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"Absolute Purity Projected into Sound": Goeyvaerts, Heidegger
and Early Serialism Author(s): Jan Christiaens Source: Perspectives
of New Music, Vol. 41, No. 1 (Winter, 2003), pp. 168-178Published
by: Perspectives of New MusicStable URL:
http://www.jstor.org/stable/25164510Accessed: 05-03-2015 11:20
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"Absolute Purity Projected Into Sound": Goeyvaerts,
Heidegger and Early Serialism
Jan Christiaens
Research Fellow of the Fund for Scientific Research? Flanders
(Belgium)
1. Introduction
At
the Darmstadt summer courses of 1951, Karel Goeyvaerts and
Karlheinz Stockhausen played the second part of Goeyvaerts's
Nr. I, the sonata for two pianos. Immediately after the
performance, Adorno, who had taken the place of Schoenberg as the
leader of the
composition seminar, discussed the disproportion between the
scoring and the economical use of the musical material: "Why did
you compose this for two pianos?" Goeyvaerts's legitimation of his
choice made clear that a composition seminar anno 1951 could not
abstain from aesthetic and philosophical issues. Confronted with
Goeyvaerts's and
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Absolute Purity Projected into Sound 169
Stockhausen's analysis of the sonata, some participants of the
seminar
pointed out the strong similarity between Goeyvaerts's aesthetic
views and the philosophy of Being of Martin Heidegger. At that
time, Goeyvaerts apparently wasn't familiar with Heidegger's
philosophy in
general, let alone his ontological aesthetics.1 In the
correspondence between Goeyvaerts and Stockhausen, which started
after the summer courses and is an important source of knowledge
concerning the aes thetic and technical aspects of early serialism,
the name of Martin
Heidegger is mentioned several times. In a letter of August
10th, 1951,2 Stockhausen makes mention of Heidegger's Holzwege, a
volume of essays published in 1950, which contains, among others,
the lecture "Der
Ursprung des Kunstwerkes" ("The Origin of the Work of Art").3
Although this lecture, originally given in 1936, was widely
known
among philosophers and artists, it is not clear whether
Goeyvaerts effec
tively read it. On the one hand, Christoph von Blumr?der states
that Herman Sabbe's mention of "an intensive occupation of both
composers [Stockhausen and Goeyvaerts] with Heidegger" must be
strongly quali fied.4 On the other hand, it seems to me that it is
a risky step to conclude, as does Eduardo Marx in his book
Heidegger und der Ort der Musik, that there exists a "principal
incompatibility" between Heidegger's aesthetics and the new music,
and that all parallels are due to a "superficial recep tion" of
Heidegger's philosophy.5 At the risk of being myself a superficial
reader of Heidegger, I will try to shed some light on this aspect
by inves
tigating whether and how certain key concepts of Heidegger's
aesthetics can be philosophically corroborating for Goeyvaerts's
aesthetic views.
In his preparations for the course on music history he was
teaching from September 1950 onwards, Goeyvaerts wrote down some
notes con
taining his aesthetic views on music of that time.6 Before
submitting these to a Heideggerian interpretation, I must for the
sake of clarity point to the following: Goeyvaerts's aesthetics are
delivered to us not in the form of an elaborated theory, but as a
relatively small collection of stray notes which aren't supported
by a strong philosophical argument. Never theless these notes have
to be taken seriously for their historical value as
much as for their contents for the following reasons. The notes
were
probably written down from September or October 1950 onwards,
i.e., just after Goeyvaerts had completed his three years of study
at the Paris Conservatoire with Messiaen and Milhaud. It is to be
expected that the ideas Goeyvaerts developed in Paris under the
influence of Milhaud's and
especially Messiaen's teachings and in the exchange of ideas
with, among others, Pierre Boulez and Jean Barraqu? can be found in
these notes in their purest form. Above all, the notes are of
importance as far as they reveal the deeper-lying aesthetic motives
for the development of total
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170 Perspectives of New Music
serialism. In this respect, their fragmentary character doesn't
detract from their value as a key to the deeper sense of
Goeyvaerts's serial procedures. On the contrary, in their reduction
to the essential, these notes form the best imaginable introduction
to Goeyvaerts's serial works.7
2. Heidegger/Goeyvaerts: Philosophical Aspects of Early
Serialism
The core of Goeyvaerts's aesthetics is formed by the thesis that
music is the objectification in sound matter of a spiritual or
mental issue. How
ever, the notes do not make clear in a univocal way what is
meant by "spiritual" or "mental issue." This can be interpreted as
the spiritual and
mental background of a composition, which bears the traces of
the per sonality of the composer as well as of the socio-cultural
context of the
composition?an aspect Goeyvaerts calls the "spirit of the age."
Accord
ing to Goeyvaerts, the artist can claim merit to himself for
penetrating this spirit of the age more deeply than the rest of
humanity, and for
materialising his insights into a work of art. Elsewhere in his
notes, how
ever, Goeyvaerts is much more explicit concerning the meaning of
the
concept "mental issue." In a note of October 23rd, 1952 he
writes that it is the task of music "to present 'Being' in time and
in sound matter." This view is on a par with another note, in which
Goeyvaerts makes a hierarchical distinction between three
fundamental levels of a composi tion. At the top of this scheme
Goeyvaerts places: "absolute 'Being': immobile." At the second
level is the general structure of the composi tion, and at the
lowest level he places the concrete composition as it exists in
time and space. In this sense, only the upper level, absolute
Being, has absolute existence for Goeyvaerts?the composition is
seen as a phenomenological appearance in time and space of this
absolute
Being.8 This distinction between various levels, and the view of
the work of art
as a phenomenological appearance of Being, is strongly related
to
Heidegger's aesthetics. In his lecture "Der Ursprung des
Kunstwerkes," the work of art is considered as the place where "die
Wahrheit des Seienden [sich] ins Werk setzt" (UdK 30).9 According
to Heidegger, the content of the work of art (he uses examples from
painting) is high lighted in its ontological quality by the simple
fact that in the work of art this content is brought to
steadfastness, to "St?ndigkeit": "... was im
Werk am Werk ist: die Er?ffnung des Seienden in seinem Sein: das
Geschehnis der Wahrheit." (UdK 33) In that way the work of art is a
dis tinctive way in which the truth, in the Heideggerian sense of
"Unverbor
genheit des Seins"?"unconcealment" of Being?becomes
operative.
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Absolute Purity Projected into Sound 171
Goeyvaerts's aesthetics are a radicalisation of this aspect
insofar as not the content of the work of art (in this case sound
matter) in its ontological quality but this ontological quality
itself, that is absolute Being itself, is
proclaimed as the proper "content" of the work of art. This
process of "unconcealment" of Being in the work of art is described
by Heidegger as the "struggle" (Streit) between two fundamental
aspects of each work of art: the struggle between Welt (World) and
Erde (Earth). Heidegger writes about the first aspect, the
Welt-dimension: "Indem eine Welt sich
?ffnet, bekommen alle Dinge ihre Weile und Eile, ihre Ferne und
N?he, ihre Weite und Enge." (UdK 41) The Welt-concept, which in
Sein und
Zeit designates the spiritual design of one's living climate and
living space, points in this context to the spiritual dimension of
the work of art, i.e., the mental or spiritual openness created by
the work of art in which the process of "unconcealment" of Being
can take place.10 This open space ("das Offene der Welt") has in a
certain sense to be occupied by the work of art in its
Erde-dimension, its material dimension. The Erde,
which Heidegger also calls Werkstoff or the material out of
which the work of art is made, is described as "das wohin das Werk
sich zur?ckstellt und was es in diesem Sich-Zur?ckstellen
hervorkommen l??t" (UdK 43). Heidegger takes a strong position by
localizing the ontological quality of the work of art not in its
spiritual dimension, but in the unique relation between the
spiritual and the material dimension. This position is not, as it
might seem at first sight, a reassertion of the old mind-matter
dualism.
According to Heidegger, the work of art is not mute matter which
only comes to speak when bestowed upon a meaning or a sense by
human kind. It is on the contrary the twofold activity immanently
at work in the work of art which generates meaning: as Welt it
opens a spiritual space in which the material, the Erde, comes to
its true being and meaning. As Welt the work of art wants to break
out of its material limits; as Erde, it holds its spiritual
dimension contained within itself. In this very relation the
ontological quality of the work of art is brought to light. As
Heidegger writes: "Aufstellend eine Welt und herstellend die
Erde ist das Werk die Bestreitung jenes Streites, in dem die
Unverborgenheit des Seienden im Ganzen, die Wahrheit, erstritten
wird." (UdK 54)
This bipolar aesthetic model offers an apt philosophical
framework to
grasp the full bearing of Goeyvaerts's stringent aesthetical
principles.11 As it appears from Goeyvaerts's notes as well as the
correspondence with Stockhausen and others, early serialism was as
much concerned with spir itual and philosophical as with technical
issues. In a letter to his cousin
Mia Greeve, Goeyvaerts describes how at Darmstadt 1951 all his
fellow
composers wanted to know the technical details of the new method
he had applied in his Nr. 1. Goeyvaerts wrote: "I don't tell them
everything
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172 Perspectives of New Music
about it, because the application of my method by composers who
do not possess the spiritual background which gave rise to it,
would lead to an academism."12
In Goeyvaerts's aesthetics, the Heideggerian open space (das
Offene der Welt) coincides with absolute Being. It goes without
saying that the
metaphysical task Goeyvaerts sets to his music makes high
demands on the musical material and its shaping. It has become
clear that music can
only succeed in fulfilling this task if the shaping of sound
matter is per fectly attuned to the spiritual dimension, i.e., to
absolute Being, or, to use Heidegger's words, if the Erde-dimcnsion
and the W?/?-dimension cover each other seamlessly. Consequently,
Goeyvaerts's shaping of his
musical material was to a large extent dictated by the
requirements of a
perfect congruence between the material and the spiritual
dimension.13 There are two main properties of absolute Being by
which Goeyvaerts wanted his sound matter to be determined:
(structural) purity and immo
bility. From 1950 onwards, structural purity was one of the main
solici tudes of Goeyvaerts, as it appears repeatedly from the
correspondence
with Stockhausen.14 This purity became most evident from
Goeyvaerts's striving for an absolute control of all properties of
the sounds he used.15 It is however especially by the application
of the second property of abso lute Being, immobility, that
Goeyvaerts's serial works reveal themselves as the most strict and
uncompromising form of serialism. In this aspect in
particular, Goeyvaerts succeeded in shaping his sound material
perfectly according to the demands of his spiritual "program"
(forgive the word). Yet, the problem this aspect poses to the
composer is not to be disre
garded: how to shape the immobility of Being in a artform which
is pre eminently spatio-temporal? Goeyvaerts tackled this problem
by banishing the traditional concept of dynamic development out of
his music, down to the smallest details. His serial technique aims
at neutralising the tem
poral dimension as completely as possible and, by so doing,
sublimating it in a static situation of absolute equilibrium. As a
result of this rigid compositorial ethic, Goeyvaerts arrived at the
cross-structure as the ideal incarnation of absolute balance, as
convincingly shown by the analyses of
Herman Sabbe and Mark Delaere.16 The causal relation which
Goeyvaerts installs between the structural
purity and the ontological qualities of a composition can also
be found in
Heidegger's lecture. Although Heidegger states that every work
of art is in a certain sense a revelation of Being, he still
recognizes that the struc tural purity of artworks, their
simplicity, their limitation to the essential is the hallmark of
the truth (here to be understood as "unconcealment" of
Being). He writes: "Je einfacher und wesentlicher das Schuhzeug
[Heidegger refers to the painting A Peasant's Shoes of Van Gogh],
urn so
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Absolute Purity Projected into Sound 173
unmittelbarer und einnehmender wird mit ihnen alles Seiende
seiender.
Dergestalt ist das sichverbergende Sein gelichtet." (UdK 55) In
this con
text, the traditional aesthetic category of beauty is given a
new definition.
According to Heidegger, a work of art can only truly be called
beautiful when the treatment of its matter (the material dimension)
fits the uncon cealment of Being as seamlessly as possible:
"Sch?nheit ist eine Weise, wie Wahrheit als Unverborgenheit west."
(UdK 55)
Taking into account that this unconcealment of Being requires
such a
precarious handling and shaping of the musical material, and
that
Heidegger describes the relation between the material and the
spiritual dimension, not without reason, as a "struggle," why ever
do Heidegger and Goeyvaerts consider the work of art as a
privileged locus for this pro cess of truth, and not, as in Hegel's
philosophy, as an imperfect and
(hence) temporary phase in the development of absolute spirit?
In their answers to this question, Heidegger and Goeyvaerts seem to
attach
importance to similar aspects of the work of art. According to
Heidegger, the spiritual openness of the work of art can only exist
by the grace of its
material, which so to speak keeps this openness open,
materialises it, and
by so doing lends steadfastness to it. It belongs to the essence
of Being to install itself in a particular and historically
determined work of art?
Heidegger calls this der Zug zum Werk. We can find a very
similar view in
Goeyvaerts's aesthetics. Although he supports the primacy of the
spiritual dimension, he still states that it is of primordial
importance that these mental or spiritual issues become
materialised in a concrete sound struc ture: "We speak of music
only when the spiritual issues step out of the individual and
become a sounding reality."17 Yet this strain on objectifica tion
implies that the work of art, that a composition, always bears the
traces of its era. Heidegger uses the term "Gestalt" to indicate
the way in
which truth becomes tangible in a specific material and
historical constel lation. In Heidegger's aesthetics this aspect
has no further implications,
whereas in Goeyvaerts's notes it functions as a criterion for a
judgment of value. The composer not only has to penetrate the
spirit of the age, he also has to translate his insights in a
musical language which is in keeping with its inherent historical
evolution (cf. Adorno's concept of "musical
material").18
3. Conclusion
The starting point of this article was an interesting
disagreement in the
secondary literature about the putative (in)compatibility
between
Heidegger's aesthetics in Der Ursprung des Kunstwerkes and
Goeyvaerts's
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174 Perspectives of New Music
serial music or new music in general. Let me review the points
in which
Goeyvaerts and Heidegger take up strikingly similar attitudes
towards the work of art and music. First, it is obvious that both
views recognize the
primacy of the spiritual, even ontological level, which, it is
true, they con ceive of as intricably bound to the material
dimension of art. But in
Heidegger's view it is the ontological quality of the particular
work of art which is aimed at (e.g., A Peasant's Shoes of Van
Gogh), whereas in
Goeyvaerts's notes the focus is directed immediately and
directly to abso lute Being itself. A second point concerns the
relation between the spiri tual and the material dimension in art.
I think Heidegger's concept of
"struggle" between Welt and Erde forms an apt framework within
which to interpret the implications of Goeyvaerts's aesthetics for
the material dimension of his music, the more so as it transcends
any interpretation in terms of a mind-matter dualism.
But there are important differences too. Firstly, the utterances
about the historical component of the work of art are a mere
statement in
Heidegger's theory, which they are not in Goeyvaerts's notes.
Secondly, Goeyvaerts tries to capture absolute Being in sound
structures which are immobile and atemporal; for Heidegger, on the
contrary, temporality is a fundamental feature of absolute Being,
as he made clear in Sein und Zeit.
Finally, I want to point out a remarkable similarity as far as
the position of Heidegger and Goeyvaerts in a broader aesthetic
context is concerned. In his lecture Heidegger denounces any
approach to the work of art as a
mere thing or object (Vorhandenes/Dingliches), because according
to
Heidegger this is an unjustified attack on the real essence of
art. Instead, he points to the unique position of art as a
privileged way in which truth
(unconcealment of Being) becomes historical and tangible.
Something similar can be said about Goeyvaerts's position within
the evolution of
musical aesthetics. Generally speaking, musical aesthetics in
the first half of the twentieth century was dominated by
positivistic tendencies, which
approached music as a factual, analysable object, as etwas
Vorhandenes. Formalism may have been one of the most influential of
these tendencies, but other approaches such as biologistic or
energetic theories also cut the romantic thread with the absolute.
In his serial works Goeyvaerts took up this thread again by
coupling his search for an absolute structural purity
with an absolute spiritual purity, with absolute Being, which is
the ulti mate foundation of what Herman Sabbe has called
"Goeyvaerts's abso lutism of purity." It is a remarkable
peculiarity of music history to see how Goeyvaerts's ideology of
purity, which is implicitly a critique of the romantic
expressionistic heritage, reverts to a pre-eminently romantic
paradigm, namely the view of music as a privileged revelation of
the Absolute. The enemy is fought with its own weapons.
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Absolute Purity Projected into Sound 175
It has become clear that?even if there was an intensive
occupation of
Goeyvaerts with Heidegger's philosophy?the similarity
between
Heidegger's and Goeyvaerts's aesthetic views is limited to some
general aesthetic attitudes and categories, and that the
differences are not to be overlooked. Since Heidegger's lecture
offers no specific theory of musical
structures, but only impulses to a general aesthetic reflection,
I've tried not to let it say more than it says. This means that the
vagueness of the indicated similarities is a conscious option on my
part.
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176 Perspectives of New Music
Notes
1. "War es Zufall, da? pl?tzlich der Schatten Heideggers
auftauchte? Der junge Belgier [Goeyvaerts] wu?te sicher nichts
von
Fundamental-Ontologie und vom Begriff der Wahrheit als
'Offen
heit,' vom 'Sein' das 'redet.' Einige der deutschen Teilnehmer
schienen den Zusammenhang zu ahnen." W. Friedl?nder, "Musikalische
Alchimie," Frankfurter Hefte 7, no. 4 (1952): 263.
2. Cf. H. Sabbe, "Karlheinz Stockhausen: . . . wie die Zeit
verging . . .",
Musik-Konzepte 19 ( M?nchen: Edition Text + Kritik, 1981), 82.
The complete letters of Stockhausen to Goeyvaerts are being pre
served in the New Music Research Center Karel Goeyvaerts of the
Katholieke Universiteit Leuven (Belgium) (University Archives,
Artistic Estate of Karel Goeyvaerts, II, no. 5).
3. Martin Heidegger, Holzwege, (Frankfurt am Main: V.
Klostermann, 1950). The lecture "Der Ursprung des Kunstwerkes" is
also edited
separately: Martin Heidegger, Der Ursprung des Kunstwerkes
(Stuttgart: Philipp Reclam, 1960) (henceforth UdK). In 2002
Cambridge University Press published the first English
translation to
bring together the texts originally published under the title
Holzwege: Martin Heidegger, Off the Beaten Track, trans, by J.
Young and K.
Haynes (Cambridge: Cambridge University Press, 2002).
4. Sabbe, "Karlheinz Stockhausen," 70, n. 39; C. Von Blumr?der,
Die
Grundlegung der Musik Karlheinz Stockhausens, (Stuttgart:
Franz
Steiner, 1993), 23: "Wenn Stockhausen in diesen Zusammenhang
Hesses Glasperlenspiel nun unter die 'Schlu?steine' rechnet, so
bedeutet das keine Abwertung, ebensowenig wie die Erw?hnung der
Holzwege Martin Heideggers als Dokument des Neubeginns ?berbe
wertet werden darf. . . . Stockhausens daraufhin gefa?ter Vorsatz
einer gr?ndlichen Lekt?re der Schriften Heideggers blieb allerdings
unausgef?hrt, und in den folgenden Briefen an Goeyvaerts ist
von
Heidegger nicht mehr die Rede."
5. Eduardo Marx, Heidegger und der Ort der Musik (Epistemata:
Reihe
Philosophie, Bd. 237) (W?rzburg: K?nigshausen & Neumann,
1998), 13.
6. University Archives of the Katholieke Universiteit Leuven
(Belgium), Artistic Estate of Karel Goeyvaerts, I, no. 4.
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Absolute Purity Projected into Sound 177
7. For a thorough introduction to Goeyvaerts's oeuvre (including
analyses, an excerpt of his autobiography, and a complete list
of
works), see Mark Delaere, "The Artistic Legacy of Karel
Goeyvaerts: A Collection of Essays," thematic issue of the Revue
Belge de Musicol
ogie 48(1994). 8. The same train of thought can be seen in a
letter of Goeyvaerts to
Stockhausen (dated September 9, 1953): "Als Prinzip [of
electronic
music] scheint mir aber nur das g?ltig zu sein, was mit der
Bewe
gungslosigkeit des Seins ?bereinstimmt. . . . Das Prinzip ist
bewe
gungslos wie der absolute Geist." (Artistic Estate of Karel
Goeyvaerts II, no. 5); see also H. Sabbe, "Das Musikdenken von
Karel
Goeyvaerts in Bezug auf das Schaffen von Karlheinz Stockhausen:
Ein Beitrag zur Geschichte der fr?hseriellen und elektronischen
Musik 1950-1956" in Interface 2, no. 1 (August 1973): 104.
9. It is a remarkable fact that Heidegger does not make any
distinction
(as do Kant and Hegel in their idealistic aesthetics) between
the dif ferent artforms as far as their character as revelation of
"Truth" is concerned. This (positive) indifference of the
truth-process towards the material dimension of the artwork entails
that music is in the same measure as the other artforms capable of
revealing the truth.
10. Cf. Gabriel Liiceanu, "Zu Heideggers 'Welt'-Begriff in
'Der
Ursprung des Kunstwerkes,'" in Walter Biemel and Friedrich
Wilhelm von Herrmann, eds. Kunst und Technik: Ged?chtnisschrift zum
100. Geburtstag von Martin Heidegger (Frankfurt am Main,: V.
Klostermann, 1989), 205-15.
11. Hartmut Flechsig has already pointed to the value of this
aspect of
Heidegger's aesthetics for a deeper understanding of musical
struc tures. Cf. Hartmut Flechsig, "Anst??e Heideggers zum
Selbstver st?ndnis in der Musikwissenschaft," Die Musikforschung 30
(1977): 29.
12. Artistic Estate of Karel Goeyvaerts, II, no. 5
13. As an example of this, Herman Sabbe mentions Goeyvaerts's
remark able attitude towards electronic music. See Sabbe,
"Karlheinz
Stockhausen," 58: "F?r Goeyvaerts gilt das Primat des Gedachten,
die Volkommenheit der Struktur, die in die Welt zu stellen ist;
die
Realisierung aber kann warten, bis die M?glichkeiten der Appara
turen dieser gerecht geworden sind."
14. Cf. Stockhausen's letter of January 25, 1954 to Goeyvaerts
(Artistic Estate of Karel Goeyvaerts, II, no. 5); cf. also Sabbe,
"Karlheinz
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178 Perspectives of New Music
Stockhausen," 58, where the author uses the following epitheta
to describe Goeyvaerts's serial music: Reinheits-Absolutismus,
the
hypostasis of a tranzendente Wahrheit, music as pures Raum
Zeitgeflecht.
15. For an account of the influence of Goeyvaerts's teacher
Messiaen on the former's development of serialism, see Mark
Delaere, "Olivier
Messiaen's Analysis Seminar and the Development of Post-War
Serial
Music," Music Analysis 21, no. 1 (March 2002): 35-51.
16. Sabbe, "Karlheinz Stockhausen," 7-16; idem, Het muzikale
serial isme als techniek en denkmethode (Doctoral dissertation,
Ghent
University, 1977), 43-87; M. Delaere, "Auf der Suche nach
serieller
Stimmigkeit: Goeyvaerts Weg zur Komposition Nr. 2 (1951)," in
Orm Finnendahl, ed., Die Anf?nge der seriellen Musik (Kontexte:
Beitr?ge zur zeitgen?ssischen Musik 1) (Hofheim: Wolke, 1999), 13
36.
17. Text to be found in Goeyvaerts's notebooks, Artistic Estate
of Karel
Goeyvaerts, I, no. 4.
18. Theodor W. Adorno, Philosophie der neuen Musik (Frankfurt:
Suhrkamp, 1976), 38-41 ("Tendenz des Materials"). However, as far
as the concrete filling in of the notion "musical material" is
con
cerned, Goeyvaerts and Adorno had totally different opinions,
as
appears from the latter's harsh critique of serial music in "Vom
Altern der neuen Musik" (1954). Later on, Adorno adopted a more
moderate critical approach, as for instance in "Vers une musique
informelle" (1961).
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Article Contentsp. [168]p. 169p. 170p. 171p. 172p. 173p. 174p.
175p. 176p. 177p. 178
Issue Table of ContentsPerspectives of New Music, Vol. 41, No. 1
(Winter, 2003) pp. 1-248Front MatterIn Memoriam Iannis Xenakis
(Part Three)Xenakis:... Tireless Renewal at Every Instant, at Every
Death... [pp. 4-64]Toward an Interpretation of Xenakis's "Nomos
alpha" [pp. 66-118]Xenakis in Miniature: Style and Structure in "
r. (Hommage Ravel)" for Piano (1987) [pp. 120-153]The Writings of
Iannis Xenakis (Starting with "Formalized Music") [pp. 154-166]
"Absolute Purity Projected into Sound": Goeyvaerts, Heidegger
and Early Serialism [pp. 168-178]Field Notes: A Study of
Fixed-Pitch Formations [pp. 180-239]Editorial Notes [pp.
240-242]Correspondence [pp. 244-246]Back Matter