50. On Bartok's chromaticism, see Gisele Brelet's study in Histoire de la musique, vol. 2,
1036-1072.
51. In his book on Debussy, Barraque analyzes the "dialogue of the wind and the sea" in
terms offerees instead of themes: pp. 153-154. See Messiaen's statements on his own works:
sounds are no longer anything more "than vulgar means of expression intended to make durations
measurable."
52. Odile Vivier describes Varese's procedures for treating sound matter, in Varese (Paris:
Seuil, 1973): the use of pure sounds acting as a prism (p. 36); mechanisms of projection onto a
plane (pp. 45 and 50); non-octave-forming scales (p. 75); the "ionization" procedure (pp.
98ff.); the theme of sound molecules, the transformations of which are determined by forces
or energies (passim).
53. See the interview with Stockhausen on the role of synthesizers and the effectively
"cosmic" dimension of music, in Le Monde, July 21,1977: "Work with very limited materials
and integrate the universe into them through a continuous variation." Richard Pinhas has
written an excellent analysis of the possibilities of synthesizers in this regard, in relation to
pop music: "Input, Output," in Atem, no. 10 (1977).
54. The definition of fuzzy aggregates brings up all kinds of problems because one cannot
appeal to a local determination: "The set of all objects on this table" is obviously not a fuzzy
set. Mathematicians concerned with the question speak only of "fuzzy subsets" because the
reference set must always be an ordinary set. See Arnold Kaufmann, Introduction to the Theory
of Fuzzy Subsets, foreword L. A. Zadeh, trans. D. L. Swanson (New York: Academic Press,
1975), and Hourya Sinacoeur, "Logique et mathematique du flou," Critique, no. 372 (May
1978), pp. 512-525. In considering fuzziness as the characteristic of certain sets, our point of
departure was a functional, as opposed to a local, definition: sets of heterogeneous elements
that have a territorial, or rather territorializing, function. But this is a nominal definitiion that
does not take "what happened" into account. The real definition can come only at the level of
processes affecting the fuzzy set; a set is fuzzy if its elements belong to it only by virtue of specific
operations of consistency and consolidation, which themselves follow a special logic.
55. Paul Klee, On Modern Art, p. 53: "The legend of the childishness of my drawing must
have originated from those linear compositions of mine in which I tried to combine a concrete
image, say that of a man, with the pure representation of the linear element. Had I wished to
present man 'as he is,' then I should have had to use such a bewildering confusion of lines that
pure elementary representation would have been out of the question. The result would have
been vagueness beyond recognition."
56. Paul Virilio, L'insecurite du territoire (Paris: Stock, 1975), p. 49. Henry Miller develops
this theme in The Time of the Assassins. A Study ofRimbaud(Norfolk, Conn.: J. Laughlin,
1956), and in the text he wrote for Varese, "Lost! Saved!" (The Air-Conditioned Nightmare
[New York: New Directions, 1945]). It is undoubtedly Miller who has taken the modern figure
of the writer as cosmic artisan the farthest, particularly in Sexus.
57. On the relation of colors to sound, see Messiaen and Samuel, Conversations, pp.
15-17. Messiaen faults drug users for oversimplifying the relation, which they make into a
relation between a noise and a color, instead of isolating complexes of sounds-durations and
complexes of colors.
58. On the crystal, or the crystalline type, added and subtracted values, retrograde
motion, see also Messiaen's texts in Samuel, Conversations, and those of Paul Klee in his
diary, The Diaries of Paul Klee, 1898-1918, ed. and intro. Felix Klee (Berkeley: University of
California Press, 1964).
59. See Roland-Manuel's article, "L'evolution de l'harmonie en France et le renouveau de
1880" (pp. 867-879), and the article by Delage on Chabrier (pp. 831-840), in Histoire de la
musique, vol. 2. And especially, Brelet's article on Bartok: "Are not the difficulties learned
