298 Notes to pages 124–135
- Newton, second letter on light and colors for the Royal Society (1675), quoted in Pesic 2005 , 192 – 193.
- For Newton ’ s “ analogy of nature, ” see Armstrong 1972 ; Newton 1984 , 1:537 – 549, especially 545, 550n10;
McLaren 1985 ; Hall 1993 , 56 – 57, 112 – 113; Sepper 1994 , 95 – 99, 205 – 270; Shapiro 1994. - See Newton 1979, Book III, 317 – 339, which ends inconclusively with Newton ’ s remark that he was “ inter-
rupted, and cannot now think of taking these things into farther Consideration, ” followed by his long series of
“ Queries, in order to a farther search to be made by others. ” - See Kepler 1997 , 138 and above. Gouk (1999 , 232 – 237) suggests that Newton ’ s choice of the Dorian mode
reflects his preference for a symmetric, palindromic sequence of ratios (namely T S T T T S T), which she
discerns in his “ ideal ” scale; see also Pesic 2006 and B ü hler 2013, 121 – 129. - For his extensive experiments following “ Grimaldo, ” see Newton 1979, Book III, 317 – 339. See also Shapiro
- For Grimaldi, Pardies, and Ango, see Darrigol 2012, 58 – 64.
- For Newton ’ s “ fits ” and his concept of “ bigness, ” see Sabra 1963 ; 1981 , 231 – 250, 273 – 342; Westfall 1967 ;
Hall 1993 , 163 – 179; Shapiro 1993, 2001 , 2002. - “ An Hypothesis hinted at for explicating all the aforesaid properties of light, ” Add. Ms. 3970, fol. 528 v.
- Ibid., fol. 521 v. Newton 1984 , 1:546 – 547n28 contains a helpful account of the development of Newton ’ s
thinking on this issue. - Newton 1979 , 200 – 201.
- Certain insects apparently have a full octave (or more) of color perception and may find what seems a
behaviorally similar identity in two wavelengths of frequency ratio 2:1 to that identity our ear perceives in
D and d. For instance, Frisch 1971, 10, notes that the spectral sensitivity of honey bees is 300 – 650 nm, which
implies the possibility of their experiencing a “ color octave ” denied to human vision (400 – 700 nm). - This is also the view of Sepper 1994 , 123 – 127, at 123. Cf. Darrigol 2012, 80 – 85, 89 – 108, which does not
comment on the problem of the color octave. - For musical analogies in Newton ’ s cosmology, see McGuire and Rattansi 1966 ; Gouk 1999 , 251 – 257; Toni-
etti 2000. - Malebranche 1997 , 689, 716 – 717.
- Voltaire 1967 , 149 – 158.
- McGuire and Rattansi 1966 ; Westfall 1980 , 510n136.
9 Euler: The Mathematics of Musical Sadness - Yushkevich, Bogolyubov, and Mikha ĭ lov 2007 , 375.
- See Tserlyuk-Askadskaya 2007. For a reproduction of Euler ’ s notebook, see Bredekamp and Velminski 2010 ,
39 – 64. - “ Dissertatio physico de sono, ” E2, III.1.183 – 196. The original text of this and other works by Euler may also
be found in Euler 1911. For convenience, I will cite them by the standard Enestr ö m number of each item, here
E2, and its place in the Opera omnia by series, volume, and pages, here III.1.183 – 296. These works (along with
helpful listing of translations and secondary literature) can be found at the online Euler Archive at http://www
.math.dartmouth.edu/~euler/. Euler ’ s very first published paper, “ Constructio linearum isochronarum in medio
quocunque resistente, ” E1, II.6.1 – 3, concerned the brachistochrone problem, finding a curve along which a
particle falls with the shortest time; see Sandifer 2007a , 3 – 5. - All my citations of E2 are from the translation by Bruce 2013.
- In his time, the flute was notably different in shape (with a U-shaped bend near the mouthpiece) than Mer-
senne ’ s straight (transverse) flute. Though he only begins to consider the effect of temperature (whose full
treatment came with Laplace and the beginnings of thermodynamics at the end of the century), Euler includes
the relative effects of varying air pressure and density, following Newton. - Ronald 1996 , 147 – 148. On Euler ’ s work in naval science, see Sandifer 2007b; 2007c , 219 – 222.
- See Busch 1970 ; Muzzulini 1994; Gertsman 2007 ; Warusfel 2009, 165 – 185; Velminski 2009b, 150 – 171. For
the context of Euler ’ s other early Petersburg works, see Calinger 1996. - Smith 1960 , 24 (preface).