1. For more information about fuzzy sets and logic see Didier Dubois and Henri Prade, Fuzzy Sets and Systems: Theory and Applications, Mathematics in Science and Engineering 144 (New York: Academic Press, 1980). Broader discussion of fuzzy sets in Penderecki can be found in Danuta Mirka, "Young Penderecki and Fuzzy Sets," in Ioannis Zannos (ed.), Music and Signs: Semiotic and Cognitive Studies in Music Proceedings of the 5th International Symposium on Systematic and Comparative Musicology, Berlin, September 10-14, 1997 (Bratislava: ASCO Art and Science, 1999).

2. Unusual means of sound generation are very characteristic of Penderecki's early scores. In this connection, early critics of Penderecki accused him of a humbug intention to shock the audience. As I have demonstrated, however, the new musical accessories and techniques of articulation were necessitated by the timbre system--the other half of the compositional method used by Penderecki in the 1960s. See Danuta Mirka, The Sonoristic Structuralism of Krzysztof Penderecki (Katowice: Akademia Muzyczna, 1997).

End of Footnotes