The Structure of Scientific Revolutions - Means
The Structure of Scientific Revolutions - Means
The Structure of Scientific Revolutions - Means
.
and mathematical conceptions of space. A particular importance is attributed to the
difference between the human experience of space (e.g. a natural space-consciousness,
action space, lived space), and various theoretical constructs of space (e.g. absolute
space, vector space, space as a set), as having vital consequences for the discourse on
space in music. Finally, in reference to "spatialization," the dissertation presents a
thesis that the commonly accepted opposition of "space and time" is fallacious in
music if the sonorous (rather than notational) dimension is taken into account; musical
sound material is essentially spatio-temporal. This thesis, grounded in
phenomenological conceptions of space (Merleau-Ponty) and art (Ingarden), provides a
foundation for the study of selected, distinct compositional approaches to
"spatialization" in the analytical portion of the dissertation (Chapters V-VIII).
The conceptual aspects of this dissertation situate it in the domain of the
history of ideas, that is, ideology, according to one of the word's senses. 7 "Space" is
one of the central notions of modem music; in this paradigmatic function it resembles
the idea of "absolute music"--the paradigm of the 19th century according ta Carl
Dahlhaus (1978/1989). "Paradigm"--a term borrowed by Dahlhaus from Thomas
Kuhn's The Structure of Scientific Revolutions--means, for Kuhn, "universally
recognized scientific achievements that for a time provide model problems and
solutions to a community of practitioners" (Kuhn 1970: viii). For Dahlhaus,
paradigms are "basic concepts that guide musical perception and musical thought"
(Dahlhaus 1978/1989: 2). The two types of paradigms differ in that, in art, the
omnipresence of an idea does not guarantee its unequivocal meaning neither does it
ascertain its normative status. Hence, the universal appeal of "space" in music has not
been accompanied by the development of a consensus about what exactly this term
1S. v. "ideology" in The Oxford English Dictionary (1989). The term refers to
(sense la) "the science of ideas; that department of philosophy or psychology which
deals with the origin and nature of ideas" or to (sense le) "the study of the way in
which ideas are expressed in language." 1 hope that this dissertation will not he
c1assified as belonging to the domain of ideology in sense 2: "ideal or abstract
speculation; in a depreciatory sense, unpractical or visionary theorizing or
speculation. "
6
means.
The dissertation relies on yet another "paradigm" in the Dahlhausian sense--the
notion of "the musical work. ft This crucial conception is borrowed from Roman
Ingarden's phenomenological aesthetics of art (Ingarden 1958/1986).8 In Ingarden's
formulation, the "work of music" is a single-Iayered, intersubjective and intentional
object with an ontological basis in the score--the work' s schema which is differently
complemented in each performance. 9 According to the philosopher, the musical work
differs both from the score, that is the work's abstract, notational schema, and from
the performance, that is its sonorous, spatio-temporal realization. The work's internal
structure consists of a single stratum of sound; music in itself bas no meaning, no
content. Such a conception is applicable (if at aIl) only to "absolute," instrumental
music of the Western high-art tradition, the domain of self-contained, unique musical
works. 10 Therefore, Ingarden's understanding of music does not embrace all possible
'musics.'11 This mode of thinking of music in terms of individual, separate and
original compositions, significantly differs from conceiving music in terms of a
process of sound-making, or as orally transmitted and variable repertory, or as a
8My use of the phenomenological method differs from that of Clifton (1983),
Smith (1979), and Ferrara (1991). Clifton and Smith borrow the idea of epoch from
Husserl's Ideas 1 (1913) and focus on descriptions of the listener's experience in
"lived time" (in addition, Clifton draws from Merleau-Ponty, Smith--from
Heidegger). Ferrara, critical of their work, attempts to create a form of a
comprehensive "hermeneutic phenomenology of music" based on ideas from Husserl
and Heidegger. None of the three authors considers consequences of Husserl's later
work (ideas of Leib, Lebenswelt) and Ingarden's phenomenology of art.
~oman Ingarden's The Work of Music and the Problem of Its Identity, written
in 1928-1957, was published in Polish in 1958 and in English translation in 1986.
lFor the notion of "absolute music" see Dahlhaus's Die Idee der absoluten
Musik (1978; English translation 1989). Recently, Lydia Goehr studied the concept of
the work, its genesis, and reception in The lmaginary Museum of Musical Worb. An
Essay in the Philosophy of Music (1992).
IIZofia Lissa criticized the social, spatial (geographic) and temporal (historical)
limitations of Ingarden's phenomenological aesthetics from a Marxist perspective
(Lissa 1966/1975, 1968/1975).
7
12For a recent vision of music as a socially conditioned art see Music and
Society. The PoUtics of Composition, Peiformance and Reception, eds. Richard
Leppert and Susan McClary (1987).
criticism, provided a key concept for many authors presenting their work at the
International Conference of the Gesellschaft fiir Musikforschung, Musik aIs Text,
Freiburg im Breisgau, September/October 1993 (Proceedings are forthcoming).
8
can be seen in the bibliography of about 400 items. 15 However, many of these
contributions examine one particular, and often quite narrow, aspect of the spatiality
of music. 16 Papers of a larger scope range from analytical investigations of various
spatial aspects of the music by one composer (e.g. Serocki studied by Davies, 1983;
Carter analyzed by Bernard, 1983; Reynolds discussed by Vrin, 1991) to thorough
and insightful examinations of chosen aspects of space or spatialization. 17 Many
smaller articles contain either information about individual projects l8 or reflections on
the new "musicalisation of space" (term from Brelet, 1967) in contemporary music.
Papers of the latter category are rather general, with the scope and nature of a
manifesto rather than of an in-depth study (e.g. Brelet 1967; Schnebel 1976; de la
Motte-Haber 1986; Dhomont 1988).
Several collections of articles on space and music include both types of brief
contributions (Die Reihe no. 7: "Form--Raum, " 1960/1965; Musik und Raum ed.
Thurig Brm, 1986; L'Espace du Son I-II, ed. Francis Dhomont, 1988, 1991).19
These collections contain papers of varied scope and quality, gathered together in
order to highlight the multi-faceted reality of space in contemporary music--linked to
considerations of form and structure, from music notation to architecture in the 1960's
(Die Reihe) to reflections on sound projection and perception in electro-acoustic music
as well as to comments about avant-garde experiments in the 1980' s (L'Espace du
Son, Musik und Raum). In addition to articles on contemporary music, Musik und
Raum includes a number of studies of various historical aspects of "space as the
carrier of musical sound" (Binkley on medieval drama, Meyer on Haydn's concert
halls, etc.).
The contributions to the general history of the 2Oth-century "music in space,"
tracing the evolution of spatialization, are few and far between: articles by Winckel
(1970, 1971), Szwajgier (1973), Angerman and Barthelmes (1984), Vande Gome
(1988); books by Sacher (1985),20 Przybylski (1984),21 and Bayer (1987).22 The
subject of spatialization may be encountered also in general histories of 2Oth-century
music (Watkins 1988), histories of music after 1945 (Schwartz and Godfrey 1993,
Nyman 1974) or studies of the music by one composer (e.g. Stockhausen: Harvey
1975, Maconie 1976/1990). So far, only the music of Henry Brant has been
thoroughly investigated from the spatial point of view (Drennan 1975); the
contributions of other composers to the development of spatialization still await full
review. Perhaps not surprisingly, entries on "space" and "spatialization" are
conspicuously absent frolli major reference works, inc1uding The New Grove's
2In his doctoral dissertation, entitled Musik ais Theater, Sacher puts forward
the thesis that all spatialization is primarily theatrical; this supposition is disputed in
Chapter IV (also in Harley 1993).
21This is a study of the spatialized compositions performed at the Warsaw
Autumn Festival in Poland.
22Bayer's enigmatic notion of "espace sonore," which is, for him, the paradigm
of aIl modem music, refers simultaneously to pitch space and acoustic space used by
contemporary composers, from Schoenberg to Cage. Thus, it embraces both "musical
space" and "spatial music."
10
the "literature on the subject" (cf. Chapter II). Such is the case with North American
doctoral dissertations in musicology that refer to "space" in their titles: by Lippman
(1952--"space"), McDermott (1966--"musical space"), Judkins (1988--"virtual space")
and Stofft (1975--"space"). The most comprehensive of these studies, and the most
valuable as a scholarly text, source of data and inspiration for further research, is the
earliest one--by Edward Lippman (cf. Chapter II). "Space" or "musical space" is also
the concem of doctoral students in other disciplines (e.g. in experimental psychology,
Monahan 1984).
Among many concepts of a phenomenal musical space (discussed in Chapter
II), Thomas Clifton's (1983) is best known in North America, while Ernst Kurth's
(1930) has been the most influential in Europe. 24 The identification of space with
stasis or with pitch has been a common phenomenon in contemporary musical-
theoretical thinking. as Compositional discussions of space and spatialization range
from comprehensive studies (e.g. Boulez 196311971), to brief reflections (e.g. Boulez
and Nattiez 1991). Stockhausen's "Musik im Raum" (Stockhausen 195911961) best
exemplifies the former category, inc1uding a survey (and an ultimate rejection) of a11
25For "stasis" see Chapter II, section 2 Ce.g. Adorno 1948, Ligeti 1960,
Rochberg 1963, McDermott 1966); for "pitch" see section 3 of the same Chapter (e.g.
Boulez 1963, Morris 1987).
11
28
1 have also presented papers relating to the dissertation at national and
international conferences: (1) "The 'work of music' revisited: Roman Ingarden's
phenomenological aesthetics" at the Annual Conference of the Canadian University
Music Society (Calgary, June 1994); (2) "American experimental tradition re-
examined: Henry Brant's 'spatial music'" at the 1994 Conference of the Sonneck
Society for American Music (Worcester, Massachusetts, April 1994); (3) "On reality,
unreality, and virtual reality in music: two dialogues with a commentary" at the
International Conference on Acoustic Ecology, The Tuning of the World (Banff,
Alberta, August 1993); (4) "On the use(fullless)ness of analysis for the performance
of 2Oth-century music (Xenakis, Bart6k, Stravinsky)" at the 1993 Conference of the
Canadian University Music Society (Ottawa, May/June 1993); (5) "The technique of
spatial sound movement in the instrumental music of Iannis Xenakis" at the FaU
Meeting of the New York State--St. Lawrence Chapter of the AMS (Albany, October
1992); (6) "The concept of 'musical space' in music theory and aesthetics (19308-
1980s)" at the 12th Congress of the International Association for Empirical Aesthetics
(Berlin, July 1992)..
13
difference between the perception and the models of space. Here, the notions of
"Lebenswelt" (Husserl) and "incarnate subjectivity" (Merleau-Ponty") are of partlcular
importance.
An outline history of the concept of "space" in musicologicalliterature
constitutes Chapter II. 29 Firstly, 1 examine different theories of the 'internaI' musical
or tonal space which manifests itself in the perceptual experience of music. The
second section of Chapter III is devoted to the concept of musical spatiality postulated
as a paradigm for the new music of the 196O's (space as stasis, spatialization of time).
The identification of space with pitch is the subject of section 2.3. Here, 1 also
present chosen mathematical concepts of space used in the research and creation of
contemporary music. Finally (in section 2.4), 1 discuss and examplify the shift in the
meaning of "musical space" towards the physical-acoustic-perceptual space. This
chapter, a comprehensive historical survey of the idea of space in music, addresses
issues of dimensions, attributes and structure of space, as well as problems of internaI
. consistency and area of applicability of the various theories and models of space.
These conceptions are placed in their appropriate philosophical and historical contexts.
For example, the conceptual dependence of various "musical spaces" on the
paradigmatic concept of an absolute, three-dimensional, physical space is revea1ed and
the futility of comparisons between the "logical spaces" of music and the perceived
qualities of the physical space is pointed out.
The third chapter of the dissertation presents the idea of "spatialization" in
contemporary music. A brief examination of the intricate relationships between
various types of space associated with music (e.g. pitch-space, represented space,
performance space) is followed by a survey of compositional concepts of
spatialization, from Ives and Varse, through Stockhausen, Boulez and Brant, to
Smalley and Dhomont.
Chapter IV contains a new definition of spatialization preceded with a review
29Here, 1 use the term "musicology" broadly, in reference to all writings about
music, including music theory, aesthetics, musicology, texts by composers, etc.
14
The dissertation realizes aH these objectives and captures in vivid detail one of
the main musical preoccupations of our times. This contemporaneous validity
highlights its merits as an original contribution to knowledge. The history of the
concepts of "musical space," and "spatialization" includes important discoveries and
reevaluations. The text emphasizes the interrelationships of ideas and articulates main
conceptual trends. The dissertation contains numerous analytical examples from a
repertory of spatialized works which has not previously attracted much critical
attention. Moreover, even well-known compositions (e.g. Bart6k's Music for Strings,
Percussion and Celeste) reveal spatial aspects unnoticed in earlier theoretical scrutiny.
Thus, the dissertation establishes a new ground for musicological research, bringing
together issues vital to composition and perception of music in space, topics pertaining
to asthetics and philosophy of music, themes of current interest and future importance.
PART ONE
CONCEPTS OF SPACE
CHAPT ER 1
1.1.
Space in langual:e
2The Oxford English Dictionary, 2nd ed., vol. 16, 1989, p. 87-89. In subsequent
citations, 1 will use the abbreviation to OED.
3The Table 1-1 (at the end of section 1.1) contains a selection from the meanings
of "space" listed in the entry in the OED. Here, 1 include sorne of the infrequently
encountered meanings of "space" to illustrate the polysemous character of this term.
4Swift's citaiton cornes from Gulliver's Travels (1726), Keats's from St. Agnes
(1820), and Stowe's from Uncle Tom's Cabin (1852); aIl from the OED.
18
19
The temporal senses of "space" associate this term with the ideas of
"measurement" an "distance." This conceptual link underlies the philosophical idea
of the "spatialization of time" (Bergson 1913; see section 1. 5 of this Chapter).
Indeed, the expression "the space of time" is as common as "the space and time"--the
former denoting the measurement of time, the latter the totality of existence. s Here,
the problematic nature of the notion of space becomes apparent. 6 The two meanings
of space as the complement and the attribute of time are diametrically opposed, yet
frequently intertwined; this "entanglement" has consequences for the meaning of space
in music (cf. Chapter II).
Another !a.rge group of the senses of space refers to area and extension.
"Spatial" is what co.,exists simultaneously, what is present at the same temporal
instant. Again, as in the group of "temporal" senses, the relation of space to
measurement is of primary importance. The 17th-century poet, John Milton writes:
"Twixt Host and Host but narrow space was left. A dreadful interval" (Milton 1667;
in the OEV: 87). Here, space means "linear distance; interval between two or more
points or objects:""" In t1:lis sense, space has one, measurable dimension. 7
"Space" may also mean "superficial area, extent in tbree dimensions." Thus,
aIl tbree-dimensional objects, including musical instruments and bodies of the
musicians "occupy a certain space." If so, space may be sufficient or insufficient for
5This conclusion may be reached on the basis of citations listed in the OED; the se
quotes are gathered to document linguistic practice, rather than delimit the range of
possibilities (i.e. the Dictionary is descriptive, not prescriptive).
rudiments of Western musical notation: notes are written on Hnes or in the spaces
"between the lines of a staff. If The same general meaning underlies a specifie
typographie sense of space as "an interval or blank between words, or lines, in printed
or written matter. "
20
9E.g. metric space, topological space, vector space. The mathematical notions
of space are discussed in Section 1. 3.
21
i
! II. Denoting area or extension.
1
1
14. (Music): One or other of the degrees of intervals between the lines
of a staff.
1.2.
Selected philosophical conce.pts of s.pace
llQuoted from Jammer (1954: 97). Source of this quotation: F. Cajori, ed., Sir
Isaac Newton 's Mathematical Principles of Natural Philosophy and His System of the
World. A Revision of Mott's Translation, (Berkeley: University of California Press,
25
God's "boundless uniform Sensorium," i.e. God's way of perceiving and creating
things (Jammer 1954: 110-112, Gosztonyi 1976: 338-344).12 The Newtonian
identification of the omnipresence of space with the omnipresence of God, used later
as a proof for the Divine existence,13 forms the basic contradiction within his
conception of space: the location of a metaphysical Being at the centre of a
hypothetical-deductive system of mechanical physics.
The universal acceptance of Newtonian physics led to the adoption of the
notion of absolute space as a basic, scientific truth, not an artifact of limited scope and
applicability. An awareness of the paradigmatic status of this notion ("paradigmatic"
in the sense introduced by Kuhn in 1962) arose only with the renewed interest in the
nature of space spurred by the development of relativity theory in the 20th century
(discussed in Section 4, below). Meanwhile, one philosopher who adopted a
Newtonian world-view, Immanuel Kant (1724-1804), formulated a new notion of
space that influenced philosophical discourse on space for several generations.
As Patrick Heelan writes, "so persuaded ... was Immanuel Kant of the
apodicticity of Newtonian physics, that he proposed as a self-evident truth that the
space of empirical objects and intuitive experience is Euclidean" (Heelan 1983: 250).
Heelan has criticized Kant's limitations from the position of a phenomenologist;
Michael Friedman points out that for the positivist as weIl, Kant's conception of space
suffers from "its too intimate connection with outmoded mathematics and physics"
(Friedman 1983: 7). Nonetheless, Kant's theory continues to influence research into
1934, 6). The notion of absolute space is contrasted by Newton with that of the relative
spaces, which are, in contemporary language, different frames of reference (cf. van
Fraassen 1985: 115).
12As Newton writes about God: "He is not eternity and infinity, but etemal and
infmite; He is not duration or space, but He endures and is present. He endures for ever,
and is everywhere present; and by existing always and everywhere, He constitutes
duration and space" (Newton/ Cajori 1934: 544; quoted by Jammer 1954: 11 0-111).
13For instance by Samuel Clarke, cf. Gosztonyi (1976: 346-348) and Jammer
(1954: 127).
26
14Kant's critical writings dealing with the topic of space inc1ude: Critique of Pure
, Reason (1781), Critique of Practical Reason (1787) and Prolegomena (1783).
27
ISIn the domain of musical thought, the Kantian legacy has particular significance
for the German theorists of "musical space (cf. Chapter II, section 1).
If
28
1.3.
Notions of s.pace in mathematics
What Kant could not have known, that space is not necessarily Euclidean, bas
slowly come to be understood over the course of the 19th century--the time of the
development of various non-Euclidean geometries. 16 Their emergence has heralded the
birth of mathematical notions of space which have little to do with the experience of
the human (bodily and environmental) spatiality. In mathematics, space is "usually
regarded as a set of points having some specified structure" (linguistic sense III. 9
listed in Section 1).17 The main stages in the evolution of such counter-intuitive
concepts of space are outlined below.
According to the classical formulation of Euclidean geometry (that of the
Elements by Euclid), spatial relations between elementary entities (point, line, plane)
are supposed to fulf five postulates, of which the fifth one, the so-called parallelism
postulate is the most questionable. Bas van Fraassen formulates these postulates in the
following manner:
(1) If x and y are distinct points, there is a straight line incident with both.
(II) Any finite straight line (segment) is part of a unique infinite straight line.
(III) If x is a point and ra finite distance, there is a unique circle with x and
radius r.
(IV) Any two right angles are equal.
(V) If a straight line falling on two straight lines makes the interior angles on
the same side less than two right angles, the two straight lines, if produced
indefmitely, meet on that side on which the angles are less than two right
angles.
(van Fraassen 1985: 117-118)
I1Whether any particular mathematical spaces can be coordinated with entities from
the physical reality (Le. discovered) or whether their existence is purely ideal (i.e.
invented or construed) is a matter of contention. Some philosophers assert that the
geometry of space has little to do with spatial intuition or experience (cf. Gosztonyi 1976:
467-473).
29
The members of T are then called T-open sets, or simply open sets, and X
together with T, Le. the pair (X,1), is called a topological space.
(Lipschutz 1965: 66)
(proposition 2.0131), "a speck in a visual field need not be red, but it must have a
colour; it has, so to speak, a colour space round it. A tone must have a pitch, the
object of the sense of touch a hardness, etc." In Wittgenstein's definition, the musical
notion of "pitch" is a logical space. 20
Bas van Fraassen explains that a logical space is "a mathematical construct
used to represent conceptual interconnections among a family of properties and
relations" (van Fraassen 1985: 102-104; cf. also Reichenbach 1927/1958: 132). This
logical.space may be used to represent physical space. If each event receives three
space coordinates (real numbers), "the logical space in which . . . all spatial
relationships are represented, is the set of all triples of real numbers" (p. 167). If, on
the other band, events are considered in a four-dimensional space-time, "the logical
space, in which, for us, all spatio-temporal relationships are represented is the set of
aIl quadruples of real numbers" (p. 167).21 In addition, van Fraassen argues that time
is a logical space, and "furthermore, that this logical space (time) is the realline being
used to represent all possible temporal relations among events and the conceptual
interconnections among these relations" (van Fraassen 1985: 102). So much for
absolute, independent time and space! Having begun this survey of concepts of space
from an intuitive conception of "the space of time " (cf. linguistic senses 1.1--1.3 in
Section 1), we reach one philosopher's conclusion that time is a logical space.
writings of those composers or theoreticians who have studied mathematics, and have
sought to transplant mathematical ideas into music (cf. Boulez, Xenakis and Morris in
Chapter II).
1.4.
Space-time theories in modem philosophy of science
22Albert Einstein expresses a similar view in his lecture of 1921, "Geometry and
Experience," (published in English translation in Ideas and Opinions, in 1976: 227-239).
2'Hans Reichenbach opposes the view advocated here and emphasizes the
distinction between space and time: "Calling time the fourth dimension gives it an air of
mystery. One might think that time can now be conceived as a kind of space and try in
vain to add visually a fourth dimension to the three dimensions of space. It is essential
to guard against such a misunderstanding of mathematical concepts. If we add time to
space as a fourth dimension, it does not lose in any way its peculiar character as time.
Through the combination of space and time into a four-dimensional manifold we merely
express the fact that it takes four numbers to determine a world event, namely three
numbers for the spatial location and one for time." (Reichenbach 1927/1958: 110).
These reservations have been shared by Henri Bergson (Bergson 1922/1965; cf. below,
section 1.5).
laws, of many distinct spacetime worlds" (Sklar 1985: 127). Hence, there is na wide
variety of spacetimes compatible with the theory, because in general relativity
Il
lt
events ) as embedded in a space-time which possesses a specific type of geometric
structure. Where the various theories disagree is what this structure really is.
According to Friedman' s view, the basic or primitive elements of space-time theories
are of two kinds: "space-time and its geometrical structure; and matter fields--
distributions of mass, charge, and so on--which represent the physical processes and
events occurring within space-time" (Friedman 1983: 32). Friedman's critique is
directed against relationalism, which does not require the existence of space-time
independently of matter and energy. As Hartry Field puts it:
According to the relational theory of space-time, the physical world contains
spatio-temporal aggregates of matter (spatio-temporally extended physical
37
30Lawrence SIdar, one of the participants in the debate between substantivism and
relationism describes the kinship of relationism to other "doctrines regarding theories,
doctrines which attribute genuine reference only to the names and predicates of the theory
which aim to denote observable entities and properties, and which treat the apparently
denoting terms which allegedly refer to nonobservable entities and properties as not reaIly
referring in nature at aIl" (Sklar 1985: Il).