288 Notes to pages 29–39
- Oresme 1971, 284 – 289
- Ibid., 288 – 311, at 295 – 297.
- Ibid., 310 – 321, at 310 – 311, 316 – 317. See also Zoubov 1961, 96 – 98.
- Oresme 1971 , 312 – 313.
- Ibid., 320 – 323.
- Oresme 1968a , 480 – 481. Zoubov 1961, 102, also thinks that the verdict goes to Geometry; see also Kassler
2001, 26 – 35. - Oresme 1968a, 480 – 481.
- Apoc. 5:9, 14:3; cf. Ps. 39:4, 143:9, 149:1.
- Oresme 1968a, 480 – 483.
- Pesic in preparation-a.
- The term ars nova as a historical epoch was only introduced by Johannes Wolf in 1904, so we cannot assume
that Oresme would have responded to this term as we would; on the other hand, the very title of de Vitry ’ s treatise
would suffice to make the connection I am putting forward here. For the ars nova and de Vitry, see Hoppin 1978,
353 – 357. - Grant 1965 , 328. De Vitry had become bishop of Meaux, hence dating this work during his bishopric,
1351 – 1361; see Oresme 1971 , 328; 1968b , 122 – 123, 447, 471 – 472, 477; 1966 , 12 – 13. For the history of
Pythagoreanism in the Middle Ages, see Joost-Gaugier 2006 , 116 – 133. - De Vitry and Plantinga 1961. See also Werner 1956 , 132, who notes that “ this new, mathematically grounded
theory of musical measurement proved serviceable to the hitherto blocked development of musical notation. ” - For Oresme ’ s references to de Muris, see Oresme 1968b , 450; 1966 , 58n, 125 – 126, 299; 1971 , 78 – 79,
97 – 103, 86 – 97. - For Gersonides, see Werner 1956 , which mistakenly refers to Gersonides ’ s work as Sefer ha-Mispar ( Book
of Number ), an earlier and less sophisticated work by Rabbi Abraham ben Meir ibn Ezra (1090 – 1167). - For the rhythmic issues, see Hoppin 1978, 354 – 357, 362 – 367.
- Oresme 1971 , 212 – 215.
- Ibid. , 294 – 295.
- Ibid. , 304 – 305.
- Ibid. , 316 – 317.
- Oresme 1968b , 222 – 225, 450, which speculates that he may have learned Archimedes ’ s ideas from de Muris.
In the following century, Nicholas of Cusa argued (incorrectly but ingeniously) that the circle can be squared
( Boyer 1991 , 271 – 272). For Oresme ’ s general approach to magnitudes and intensities, see Taschow 1999; 2003,
59 – 199; and Heller-Roazen 2011, 49 – 59. - Oresme 1968a , 482 – 483.
3 Moving the Immovable - Tinctoris 1961 , 77. Regarding the fate of the spheres, see Donahue 1981.
- For the relation between theory and practice in Gaffurius, see Westman 2011 , 41 – 42.
- For its history, see M. Lundberg 2011.
- Glarean 1965 , 87; he discussed this adage with his friend Erasmus, who had included it in his Adagia.
- Aristotle, Politics 1342b9 – 11 (1984, 2129); note that the poet, Philoxenus, is one of the avant-garde practi-
tioners of the New Music. See Csapo 2004 , 233 – 234. - Glareanus 1965, 87. Zarlino lists this motet under mode 4, which “ accommodates itself marvelously to
lamentful words which contain sadness or supplicant lamentation ” ; he does not remark on the mode altering in
this motet. See Zarlino 1983 , chap. 21. Glarean ’ s attribution of this motet to Josquin is now considered dubious;
Macey (2009) argues in favor of Nicolas Champion being its composer. Glarean ’ s arguments are not affected,
however, so my text continues to follow him in referring to the composer as Josquin. Thomas (2009) surveys
the evidence that Absalon fili mi is by Pierre La Rue.