apres la Quarte; ce qui monstre qu’elle est la plus excellente de toutes les simples Consonances apres la Quarte.’ Mersenne, Harmonie universelle, Livre premier des consonances, prop. 32, 79.

⁵⁹ 三音之四分與首音之五分相近，第六音之三分與首音之五分相遠。Lülü jieyao, p. 53.

⁶⁰ Ibid., p. 54.

⁶¹ Hobbes, Elements of Philosophy: The First Section, Concerning Body, p. 366.

⁶² Lülü jieyao, pp. 64–7.

⁶³ Tao, ‘Lülü zuanyao ji qi yu Lülü zhengyi xubian de guanxi’, pp. 48–53.

⁶⁴ Lülü jieyao, pp. 41, 5.

⁶⁵ Lülü zuanyao, pp. 347–8.

⁶⁶ Irving, ‘The Dissemination and Use of European Music Books in Early Modern Asia’, p. 58.

⁶⁷ Yunzhi etal., Kangxi neifu ben Lülü zhengyi, ii, pp. 625–7.

⁶⁸ Ibid., p. 632; see also pp. 684, 686, 689, 692.

⁶⁹ Zhongguo diyi lishi dang’anguan [The First Historical Archives of China], ed. Kangxi chao Manwen zhupi zouzhe quanyi 康熙朝滿文朱批奏摺全譯 [Complete Translation of Manchu Memorials to the Kanxi Emperor] (Beijing, 1996), p. 914.

⁷⁰ Yunzhi etal., Kangxi neifu ben Lülü zhengyi, i, pp. 151–6.

⁷¹ Y. Fan and B. Sima, Hou Han shu 後漢書 [Book of the Eastern Han], vol. 11 (Beijing, 1965), p. 3001.

⁷² H. L. Goodman and Y. E. Lien, ‘A Third Century AD Chinese System of Di-Flute Temperament: Matching Ancient Pitch-Standards and Confronting Modal Practice’, Galpin Society Journal, 62 (2009), pp. 3–24; N. Dai, Zhongguo shengxue shi 中國聲學史 [A History of Acoustics in China] (Shijiazhuang Shi, 1994), pp. 347–64.

⁷³ M. Mersenne, Harmonie Universelle: The Books on Instruments, trans. R. E. Chapman (The Hague, 1957), p. 417.

⁷⁴ 因管八音之為高低在於管之長短，為互相合不相合又在於管粗細之故。Lülü jieyao, p. 68.

⁷⁵ Ibid., p. 66.

⁷⁶ Cun is a unit of length.

⁷⁷ Yunzhi etal., Kangxi neifu ben Lülü zhengyi, i, pp. 151–6; Lülü jieyao, pp. 42–55.

⁷⁸ ‘Strings have solid bodies. They produce sound by being struck. Long strings vibrate slowly; short strings vibrate quickly. A full-length string vibrates slowly because it is long; a half-length string vibrates quickly because it is short. Let a full-length string be 36 fen and a half-length string be 18 fen. During the period when the full-length string vibrates one time, the half-length string definitely vibrates two times; when the full-length string vibrates one and a half time, the half-length string definitely vibrates three times. Since their vibration periods meet at the same time, they resonate with each other and produce the same sound.’ 絃之實體，實賴人力鼓動而生聲。絃之長者，其音緩 ；絃之短者，其音急。全絃長故得音緩，半絃短故得音急。長短緩急之間，全半相應之理生焉。今以全絃為三十六分，則半絃為一十八分。其全絃鼓動一次之分，則半絃必鼓動二次。全絃鼓動一次半，則半絃必鼓動三次。兩絃鼓動之分，恰相值於一候，是以相應而同聲也。Yunzhi etal., Kangxi neifu ben Lülü zhengyi, i, pp. 149–50.

⁷⁹ Lülü jieyao, pp. 40–1, 62–3.

⁸⁰ Ibid., pp. 67–80.

⁸¹ Ibid., p. 61.

⁸² Ibid., p. 39.

⁸³ The National Library of China only holds copies of A Compilation but not A Summary. One of the two manuscripts of A Compilation in the Library was presented as a gift to an anonymous writer by Yinzhi, the chief editor of The True Doctrine of Music and the third prince of the Kangxi emperor. Lülu zuanyao 律呂纂要 [A Summary of the Essentials of Music], vol. 4 (1644–1911), National Library of China, 15251, fol. 119^r.

⁸⁴ Zhongguo guji shanben shumu: jing bu, fol. 53^r. One more official edition printed during the Qing dynasty is the one in the Complete Collection of Four Treasures (Siku quanshu 四庫全書), a collection of books commissioned in 1772 by the Qianlong emperor, who ordered seven manuscript copies of the collection. Often translated as ‘scroll’, ‘fascicle’ or ‘chapter’, a juan 卷 is one of the parts that a piece of classical Chinese writing is divided into. In antiquity, vertical bamboo slips were tied together as writing material and were rolled up for storage. A piece of writing often consists of more than one juan (scroll) of bamboo slips. The term was later applied to the codex form of books. Although it often has the same length as a chapter, it can also contain more than one chapter.

⁸⁵ C. J. Brokaw, ‘On the History of the Book in China’, in C. J. Brokaw and K.-w. Chow (eds.), Printing and Book Culture in Late Imperial China (Berkeley, 2005), pp. 3–54, at p. 9.

⁸⁶ Ibid., pp. 3–54.

⁸⁷ X. Xiang, ‘Qinggong Kang-Yong shiqi tonghuozi yinshu shulun 清宮康雍時期銅活字印書述論 [A Study on Imperial Bronze Type during Kangxi and Yongzheng’s Reigns]’, Lishi dang’an 歷史檔案 [Historical Archives], no. 3 (2015), pp. 86–91, at pp. 87–9.

⁸⁸ Quoted ibid., p. 89.

⁸⁹ The different context of circulation and the increasing deterioration of reused printing blocks have left material traces in later printings. Judging from the book layout, font and the locations of missing details, copies from the Harvard-Yenching, the Princeton University Library, the University of California at Berkeley Library and the National Taiwan University Library were likely to be printed from the same set of woodblocks, but they were printed in different print runs. All three copies have different book covers. The Harvard-Yenching copy’s book covers are in yellow, the imperial colour. Moreover, it is of better quality than the other two copies in terms of page alignment and evenness of ink density. The colour of its book cover and its better quality suggest that it is an earlier print for circulation within the court. The Princeton University copy, in contrast, has more instances of missing lines, faded ink, and occasional marks of a cracking woodblock, suggesting that it was printed later than the other two copies. The printing block was gradually damaged as the number of printings increased. Compare Yunlu et al., Yuzhi lüli yuanyuan: sizhong 御製律曆淵源: 四種 [The Imperial Compendium of Music and Calendrical Astronomy], vols. 40–4 (Beijing, 1724–56), Harvard-Yenching Library, accessed 8 July 2018, http://nrs.harvard.edu/urn-3:FHCL:27272446; Yunzhi etal., Yuzhi lülü zhengyi 御製律呂正義 [The Imperial Correct Principles of Music] (Beijing, 1723–35), Department of Rare Books and Special Collections, Princeton University Library; and Yunlu etal., Yuzhi lülü zhengyi 御製律呂正義 [The Imperial Correct Priniples of Music] (Beijing, 1713–22), Berkeley Library, University of California. The Berkeley copy is catalogued as a Kangxi reign movable-type edition, but it is more likely to be the Yongzheng reign woodblock print edition. On the differentiation of first print, reprint and re-engraved edition, see L. Guo, Zhongguo guji yuanke fanke yu chuyin houyin yanjiu 中國古籍原刻翻刻與初印後印研究 [A Study on the First Edition and Re-engraved Editions, the First Print and Reprints of Chinese Ancient Books] (Shanghai, 2015).

⁹⁰ 現今書板存貯禮部，外間並無翻刻之板，是以未能流通。Yunlu etal., ‘Zouyi 奏議 [Memorials]’, in Yuzhi lixiang kaocheng houbian 御製曆象考成後編 [Sequel to the Imperial Compendium of Calendrical Astronomy] (Beijing, 1742), fol. 2^v.

⁹¹ Zhuli is the province directly administered by the central government. The other provinces are Shandong, Shanxi, Henan, Jiangsu, Anhui, Jiangxi, Fujian, Zhejiang, Hubei, Hunan, Shaanxi, Gansu, Sichuan, Guangdong, Guangxi, Yunnan and Guizhou.

⁹² Yunlu etal., ‘Zouyi 奏議 [Memorials]’, fol. 2^v.

⁹³ Qing neifu keshu dangan shiliao huibian 清內府刻書檔案史料彙編, ed. L. Weng [Collection of Archival Sources on Book Printing in the Qing Imperial Household] (Yangzhou, 2007), p. 108.

⁹⁴ Y. Zhang, ‘Qingdai zhongyang guanzuan tushu fahang qianshi 清代中央官纂圖書發行淺析 [A Brief Analysis of the Distribution of Central Governement Publications in the Qing Dynasty]’, Palace Museum Journal 故宫博物院院刊, no. 4 (1993), pp. 88–92, at p. 91.

⁹⁵ L. Weng, Qingdai neifu keshu yanjiu 清代內府刻書研究 [A Study on Book Printing in the Qing Imperial Household] (Beijing, 2013), pp. 338–9.

⁹⁶ Yaodou Lü 呂耀斗, (Guangxu) Dantu xianzhi (光緒)丹徒縣志 [(Guangxu) Gazetteer of Dantu County], juan 37 (China, s.n., 1879), fol. 8^r.

⁹⁷ Furen Gu 顧福仁, (Guangxu) Chongxiu Jiaxian xianzhi (光緒)重修嘉善縣志 [(Guangxu) Gazetteer of Jiaxian County], juan 24 (China: s.n., 1879), fol. 33^r–v.

⁹⁸ T. Cao, Qin xue 琴學 [Qin Studies], Xuxiu Siku quanshu 續修四庫全書 1095 (Shanghai, 1995), pp. 373–444, at p. 10; T. Wang, Qin zhi 琴旨 [Qin Studies], Jingyin wenyuange Siku quanshu, 220 (Taipei, 1984), pp. 687–785, at p. 695.

⁹⁹ Wang, Qin zhi, p. 695.

¹⁰⁰ Cao, Qin xue, p. 410.

¹⁰¹ Mengyao He, Genghe lu 賡和錄 [Annotations], Lingnan yishu 嶺南遺書 [Heritage Books in Lingnan] (Hainan, 1831).

¹⁰² M. You, ‘He Mengyao shengping kaozheng yanjiu 何夢瑤生平考證研究 [A Study of He Mengyao’s Biography]’, Xinjiang jiaoyu xueyuan xuebao 新疆教育學院學報 34, no. 1 (2018), pp. 56–62.

¹⁰³ He, Genghe lu, fols. 1^r, 2^v.

¹⁰⁴ Yunzhi etal., Kangxi neifu ben Lülü zhengyi, i, pp. 151–6.

¹⁰⁵ He, Genghe lu, fols. 10^v–11^r.

¹⁰⁶ Ibid., fol. 11^r.

¹⁰⁷ Ibid.

¹⁰⁸ Ibid., fol. 10^r. For the original text in The True Doctrine of Music, see n. 78.

¹⁰⁹ A. Rehding, ‘Instruments of Music Theory’, Music Theory Online, 22, no. 4 (2016), https://mtosmt.org/issues/mto.16.22.4/mto.16.22.4.rehding.html (accessed 29 Dec. 2019).

¹¹⁰ A long and heavy string vibrates slower than a short and light string.

¹¹¹ T. Irvine, Listening to China: Sound and the Sino-Western Encounter, 1770–1839 (Chicago, 2020), p. 50.

¹¹² Charles Burney’s (1726–1814) accounts of Chinese listeners being non-receptive to polyphonic music by no means represent the general reception of European music in late imperial China. There were also Chinese writers who sang praises of the organ in their poems, which often characterise the instrument as one that can produce many sounds simultaneously. Irvine, Listening to China, p. 147; J. Lindorff, ‘Burney, Macartney and the Qianlong Emperor: The Role of Music in the British Embassy to China, 1792–1794’, Early Music, 40 (2012), pp. 441–53, at p. 449; D. F. Urrows, ‘The Pipe Organ of the Baroque Era in China’, in H.-L. Yang and M. Saffle (eds.), China and the West: Music, Representation, and Reception (Ann Arbor, 2017), pp. 21–48, at pp. 28, 38, 40.