Figures
4.1Part of Schoenberg’s set tables for the Suite op. 25, with a pitch-class map
5.1Berg’s illustration of the row set in the Lyric Suite, borrowed from F. H. Klein (Berg 2014: 203)
5.2Berg’s illustration of the all-notes and all-intervals chord
5.3Berg’s illustration of axis of rotation generating the C major and G♭ chords and scales
5.4Pitch reduction of Berg’s Violin Concerto, Part ii, bb. 125–37; after Österreichische Nationalbibliothek Musiksammlung F21 Berg 27, fols. 20 v–21 r
6.1Webern, string trio fragment, M. 273, bb. 1–5 and 2{a}, accompanied by some analytical annotations, based on a transcription of the manuscripts and sketches as provided in Wörner (2003: 75 and 88); the sources are archived at the Paul Sacher Foundation, Basel
6.2a, b, and cKlumpenhouwer network interpretation of Webern’s string trio fragment M. 273, bb. 1–2 and 2{a}, as defined by Lewin (1990) and Klumpenhouwer (1991)
6.3a, b, c, and dWebern, ‘Dein Leib geht jetzt der Erde zu’, M. 276: transcription of the sketch of the first melodic idea and twelve-tone row, ‘Sketchbook i’, p. 11, archived at the Morgan Library & Museum, New York, accompanied by some annotations highlighting the constitution of the interval vector space as illustrated in Table 6.1
6.4Reconstruction (modified transcription) of Webern’s fragment ‘Dein Leib geht jetzt der Erde zu’, M. 276, ‘Sketchbook i’, p. 11, archived at The Morgan Library & Museum, New York
6.5 a and bWebern, Symphony, op. 21/ii, final variation (reduction), accompanied by some analytical annotations
7.1Trichordal array composed into fifteen subsets of four elements
7.2Trichordal disposition in the last section of Composition for Four Instruments
8.1Pitch-class multiplication as described by Boulez. e*c (ec) results from realising each one of the ordered pitch-class intervals that occur above the bass in e (the multiplicand) over each pitch-class of c (the multiplier)
8.2Annotated reproduction of pre-compositional table for ‘Séquence’, from Third Piano Sonata. Paul Sacher Foundation, Pierre Boulez Collection (Mappe H, Dossier 2 f,1)
8.3a and bTransformation graph modelling the partitioned row and other levels of structure in ‘Séquence’, from Third Piano Sonata; partitioned row for ‘Séquence’
8.5The consequence of transposing a chord by the retrograde of embedded pitch intervals (in registral space) is a common tone in pitch space
10.1a and bComposizione per orchestra [No. 1] (1951). Sketch of the precompositional material for bb. 17–25, Archivio Luigi Nono (facsimile)
10.2a and bPolifonica–Monodia–Ritmica (1951). Generation of ‘degrading’ intervallic material of the opening four-part canon of Polifonica (bb. 1–40)
10.3Polifonica–Monodia–Ritmica (1951). Four-part canon (bb. 1–40) built by reading each of the four derivations right to left, bottom up, beginning with sparse sounds and gradually filling the space (score, Ars Viva, excerpts: bb. 1–28)
10.4Polifonica–Monodia–Ritmica (1951). Serial permutations of the Afro-Brazilian rhythm (‘Jemanjá’) employed in the movement Polifonica (sketch, Archivio Luigi Nono; facsimile)
10.5Typescript of Luigi Nono with text selection and sketches for Cori di Didone (Archivio Luigi Nono)
10.6Il canto sospeso, no. 2: schematic rendering of the first three rotations of the parametric series
10.7Il canto sospeso, no. 2: the final outcome of Nono’s compositional device as represented in the score (Ars Viva AV 50)
10.8Multi-parametric module prepared for Sarà dolce tacere (used in the second section, bb. 26–67)
10.9Representation of the various group types obtained from the transformation of an original group
11.3In memoriam Dylan Thomas, diplomatic transcription of sketch page
11.5Threni condensed orchestral score, bb. 5–18. © 1958 by Boosey & Co. Ltd. All Rights Reserved. Reprinted by Permission.
11.6Movements, original (prime) row, split into hexachords α and β
11.7Movements, diplomatic transcription of sketch page, annotated with rotation of hexachord 6–7
11.8Elegy for J.F.K., diplomatic transcription of sketch page
12.1a and bO. Messiaen, ‘Île de feu 2’ (scale subjected to permutation) and ‘Île de feu 2’, bb. 8–27. © Durand S.A.
12.2Michel Fano, Étude for 15 instruments, bb. 1–10 (sounds as written)
12.3Bo Nilsson, Zwanzig Gruppen, excerpt from the piccolo part
17.1a and bLuo Zhongrong’s tone row and Picking Lotus Flowers, bb. 1–8
17.2a, b, and cGagaku melody, tone row, and Yoristsune Matsudaira, ‘Variations’, bb. 1–3
18.1Anton Webern, draft of first variation, third movement of Piano Variations op. 27, bb. 12–23
18.2Anton Webern, draft of fourth variation, third movement of Piano Variations op. 27, bb. 56–66
20.1Milton Babbitt sketch, perhaps for Composition for Synthesizer (1961) or Ensembles for Synthesizer (1964), showing how music notation was translated into the five-channel parameters of the RCA Mark II. Columbia-Princeton Electronic Music Center Records, 1958–2014. Rare Book & Manuscript Library, Columbia University Libraries. Temporary inventory box CPEMC-00264
20.2Yellow Magic Orchestra, ‘Technopolis’, sectional formal plan. Dotted line marks temporal halfway point. X = groove, A = Japanese melody, B = flute melody, C = trumpet canon
20.3Programming the MC-8 using numeric translations of pitch and duration at specific timepoints (for example, measures and beats or ‘steps’). Owner’s manual, p. 24
