Generating New Musical Works in the Style of Milton Babbitt

Brian Bemman and David Meredith Generating New Musical Department of Architecture, Design, and Media Technology Aalborg University Works in the Style of Rendsburggade 14, 9000 Aalborg, Denmark Milton Babbitt {bb, dave}@create.aau.dk Abstract: Milton Babbitt is noted for composing twelve-tone and serial music that is both complex and highly constrained. He has written extensively on a variety of topics in music and his writings have had a profound and lasting impact on musical composition. In this article, we first review in detail his compositional process and the techniques he developed, focusing in particular on the all-partition array, time-point system, and equal-note-value strings used in his later works. Next, we describe our proposed procedure for automating his compositional process using these techniques. We conclude by using our procedure to automatically generate an entirely new musical work that we argue is in the style of Babbitt. Introduction time are strict, and his application of these techniques follows an often well-defined procedure. For Milton Babbitt (1916–2011) was a composer of this reason, we suggest that Babbitt’s compositional twelve-tone and serial music whose works and the- process is inherently algorithmic in nature and that, oretical writings had a profound impact on modern therefore, many of these techniques can be modeled musical composition. Beginning in the 1950s and by machine. This line of reasoning follows years over the course of the next two decades, Babbitt of research in the field of computational music formalized the twelve-tone system and established analysis and generation, with similar efforts having techniques such as the time-point system and the been made, for example, to harmonize chorales in all-partition array (Babbitt 1955, 1960, 1961, 1962, the style of Bach (Ebcioglu˘ 1987) and, more recently, 1973). Many of these techniques remain of interest to generate the structures found in Babbitt’s own to composition and music research today (Tanaka, music (Bemman and Meredith 2016; Tanaka, Bem- Bemman, and Meredith 2016b; Bernstein 2017; man, and Meredith 2016a,b). The primary purpose Bemman and Meredith, forthcoming). Indeed, music of this article, however, is simply to provide further theorists and computer scientists alike have writ- insight into the nature of Babbitt’s compositional ten at length on these techniques and the highly process, notably through the creation of an algorith- constrained and often complex structures in Bab- mic model. We should note that this model is not bitt’s music that result (Mead 1987, 1994; Bemman necessarily intended to be a tool for computer-aided and Meredith 2015, 2016; Tanaka, Bemman, and algorithmic composition nor an explanation for Meredith 2016a; Bernstein 2017). In recent years, how other twelve-tone composers (e.g., Webern, the sketches for many of his works have been made Schoenberg, Carter) might have composed their publicly available by the Library of Congress in music, although such uses would be welcomed. Washington, DC (http://lccn.loc.gov/2014565648). In the remainder of this article, we present Researchers are now able to examine Babbitt’s our proposed procedure for automating Babbitt’s compositional process in much greater detail than compositional process in his later works. First, we before. introduce a method for generating the pitches and In this article we describe the process Babbitt time points of a piece from its all-partition array. devised in composing his later works (from approxi- Then we show how this same method can be used mately 1980 to 2011), focusing in particular on the to generate pitch repetitions (i.e., a single pitch that notions of the all-partition array, the time-point occurs at more than one point in time), which occur system, and the equal-note-value string. The con- frequently in Babbitt’s music. Next we describe a straints under which he composed his music at this method for determining the rhythms in a piece as well as the placement of rests and ties. We conclude by using this procedure to automatically generate Computer Music Journal, 42:1, pp. 60–79, Spring 2018 doi:10.1162/COMJ a 00451 a novel musical work that we believe to be in the c 2018 Massachusetts Institute of Technology. style of Babbitt. 60 Computer Music Journal Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/comj_a_00451 by guest on 24 September 2021 Figure 1. Excerpt mosaic is a partitioning of containing three ordered the aggregate that has mosaics from the been ordered from top to all-partition array found in bottom into sets of pitch Babbitt’s None but the classes each ordered from Lonely Flute. Each ordered left to right. and 6 from the first ordered mosaic and pitch class 4 from the second ordered mosaic. An all-partition array must contain a number of ordered mosaics equal to the number of distinct ways in which twelve can be partitioned into k parts (i.e., lynes) or fewer, with each of these partitions represented by a distinct ordered mosaic. Babbitt used four-, six-, and twelve-part all-partition arrays containing 34, 58, and 77 ordered mosaics, respectively. In earlier All-Partition Array publications we provide a more detailed look at the mathematical construction of an all-partition array Both the pitch and the rhythmic content in Babbitt’s and the difficulty associated with generating one later works are organized according to a structure (cf. Bemman and Meredith 2016 and Tanaka et al. known as the all-partition array (Mead 1994; Bem- 2016a,b). man and Meredith 2016). In an all-partition array, Babbitt constructed aggregates (i.e., collections of the twelve musical pitch classes) so that each was a Time-Point System distinct set of partitioned pitch-class segments called an ordered mosaic (Bemman and Meredith 2016). Babbitt himself laid the foundations for his time- For example, 2, 0, 1, 3, 5, 4, 6, 7, 8, 9, 11, 10 is point system and outlined general principles for one ordered mosaic made up of three pitch-class applying it to composition (Babbitt 1962). With segments of length 4. We denote ordered sets using the time-point system, Babbitt sought to derive a angle brackets, ·, and unordered sets with braces, correspondence between the twelve-tone row and {·}. As is standard in musical set theory, we use num- time. By replacing the interval of a half-step in a bers to denote pitch classes of the equal-tempered twelve-tone row with a fixed period of time called a chromatic scale independent of octave register, unit, the time-point intervals (analogous to directed where C = 0, C = 1, D = 2, ...,B= 11. A second pitch-class intervals) between adjacent members ordered mosaic might contain three pitch-class become lengths of time measured in units rather segments in which two are of length 5 and one is than pitch intervals measured in semitones. In his of length 2, e.g., 6, 1, 11, 4, 2, 5, 7, 0, 9, 8, 3, 10. later works, Babbitt typically used a sixteenth note Each pitch-class segment in an ordered mosaic is as the unit (Bernstein 2017). Figure 2 shows a left- then assigned to a “voice” on the musical surface, to-right linear ordering of twelve time points from forming what is known as a lyne (Mead 1994). the opening of Babbitt’s None but the Lonely Flute Collectively, these pitch-class segments in each using a sixteenth note as the unit and one possible lyne for all ordered mosaics form a concatenation rhythmic representation (not used by Babbitt in this of twelve-tone rows that may or may not contain piece). repetitions. Figure 1 shows an excerpt from the Note, in Figure 2, how time points denote onsets all-partition array in Babbitt’s None but the Lonely in time corresponding to new rhythmic events. In Flute with six such lynes and the first three of its Figure 2b, these rhythmic events have a duration ordered mosaics. equal to the interonset intervals of each time Note, in Figure 1, that the pitch-class segments in point. Babbitt often sought less straightforward the first ordered mosaic are distributed across each rhythmic interpretations of his time points than of the six possible lynes but that in the third ordered that shown in Figure 2b, however, and in the mosaic, these pitch-class segments appear in only following sections we will see in greater detail how three lynes—1, 2, and 5. In the third ordered mosaic, his use of additional techniques gave his later works the first pitch class in each segment is a repetition their characteristically varied and often complex from the previous ordered mosaics: pitch classes 2 rhythms. Bemman and Meredith 61 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/comj_a_00451 by guest on 24 September 2021 Figure 2. A linear ordering ordering (b), in which Figure 3. Pitch-class of twelve time points set duration is equal to ordered mosaic (PcOM) against a grid of interonset interval, distinguished by register sixteenth-note units (a) meaning there are no rests (a) and time-point class and one possible rhythmic or overlapping notes. ordered mosaic (TpcOM) interpretation of this distinguished by dynamic level (b). Babbitt’s Compositional Process in Later Works In this section, we describe in detail Babbitt’s compositional process as found in his later works. Many of the techniques he used in this process have been described elsewhere (Mead 1994; Bernstein 2017), yet a thorough understanding of how exactly this process comes to form the musical surface of his works is essential in explaining how we have automated this process.

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