From French to German

Tonietti, Tito M.

doi:10.1007/978-3-0348-0675-6_6

Tito M. Tonietti⁵

Part of the book series: Science Networks. Historical Studies ((SNHS,volume 47))

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Abstract

Luigi Giuseppe Lagrange (1736–1813) entered into the controversy about the forms assumed by a string made to vibrate, with some articles about sound. However, we will overlook the details of how much he felt himself, at least at the beginning, closer to Euler than to d’Alembert or to Daniel Bernoulli, as is well known. Among other things, our mathematician from Turin believed in the possibility that mathematics could illuminate physics; indeed, in his famous book about analytical mechanics, he would have desired to reduce the latter to the former.

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Notes

1.
Lagrange 1759, pp. 45 and 144–147.
2.
Lagrange 1760–1761, p. 316.
3.
Lagrange 1759, p. 147. Quoted in Christensen 1993, p. 155.
4.
Quoted in Bailhache 1995a, p. 33.
5.
Itard 1981. Boyer 1990, pp. 544–545 and 566. Kline 1972, pp. 583–586.
6.
Grattan-Guinness 1970, p. 20; Grattan-Guinness & Ravetz 1972, pp. 250–253, 445–446, 450–453, 457 and passim. Ravetz & Grattan-Guinness 1981. Kline 1972 , pp. 672–679. Cf. Bottazzini 1981.
7.
Truesdell 1960, p. 299 and passim. Ravetz 1961 . Grattan-Guinness 1970, pp. 1–21. Grattan-Guinness & Ravetz 1972, passim.
8.
Bibliothèque Nationale Paris, Manuscrits fond français 22501. Grattan-Guinness & Ravetz 1972, p. 496.
9.
Ravetz & Grattan-Guinness 1981, p. 97.
10.
Serres 1989, pp. 337–361 and passim.
11.
Agnesi 1748, tome I, pp. 380–382, Fig. 135. Kramer 1981.
12.
Dostrovsky 1981c. Resnick & Halliday 1961, p. 435.
13.
Kramer 1981 a.
14.
Dostrovsky 1981b.
15.
Dobrzycki 1981, supplements. Orcalli 1996, pp. 128–136 and 143–144.
16.
Riemann 1990, p. 262; French transl. Riemann 1968, p. 229.
17.
Riemann 1990, p. 210; French transl. Riemann 1968, p. 206.
18.
Thom 1980, pp. 71–72. Tonietti 2002a, Chaps. II and III.
19.
Riemann 1990, 370–382.
20.
Riemann 1990, pp. 372–373.
21.
See above, Sect. 12.2.
22.
Riemann 1990, p. 374.
23.
See above, Sect. 10.2.
24.
Riemann 1990, pp. 376 and 380.
25.
Riemann 1990, p. 373.
26.
Riemann 1990, pp. 589–590. Freudenthal 1981.
27.
Riemann 1990, pp. 843 and 589.
28.
See above, Sects. 10.2 and 11.1.
29.
Riemann 1990, pp. 304–305, 318, 539–570 and passim. Riemann 1968, pp. xiii–xxxv, 281 and 297. Freudenthal 1981. Bottazzini 1981, pp. 169–213. Tonietti 1992b and 1994.
30.
Persico 1960, Chaps. II and III. Kline 1972 , p. 685.
31.
We can read this in the French edition, approved by the author. Helmholtz 1868.
32.
Helmholtz 1868, pp. 2, 6–7 and 21.
33.
Helmholtz 1868, p. 20.
34.
See above, Sect. 8.2.
35.
Helmholtz 1868, pp. 25, 27 and passim.
36.
Helmholtz 1868, pp. 44–45, 47, 58.
37.
Helmholtz 1868, pp. 73–74, 78 and passim.
38.
Dostrovsky 1981d.
39.
Helmholtz 1868, pp. 154–155, 159–163, 166–188 and passim.
40.
Helmholtz 1868, pp. 230–239, 247 and passim.
41.
Helmholtz 1868, pp. 261, 263, 265 and passim.
42.
See above, Sect. 11.2.
43.
Helmholtz 1868, pp. 266, 280–281 and passim.
44.
Helmholtz 1868, pp. 291–293 and passim.
45.
Helmholtz 1868, pp. 294–295 and passim.
46.
See above, Sect. 8.3.
47.
Helmholtz 1868, pp. 295–297 and passim.
48.
See above, Sect. 11.1.
49.
Helmholtz 1868, p. 298 and passim.
50.
Helmholtz 1868, pp. 300, 306 and passim. The criticism of Helmholtz that the others above referred to the “natural” may likewise be extended to himself.
51.
Helmholtz 1868, pp. 300, 306, 323 and passim.
52.
Helmholtz 1868, pp. 328, 334 and passim.
53.
See above, Sect. 8.1.
54.
Helmholtz 1868, pp. 334, 339 and passim. See Part I, Chaps. 3 and 4.
55.
Helmholtz 1868, pp. 356, 365–366 and passim.
56.
Helmholtz 1868, p. 371 and passim.
57.
Helmholtz 1868, pp. 372, 374 and passim.
58.
See Part I, Sect. 6.7.
59.
See Part I, Chap. 5.
60.
Helmholtz 1868, Chap. XV pp. 396–397, 406 and passim.
61.
Helmholtz 1868, pp. 411, 415–416, 421 and passim.
62.
Helmholtz 1868, pp. 422, 425–426, 429 and passim. For the different version of musicians, see below, Sect. 12.3.
63.
Helmholtz 1868, pp. 430, 432 and passim.
64.
Helmholtz 1868, pp. 436, 469 and passim.
65.
Helmholtz 1868, pp. 481–482, 486 and passim. In italics and in Italian in the text.
66.
Helmholtz 1868, pp. 493–497, 507–509 and passim.
67.
Helmholtz 1868, pp. 532–534, 537–538 and passim.
68.
Helmholtz 1868, pp. 86–87, 482. Turner 1981 , pp. 246–247.
69.
Turner 1981 , pp. 243–244.
70.
Riemann 1990, pp. 345 and 349.
71.
Turner 1981 .
72.
Helmholtz 1868, p. 16.
73.
Helmholtz 1868, p. 71 and passim.
74.
Morse 1981.
75.
Ohm 1843; 1844, pp. 7 and 15.
76.
Ohm 1844, pp. 15–18.
77.
Seebeck 1843, passim. Ohm 1844, p. 10.
78.
Seebeck 1843, pp. 449, 452–453 and 480–481.
79.
Ohm 1844, pp. 14–15.
80.
Caneva 1981.
81.
See Part II, Sect. 8.2. Tonietti 2006a.
82.
Martzloff 1988, pp. 318–325. Martzloff 1992, pp. 32, 36–37.
83.
Wylie 1897, pp. 193–194.
84.
Hulin 1979, pp. 150, 152.
85.
Hulin 1979, pp. 163, 168, 171.
86.
Hulin 1979, pp. 179, 188.
87.
Hulin 1979, pp. 190–191, and passim.
88.
Hulin 1979, p. 213.
89.
Joseph 2003, pp. 11–13, 289–290.
90.
Chern 1990, p. 685–686, 649. Zhang 1993. Roman 1964, pp. 238–239. Tonietti 1966. Tr. Harry Wang.
91.
Boltzmann 1876. Riemann 1990, pp. 188 and 208; Riemann 1968, pp. 177 and 204. Weber 1877, p. 71. Schoeneberg 1981.
92.
Boltzmann 2004. Brush 1981 .
93.
Boltzmann 1905, p. 73.
94.
Boltzmann 2004, p. 183.
95.
Boltzmann 1905, p. 421. Boltzmann 1993, pp. 18–19, 37–38 and passim. In his youth, he had studied the threshold of intensity for sounds. Rayleigh 1945, pp. 433 and 438.
96.
Boltzmann 1905, pp. 385 and 391.
97.
Dieudonné 1981a.
98.
Poincaré 1905–1910, t. III, p. 305. Poincaré 1989, v. I, p. 320, 329; v. II, p. 190. Volterra, Hadamard, Langevin & Boutroux 1914. Boyer 1990, pp. 689–693. Kline 1972 , pp. 706–707, 1025–1026, 1170–1179 and passim. Tonietti 1982b; 1983a; 1990.
99.
Planck 1893, p. 418.
100.
Kangro 1981. Heilbron 1986.
101.
Planck 1893, pp. 425, 419–421 and passim. Planck 1958, B. I, pp. 435–436.
102.
Planck 1893, p. 423 and passim.
103.
Planck 1893, pp. 423–424, passim.
104.
Planck 1893, pp. 425–426, and passim.
105.
Planck 1893, pp. 428–429 and passim.
106.
Planck 1893, p. 429 and passim.
107.
Planck 1893, pp. 434–439.
108.
Planck 1893, pp. 439–440.
109.
Heilbron 1986.
110.
Planck 1958, B. I, p. 436.
111.
Planck 1958, B. I, p. V.
112.
Planck 1958, B. III, pp. 383–384.
113.
Serravezza 1996, pp. 79–80.
114.
Planck 1958, B. III, p. 421. Heilbron 1986, p. 34.
115.
Kangro 1981, p. 7.
116.
Forman 2002. Heilbron 1986, p. 186.
117.
Serravezza 1996, pp. 65–66 and 206.
118.
See Sect. 10.2.
119.
Mach 1977, pp. 36–37, 451, 492 and passim.
120.
Kalbeck 1976, B. I, p. 279. Cf. Serravezza 1996, p. 80. Grassmann 1973, pp. 92–94, 96 and passim.
121.
Kangro 1981. Heilbron 1986, pp. 54, 58, 66 and passim. Forman 2002. Giovannini & Tonietti 1968. Tonietti 1976. Tonietti 1980.
122.
Grassmann 1973, p. 96. Heilbron 1986, p. 34. Tonietti 2005.
123.
Serravezza 1996, pp. 56–57, 315 and passim. In contrast with Helmholtz , Stumpf maintained that in consonances, sounds fused together, whereas in dissonances, they did not. He confirmed his theory of “fusion” by studying the judgement of listeners directly. For him, basically, the phenomenon of music manifested that psychological unity which could not be broken down into mechanical elements without losing its main characteristics. Green & Butler 2004.
124.
See below.
125.
Serravezza 1996, pp. 74, 76.
126.
Serravezza 1996, pp. 90, 96 and passim.
127.
Serravezza 1996, pp. 83–85 and passim. See above, Sect. 11.1.
128.
Serravezza 1996, p. 110 and passim.
129.
Tonietti 1997; Tonietti 2004.
130.
Tonietti 1997, pp. 1–2. Tonietti 2004, pp. 1329–1330.
131.
Tonietti 1997, p. 12. Tonietti 2004, pp. 1351–1352.
132.
Tonietti 1997, p. 13. Tonietti 2004, p. 1352.
133.
See below.
134.
Forman 2002, pp. 66–67.
135.
See above, Sect. 8.3.
136.
Schönberg 1917/1977, pp. 98–99, bars 360–363.
137.
Baumgardt 1951, p. 13.
138.
See above, Chap. 8.3.
139.
Einstein 1980.
140.
Jung & Pauli 1955.
141.
Einstein 1934, p. 179. Einstein 1991, p. 52.
142.
Tonietti 2004, Chap. 58.
143.
Schönberg 1922/1963, pp. 494–495, 81–82, 512–513, and passim.
144.
Schönberg 1922/1963, pp. 59, 82, 116, 119, and passim.
145.
Schönberg 1922/1963, pp. 22–23, 29–30, 31–32, and passim.
146.
Schönberg 1922/1963, pp. 37, 396–397, and passim.
147.
Schönberg 1922/1963, pp. 20-21-22, and passim. Tonietti 2004.
148.
Tonietti 2004, p. 733.
149.
Schönberg 1922/1963, pp. 518, 521–522 and passim.
150.
Tonietti 2004.
151.
Max Weber 1980, pp. 67–68 and passim. Cf. above, Part I.
152.
Tonietti 2004, pp. 714–721.
153.
Tonietti 2004, Chap. 49.
154.
Tonietti 1988.
155.
Weyl 1932, p. 22.
156.
Weyl 1962, p. 59. Speiser 1932, pp. 23–36.
157.
Speiser 1932, pp. 30–31 and passim.
158.
Speiser 1932, pp. 32, 33 and passim.
159.
Speiser 1932, p. 36.
160.
Birkhoff 1950, vol. III, pp. 288–306, 320–333, 382–535, 755–777, pp. 435, 446, 524 and passim. Birkhoff 1933.
161.
Knobloch 1995.
162.
Archibald 1924. Hiebert 1981, pp. 434 and 449.
163.
Tonietti 1992a; 1992b; 1994.
164.
Enriques & De Santillana 1932, p. 86. Enriques 1949, pp. 464 and vii. Enriques & Castelnuovo 1996, p. xxx.
165.
O’Keefe 1972.
166.
Knobloch 1992; 1995.
167.
Bailhache 1989; 1996, pp. 1, 27 and passim.
168.
Simonini 1995.
169.
Asinari 1997. Gozza 1996.
170.
Pekonen 1993. Klotz 1995. Bizzi 198?. Scimemi 1990.
171.
Anfilov 1966, p. 128. Cingolani 1995. Lindsay 1972. Lindsay 1981.
172.
Xenakis 1963. Napolitano & Tonietti 1972.
173.
Domínguez & Pecci 199?.
174.
Hofstadter 1980. Cf. Nolan 2004.

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Dipartimento di matematica, University of Pisa, Pisa, Italy
Tito M. Tonietti

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Tonietti, T.M. (2014). From French to German. In: And Yet It Is Heard. Science Networks. Historical Studies, vol 47. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0675-6_6

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DOI: https://doi.org/10.1007/978-3-0348-0675-6_6
Published: 23 December 2014
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