Some reflections on the use of 'styles of scientific thinking' to disaggregate and sharpen comparisons between China and Europe from sòng to Mid-Qing times (960-1850 CE)

History of Technology

Volumn 25, Issue , 2004, Pages

  Elvin, Mark ^a  

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References (175)

1. A. Crombie, Styles of Scientific Thinking in the European Tradition. The history of argument and explanation especially in the mathematical and biomedical sciences and arts (London, 1994), 3 vols
2. Crombie, Styles (1), 46
3. R.M. Grove, Green Imperialism: Colonial Expansion, Tropical Island Edens and the Origins of Emironmentalism, 1600-1860 (New York, 1994), esp. 355, 360-4
4. R. Iliffe, 'Rational Artistry', History of Science 36, 1998
5. M. Elvin, 'Personal Luck: why premodern China - probably - did not develop probabilistic thinking'. Paper deposited with the Needham Research Institute, 8 Sylvester Road, Cambridge, UK, 2000. Scheduled for publication in 2004 in a volume edited by G. Dux and H.U. Vogel. There is a Chinese version in Liú Dù and Wáng Yángzong (eds.), Ehonggúo kèxuéyú kèxué géming. Lî Yuesè nánti jí qí xiangguan wèntí yánjiù lúnzhù xuân [Chinese science and scientific revolution. Selected research on Needham's conundrum and related questions] (Shenyáng, 2002)
6. Tones are shown for modern characters as follows: 'a' - level (unmarked), also used for neutral tones; 'á' - rising; 'â' - dipping-rising; 'à' - falling and dynamically fp. Where the tone in some personal and place names can be read in one of two ways, I have not always been able to determine which is correct. Tones for premodern words are not shown
7. For the main participants see references to Chén Dí, Gù Yánwû, Dài Zhèn, Qián Dàxin, Duan Yùcái, Wáng Niànsun, Jiang Yôugào, Ýn Ruòju, and Cúi Shùin A. Hummel (ed.), Eminent Chinese of the Ch'ing Period (1644-1912) (Washington, 1943-4), 2 vols. (An asterisk indicates an entry dedicated to the scholar concerned.) There is a survey in B.A. Elman, From Philosophy to Philology: Intellectual and Social Aspects of Change in Late Imperial China (Cambridge, Massachusetts, 1984), 212-21. He sees the historicization of approach as being particularly the achievement of Jiang Yông (1681-1762)
8. M. Elvin, 'Who was responsible for the weather? Moral meteorology in late imperial China', in M.F. Low (ed.), Beyond Joseph Needham, Technology, and Medicine in East and Southeast Asia, Osiris 13, 1998
9. and M. Elvin, 'The Man Who Saw Dragons: Science and Styles of Thinking in Xie Zhaozhe's Fivefold Miscellany', Journal of the Oriental Society of Australia, 25 and 26, 1993-4
10. Elvin, 'Personal luck' (5)
11. Zhu Zàiyù [Míng], Lüxué xinshuo [A new theory of the science of the pitch-pipes], Féng Wéncí (ed.) (annotated reprint of the 1584 edition: Bêijing, 1986), 19
12. M. Elvin, 'The unavoidable environment: reflections on premodern economic growth in China,' in Ts'ui-jung Liu [Liú Cùiróng] and Shou-chien Shih [Shí Shôuqian] (eds.), Economic History, Urban Culture and Material Culture (Táibêi, 2002)
13. E.S. Rawski, Education and Popular Literacy in Ch'ing China (Ann Arbor, 1979)
14. For example, E. Eisenstein, The Printing Press as an Agent of Change (Cambridge, 1980)
15. or A. Johns, The Nature of the Book: Print and Knowledge in the Making (Chicago, 1998)
16. M. Elvin, 'Skills and resources in late traditional China', in D. Perkins (ed.), China's Modern Economy in Historical Perspective (Stanford, 1975)
17. reprinted in Elvin, Another History. Essays on China from a European Perspective (Sydney, 1996)
18. E.g., J. Besson, Theatrum Instrumetarum et Machinarum (Paris, 1573)
19. A. Ramelli, Le diverse et artificose machine del capitano Agostino Ramelli (Paris, 1588)
20. and G.A. Böckler,Theatrum machinarum novum (Nuremberg, 1662)
21. I. Newton, The Principia. Mathematical Principles of Natural Philosophy, translated by I. Bernard Cohen and Anne Whitman (Berkeley, 1999), 418
22. Discussed in footnote 68 of M. Elvin and N. Su, 'Action at Distance. The Influence of the Yellow River on Hangzhou Bay since A.D. 1000', in M. Elvin and T-J. Liu, (eds.), Sediments of Time. Environment and Society in Chinese History (New York, 1998)
23. Sòng Yìngxing, 'Lùn qì' [A discussion of matter-energy], in id., Yêyì, Lùn qì, Tán Tian, Silián shi [Unofficial policy papers, A discussion of matter-energy, On the heavens, and Poems of pity] (Shanghai, 1976), 68
24. On Sòng generally, see C. Cullen, 'The Science/ technology interface in seventeenth-century China: Song Yingxing on qi and the wuxing', Bulletin of the School of Oriental and African Studies 53.2, 1990
25. Elvin, 'Skills' (14), and M. Elvin, 'Blood and Statistics: Reconstructing the Population Dynamics of Late Imperial China from the Biographies of Virtuous Women in Local Gazetteers', in H. Zurndorfer (ed.), Chinese Women in the Imperial Past: New Perspectives (Leiden, 1999)
26. Wáng Jiànqiu, Sòngdài Tàixué yû Tàixuésheng [The Great School and its students in the Sòng dynasty] (Táibêi, 1965)
27. See also J. Needham and Lu Gwei-djen [Lu Gùizhen], 'China and the origin of examinations in medicine', Proceedings of the Royal Society of Medicine LVI.2, Feb. 1963
28. E. Grant, The Foundations of Modern Science in the Middle Ages. Their Religious, Institutional, and Intellectual Contexts (New York, 1996)
29. T. Grimm, 'Academies and Urban Systems in Kwangtung', in G.W. Skinner (ed.), The City in Late Imperial China (Stanford, 1977)
30. G. Bachelard, La formation de l'esprit scientifique (Paris, 3rd ed., 1957)
31. W. Eamon, Science and the Secrets of Nature. Books of Secrets in Medieval and Early Modern Europe (Princeton, 1994)
32. On Xiè see Elvin, 'Dragons' (8)
33. Even he got the wrong empirical numerical results as Mersenne complained from Paris. See Crombie, Styles (1), 675, 817-19
34. S. Kuznets, Modern Economic Growth. Rate, Structure, and Spread (New Haven, Connecticut, 1966), 9. Kuznets provides useful benchmark tests for 'modern' economic growth, such as the decline of the proportion of the labour force engaged in primary production (essentially agriculture and stockraising)
35. M. Elvin, The Pattern of the Chinese Past (Stanford, 1973)
36. W. Van O. Quine, Set Theory and Its Logic (Cambridge, Massachusetts, 1963), 2-3 and ch. 11
37. A.C. Graham, Later Mohist Logic, Ethics and Science (London, 1978), 40, 440-1
38. Graham, Mohist Logic (30), 58
39. Retranslated from Graham, Mohist Logic (30), 439
40. See M. Elvin, 'The Logic of Logic. A Comment on Mr. Makeham's Note', Papers on Far Eastern History 42, 1990
41. C. Harbsmeier, C., Science and Civilisation in China VII.1, Language and Logic (Cambridge, 1998), 358-408
42. K. Chemla, 'Relations between procedure and demonstration. Measuring the circle in the Nine Chapters on Mathematical Procedures and their commentary by Liu Hui (3rd century)', in H.N. Janke, N. Knoche and M. Otte (eds.), History of Mathematics and Education: Ideas and Experiences (Göttingen, 1996)
43. K. Chemla, 'What is at stake in mathematical proofs from third-century China?', Science in Context 10.2, 1997
44. and K. Chemla, 'Fractions and irrationals between algorithm and proof in ancient China', Studies in the History of Science and Medicine XV.1-2 (1997-8)
45. C. Jami, Les Méthodes Rapides pour la Trigonométrie et le Rapport Précis du Cercle (1774). Tradition chinoise et apport occidental en mathématiques (Paris, 1990), 41
46. P. Engelfriet, 'The Chinese Euclid and its European Context', in C. Jami and H. Delahaye (eds.), L'Europe en Chine. Interactions scientifiques, religieuses et culturelles aux XVII et XVIII siècles (Paris, 1993)
47. Xiè Zhàozhè, Wû zázû [Fivefold miscellany] (1608. Reprinted: Táibêi, 1971, 2 vols.), 360-1. There is another account at ibid. 272 stressing the 'minute particularity' with which the seafarers saw the dragons
48. Xiè Zhàozhè, Miscellany (37), 127
49. For background, see J. Needham and Lu Gweidjen [Lu Gùizhen], 'The earliest snow crystal observations', Weather XVI.10, Oct. 1961
50. What Lî says is 'I have cut open the stomach [whether of one or more is not clear] and there are, in approximate terms, somewhat over a catty [jin] of ants [inside].' See Li Shizhen, Béncâo gangmù [Pharmacopeia arranged by headings and subheadings] (1596, reprinted, Shangwù yinshuguân edition: Shànghâi, 1930, 5 vols, and index), 22:60, juàn 43. On another edition of this work see note 68
51. J. Needham, Lu Gwei-djen [Lu Gùizhen] and Huang Hsing-tsung, Science and Civilisation in China, VI.1: Botany (Cambridge, 1986), 318
52. What Li says is: 'The old prescriptions say that soya-beans dissolve the effects of numerous drugs and poisons [bâiyàodú], but every time I tried this they have been quite ineffective. If one adds "liquorice" [gancâo] their efficacy is remarkable. It is essential to know this.' Lî Shizhen, Pharmacopeia (39), 16:90, juàn 24
53. Xiè Zhàozhè, Miscellany (37), 1080-1
54. Shicháo Shèngxùn [The sacred instructions of ten reigns] (99 vols, 1616 to 1874, with prefaces from 1666 to 1880. Referred to in the text by reign-period. Publication details are not specified, but the work was presumably issued by imperial order in Bêijing during the Guangxù reign-period), Yongzhèng 8:lab
55. Sacred Instructions (42), Yongzhèng 8:7a
56. Yáng Qîqiáo, Yongzhèng-dì jí qí mìzhé zhìdùyánjiù [The Yongzhèng emperor and his system of secret memorials] (Hong Kong, 1981), 27
57. These issues are discussed in more detail in Elvin, 'Weather' (8, 1998)
58. J. Needham, Ho Ping-yü [Hé Bîngyù] and Lu Gwei-djen [Lu Gùizhen], Science and Civilisation in China V.3: Chemistry and Chemical Technology: Part 3: Spagyrical discovery and invention: historical survey, from cinnabar elixirs to synthetic insulin (Cambridge, 1976), 108, make the intriguing off-the-cuff remark about Gé Hóng (3rd to 4th century CE), 'How did he manage to make so many true observations of chemical behaviour, and carry out so many interpretable experiments, even though he himself could never interpret them?' It has to be asked to what extent they involved 'experimental' thinking in the relatively strict sense given to the term in the present discussion. It needs to be distinguished, for example, from the everyday sense of 'experimentation' in the sense of 'trying out' - new recipes, for example
59. Xiè Zhàozhè, Miscellany (37), 940
60. Xiè Zhàozhè, Miscellany (37), 857
61. Tián Wén, (QJng), Qián shu [The book of Gùizhou] in Yan Yiping (ed.), Yuèyâ-táng cóngshu, case 36 in Bâibù cóngshu jíchéng [Collection of collections on all topics] (reprinted by Yiwén Yinshuguàn: Táibêi, 1965-8, in 830 cases), 4::4:5ab. The '::' in citations indicates the number preceding is that of the 'case'. I have found Lombard-Salmon's translation very useful, even if I have often, with hesitations, differed from it
62. See C. Lombard-Salmon, Un exemple d'acculturation chinoise: la province de Guizhou (Paris, 1972), 190-1
63. Twenty sheng. The Qing sheng was 1035 ml
64. G. Bauer, [Agricola, Georgius ], De Re Metallica (1556), H.C. and L.H. Hoover, transl, and ed. (1912. Reprinted, New York, 1950), notably the methods on 430-2
65. I owe these explanations to Dr Ian Williams of the Research School of Earth Sciences, Australian National University, and would like to express my thanks
66. Xiè Zhàozhè, Miscellany (37), 68-9. Xiè also used other arguments: a quotation from scripture, and theoretical considerations based on yin-ydng theory
67. Sòng Yingxing, 'Lùn qì' (18), 72, 69 and 70 respectively
68. Personal observations in 1994 of the 70-metre scale model of the inner Hángzhou Bay, Zhèjiang Province, used for simulations in Hángzhou
69. Here, presumably the seasons when certain plants blossomed or migrant birds appeared
70. J. Needham and Wáng Líng, Science and Civilisation in China III: Mathematics and the sciences of the heavens and the earth (Cambridge, 1959), 359. Notes and transliterated Chinese characters omitted
71. J. Needham and Wáng Líng, Science and Civilisation in China III (58), 361. On the history of the mechanical details see J. Needham and Wáng Líng, Science and Civilisation in China IV.2: Physics and physical technology, part 2, Mechanical engineering (Cambridge, 1965), section 27j
72. Shi Sù et al., (eds.), revised by Shên Zuòbin, Jiatài Gùiji zhì [Jiatài reign-period gazetteer for Gùiji] (Reprinted in vol. 7 of Sòng-Yudn fangzhî cóngkan [Collection of Sòng- and Yuán-dynasty local gazetteers] (Bêijing, 1992), 7065
73. See also Needham and Wang, Science and Civilisation in China III (58), 491
74. The term qi in this phrase properly means 'stones on the side of a mountain', or scree
75. Zhang Hào (ed.), Bâoqìng Gùiji xù-zhi [Bâoqìng reign-period continuation of the gazetteer for Gùiji] (Reprinted in vol. 7 of Sȯng-Yúanfangzhi cóngkan [Collection of Sòng- and Yúan-dynasty local gazetteers] (Bêijing, 1992), 7180
76. J. Brown et al., Waves, Tides and Shallow-Water Processes (Oxford, 1989. Produced by the Open University), 62
77. W. Debler, Fluid Mechanics Fundamentals (Englewood Cliffs, 1990), 250-1
78. Elvin and Su, 'Hangzhou Bay' (17), 368 and 370
79. Crombie, Styles (I), II, ch. 15
80. Grove, Green Imperialism (3); K. Reeds, 'What the Nahua knew. The secrets of Mexico's plants had been revealed by the sixteenth century', Nature 6879 (28 Mar. 2002), 369-70
81. References are to the five-volume Shangwù yinshuguân edition published in Shànghâi in 1930 (as in note 39). Readers may however find Lî Shízhen, Bêncâo gangmù: [Pharmacopoeia arranged by headings and subheadings] (1596. Reprinted, Rénmín wèisheng chubânshè: Bêijing, 1975. 4 vols). easier to access. Juàn numbers have been included in these references to facilitate location of passages
82. N.R. Scott-Ram, Transformed Cladistics, Taxonomy and Evolution (Cambridge, 1990)
83. Crombie, Styles (1), II, 1267
84. W. Blunt, The Compleat Naturalist. A Life of Linnaeus (first published in 1971, reprinted, London, 2001), appendix I by W.T. Stearn, 246-8
85. Quèxíng here might also be translated as 'move backwards', but it is hard to see how this could make any zoological sense. Què can mean yâng, 'face upwards', and this gives a more intelligible rendering
86. Li Shizhen, Pharmacopeia (39), 21/55, juàn 39
87. Lî Shizhen, Pharmacopeia (39), 6/33, juàn 3.1 use the translation 'quasi-cholera' as it is unlikely that the disease called hùoluàn before the 1820s was true classic cholera
88. See K. MacPherson, 'Cholera In China, 1820-1930: An Aspect of the Internationalization of Infectious Disease', in Elvin and Liu (eds.), Sediments of Time. Environment and Society in Chinese History (New York, 1998). Emphasis added
89. Lî Shízhen, Pharmacopeia (39), 21/89-90, juàn 40
90. Lî Shízhen, Pharmacopeia (39), 6/32-3, juàn 3. The last example has been very slightly rearranged so as to show the structure more clearly. Emphases added
91. Lî Shízhen, Pharmacopeia (39), 6/34, juàn 3
92. Lî Shízhen, Pharmacopeia (39), 6/36, juàn 3
93. This provisional conclusion is based mainly on P. Huard and M. Wong, 'Évolution de la matière médicale chinoise', Janus 47, 1958, 45-50
94. The answer is 2: a 5 and a 6, or a 6 and a 5. Leibniz is said to have failed to solve this correctly
95. I am grateful to Professor Jochi Shigeru for drawing this passage to my attention
96. Bái Shàngshù, 'Jiûzhang suàn shù' zhùshì [Annotated explanations of Nine Chapters on the Mathematical Art] (Bêijing, 1983), 21-3
97. Qián Bâocong (ed.), Suànjing shíshu [Ten mathematical classics], II, Jiûzhang suànshù [Nine chapters on the mathematical art], with commentary by Liú Hui (3rd c. CE) (Bêijing, 1963), 71-2
98. Wú Wénjùn (ed.), Zhongguó shùxué dàxi [Compendium on Chinese mathematics] (Bêijing, 1998), Volume 2
99. Shên Kangshen (ed.), Zhongguó gûdài shùxué míngzhù 'Jiûzhang suànshù ' ['Nine Chapters on the Mathematical Art': A masterpiece of ancient Chinese mathematics], 11.59-60
100. On text of the 'Nine Chapters' see J-C. Martzloff, A History of Chinese Mathematics (original edn., 1987; rev. English edn., Berlin and Heidelberg, 1997), translated from the French by S.S. Wilson, 127-36
101. Qián Bâocong, Nine Chapters (82), 6:1-2. Bái Shàngshù (82),184-7 gives the method
102. See also Wú Wénjùn/Shên Kangshen, Nine Chapters (82), II.85-6
103. The exact meaning of the terms in quotes in this sentence is not relevant here, and they should be taken as approximations only
104. There is a brief history in Wu Kang, Outline of the Changes of the Zhou
105. For the general background, see Needham and Wang, Science and Civilisation in China II: History of Scientific Thought (Cambridge, 1956)
106. R. Wilhelm, The I Ching or Book of Changes, transi. C.F. Baynes (New York, 1950, 2 vols), I.xl-xli
107. See Lî Lîng, Zhongguó fangshù kâo [A study of magical techniques in China] (rev.ed., Bêijing, 2000), ch. 4
108. Wú Kang, Shào-zî Yi-xué [Master Shào's study of the Changes] (Táibêi, 1959), 37
109. Chéng Shìquán, 'Zhou Yi chéng guà ji Chun-qiu shifâ' [The transformation of the Changes of Zhou into hexagram form and methods of divining by plants during the Springs and Autumns period], in Huáng Shòuqí and Zhang Shànwén (eds.), Zhou Yi yánjiù lùmvénjí [Collected essays on the Changes of Zhou] (Bêijing, 1989), II, 377
110. Sometimes given as ptarmica or sibirica by earlier writers
111. I follow the formulation given by Wilhelm, The I Ching (1950), 86
112. There is a version of this table, with other matter, in Wáng Qi, San Cái túhùi [Illustrated encyclopaedia of the Three Principles] (1607. Reprinted Táibêi, 1970, 6 vols.), vol. 4, 10:18ab,/1795-6. The three differing derivations of the young yin and young yáng are each seen as having a distinctive nature. They are each described by one of the hexagrams that is the reduplicated form of a trigram. Thus (9, 4, 8) is symbolized by kân 'the abysmal'
113. Needham and Wang, Science and Civilisation in China III (58), 140, hint at the existence of 'an esoteric doctrine', without elaborating further
114. 3 = 8
115. Martzlofr, Chinese Mathematics (82), 17, 230-1, 304-5
116. Luó Xinbén and Xû Róngsheng, Zhongguó gûd ài dûbó xísú [Gambling customs in ancient China] (Xi'an, 1994), 106-8
117. Mèng Yuánlâo, Dongjng mènghuà lù [Dream of the Glories of the Eastern Capital], with notes by Dèng Zhichéng (Bêijing, 1959), 162
118. I have also consulted the Japanese translation by Iriya Yoshitake and Umehara Kaoru, Tôkyô muka roku (Tokyo, 1996), 199
119. Note cited by Dèng Zhichéng in Mèng Yuánlâo, Dream (97), 164
120. Note cited by Dèng Zhichéng in Mèng Yuánlâo, Dream (97), 163
121. Note cited by Dèng Zhichéng in Mèng Yuánlâo, Dream (97), 163-4
122. Lî Kuangyì, Zixià lù [Providing For Leisure Time], in Qindìng sìkù quánshu (Táiwan shangwù yinshuguân edn.: Táibêi, 1983), zibu 10, vol. 850, 157
123. Guó Shuanglín and Xiào Méihua, Zhongguó dûbó shî [A history of gambling in China] (Bêijing, 1995), 181-3
124. This reconstruction is based on the most coherent compromise I can devise from the somewhat conflicting accounts in Guó and Xiào (104), and in Luó and Xû (98)
125. We have also to consider the possibility that the rules may have the special feature that the principal had to be the first of the pair. In other words: 2′. Permitted: 12, 23, 34, and 41. Not permitted: 12, 23, 34, or 41; 13, 13, 24, or 24
126. Gù Yánwû, Yinxué wû shu [Five works on phonology] (seventeenth century. Reprinted, Sixián jiángshè : n.p., 1890, 12 vols.). There is a modern single-volume reprint in the Yinyùnxué cóngshu [Series on phonology] published by the Zhonghuá shujú, Bèijing, in 1982
127. E. Pulleyblank, Lexicon of Reconstructed Pronunciation in Early Middle Chinese, Late Middle Chinese, and Early Mandarin (Vancouver, 1991), divides Middle Chinese into Early and Late
128. B. Karlgren, Grammata Serica Recensa. (Stockholm, 1957), 650a and 663a. Karlgren's phonetic typography cannot be reproduced here without fonts not available to me
129. See also Gù Yánwû, Pronunciations (105), zhong:lb. I have used 'ε' to represent Karlgren's inverted 'e'
130. Gù Yánwû, Pronunciations (105), zhong:la. I have not included the more recent reconstructions in Pulleyblank, Lexicon (106) as these, though superior, do not affect the argument put forward here
131. This xié is Karlgren, Grammata Serica (107), 639c, and different from the xiéin xiésheng given earlier, which is ibid., 599g
132. Gù Yánwû, Pronunciations (105), zhong: 6a
133. Gù Yánwû, Pronunciations (105), zhong: 1b-2a
134. The first was probably Zhou Yong in the 5th century CE
135. Not of course the same as the four tones of modern standard Chinese
136. A feature of the Qièyùn was that it differentiated words according to their tone
137. Gù Yánwû, Pronunciations (105), author's preface: 2b
138. It has been suggested by Fang Chaoying [Fáng Zhàoyí ng] in L. Goodrich and Fang Chaoying [Fáng Zhàoying] (eds.), Dictionary of Ming Biography (New York, 1976, 2 vols.), 180-4, that Chén Dì may possibly have been influenced by the Jesuits as he had a good friend who also knew Ricci, and Ricci had made Western alphabetic writing known to Chinese scholars at the opening of the seventeenth century and maybe, informally, earlier. Chén's key study of the Songs was published in 1606. There is no internal evidence to support this idea, however
139. Pulleyblank, Lexicon (106), 3-4
140. H.F.Cohen, The Scientific Revolution. A Historiographical Enquiry (Chicago, 1994), esp. ch. 8
141. The Sòng foot was approximately 31.6 cm; there were 5 feet per double pace [bù], and 360 double paces per lî, which was thus about 569 metres, or a little over half a kilometre. See Qiu Guangmíng, Zhongguó lidài dù-liàng-he'ng káo [Measures of length, capacity, and weight under successive Chinese dynasties] (Bêijing, 1992), 98
142. Aoyama Sadao, Tô-Sô jidai no kôtsû to chishi chizu no kenkyû [Researches on communications and topographies and maps in Táng and Sòng China] (Kyòto, 1963), pt 2
143. J. Needham, Wang Ling and K. Robinson, Science and Civilisation in China, IV: Physics (129), 220-4
144. What would be needed is a treatment of Chinese musical theory at this period that addressed the multifaceted discussion in H.F. Cohen, Quantifying Music. The Science of Musìc at the First Stage of the Scientific Revolution, 1550-1650 (Dordrecht, 1984)
145. Zhu Zàiyù, New Theory (10), 42
146. The Transforming Force was not a creator but had some of the same attributes as a god
147. Zhu Zàiyù, New Theory (10), 1
148. Zhu Zàiyù, 'Jin lüshu zòushù' [Memorial on the presentation of books on pitch], in Zhu Zàiyù (Ming), Lülü jingyi [The quintessential significance of the standard pitchpipes], Féng Wénci (ed.) (annotated reprint of the 1584 edition: Bêijing, 1998), separate section, 1
149. Zhu Zàiyù, New Theory (10), 2
150. So called as its 'tone' was the proportional mean between the 'major' and 'minor' tones, or √ ((8/9)(9/10)). See Cohen, Qualifying Music (132), 42
151. Cohen, Quantifying Music (132), 41. The earliest recorded case is from 1511, but presumably it was done earlier
152. P.A. Scholes, The Oxford Companion to Music (tenth ed., rev. J.O. Ward; London, 1970), 1012-17
153. Cohen, Quantifying Music (132), 43
154. Thís pronunciation is used for that character zheng ('show', 'prove', 'tax', etc.) when used in this musical sense
155. See the diagram and explanation in Dài Niànzû, Zhu Zàiyù - Mingíài-de kexué héyì shù jùxing [Zhu Zàiyù - megastar of the science and arts of the Míng dynasty] (Bêijing, 1986), 48-50
156. See Dài Niànzû, Zhu Zàiyü (153), 48-54, and Needham, Wáng and Robinson, Science and Civilisation in China IV. 1 (129), 172-3
157. Needham, Wáng and Robìnson, Science and Civilisation in China IV. 1 (129), 185
158. Needham, Wáng and Robinson, Science and Civilisation in China IV.1(129), 181-2
159. Zhu Zàiyù, New Theory (10), 23
160. Needham, Wáng and Robinson, Science and Civilisation in China IV. 1 (129), 213, note that 'a pîpe half the length of another pipe... does not necessarily give its octave'. The reason is that the 'effective length' of a pipe with open ends, in the sense of length of the resonating column of air, also depends on the diameter
161. From the Shîji [Records of the Grand Historian], the Hànshu [History of the Hàn dynasty], the Huáinánzî [The book of the Prince of Huáinán] together with the Jinshu [History of the Jin dynasty] and the Sòngshu [History of the Líú Sòng dynasty], and the .Xù Hànshu [Continuation of the Hàn history]. See Féng Wénci's notes in Zhu Zàiyù, New Theory (10), 19. These 'methods' differed only in the numerical values they used, not in procedures
162. Zhu Zàiyù, New Theory (10), 19. Emphasis added
163. Zhu Zàiyü, Pitchpipes (136), 7-10
164. Dài Niànzû, Zhu Zàijù (153), 226-7
165. Dài Niànzû, Zhu Zàiyù (153), 296-7
166. Needham, Wang and Robinson, Science and Civilisation in China IV. 1 (129), 218-20
167. and Dài Niànzû, Zhu Zàiyù (153) 224-5
168. Literally 'mutual generation by intervals of 8'. There are 8 notes, with 7 semitones between them, defining a fifth
169. Zhu Zàiyù, Pitchpipes (136), 'Jin lüshu zòushù' [Memorial on the presentation of books on pitch], separate section, 2. Also cited in Dài Niànzû, Zhu Zàiyù (153), 112
170. The Guózijian. The translation is the standard one, following C. Hucker, 'An Index of Terms and Titles in "Governmental Organization of the Ming Dynasty"', Harvard Journal of Asiatic Studies 23, 1960-1, 138, but it was not a university in the full sense
171. Zhu Zàiyù, Pitchpipes (136), 'Memorial on the presentation of books on pitch', 2-5
172. Hummel, Eminent Chinese (7), I, 24-5
173. Zhu Zàiyù (Ming), Tuèxuéxinshuo [A new theory of musicology], in id., Yütlü quánshu [Complete works on music and pitches], number 735 in the Wànyôu wénkù, first series, Wáng Yûnwû (gen. ed.), (Shànghâi, 1929), 5.17
174. Also cited in Dài Niànzû, Zhu Zàiyà (153), 225
175. Dài Niànzû, Zhu Zàyù (153), 235