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Music in the Late Twentieth Century


CHAPTER 1 Starting from Scratch
Richard Taruskin

The earliest actual piece of music that can be securely identified as belonging to the “Darmstadt school” was not by any of the composers recalled by Henze, nor was it even a twelve-tone piece. It was a work for piano by Messiaen called Mode de valeurs et d'intensités (roughly, “Scheme of note values and dynamics”), which he composed (or began composing) during the summer of 1949 while engaged as an instructor at the Summer Courses. Published the next year as the second in a set of four Études de rhythme, it is in fact a study in “hypostatization,” the total determination (“fixing”) of a limited assemblage of sonic elements or events. This idea had a direct precedent in Webern, who in his Symphony, his String Quartet, and his Piano Variations had experimented with the fixed assignment of particular pitches to particular registers. As his title suggests, Messiaen thrust this principle of fixed assignment into three additional domains.


ex. 1-3 Olivier Messiaen, Mode de valeurs et d'intensités, prefatory table

The material out of which Messiaen assembled the composition consisted of thirty-six different notes, each characterized by a unique combination of pitch, duration, loudness, and attack. They are all systematically catalogued in a table (Ex. 1-3) that precedes the score. The thirty-six pitches are laid out in three overlapping registral domains (or “divisions,” as Messiaen calls them) containing all twelve notes of the chromatic scale, each represented once. In the score, of which the first page is given in Ex. 1-4, each division has a staff to itself. No pitch appears in the same register in more than one division. Within each division, a given pitch is assigned a duration from another set of three overlapping “divisions.” The first consists of all the durations between a thirty-second note and a dotted quarter (= twelve thirty-seconds), laid out in thirty-second-note increments: a sort of “chromatic scale” of thirty-seconds. The second division doubles everything: a chromatic scale of sixteenths, from one to twelve (= a dotted half); and the third doubles everything again: a chromatic scale of eighths, from one to twelve (= a dotted whole note).


ex. 1-4 Olivier Messiaen, Mode de valeurs et d'intensités, mm. 1–10

Within each domain there is thus a fixed correspondence between pitch and duration, and a systematic lengthening of durations as pitches descend. The highest note in the piece is also the shortest, and the lowest the longest. In addition, each note is assigned a mode of attack from an arbitrary list of twelve (the number corresponding again with the number of elements in the chromatic scale) and a loudness from an incremental list of seven. Thus every “pitch-class” (or “note-name,” e.g. A, B♭, B, etc.) is represented in three different registers, each time with a different duration, loudness, and mode of attack. But since no combination of pitch, duration, loudness, and attack ever recurs within the scheme, every note is a completely discrete element. No special significance attaches to octave equivalency; the texture is utterly “atomized.” The only notes that recur in melodic conjunction are the ones that come under slurs (the first two in Division I; nos. 2–3, 4–5 and 6–8 in Division II; nos. 4–5 in Division III). To be fastidiously exact, then, the number of “elements” in the piece is thirty: twenty-five single notes, four two-note groups, and one three-note group.


ex. 1-5 Olivier Messiaen's scheme reduced to a single succession (after R. S.Johnson)

The music consists of a ceaseless “counterpointing” of elements drawn from the stringently limited menu just described, individual hypostatized objects in seemingly fortuitous relationships. Stockhausen called it “a mosaic of sound.” Calling it a sonic “mobile” might come even closer to its effect. Some sense of overall progression emerges from the general tendency of all three domains to descend and slow down; the thundering low C♯ at the end of Division III comes three times and seems to divide the piece into three sections, the last time (in the words of the critic Paul Griffiths) effectively “stopping the music in its tracks.”32 (Not much of a surprise, really; ending a piece with a long loud low note is not exactly unheard of.) Different registers, regardless of “division,” have characteristic attack and loudness features as well, as may be seen in Ex. 1-5, a summary devised by the pianist and Messiaen scholar Robert Sherlaw Johnson, in which the complete array of “particles” is laid out in a single succession. Finally, the middle staff, with its three slurred groups, possesses in consequence a certain amount of “motivic consistency,” so that despite the arbitrariness of its constituent elements and its atomized texture, the music never sounds entirely random.

Still, one may fairly wonder why Messiaen would have wished to court an impression of randomness; or (perhaps more to the point) why one would wish to plan such an apparently haphazard outcome in such meticulous detail. (Even when the three staves line up on a plain old diminished triad, as happens in m. 56, it's just a “happening,” and more likely to be spotted by eye than by ear; see Ex. 1-6.) In the case of Messiaen himself, answers are probably to be sought in his religious philosophy, in which the incomprehensible results of unknowable plans can symbolize the relationship of man and God.


ex. 1-6 Olivier Messiaen, Mode de valeurs et d'intensités, mm. 54–56

Arcane structures, reminiscent of medieval speculations in sound, were an old story with Messiaen. They conveyed the “charm of impossibilities” — sublime truths that we may apprehend only with our minds, not our senses. Shortly after composing the Mode de valeurs et d'intensités, Messiaen wrote an organ piece called “Soixantequatre durées” (“Sixty-four durations,” the seventh and last item in his Livre d'orgue or Organ Book); its title refers to a “chromatic” series of note values, increasing from one thirty-second all the way to a breve (or “double whole note”), which makes the divisions in Mode de valeurs seem like child's play. Is a listener expected to distinguish a duration of 57 thirty-seconds from one of 56 or 58? Or is all the elaborate rational calculation a “theological” ploy to boggle (yet somehow comfort) the mind?

But Mode de valeurs et d'intensités was special in its obsession with the number twelve; and that made it a sign of the times. As laid out in the preliminary table, the three pitch “divisions” looked like tone rows, even though in practice they were unordered rather than ordered sets. Moreover, by conceiving the durations as “chromatic scales,” and mapping them onto the pitches in a one-to-one relationship, Messiaen seemed (or could seem) to be doing something about that perceived gap between serial pitch structure and garden-variety “classical” rhythm that so bothered his pupil Boulez.


(32) Paul Griffiths, Olivier Messiaen and the Music of Time (Ithaca: Cornell University Press, 1985), p. 151.

Citation (MLA):
Richard Taruskin. "Chapter 1 Starting from Scratch." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 16 Sep. 2021. <https://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-001009.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 1 Starting from Scratch. In Oxford University Press, Music in the Late Twentieth Century. New York, USA. Retrieved 16 Sep. 2021, from https://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-001009.xml
Citation (Chicago):
Richard Taruskin. "Chapter 1 Starting from Scratch." In Music in the Late Twentieth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 16 Sep. 2021, from https://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-001009.xml