Music and the Making of Modern Science

Notes to pages 217–231 305

14 Helmholtz and the Sirens

1. Helmholtz 1882 , 1:12 – 75; see also Bevilacqua 1993.


2. Helmholtz 1882 , 2:760 – 839.


3. Ibid. , 2:858 – 880; see also Debru 2001; see Meulders 2010 , 89 – 106.


4. Helmholtz 1882 , 2:229 – 260.


5. Helmholtz 1971 , 144 – 22, at 213 – 222; Hatfield 1990 ; Lenoir 1993 , 124 – 126; Hui 2008 , 77 – 79.


6. For the relation between his physiological, mathematical, and philosophical work, see Richards 1977.


7. Helmholtz 1882 , 2:45 – 70; on the relation between visual color and sound-color ( Klangfarbe ), see Kursell


8. 
   


9. Helmholtz 1867 , 282 – 288, 293, which incorporated the work of Grassmann 1854 ; MacAdam 1970 , 53 – 60.


10. Helmholtz 1962a , 2:64; see also Lenoir 1993.


11. Helmholtz 1962a , 2:76.


12. Ibid. , 2:66.


13. Ibid. , 2:77, originally published in Helmholtz 1882 , 2:78 – 82.


14. Helmholtz 1962a , 2:117.


15. Ibid. , 2:77.


16. For excellent discussions of Helmholtz within his larger musical and cultural milieus, see Hiebert and Hiebert
    1994; Jackson 2006 , 146 – 148; Hui 2008 , 39 – 82; Erlmann 2010 , 217 – 270; Hui 2013a.


17. Koenigsberger 1965 , 14; Helmholtz 1993 , 43n2, 68.


18. Helmholtz 1962b , 250 – 286. Regarding the relation between painting and visual science in Helmholtz, see
    Hatfield 1993 , 522 – 588, at 535 – 540. On the significance of the Kulturtr ä ger in science, see Sonnert 2005.


19. Helmholtz 1882 , 1:256 – 302, 420 – 423, 424 – 426.


20. For helpful overviews of his project, see Vogel 1993 ; Meulders 2010 , 153 – 199; Fowler 2004.


21. For Helmholtz ’ s use of “ instruments as agents of change, ” see Pantalony 2009 , 20 – 36. For Weber ’ s anticipa-
    tion of Helmholtz ’ s recording technique, see Kittler 1999, 26.


22. Helmholtz 1954 , 229 – 233.


23. For the larger context of this instrument, see Rehding 2014. See also Kursell 2013.


24. Helmholtz 1954 , 8, 11, 13.


25. Ibid. , 155 – 159, at 157, with mathematical details at 411 – 413, 418 – 420. See also Jackson 2006, 178 – 179.


26. Helmholtz 1954 , 158.


27. Ibid. , 170, 173.


28. Helmholtz 1903 , 1:265 – 365, at 309; Helmholtz 1962b , 93 – 185, at 130 – 131.


29. Helmholtz 1903 , 1:120 – 155, at 122; Helmholtz 1962b , 22 – 58, at 23.


30. Helmholtz 1954 , 369 – 370. In the second edition, following this paragraph the text then cuts to the final
    paragraph on 371. Regarding the importance of invariance in his thinking, see Hatfield 1993 , 552 – 553.


31. Meulders 2010 , 71.
    15 Riemann and the Sound of Space


32. Koenigsberger 1965 , 207 – 208.


33. Gauss 2005.


34. Riemann 1990 , 304 – 319; quoted in Pesic 2007 , 23 – 45.


35. See Pesic 2007 , 2; see also Scholz 1982 ; Nowak 1989.


36. Riemann 1990 , 318; quoted in Pesic 2007 , 33; see also Grattan-Guinness and Cooke 2005 , 506 – 520.


37. Riemann 1990 , 304, 306; quoted in Pesic 2007 , 23, 24.