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2. Exploring structure
“We are all more or less treading on ice, and as long as this is the case, the organizational
systems being put forward represent guidelines to prevent the composer from faltering.
And one has to face the fact that there are as many systems as there are grains of sand,
systems that can be dreamed up and set in motion as easily as clockwork. Their number is
probably infinite, but certainly only a very few of them are acceptable systems, compatible
with their means of expression, and applicable without self-contradiction to all the
dimensions of music. Of these, still fewer are so perfectly prefigured that they yield
beautiful and interesting music.” Stockhausen, Texte, i, 47.
The Gardener: Structure from Within
Stockhausen
Kontra-Punkte (1952-53) for ten instruments: ausmultiplikation
Gruppen (1955-57) for 3 orchestras: rhythm-harmony
in Gruppen ... whole envelopes of rhythmic blocks are exact lines of mountains that I saw in
Paspels in Switzerland right in front of my little window. Many of the time spectra, which are
represented by superimpositions of different rhythmic layers—of different speeds in each
layer—their envelope which describes the increase and decrease of the number of layers,
their shape, so to speak, the shape of the time field, are the curves of the mountain's
contour which I saw when I looked out the window. (Cott 1973, 141)
Klavierstück X (1961): extreme parametricization
Mantra for two ring-modulated pianos, crotales, woodblock, radio (1970): formula technique
Boulez
Le Marteau sans maître (1955): structure from poetry, and the irrational turn
By applying himself thoroughly to the text, the composer would uncover “a whole web of
relationships… including, among others, the affective relationships, but also the entire
mechanism of the poem, from its pure sound to its intelligible organization.” Boulez, quoted
in Griffiths, Modern Music and After.
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“one soon realizes that composition and organization cannot be confused without falling
into a maniacal inanity.” ibid.
“One used to find, especially in country towns, cafés where two walls with mirrors ran
parallel. And when you entered these cafés you saw yourself to infinity; but if you took one
mirror away, you saw only one reflection. I think the imagination is situated between
irrational and rational invention just as between two mirrors: if it deprives itself either of the
irrational or the rational, then it can see itself only once.” ibid.
Text by René Char (in translation)
The furious craftsmanship
The red caravan on the edge of the nail
And corpse in the basket
And plowhorses in the horseshoe
I dream the head on the point of my knife Peru.
Hangmen of solitude
The step has gone away, the walker has fallen silent
On the dial of Imitation
The Pendulum throws its instinctive load of granite.
Stately building and presentiments
I hear marching in my legs
The dead sea waves overhead
Child the wild seaside pier
Man the imitated illusion
Pure eyes in the woods
Are searching in tears for a habitable head.
Berio
Nones (1954) for orchestra
“[Serialism] never gave relevant results…. What I’m against is the use of serialism in the
abstract sense without taking into consideration the sound process…. It becomes a sort
of immobile, static world revolving around itself.” “Luciano Berio on New Music: An
Interview with David Roth,” Musical Opinion 99 (September 1976): 548.
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The Sculptor: Structure from Without
Physical Metaphors
“When new instruments will allow me to write music as I conceive it, the movement of
sound-masses, of shifting planes, will be clearly perceived in my works, taking the
place of linear counterpoint. When these sound-masses collide, the phenomena of
penetration or repulsion will seem to occur… In the moving masses you would be
conscious of their transmutations when they pass over different layers, when they
penetrate certain opacities, or are dilated in certain rarefactions.” Varèse 1967 p197.
“First I chose types with various group-characteristics and various types of internal
organization, as: grainy, friable, fibrous, slimy, sticky and compact materials. An
investigation of the relative permeability of these characters indicated which could be
mixed and which resisted mixture.” Ligeti about his Artikulations. Ligeti, The
Metamorphosis of Musical Form, Die Riehe.
Iannis Xenakis
Metasteseis (1953-54): hyperbolic paraboloids
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Pithoprakta (1955-56): Brownian motion
“Everyone has observed the sonic phenomena of a political crowd of dozens or hundreds
of thousands of people. The human river shouts a slogan in a uniform rhythm. Then another
slogan springs from the head of the demonstration; it spreads towards the tail replacing the
first. A wave of transition thus passes from the head to the tail. The clamour fills the city, and
the inhibiting force of voice and rhythm reaches a climax. It is an event of great power and
beauty in its ferocity. Then the impact between the demonstrators and the enemy occurs.
The perfect rhythm of the last slogan breaks up in a huge cluster of chaotic shouts, which
also spreads to the tail. Imagine, in addition the reports of dozens of machine guns and the
whistle of bullets adding their punctuations to this total disorder. The crowd is then rapidly
dispersed, and after sonic and visual hell follows a detonating calm, full of despair, dust
and death. The statistical laws of these events, separated from their political or moral
context... are the laws of the passage from complete order to total disorder in a continuous
or explosive manner. They are stochastic laws.”
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Evryali (1973) for piano: arborescences
Pléïades (1979) for percussion
Ligeti
Atmosphères for orchestra (1961)
Volumina (1961-62)
Lux Aeterna (1966)
Lontano (1967)
“Technically speaking I have always approached musical texture through part-writing. Both
Atmosphères and Lontano have a dense canonic structure. But you cannot actually hear
the polyphony, the canon. You hear a kind of impenetrable texture, something like a very
densely woven cobweb. I have retained melodic lines in the process of composition, they
are governed by rules as strict as Palestrina's or those of the Flemish school, but the rules
of this polyphony are worked out by me. The polyphonic structure does not come through,
you cannot hear it; it remains hidden in a microscopic, underwater world, to us inaudible.”
Ligeti, quoted in Bernard, Jonathan. “Voice Leading as a Spatial Function in the Music of
Ligeti”. Music Analysis 13, nos. 2/3 (July–October): 227.53.
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Penderecki
String Quartet no. 2 (1968)
Threnody for the Victims of Hiroshima (1960)
Xenakis
Kagel
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Open Structures
Raymond Queneau
Cent mille milliards de poèmes (1961)
Stockhausen
Klavierstück XI (1956)
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Momente for 13 instruments, 4 mixed choirs, solo soprano (1962-69): momentform
A moment is any “formal unit in a particular composition that is recognizable by a
personal and unmistakable character.”
Moment form musics “neither aim at the climax, nor at prepared (and consequently
expected) multiple climaxes, and the usual introductory, rising, transitional and fadingaway stages are not delineated in a development curve encompassing the entire
duration of the work. On the contrary, these forms are immediately intense and seek to
maintain the level of continued "main points", which are constantly equally present, right
up until they stop. In these forms a minimum or a maximum may be expected in every
moment, and no developmental direction can be predicted with certainty from the
present one; they have always already commenced, and could continue forever; in
them either everything present counts, or nothing at all; and each and every Now is not
unremittingly regarded as the mere consequence of the one which preceded it and as
the upbeat to the coming one—in which one puts one's hope—but rather as something
personal, independent and centred, capable of existing on its own. They are forms in
which an instant does not have to be just a bit of a temporal line, nor a moment just a
particle of a measured duration, but rather in which concentration on the Now—on
every Now—makes vertical slices, as it were, that cut through a horizontal temporal
conception to a timelessness I call eternity: an eternity that does not begin at the end of
time but is attainable in every moment. I am speaking of musical forms in which
apparently nothing less is being attempted than to explode (even to overthrow) the
temporal concept—or, put more accurately: the concept of duration. . . .” (Stockhausen,
Texte, i, 189-210.)
Boulez
Third Piano Sonata (1955-57)
Pli selon pli (first version, 1957-1962)
Lutoslawski
Jeux vénitiens (1960-61)
“While listening to [Cage’s Concerto for Piano and Orchestra], I suddenly realized
that… I could progress toward the whole not from the little detail but the other way
around – I should start out from the chaos and create order in it, gradually. That is when
I started to compose Jeux vénitiens” Lutoslawski, 1976, 12.
Kagel
Transición II (1958-59) for piano, percussion, and two tapes
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Prima Vista (1962-63)
Roman Haubenstock-Ramati (1919-1994)
Mobile for Shakespeare (1960)
Streichquartett (1977)
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Game Music
Xenakis: Strategie (1962)
Xenakis: Duel (1959)
Christian Wolff: For 1, 2 or 3 people
John Zorn: Cobra, Hockey, Lacrosse, Xu Feng
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