* This paper is a revised version of a paper presented at the Society for Music Theory National Conference, Seattle, 2004. The presentation featured live demonstration of the musical examples, and concluded with a complete performance of Lonely Flute. For this Music Theory Online version, we are grateful to Andrew May and Daryl Burghardt for their assistance in recording and converting files to suitable formats.
1. Andrew Mead, An Introduction to the Music of Milton Babbitt (Princeton: Princeton University Press, 1994), 52. See also Joseph Dubiel, "Three Essays on Milton Babbitt," Perspectives of New Music 28/2 (1990): 216-261, 29/1 (1991): 90-122, 30/1 (1992): 82-131 for an intrepid exploration of "the chasm between twelve-tone �background' and �immediate musical foreground'" in Babbitt's music (Dubiel 1990, 218).
2. Luciano Berio, Two Interviews with Rossana Dalmonte and B�lint András Varga, tr. and ed. David Osmond-Smith (New York: Marion Boyars, 1985), 90.
3. Sebastien de Brossard, Dictionary of Music, tr. and ed. Albion Gruber of Dictionnaire de Musique (Paris 1703) (Ottawa: Institute of Mediaeval Music, 1982), s.v. "virtu."
4. EM calls these phases of learning "orientation, demystification, internalization and identification." They correspond to Edward T. Cone's "three readings" of a detective story; see Cone, "Three Ways of Reading a Detective Story--Or a Brahms Intermezzo," in Music: A View From Delft (Chicago: University of Chicago Press, 1989), 77-94.
5. See, for example, Mead, Introduction; for "maximal diversity," see pp.19-20, 33-34.
6. The array is T5 of the array of Joy of More Sextets. As is usual with Babbitt's all-partition arrays, the three hexachordally-combinatorial lyne pairs exhaust the distinct mosaics for the segmental hexachord. See Mead, Introduction, 34 for the term "hyperaggregate."
7. T6 preserves the array's hexachordal mosaics.
8. In a few cases (mm.40, 145, 151), flutter tongues entering on tied notes perform the same function.
9. We are grateful to Andrew Mead for illuminating this aspect of Babbitt's practice in a discussion during an early phase of our analysis.
10. In early time-point works such as String Quartet 3 and My Ends are My Beginnings, the notated meter, which remains relatively constant, often corresponds to the array modulus and is frequently articulated at the work's opening. In later works such as Lonely Flute and Soli e Duettini, however, meters change frequently (including alterations such as 3/4 +1/16) and evade a close correspondence to the time-point grid. See Andrew Mead "About About Time's Time: A Survey of Milton Babbitt's Recent Rhythmic Practice," Perspectives of New Music 25/1 (1987): 195, 227; and Mead, Introduction, 257.
11. Unlike Babbitt's early tp practice, subdivisions in Lonely Flute do fall on the16th-note tp grid; sometimes even entire equal-duration strings consist of 16th or 8th notes. Furthermore, equal-duration strings often begin or end within held notes or rests, thus obscuring their boundaries. Time points themselves occasionally fall on or within rests (e.g., m.39, m.42).
12. Joel Lester, "Notated and Heard Meter," Perspectives of New Music 24/2 (1986): 116-128.
13. Commercial recordings include those by Dorothy Stone (for whom the work was written), New World Records 80456-2 (1994); and Rachel Rudich, Koch International Classics 7335.
14. The earlier LH's refer to the motive more generally, as a large downwards leap to a repeated pitch.
15. The soliloquy is bounded at its beginning by a rest and repetition of pc Eb across registers, and at its end by a mf F-Bb "cadence."
16. and only one other aggregate restricted to two contiguous dynamics (mp / mf ). That other tp aggregate also associates with a single-register pc aggregate.
17. Although there are other aggregates confined to a single register, they occur in the middle and low registers, and involve two lynes rather than one.
18. The wide variation in pacing results from differences in basic durational units (dotted 16th versus dotted 32nd), and in frequency of articulation of these units: the climactic passage articulates its equal subdivisions only sporadically, while the later passage attacks almost every one of its equal subdivisions.
19. Repeated tps and equal-duration strings do not necessarily expand inter-tp durations: they can simply fit in between tps. Where they do lengthen inter-tp durations, they do so by some multiple of twelve 16ths.
20. The pacing of pc aggregates is largely determined by the surface rhythm articulated by tps and equal-duration strings, although pc aggregates can also expand their length by repeating pcs or inserting rests.
21. Example 9a adjusts the = 90 section so that it is proportional in absolute time to the remainder of the piece.
22. Example 9a elucidates these ratios. At (a) the opening pc and tp aggregates have similar durations (very slow for pc aggregates, and relatively fast for tp aggregates). At (b) (the = 90 section), both pc and tp aggregates unfold relatively quickly. This section (pc aggregates 15-21) is the shortest block in the pc array; coincident tp aggregate 8 is the second shortest aggregate in its array. At (c), the work's "climax," both series slow: the work's longest pc aggregate (39) occurs against a relatively long tp aggregate (15). Near the end of the work (d), the slowest tp aggregate occurs against the fastest pc aggregates. (Tp aggregate 19 accompanies pc aggregate 51, the second-fastest pc aggregate, and immediately precedes pc aggregate 56, the fastest pc aggregate (the "riff")). The closing pc and tp aggregates at (e) again exhibit similar durations (the work's fastest tp aggregate against a pc aggregate undistinguished in duration).
23. Edward T. Cone, Musical Form and Musical Performance (New York: Norton, 1968), 57-87, especially 66, 72, 79.
24. The resemblance extends to other features such as counterpoint, basic homogeneity, and tight structure.
End of footnotes