Print Article - Journal of Music and Meaning

JMM: The Journal of Music and Meaning, vol.4, Winter
2007, section 3. [Do not cite or quote from this version, but only
from the online version]
Lasse Thoresen
with the assistance of Andreas Hedman and Olav Anton Thommessen
FORM-BUILDING TRANSFORMATIONS: AN APPROACH
TO THE AURAL ANALYSIS OF EMERGENT MUSICAL
FORMS.
1.0 On the Theoretical Background of Aural Sonology.
The present approach to analysis, termed Aural Sonology, results from an
attempt to analyze music as represented on a phonogram, rather than on a
score. This approach is particularly useful for dealing with music for which
no score is available (e.g. electroacoustic music) or music in which there is
no simple one-to-one correspondence between score and the aural
phenomenon (which is often the case with late romantic and impressionist
music as well as contemporary music), although music in which such a
correspondence is evident (e.g. classical Western music) is by no means
excluded, as long as the piece is represented on a phonogram. Aural
Sonology shifts the focus of musical analysis from applying analytical
concepts to what the analyst sees in a score, towards what she hears. The
musical object is not entirely an objective fact but is partly constituted by
the listener’s intentions. Accordingly, in order to achieve a systematic
analytical approach with a degree of intersubjective consensus, the analysis
must be backed up by a theory of listening intentions, and these must not
only be identified but practiced by the analyst: she must learn to observe,
discern and select a specific listening intention of her own mind, as well as
be able to set and maintain a consistent focus on selected strands of the
multidimensional reality of music as heard. 1
The objective of this article is to present one particular method of analysis
developed within the framework. However, since Aural Sonology differs from
most other scholarly approaches to analysis, it will be useful for the reader
to have a condensed introduction to some of the theoretical and aesthetic
assumptions on which it rests.
1.1 Background and Aesthetic Orientation
The Aural Sonology Project began in the 1970s. The two main influences
were Sonology as taught at the Institute of Sonology, Utrecht Netherlands
(today moved to the Royal Conservatory at the Hague), and the
phenomenologically oriented, spectromorphological point of view articulated
by Pierre Schaeffer’s “Traité des objets musicaux”, and further expanded at
INA/GRM, Paris, France. The ideas gathered were subsequently refined at

the Norwegian Academy of Music in Oslo, through a collaboration between
Professor Olav Anton Thommessen and the present author, both of us
professors of musical composition. The development of the methods of
analysis took place within the context of a circle comprising performers and
composers, which accounts for the general orientation towards an applied
branch of music theory designed to enhance artistic sensibilities and
cognition. Aural Sonology has been regularly taught at the Academy since the
beginning of the 1980s, and has continued to evolve interactively in the
dialogue between students and teachers It has been the aim of the project
to develop a conceptual structure of analysis and theory that is not uniquely
reserved for a particular compositional style or expression, but addresses
music appreciation in Western art music on a general basis.
Aural Sonology has consistently been concerned with aural consciousness
during a period of music history in which creative musical thinking has
largely been concentrated on the development of novel compositional
techniques and technology. The serial composition technique depended on
the written medium as its extratemporal support; algorithmic approaches to
music tended to substitute the sonic representation of music with a model. 2
The motivation for launching the Aural Sonology Project was a strong
impression that the aural aspect of contemporary music was being neglected
by contemporary composers to the detriment of its ability to communicate
with a non-specialized audience. The Aural Sonology Project therefore seeks
to enhance the listeners’ ability to encounter and evaluate the sonic results
of any technical procedure, by an explication and conceptualization of its
perceived, aural syntax. Moreover, Aural Sonology intends to benefit from
the study of the aural syntaxes and principles of form in music that have
already proven to make sense in a greater community of listeners. This will
be done through an effort to formulate observations in an abstract way such
as to facilitate its eventual transfer to new sonic materials. Therefore, Aural
Sonology seeks to conceptualize and represent graphically that which makes
syntactical sense in music as heard. That music – even new music - ought to
make sense to the average listener, not only to the composer or the
intellectual elite, was a position occasionally attacked by the most fervent
adherents of the avant-garde, for whom alienation, negation and
fragmentation were the highest ideals for contemporary music.
The methodological approach chosen combines a phenomenological
perspective with a pragmatic use of selected structuralist techniques.
Phenomenology provides the global outlook, with its emphasis on the life
world (hence music as heard), its explication of intentionalities, and its
emphasis on describing and reflecting on an experienced object, rather than
on its explanation. 3 Although a number of books and essays have been
written on the subject of musical phenomenology, as well as on music from a
phenomenological perspective, all seem to overlook the need to develop a
terminology suitable for describing the phenomenon of music in experiential

terms, falling back either on philosophical jargon, everyday language, or a
terminology of traditional musicological or acoustics, employing terms that
are not coined within a consistent phenomenological point of view. Aural
Sonology has taken the step to construct a new and consistent terminology
based on aural experience and correlated through specified structural
relationships. While structuralist techniques provide helpful schemata for
organizing a conceptual world, structuralism as such lacks the concept of a
conscious, perceiving subject, and has a tendency to overlook the particular
in favour of a postulated universality. The phenomenological perspective
counterbalances this deficiency of structuralism. All the structural concepts
developed are condensed into a set of graphic symbols, so that the concepts
can be used in practical analysis.
1.2 Listening Intentions, Listening Behaviours
Music as heard is a phenomenon of enormous richness and ambiguity. People
make sense of music in a number of very different ways, which tends to
make a meaningful discussion about music problematic. Even when listening
to the same piece of music, interpreted by the same musicians, the listening
experience itself, and its interpretation in words, varies greatly. The musical
experience consists of a synthesis of signs and signals transmitted as sound,
and of the listening subject’s own perceptions and conceptions of the music,
i.e. his constitution of the musical object. Different listening intentions
constitute different musical objects.
Based on analysis of interviews with listeners, Francois Delalande, researcher
at INA/GRM, has come up with suggestions for a number of listener
behaviours, each of which is representative of different musical listening
intentions that constitute widely different musical objects and
interpretations. The present project can be seen as a specialized
development of one of these listener behaviours, that which has been
termed taxonomic listening. Francois Delalande (1998, pp. 26-27) defines
this listening behaviour in the following way:
Taxonomic listening is manifest through the listener’s tendency:
- To distinguish sufficiently large morphological units such as sections
or chains and to make a mental list of them;
- To qualify these, but just enough to distinguish them from each
other,
- To notice how these units are arranged in relation to one another,
- To try and memorize all this data.
This is a listening behaviour that leads to the most neutral perceptual
image possible in the sense that the subjects who practice it aim: (1)
to give a complete picture with little detail, a map on a large enough
scale without distorting the design; (2) to parenthesize subjective
characteristics which might affect the true image of the object… For
these subjects… it is a canvas on which one will subsequently be able
to plot more personal observations. It is conceived as a practical

eference ... It is possible that these ideas of pictures, maps and score
– graphic representations on paper – correspond to what happens in
listening. Paper as a medium is associated with a double function: (1)
a memory aid; (2) an analytical tool for laying out the relative nature
of units.
(Delalande, 1998, pp. 26-27)
Expanding upon Francois Delalande’s observation, it could be said that such
a listening attitude would favour the observation of forms, e.g. the study of
how identifiable smaller parts would integrate into greater wholes. In Aural
Sonology we develop this listening intention in a systematic fashion. The
musical phenomenon, and the aural investigation of it are generally divided
into three levels:
• Level 1: sound objects i.e. single sound objects, analyzed in
spectromorphologic terms.
• Level 2: elementary gestalts i.e. combinations of sound objects into
small patterns.
• Level 3: form gestalts i.e. patterns of elementary gestalts.
Traditionally, music theory and analysis has taken for granted the nature of
the sound objects being dealt with. However, it is clear that the pitched,
stable sounds on which traditional music theory are built is a special case in
the larger world of sounds. The main focus of traditional theory has been a
discussion of how pitched sound objects can be combined in scales, and
chords and into larger compounds such as harmony progressions, etc., all of
which are clearly level 2 phenomena. Studies of contemporary music are also
largely concentrated on this level.
The focus of the Aural Sonology Project is on levels 1 and 3, with a clear
emphasis on level 3. Thus the analysis of musical forms as heard, level 3, is
the focus of the present article. This means that e.g. the harmonic structure
of a piece will not be analyzed on its own terms, and will only be significant
to the extent its effect is deemed relevant for the conception of an abstract
formal model on level 3.
1.3 The Semiologic Tripartition
To analyze means to reflect, and to reflect is a complex process that both
articulates the perception of music into more details, and seeks to integrate
the details into a comprehension of the greater whole. Since the analytic
process of reflection evolves over time, it presumes that the object of
reflection remains static. Thus the object must be contained in an extratemporal,
stable, material medium permitting identical repetition of the
object researched. Moreover, the object under study should be represented
in such a way that it can be shared with others. For centuries, musical
notation has provided such a representation of the musical work in the
Western context, and has been a prerequisite for reflection and analysis.

Therefore it has been accorded the status of a kind of neutral, objective
reality to which the community of researchers could return in order to check
one another’s conclusions.
The present approach to analysis consistently replaces the score with the
phonogram as the extra-temporal, material support of analytical reflection.
The advent of recording technology and loudspeakers has opened new
horizons for analyzing music as heard. The only reason why this approach
does not seem to be much exploited in music theory, analysis, and in
musicology in general, seems to be a general scepticism towards the ear as a
sufficiently objective instrument of observation. Aural Sonology insists that
consensus with regard to listening intentions will solve this predicament and
open a new field of research, complementary to other, established
disciplines. This is made possible thanks to the heritage of Pierre Schaeffer,
and his successors at GRM such as Guy Reibel, Michel Chion, Francois Bayle,
and Francois Delalande, who have carried out pioneering efforts in sorting
out the dimensions of the listening consciousness.
The semiologic tripartition may serve as an initial help in sorting out
listening intentions by correlating these to three aspects of the musical
object. 4 The three domains are the poïetic domain (related to the process of
creating a piece of music, thus dealing with the composer’s techniques,
strategies and expressive intentions, and also the performers’ interpretative
intentions), the esthesic domain (dealing with the listeners’ reception of the
music) and a neutral domain (the uninterpreted, observable aspect of
music).
Although initially useful, the semiologic tripartition, as proposed by Molino
and Nattiez, is problematic in a few respects. The third neutral domain
appears by and large to be a musicological construct since it is not clearly
related to music as a system of signs. 5 In a life world perspective, it is above
all music as heard (the esthesic domain) that is associated with meaning
formation. The creative aspect of music (the poïetic domain) is also relevant
to meaning formation, first of all the intentions of composers and performers
and their personal and cultural context, and the processes and techniques of
composing and performing. It is therefore reasonable to propose a
reorganization of the semiotic tripartition, in which the neutral domain is
seen as the observable aspects of the esthesic and the poïetic domains,
respectively, and its status as an independent domain of research is reduced
considerably.
Hermeneutical side of
the esthesic domain:
‘Immaterial aspects’ of
the listening experience:
musical meaning (such as
Esthesic domain Poïetic domain
Neutral side of the
esthesic domain
‘material aspects’
of the listening
experience as
Neutral side of the
poïetic domain: ‘material
aspects’ of the creation of
a piece of music as
documented by material
Hermeneutical side of
the poïetic domain:
‘Immaterial aspects’
of the production
aspect of music

feelings, associations,
related world views) as
constituted through
different reception
behaviours.
documented on
phonograms: sound
heard as sound,
music heard as
sonic gestalts.
traces (sketches,
computer programs,
performers’ annotations)
as well as interviews etc.
Neutral domain
(interpretations of
composers’ or
performers’
intentions, feelings,
ideas, world views
etc.)
The restructuring of the semiologic tripartition proposed above, suggests
there is a “manifest” and a “hidden” side to the esthesic and the poïetic
domains, respectively. The manifest side comprises the material traces of
the work, while the hidden comprises the expressive aspect, that which is
concerned with “meaning” or musical sense. The manifest side always has a
potential for being “neutral”, in the sense that it is observable, and since it
is observable it can be shared with others and form the basis for shared
understanding. Admittedly, isolating the neutral sphere of music is somehow
artificial, since many listeners’ behaviours do not favour giving focused
attention to the material aspect of the sound experience, such as the sound
itself. When diverting from the listener behaviour that is the preferred when
listening to a particular kind of music, one risks missing features that are
pertinent to the formations of musical meaning understood as feelings,
general ideas, world views etc. This can only be compensated for by the
analysts’ consciousness of the artificiality of isolating one aspect of music as
heard, and by his mastery of other, complementary listeners’ intentions. In
other words: the ability to shift between different listener attitudes
becomes a prerequisite for relating to music in a way that avoids the
disadvantages of reductionism.
The analytical focus of Aural Sonology, then, is the neutral side of the
esthesic domain, i.e. the material, observable aspects of the aural
experience. The neutral side of the esthesic domain must be constituted by
an act of the listener through his choosing the requisite listening intention.
The two listener intentions preferred for our analytical purposes are the
reductive listening intention (for level 1 this is, briefly, the intention to hear
sound as sound, and will not be further dealt with in this article) and the
taxonomic listening (levels 1 and 2). 6
A study of the neutral domain (as defined above) will in fact be a study of
the signifiant of the musical sign. In a semiotic perspective, such a study
may only be relevant for approaching its signifié (interpreting its meaning)
to the extent that the musical signs used are motivated signs (dealing with
iconic or indexical links between expression and content) rather than
arbitrary ones (defined purely by convention). The relative lack of musical
vocabularies suggests that music is mostly a system of motivated signs. 7 Thus
studies of the neutral aspects of music are potentially relevant also for
approaching musical meaning – the signifié.

The analyses produced by the methods introduced by Aural Sonology are
definitely not compositional techniques. Nevertheless they may be of great
value to composers and performers, since listening and reflecting on the
aural reality of music in most cases contributes positively to the quality of
music making and performing. Thus while Aural Sonology analyses are
focused on the neutral side of the esthesic domain, the exercise of
conducting such analyses is a useful one for giving the composer a number of
more specific ideas about the shaping of his compositions, as it develops his
ability to conceive of what he eventually would like to hear when the piece
is being performed; such an exercise also encourages performers to shape
their interpretations guided by a greater awareness of how musical gestalts
evolve in time and affect the listener.
1.4 Gestalts and Structures
Music exists in our life world long before we learn to discuss language and
grammars conceptually. We are able sing a melody long before we can
define what pitch is verbally; music makes sense to us as listeners and
performers long before we can describe musical form. Music is mostly learnt
like a mother tongue; we learn to speak it before we learn its grammar. A
native speaker relies on his ear to determine whether a certain combination
of words is acceptable and correct. Similarly, musical thought understands in
terms of aural gestalts, whose wellformedness is judged in an analogous
fashion, relying on the ear. Music theory and analytical methods generally
try to comprehend music in a conceptual way, describing the intrinsic
coherence of the gestalts through structural terms, which is basically what
grammars do in relation to spoken language. Grammars do not define a
language; they describe a language that is already given in the life world.
Similarly, the comprehension of musical structure, which is a central concern
to the Aural Sonology Project, will always be a subset of what can be
understood by a listener subjected to the temporal flow of musical gestalts.
Aural Sonology takes as its starting point the experience of ordered,
sonorous gestalts in music as heard. The point of departure of the analyst is,
accordingly, an emergent phenomenon; from here, she proceeds in the
direction of defining her experience by assigning to her experience a
description in terms of structure. The initial perspective is holistic: the
analyst starts with a concrete phenomenon as a given whole, meeting it with
an attentive and receptive consciousness. The holistic orientation in
combination with elements of applied phenomenology and structuralism,
make the present project different from a number of more traditional
approaches to analysis; e.g. it differs from the methodological position of
operational structuralism that tries to explain phenomena through the
disclosure of generative relationships within the object researched. 8
Aural Sonology is characterized by an effort to develop means for the
description of the perceived musical order, and, to the extent possible,
correlate the order or gestalt heard with a theoretical structure (which is
an ideal object in phenomenological terms). It must be underlined again that

the kind of structure found by our methods of analysis is not one that is
intrinsic to the construction of the object studied, as it does not necessarily
explain its genesis. Rather, it is a concrete instance of experienced order of
an object; and this experience is founded both in objective musical reality
and at the same time in certain constitutive intentions on the part of the
listener. The equivalent of musical structure in the esthesic domain is
actually the experience of order, pattern and regularity. Thus the object
analyzed presupposes an active constitution on the part of the listener.
Combining this with the vehicle of a defined method of analysis, it may be
possible to make pertinent statements about the experience of music that
can be communicated to others who share the same conceptual orientation
and master the requisite listening intention. Of course, what the analyst
finds in this way is not necessarily an intrinsic or essential part of the music’s
purported meaning, which, in its original traditional context, might
presuppose another constitutive intention. Accordingly, using the methods of
Aural Sonology, one cannot without further qualifications make definite
judgments about the total aspect of meaning and signification of the work
analyzed. This will have to be dealt with by methods complementary to ours,
i.e. the hermeneutical methods often used by traditional musicology and
semiology. However, every scientific methodology constitutes its own object
of research, and in the final analysis, there is no definite and conclusive
truth that can be stated about a work of art. Only by approaching music
from many sides, i.e. through the use of complementary methods, can one
see to achieve a more complete understanding. 9
Aural Sonology as a method can thus be seen as an effort to correlate the
experience of musical gestalts with a set of structured concepts. The nature
and number of these concepts are largely inconstant, and what we can
propose probably only represents a beginning that serves to lay down certain
basic features of musical perception and cognition as related to form.
1.5 Isotopy and Selective Listening.
The structural models devised in Aural Sonology will all have to be related to
a consistent selection of features in the perceived music. Music as heard is a
concretum, and is therefore a composite of several attributes, containing an
almost infinite amount of information, given the number of listener
intentions by which it can be heard. In our analytical context, the analyst
will have to select and focus consistently on one strand of aural order; one
that seems to be of importance to the organization of the music as a whole.
Such a consistent focus on organizing features within the musical context
could be termed an isotopy with a term adopted from structural semantics. 10
An isotopy in our context is a consistent strand of aural gestalts perceived
to contain features essential for the organization of long stretches of the
musical discourse. An isotopy may be said to be the underlying problem
space of a piece of music, thus the overarching aspect of complementary
opposites. Organization is not here seen as being primarily a compositional

strategy (which is a fact belonging to the poïetic domain); it is what the
listener perceives as coordinating or creating coherence in the musical
discourse, by means of recurrent patterns and related contrasts. For each
particular musical isotopy there is a corresponding particular selective
listening intention.
The Aural Sonology Project has thus far focused mainly on level 3 in creating
methodical approaches to isotopic structures. The general isotopies relevant
to form building that we at present have managed to develop are: 11
• Time-fields (the temporal segmentation of the musical discourse)
• Layers (the synchronous segmentation of the musical discourse)
• Dynamic form (time directions and energetic shape)
• Thematic form (recurrence, variation, and contrast)
• Formal transformations (looser and firmer gestalts, transformations
between them).
The present article will concentrate on Formal transformations, while
touching on thematic form (form-building processes) as well. In addition to
such general formal isotopies, there are other types as well:
• Actual, thematized isotopies: Each piece may have its individual musical
isotopy, i.e. recurrent patterns and related opposites that take place
within the same isotopy, and/or interrelated passages between different
isotopies.
• Condensed, essential isotopies: Recurrent features may be given a
condensed representation in which the isotopic fields are reduced to
essential formulae. Such an essential isotopy can combine several strands
of isotopical description, and define a musical deep structure.
• Condensed isotopies can be seen as contextual meanings, i.e. as the
observable side of an iconic sign with a signifié in the extra-musical
domain.
2.0 Musical Form
In his concise book on traditional forms in Western art music, Arnold
Schoenberg (1977, p. 20) makes a number of interesting observations
concerning the nature of musical forms in general, and their importance for
the reception of the music: Form means that the piece is organized, and
organization means that the music “consists of elements functioning like
those of a living organism.” Like the elements of an organism, the
constituent parts of music must be differentiated according to their
importance and function, but the differentiation must never endanger the
underlying unity of the composition. Form in this sense ensures intelligibility,
logic and coherence; it is what makes the music comprehensible. Concern
about form is a means of surmounting limited powers of human
understanding; as a person is unable to keep in mind very long time
stretches, the musical discourse must be subdivided into manageable

segments. However, these shorter segments must again be joined by relation
to the others in such a way that one segment presupposes the other and vice
versa. This is what one could call formal functions, in a sense similar to that
we have with harmonic functions. Variety can endanger comprehensibility
and logic, and this can be avoided by subjecting the musical elements to
appropriate constraints. Delimitation, subdivision and simple repetition are
useful in counteracting the tendency toward disproportionate variety. In
fact, Schoenberg states that musical comprehension is impossible without
repetition. But repetition can easily cause monotony and boredom on the
part of the listener. This must be counteracted by variation of the repeated
elements. In a true work of music that obeys the classical laws of internal
unity, even musical contrasts should be related.
The ideal of organic form as discussed by Schoenberg is also essential to our
approach. When it comes to form, we are concerned with subdivisions in the
sense of how the musical object can be articulated through phrases and
sections, as well as through simultaneous layers. Proceeding from here, we
are also concerned with the functions these subdivisions have in relation to
one another. Aural Sonology discusses form as an emergent phenomenon,
i.e. it takes account of the phenomenon as such, without giving an account
of why or how the form shows up the way it does. This means that whether
the form is based on harmonic fields, thematic recurrence, tensions and
relaxations, or contrasting textures, the form is accounted for in an abstract
sense. Our study of form is confined to level 3, and does not offer insight
into what happens on level 1 or level 2 (referring to the levels we defined in
chapter 1.2). This level of abstractness will enhance the potential of our
method to cross over stylistic borders, while it renounces the precision and
specificity of an analysis that shows how the forms are founded in concrete
musical realities.
Approaching musical forms as emergent forms is fundamentally different
from approaching musical forms as normative conventions. The difference
lies more in the attitude than the facts; when looking for emergent forms
the music itself has to be allowed to present its own form, its own rationality
to the listener’s ear, and this presupposes a listener who ideally should be
willing to bracket her preconceptions of form during the first hearings of a
piece of music, and only afterwards apply his already acquired assumptions
of form with sensitivity and honesty in order to avoid forcing the music into a
wrong or inadequate mould. The aesthetic implication of this is a conception
of musical form that would regard good form more in terms of its emergent
wholeness and rationality, rather than as compliance to formal conventions
and codes. The concept of emergent forms is closely linked to the idea that
musical comprehension can never entirely match musical understanding,
which means – paraphrasing Pascal - that the ear can have reasons that the
reasoning mind has not yet grasped.
Aural Sonology has developed consistent approaches to three aspects of
musical form: form-building functions (dynamic forms), 12 form-building
processes (forms based on recurrence and contrast), and form-building

transformations (forms contrasting ‘loose and firm gestalts’). 13 The
remainder of our presentation will focus on the latter, the form-building
transformations, and in no way aspires to deal exhaustively with musical
form in general.
2.1 Typology of Form-Building Elements
The perception of musical form arises from the perceived interrelationships
between certain constituent elements. The elements constitutive of form
will be called form-building elements (or simple form elements). These are
often found in the melodic/rhythmic lines in the foreground layer(s). 14 Most
of the time background elements can be left out. There are, however, cases
in which musical textures as such obtain form-building significance. Thus the
discussion of the complexity of form-elements will have to apply both to
lines (i.e. melodic/rhythmic elements) and to textures. 15
The typology of form-building elements is based on their complexity (see
Figure 1):
Figure 1.
-Very simple elements. Examples: repetitive figures with a couple of pitches
and even rhythmical values such as very simple accompaniment figures
(lines); monophony or basic homophony (texture).
-Relatively simple elements. Examples: articulated yet simple figures such as
scales/passages or refined accompaniment figures (lines); heterophony, or
homophony with slight polyphonic elements (texture).
-Medium complex elements. Examples: a classical, simple theme (lines); a
two- or three-part simple polyphony (texture).
-Relatively complex elements. Examples: complex themes with great
diversity of pitch and rhythm (lines); complex polyphony (texture).
-Very complex elements. Examples: extremely asymmetric lines using a large
number of values in an unpredictable manner (lines); accumulations in
electroacoustic and avant-garde music (texture).
The scale of complexity may to some extent be considered relative to the
composition or to the style of the composition that is being analyzed.
A form-element, e.g. a theme, will often be presented in its integral form,
then broken down by being partitioned into smaller units. The symmetrically
opposite shapes of the sign for partitioned elements may be used to suggest
the opening or closing features of the context or of the (often preceding)
integral element from which they have been partitioned.

The simple arrangement of degrees from simple to complex is, however, not
sufficient to describe a range of phenomena that is perceived as pertinent
for the aural experience of musical form. One such phenomenon is that of
articulation, another that of distinction (i.e. of being characteristic). When a
form-element is well articulated, it is in possession of a reasonable number
of details that are distinctly perceivable as such. A high articulation will be
an additional feature of the middle range complexities. Most classical
themes are well articulated. However, passagework, soloist figurations etc.
may have medium complexity without being highly articulated; theme-like
passages have “structural” complexity, passagework “ornamental”
complexity. Structural complexity is by definition highly articulated, while
ornamental complexity is not.
When a form-segment is distinctive, it has a character that tends to set it
apart in the particular piece in which it occurs to such a degree that, in
hindsight, it could be considered typical or representative for the piece as a
whole. Distinction also means that certain form-elements are unique to the
particular piece in question, setting it apart from other pieces within the
same style. As an example, one may think of a piece of bebop jazz that
presents the theme to begin with; this will be a distinctive element. The
improvisations that follow will be characterized by passages and figurations,
often rather complex, but they will mostly be more typical of the genre of
bebop jazz, or of the player, than of the piece as such. These form-elements
will not be marked out as distinctive in our analysis. In order not to unduly
complicate the method of analysis, we have opted not to develop separate
analytical tools for articulation and distinction, since they often seem to be
connected. If the need to draw a distinction were to arise, it would be
better to do so in a verbal commentary to the analysis.
The linear arrangement of elements from simple to complex will have to be
reorganized since that which was formerly a middle value, i.e. the medium
complex form-element, has now been taken to represent a maximum of
distinction or articulation. At the opposite extreme of high articulation and
distinction we thus find the very simple and the very complex grouped
together as equivalent in being unarticulated and anonymous. 16
A form-building element that possesses high articulation or distinction will
have a horizontal line drawn through its sign. The signs for articulation and
distinction can also be used to qualify textures when these are sufficiently
unique and characteristic. A conceptual space that has been reorganized
according to criteria of articulation and distinction will look more like a
circle than a line. To close the circle a new sign has been added, one
designed to show the combination of an internally complex, yet globally
simple form-building segment (see Figure 2).
Figure 2.

2.2 Context Organization of Form-Elements
Form-building segments will be defined through the combination of formelements
(as presented in the typology above) into an organized context. A
form-segment is a coherent succession of form-elements, where the
evaluation of similarity and contrast between adjoining elements will serve
as the main criterion for determining what belongs to the form-segment and
what does not. Thus, when there is similarity between juxtaposed formelements,
a coherent form-segment is easily created. Contrasts tend to
fragment coherent segments or set them off from each other; however,
fragmented form elements, too, can be held together in unifying gestalt (a
phrase) due to other musical dimensions, such as harmony, or constant
background layers. Although the form-segments generally tend to be a
succession, there are also situations in which elements are superposed in
simultaneity.
In order to demarcate a form-segment in notation, a number of constituent
form-elements will be joined together by lines indicating identity or
similarity (see Figure 3).
Figure 3. L. v. Beethoven’s Piano Sonata op. 2:1, movement I, first phrase.
Breaking the line joining similar form-building segments indicates a greater
degree of contrast (see Figure 4).
Figure 4. L. v. Beethoven’s Piano Sonata op. 2:1, movement I, beginning of
development.
In the above example, further precision is added through a sign specifying
the degree of similarity. This is one of a scale of 6 signs suggesting degrees
of similarity (see Figure 5). 17
Figure 5.
A partitioning of an integral element will become a fragment if it is further
abbreviated or set off by pauses. A dot over the partitioned element or one
breaking the line that connects the form-elements of greater similarity will
be used (see Figure 6).
Figure 6. L. Janacek, String Quartet, Kreutzer Sonata, movement 3.
The context organization will often reveal hierarchical structures in which
shorter form-segments combine to form larger segments (see Figure 7).
Figure 7. L. v. Beethoven op. 2:1 beginning movement I.

When form-elements are superposed simultaneously in different layers, they
may be drawn on the vertical line. The preferred upper limit for displaying
form-elements in synchronicity would be no more than four elements on one
line. As mentioned, background elements may generally be left out (see
Figure 8).
Figure 8. J. S. Bach, Ihr aber seid nicht fleischlich.
If a more detailed analysis of simultaneous form-elements is desirable, the
specific indications of complexities can be integrated into a supplementary
layer analysis.
When the superposition of form-elements reaches a certain complexity or
merge perceptually, they should be denoted as a texture, rather than single
elements. Slurs mark the transition from single elements to texture (see
Figure 9).
Figure 9.
2.3 Form-Building Transformations
The term form-building transformations describes a set of patterns that
result from characteristic combinations of types of form-elements. While the
form-building processes are concerned with patterns of recurrence,
variation, and contrast, form-building transformations are concerned with
the logic of the organization of complexity vs. simplicity, wholeness vs.
division, lines vs. textures, distinctive vs. anonymous passages.
Form-transformations can be either discontinuous or continuous. In a
continuous transformation the passage from one state to the opposite takes
place in a linear fashion; in the case of a discontinuous transformation (the
normal case in classical music) the passage may be step-wise, or may simply
contrast the initial state of the transformation with its end or its inverse.
The transformation is also discontinuous when a linear transformation is
interrupted by sections of another character (see Figure 10).
Figure 10.
Form-building transformations can take the form of alternation: the musical
discourse moves to and fro between two different states of a transformation.
Different types of form transformations are listed below. The
transformations are non-exclusive; i.e. they may be combined. For the sake
of conceptual simplicity, they are divided into four types:
Simple vs. complex, part vs. whole; few vs. many; distinctive vs.
anonymous. Each category is exemplified with two examples, one in a

classical or romantic repertoire, one from the modern repertoire (see Figure
11).
Figure 11.
-The transformation from complex to simple is termed simplification. The
inverse transformation is termed complication.
Figure 12. Simplification: F. Mendelssohn Bartholdy, String quartet
op.44:1.
Comments to the analysis:
This simplification comes after a process of partitioning the main theme, and
recombining the parts into a polyphonic play. (The transformations liquidation and
crystallization will be discussed in detail in the next chapter). The relative contrast
between the two simple bars at the end, and the relative complex texture of the
preceding fugato, may qualify it as a discontinuous transformation, although the
collection of the preceding polyphony into a synchronized chordal descent serves to
round it off, and prepare the introduction of the simple final section.
Figure 13. Simplification: G. Grisey, Modulations.
Comments to the analysis:
This example shows a continuous transformation of textures that become simpler
and simpler. The example has been considerably abbreviated.
Figure 14. Complication: L. v. Beethoven, Diabelli Variations, op 120.
Comments to the analysis:
The example presents the beginning of three consecutive variations (nos. 15, 16,
17) each of them with the same, underlying chordal progression. The motivic
elements remain relatively simple; however the textural element seems to
dominate over the melodic, and accordingly the analysis shows the development of
textural complexity. The transformation is discontinuous. The build-up in
complexity is supported by a step-wise increase in energy (dynamics, tempo,
register); this, however, is part of the dynamic form, thus belonging to another
formal isotopy. Nonetheless, the synergy between the two isotopies is evident.
Figure 15. Complication: I. Xenakis, Persephassa.
Comments to the analysis:
A continuous transformation (complication) passes from regular pulses with some
irregular elements, to a texture of irregular pulses, thus from relatively simple to
very complex texture.
-The transformation from integral (undivided) to partitioned (divided) is
called partitioning. The inverse transformation is called integration. This
transformation is also applicable to both lines and textures.
Figure 16. Partitioning: L. v. Beethoven, Piano Sonata op. 2:2.

Comments to the analysis:
This is a classical theme presentation, in which the characteristic head of the
theme is repeated and partitioned in order to perform a liquidation of the
characteristic features, while at the same time allowing the theme to be absorbed.
The partitioning transformation happens two times; the ascending fourth at the end
of the initial motive ends up as an anonymous ‘om-pa’ figure between left and right
hand.
Figure 17. Partitioning: W. Walton, Symphony no 2.
Comments to the analysis:
The principal motive, itself relatively short, is presented twice, first in woodwinds,
then in the violins. After an inserted fragment (serving as an alert) there follows a
series of partitioned motives, and then a new series, this time consisting only of
two notes; the partitioning transformation is exacerbated and the final strokes
could be considered fragments. A new motive is introduced; it is less distinctive
than the initial one, and less complex since it actually consists of fewer durational
values. The fact that the sonority itself is more complex (tremolo articulation of
melody notes) is regarded as not being pertinent to the specific focus of this
analysis, which is more concerned with “structural intensity” than “perceptual
intensity” (the latter being a concern for the analysis of dynamic form). The second
motive is also partitioned.
Figure 18. Integration: F. Liszt: Eine Faust Symphonie, first
movement.
Comments to the analysis:
The motive of (one of) the contrast theme(s) is prepared by a few notes set apart
by inserted brass fragments. The initial motive, despite taking part in an
integration transformation, is itself first partitioned, while the dynamic form leads
the process on to the forte presentation of the integrated theme.
Figure 19. Integration: A. V. Mosolov, Savod.
Comments to the analysis:
An ostinato is presented, and different fragments are added into a more or less
coherent, repeated pattern. When the trombone enters with a melody, the pattern
is turned into an accompaniment (background or middleground, in relation to the
foreground melody). This transformation might also be seen as a proliferation and
fusion, explained later.
-The exacerbation of the latter transformations is termed fragmentation and
synthesis, respectively. This transformation can also take place both with
lines and textures.
Figure 20. Fragmentation: C. P. E. Bach, Keyboard Sonata in F sharp
minor, Wq 52/4, H37: No. 1.
Comments to the analysis:

The music alternates between two highly divergent characters, and there is no
attempt to pave the way for the new by a rounded or finished ending of the
respective segments. The context, therefore, is fragmented.
Figure 21. Fragmentation: G. Ligeti, Etude 3 (Book 1) Touches
bloquées.
Comments to the analysis:
The end of this etude is a gradual transformation, brought about by an increasing
number of ‘muted’ keys between the sounding ones. In the preceding form segment
(not presented here) there is another, more dramatic presentation of a fragmented
texture. It would be reasonable to state that synthesis (opening of the piece) vs.
fragmentation is an actual or thematized isotopy underlying this piece, the
indexical logic of which is derived from the play on muted vs. sounding keys.
Figure 22. Synthesis: F. Liszt, Piano Sonata in b-minor.
Comments to the analysis:
Two different motives, a and b, are presented twice in a fragmented context.
Following an interlude with a forward leaning dynamical shape, and using materials
only marginally related to the main motive a, we are made to expect a culminating
statement, which is to be the presentation of a full thematic statement. However,
the listener is still left in suspense while the separated a and b are repeated.
Eventually the synthesis arrives, and we have a full statement of the theme.
Figure 23. Synthesis: L. Thoresen, Tradlarudl.
Comments to the analysis:
The analysis is concentrated on the solo line. The fully synthesized, melodic
gestalt occurs towards the end, preceded by fragments of increasing length.
- The transformation from single lines to several superposed lines (that still
are perceptible as lines) is termed proliferation, typical for starting with a
few simple elements, to which more are added. The inverse transformation
is called collection: It starts with a number of superposed elements, and
ends with a simple one, or a simple collection of the elements.
Figure 24. Proliferation and Collection: J. C. Bach, Sinfonia op. 18, no
1.
Comments to the analysis:
One evident example of proliferation, the opening of a fugue, was already
demonstrated in Figure 8. Johann Christian Bach’s Sinfonia demonstrates another,
less polyphonic realization of the same formal archetype. For the sake of simplicity,
the proliferation and collection transformations are shown together in a single
example. The selected section of the piece shows a discontinuous alternation
between collection (generally unison sections) and proliferation (sections with
several layers, and generally figurations in the foreground, rather than melody).
Around the middle of the example (following the antecedent and its consequent), a

gradual build-up begins, preparing for an eventual dispersion of the proliferating,
ascending lines, as if the lines were cast into the open. Through their descent, they
are nicely collected into the closing unison section, as if elegantly gathered and
knit in a bundle (collection).
Figure 25. Proliferation: K. Stockhausen, Gruppen (1).
Comments to the analysis:
The proliferation is based on single notes and tiny cells, rather than on motives of
thematic relevance. Although the rhythm is irregular, the increasing temporal
density and expanding register leave no doubt about the overall tendency.
However, as a conceptual counterpoint to this linear growth, there are chordal
coincidences that in short moments suggest a gathering of the points (collection;
not represented in the analysis). The evolution of the same music example is shown
in Figure 28 (fusion and anamorphosis).
Figure 26. Collection: W. Lutoslawski, Paroles Tissés.
Comments to the analysis:
The selected example begins with a proliferation of small cells; eventually they
fuse into a texture, while a new linear element is added on top, continuing the
proliferation. The sudden introduction of the solo line represents a discontinuous
collection of the previous proliferation.
- A further development of the previous transformation happens when many
superposed lines become a texture (everything from a chord to a more
intricate pattern); this transformation is called fusion. The inverse
transformation is called fission (beginning with a texture which is dissolved
into the perception of individual elements). A common example in classical
and baroque music would be the contrasting of polyphony and homophony. A
proliferation transformation – a multiplication of elements - can halt before
the lines start integration into a texture; however if it does, the
proliferation may be seamlessly followed by a fusion. The Example from K.
Stockhausen’s Gruppen is a demonstration of this; it moves from
proliferation to fusion.
Figure 27. Fusion: J. S. Bach, “Omnes Generationes” from Magnificat
in D major.
Comments to the analysis:
The sound example fades in the middle of a dense, fugal stretto. To suggest what is
heard, two distinctive linear elements in superposition are shown (suggesting the
two upper lines of the thematic stretto); below these is shown a texture of medium
complexity, suggesting the web of parts not heard as a foreground. The fusion
transformation goes on to simplify the background into simple chords, and reduces
the number of foreground elements. However, the situation does not proceed in a
fully linear way to the fermata chord, indicated by the simple texture; it spreads
out (proliferates) again before the fermata chord is reached. As the fugue
proceeds, a brief fission is heard before all the forces again fuse into the
concluding tonic chord.

Figure 28. Fusion: K. Stockhausen, Gruppen (2 & 3).
Comments to the analysis:
The sound example begins more or less where the previous recording of Gruppen
stopped, i.e. at a stage in which the linear element – identification of individual
lines and instrument sounds – tends to become difficult and the listening mind
changes its intentions from trying to perceive individual parts to grasping a global
object. At this point, the fusion takes place. This spot is not in any way marked by
the music; it takes place solely in the listener’s mind, and the exact spot where it
occurs, cannot be objectively determined. At a certain point the complex texture
(“accumulation” it could be called, using a term from Schaeffer’s
spectromorphology) turns into a simpler texture of huge chords. This can be seen as
another fusion; or it could be conceived as an anamorphosis (discussed later).
Long, linear evolutions, like the one shown through the two examples from
Gruppen, can sometimes be too predictable to keep the listeners’ attention; but
not so in this case. The composer has ingeniously interspersed the evolution with
surprises: sudden, interpolated single notes. Thus a secondary element of collection
runs counter to the general evolution (proliferation). This aspect is not represented
in the analysis shown.
Figure 29: Fission: G. F. Händel, “All We Like Sheep” from The
Messiah.
Comments to the analysis:
The first words “All we like sheep” are presented in a simple, unison rhythm, once
echoed by the orchestra (the inverted form segment). The words ‘have gone astray’
increase the melodic range and are set in a more agile rhythm. The echo in the
bright voices suggests a two part texture. With the words ‘We have turned’ we are
back to very elementary materials; however, each short cell is set apart by being
distributed among different groups of singers as a part of the ongoing fission or
dispersion transformation. As the last stage of fission, a fully developed fugal
theme starts. The formal transformation of fission iconically represents the
metaphors used in the text (‘we all … have gone astray’, ‘we have turned everyone
to his own way’).
Figure 30. Fission: W. Lutoslawski, Jeux Vénitiens.
Comments to the analysis:
The first forty seconds of this example are basically a discontinuous alternation
between simple textures with a great degree of fusion, and complex textures, with
much greater inner activity, i.e. textures that tend towards fission. This alternation
prepares for the more radical fission to take place: more and more individual lines
emerge in a dramatic continuous transformation leading towards the climax of the
piece.
- A further development of the two previous cases occurs when a form
segment becomes extremely complex, loses inner articulation and is
ultimately turned into a simple, unarticulated segment. The transformation
from extremely complex directly to simple form segments is called
anamorphosis; the inverse transformation catamorphosis. Examples of this

pair of transformations are rarely, if at all, found in classical music, although
they do occur occasionally in the avant-garde music of the 20 th century.
These transformations pass out from the ordinary context of polyphony vs.
homophony (fission vs. fusion), in that they carry the transformation to a
complete extreme by transforming texture into a simple sound object.
Figure 31. Anamorphosis: L. Thoresen, Ovringar, ending.
Comments to the analysis:
The example shows the end of Ovringar. It begins in the middle of a very complex
texture, which still can be heard as separate parts. From here a fusion begins,
which eventually (after the cut in the examples) continues as an anamorphosis: the
transformation of texture into sound, in this case noise (examples of similar
transformations are found e.g. in the music of T. Murail (Memoires, Erosions), G.
Grisey, and K. Saariaho).
Figure 32. Catamorphosis: L. Thoresen, Ovringar, opening.
Comments to the analysis:
This example shows the opening of Ovringar, analyzed as a catamorphosis, the
symmetric opposite of anamorphosis, which is the transformation ending the piece.
It shows the gradual passage from a relatively simple noise sound into textures of
increasing inner activity and articulation. Eventually a fission takes place and a
melodic element emerges.
The final pair of transformations listed, liquidation and crystallization,
require a definition of Prägnanz to be understood, and examples will be
given at the end of the next chapter.
2.4 Prägnanz
In the last pair of form-transformations discussed above, that of
liquidation/crystallization, one other characteristic of musical form is
involved, namely that of Prägnanz. This is an emergent quality considered
essential for the presentation of the classical theme, which thus deserves a
more detailed discussion. The word Prägnanz used in a musical context could
be said to have two meanings: One would suggest that we have an idea that
gives birth to materials and ideas that are essential to the further
development of the composition. A theme in a sonata, as opposed to a
melody in a song, would have this quality. 18 The word can also refer to the
gestalt quality of the statement itself, and it is on this aspect of the concept
we shall concentrate in this context. In the latter sense, a pregnant formsegment
is characterized by an optimal combination of articulated,
distinctive form-elements, contextual self-affirmation and well-defined
boundaries, and good continuation. Moreover, the form-elements have to be
sufficiently complex and articulated, and they can never belong to the
lowest category of differentiation (simple form-elements) or to that of
extreme complexity. The tendency towards articulation and complexity

must, however, be counterbalanced by a self-affirming or redundant
context, which means that the form-elements or segments must be repeated
(exactly or varied) in the immediate context.
It would be reasonable to assume that the more complex the form-elements
are, the more repetitions could be allowed without losing Prägnanz (this still
remains to be demonstrated). Too much repetition, however, will lessen the
Prägnanz of the form-segment, just as, symmetrically, too much information
will threaten its unity and comprehensibility. To have well-defined
boundaries, the pregnant gestalt needs to occur in a phrase whose ending is
clearly marked out in the context.
The criterion of a good continuation applies to the immediate surroundings
of the distinctive core statement of a pregnant gestalt. The beginning of the
score statement should preferably be well prepared by the previous score
statement so the listener is alerted to the coming of something important.
After the important information there should be a phase that allows for
absorption of the information without introducing anything significant and
new, and the listener should moreover be alerted to the imminent ending of
the pregnant statement. In this way the listener will be able to ‘detach’ the
information from the context, remember it outside the general flow of
temporal retentions and protensions, and transfer it to his/her long-term
memory. The musical information may now be consciously recalled and its
return expected. The articulated part of a pregnant statement should be
surrounded by less important surroundings (thus materials with more
anonymity).
In a larger musical context, a pregnant theme presentation mostly serves to
present musical information in a fashion that is both comprehensible and
memorable. Therefore, a pregnant organization of the constituent motives
of a particular piece into a distinct theme will enhance the ability of the
listener to comprehend the piece as a whole, provided the remaining piece
avails itself of the musical elements presented in the initial gestalt. This
latter condition is, in fact, one attribute of the phenomenon of Prägnanz
itself, namely the law of good continuation, and is moreover intrinsic to the
understanding of a theme as opposed to a melody.
One instance of the presentation of a distinctive thematic motive could look
like this (see Figure 12):
Figure 33.
Here, two well articulated/distinctive form-elements are repeated in a
clearly demarcated phrase. What is not shown in this example is whether the
criterion of good continuation is fulfilled. The form-building transformation
of liquidation creates a context for the distinctive form elements that allows
them both to stand out, and to be absorbed by the listener. The liquidation

process thwarts the balance between information and redundancy in favour
either of differentiation, or of redundancy, so that distinctive materials can
stand out in relation to less distinctive materials. If the less distinctive
materials are related to the distinctive ones, the effect of the liquidation is
also to allow the information to ‘sink in’ and to be absorbed by the listener.
The inverse transformation we have termed crystallization suggesting the
movement from looser to firmer gestalts. 19
The classical theme is the ultimate example of Prägnanz, combining firm
gestalts with the loosely organized form-segments, such as the ones used in
passagework, transitional passages etc., in the same way that a foreground
presupposes a background. The combination of repeated, self-affirming,
characteristic motives in a context with looser forms gives us the
prototypical shapes of the ways in which a theme is presented in a classical
work: The Period (consisting of two major time segments, i.e. an antecedent
and a consequent, each of which begins with a distinctive motive followed
by less distinctive materials), and the Sentence (an initial repetition of the
distinctive motive, followed by transformations of the same motive,
breaking it down to less characteristic configurations) (see Figure 13).
Figure 34a. Period: Mozart, Piano Sonata in A minor KV 310, 2nd movement.
Figure 34b. Sentence: Beethoven, Piano Sonata in C major op. 2:2.
Crystallization is a less studied phenomenon; as a musical form it is probably
the creation of late classicism or early romanticism. It inverts the position of
firm and loose gestalts that we find in the classical sentence, by placing the
loose material in front of the core motive. One is given the impression of
witnessing the genesis of a theme, rather than being faced with a finished
statement that has to be absorbed. The definitive example of this type of
transformation is the opening of Beethoven’s ninth symphony.
Figure 35. Crystallization: L. v. Beethoven, Symphony no. 9, mov. I.
Comments to the analysis.
Two note fragments of the theme are presented over a drone. The fragments move
closer, and more notes are included in greater speed, all supported by a forward
oriented dynamic form function. Eventually, these fragments are synthesized into
the first motive of the theme, which is a pregnant statement in view of the way it
is prepared (synthesis of related motive fragments), and its repetition shortly after.
A moment of great impact takes place exactly before the beginning of the theme,
and it is interesting to note how it is brought about: What precedes the theme is
not a fragment of the theme, but a fusion of the fragments with the tremulato
background chord. The synthesis process, therefore, does not proceed in a linear
way towards the theme; the speeding up of the fragments leads to fusion into a
texture, and while clearly leading up to the theme, the theme itself is nevertheless

allowed to enter with the greatest possible contrast in relation to what immediately
precedes it.
While liquidation and crystallization are linked to distinctiveness, they can
be supported by most of the aforementioned transformations. Examples have
already been shown:
-Figure 12 (Mendelssohn's Quartet in D major) demonstrates a liquidation by
partitioning and followed by proliferation, terminating by simplification.
-Figure 18 (contrast theme in Liszt’s Eine Faust Symphonie) and 22: (The b-minor
sonata by F. Liszt) show a similar formal construction: The synthesis transformation
supports the crystallization transformation. After the theme is presented in a firm
gestalt, a liquidation through partitioning follows. The formal pattern suggested is
therefore symmetric: crystallization, repeated presentation of distinctive
materials, liquidation.
-Figure 24 (Sinfonia op. 18, no 1 by J. C. Bach) the transformations of collection
and proliferation are organized as a period: The antecedent consists of a focused
main motive (collection) followed by a proliferating segment; then a consequent is
constructed in the same way. The focus on collection and proliferation is
maintained in the transitional passage that follows, although the motives used may
only be distantly related to that of the characteristic motive.
-Figure 32 (Thoresen, beginning of Ovringar) shows a catamorphosis that is being
followed by a fission, as the result of which a melodic shape emerges (a motive
from a piece of archaic fiddle music. The catamorphosis and fission realize a longrange
crystallization transformation, reinforced by the forward-oriented dynamic
function, thus preparing the arrival of the folk tune in a pregnant context (not
included in the sound example).
The pregnant formulation of a musical statement is very much linked to the
classical conception of a characteristic and memorable theme – ‘the theme
as the theorem’. This particular musical feature is seldom found in the
contemporary music created during the last 60 years; many composers
whether of the serialist, spectralist, electroacoustic, or minimalist schools,
insisted on the importance of avoiding pregnant statements. An example of a
contemporary use of materials for this purpose is demonstrated in Figure 36.
Figure 36. Liquidation: L.Thoresen Illuminations.
Comments to the analysis:
At the very opening of this double concerto for two violoncelli and orchestra a
static sound prepares the listener to prepare for the erupting fortissimo texture.
This texture has a medium complexity, and is one of the most characteristic
textures of the piece. The next texture suggests a fission, presenting melodic
elements deduced from the motives used by the two solo cellos (not included in the
sound example); however the next textures are less articulated and of a simpler
kind. A backward leaning or reclining dynamic function supports the transformation
from complex to simple texture. Thus a virtual liquidation transformation is made
without linear elements.

In classical music, the normal way to carry out liquidation is through
partitioning and fragmentation. However, simplification, proliferation,
fusion and anamorphosis are also potential vehicles of liquidation. Similarly,
the vehicle of crystallization is normally integration, but can also be
synthetization, complication, collection, fission and catamorphosis.
However, the context organization of the form segments can also exert an
influence on the perception of Prägnanz. E.g. if the same distinctive element
is repeated excessively, it will become redundant and devoid of interest,
thus in effect resembling a simplification transformation that affects the
very substance of the musical material.
2.5 Closing Comments
The preceding presentation of form-building transformations is not entirely
complete, since a study of listener modalities in relation to form-building
transformations has been left out in order to keep the length of this paper
within reasonable limits. However, even if that study had been included, the
discussion of musical form would by no means be comprehensive. At least
two other form-building isotopies, namely form-building functions, and formbuilding
processes, still need to be discussed. Moreover the articulation of
musical gestalts into successive and simultaneous units will need to be
treated in detail. The Aural Sonology Project has developed detailed
analytical instruments for dealing with all of these dimensions. Additionally,
the numerous ways in which form-building isotopies interact remain to be
examined. The form-building isotopies mentioned in this article are basically
syntactic; nevertheless, they can occasionally be interpreted as metaphors
for non-musical meanings. Semantically oriented logics, e.g. narrative
schemes, may interact with or override these three isotopies. Indeed,
neither theoretical, nor rational, nor structure-oriented discourses will
adequately and a priori cover the immense field of musical form.
It should be understood that the findings presented here are merely one
component of an inquiry that can probably never be carried to a conclusive
end. As a composer I am immensely grateful that this ultimate end is out of
the reach of the theory, as the field of creation thus remains open, and
musical reality will always remain a source of wonder, discovery and
surprise.
In the early 19 th century, the musical forms that were more or less
spontaneously created during the 18 th century were analyzed and made into
normative theory. For a relatively short period of European music history,
musical form was, at the same time, a spontaneous musical practice and a
normative theory. The more advanced composers of the 19 th century were,
however, already developing formal conceptions that had by then bypassed
theoretical dogma. In ways that were not explicable, new musical forms
often made sense to the unprejudiced listener, not through their conformity
with normative conventions that existed in the listeners’ minds prior to

hearing the music, but because of the intrinsic logic of the sonic gestalts.
The listeners were made to marvel at the discovery of rational forms that
eluded conceptualization. The rational syntax of the music emerged to the
listener as the music unfolded, quite independently of the listener’s
preconceived notions of conventions for musical forms. The present
approach focuses primarily on such emergent musical forms.
The dissolution of tonality and the wish to avoid trite clichés has led
composers and theorists of the 20 th century to become concerned with
musical morphology. Modality, polytonality, atonality and spectrality have
been explored and explained. Moreover, the desire to include new sonorities
and textures in music (e.g. complex spectra, glissandi, sound accumulations)
has made it necessary to conceive of completely new relationships between
sound qualities and overall shape. However, the need to come to grips with
the new musical materials and their technique has allowed the discussion of
technical aspects of music production to monopolize the theoretical
discourse on contemporary music.
By conceptualization and objectification of certain emergent, form-building
musical gestalts, the present article has tried to give focus to possible
patterns of musical order at the level of musical form as heard. When a
musical form makes sense, music enters the mind of the listener, and this
act of internalization is a prerequisite for the listener’s act of further making
sense of the music: When coherent musical gestalts are formed and
internalized with the listener, they may in turn be understood in iconical and
indexical ways. In the examples above, we saw one clear example of this,
when the formal function of fission was used to symbolize sheep that had
gone astray (Figure 29).
We have insisted on a “blindfolded” approach to analysis – i.e. not using the
score during the process of making the analysis; this is one essential, though
not exclusive, way of accessing the musical phenomenon. Through this
approach we hope to stimulate and crystallize patterns of musical thinking
that are sufficiently close to music for it to be helpful for the reflected
musician and composer. At the same time it represents a fresh approach and
a challenge to traditional academic approaches to musical theory and
analysis.
References: Literature.
Bent, I. with Drabkin, W. (1998). Analysis. The New Groves Handbooks in Music.
London.

Bortoft, H. (1996). The Wholeness of Nature. Goethe’s Way of Science. New York:
Lindisfarne Books.
Caplin, W. E. (1998). Classical form: a theory of formal functions for the
instrumental music of Haydn, Mozart, and Beethoven. Oxford: Oxford University
Press.
Chion, M. (1983). Guide des Objets Sonores. Paris: INA & Éditions Buchet/Chastel.
Clifton, T. (1983). Music as Heard: a Study in Applied Phenomenology. New Haven:
Yale UP.
Dalbavie, M.A. (1991). “Pour sortir de l’avant-garde.” In Le Timbre, métaphore
pour la composition. Barrière, Jean-Baptiste (éd.) Paris: IRCAM et Christian
Bourgois.
Delalande, F. (1998). “Music Analysis and Reception Behaviours: SOMMEIL by Pierre
Henry.” Journal of New Music Research, Vol. 27, no. 1-2.
Dreyfus, H.L. (1991). Being-in-the World. A Commentary on Heidegger’s Being and
Time, Division I. Cambridge, Massachusetts; London, England: The MIT Press.
Ferrara, L. (1984). “Phenomenology as a Tool for Musical Analysis” The Musical
Quarterly, vol. LXX, No.3. New York, London: G. Schirmer.
Ferrara, L. (1991). Philosophy and the Analysis of Music. Bridges to Musical Sound,
Form, and Reference. New York; Westport, Connecticut; London: Greenwood Press.
Greimas, A.J. (1983). Structural Semantics. An Attempt at a Method. Introduction
by Ronald Schleifer. University of Nebraska Press.
Hatten, R. (2004). Interpreting Musical Gestures, Topics, and Tropes. Bloomington:
Indiana University Press.
Kühn, C. (6. edition, 2001). Formenlehre der Musik. Kassel, Basel, London, New
York, Prague: Bärenreiter Verlag.
Marx, A.B.(1837-47). Die Lehre von der musikalischen Komposition, praktisch und
theoretisch. Vol. I, seventh edition 1868. Leipzig.
Miller, I. (1984). Husserl, Perception, and Temporal Awareness. A Bradford Book.
Cambridge, Massachusetts; London: The MIT Press.
Monelle, R. (2000). The Sense of Music. Princeton University Press.
Nielsen, P. (1971). Den musikalske formanalyse. Copenhagen: Borgen forlag A/S.
Nattiez, J.J. (1990). Music and Discourse. Toward a Semiology of Music. Carolyn
Abbate (transl). Princeton, New Jersey: Princeton University Press.

Piaget, J. (1968). Le Structuralisme. Presses Universitaires de France
Schaeffer, P. (1966). Traité des objets musicaux. Éditions du Seuil. Paris.
Schoenberg, A. (1977). Fundamentals of Musical Composition. Gerald Strang &
Leonard Stein (eds.). London: Faber and Faber Ltd. (Reprint).
Smith, F.J. (ed.) (1976). In Search of Musical Method. London, New York, Paris:
Gordon and Breach Science Publishers.
Sokolowski, R. (2000): Introduction to Phenomenology. Cambridge: Cambridge
University Press.
Sokolowski, R. (1974): Husserlian Meditations. Evanston: Northwestern University
Press.
Stoïanova, I. (2000): Manuel d’analyse musicale. Variations, sonate, formes
cycliques. Minerve. France.
Tarasti, E. (1994). A Theory of Musical Semiotics. Bloomington: Indiana University
Press.
Thoresen, L. (1987). “An auditive analysis of Schubert’s Piano Sonata Op. 42.” In
Semiotica 66-1/3. Amsterdam: Mouton de Gruyter.
Thoresen, L. (1996). ”Flerskiktighet i Olav Anton Thommessens orkestermusikk.” In
Olav Anton Thommessen, Inspirator, Tradisjonsbærer, Rabulist. Oslo: Norsk
Musikkforlag.
References: Recordings.
Bach, C.P.E. Sonatas & Rondos. Mikhail Pletnev. Deutsche Grammophon 459 614-2
GB.
Bach, J.C. Sinfonia. Netherlands Chamber Orchestra; David Zinman. Phillips
442275-2.
Bach, J.S. Magnificat BWV 243. La Chapelle Royale, Collegium Vocale;
Philippe Herreweghe. HMC 901326.
Bach, J.C. Jesu Meine Freude. Die 6 Motetten. Bachchor Stockholm, Concertus
Musicus Wien; N. Harnoncourt. Das Alte Werk, 1989 Teldec Record Service Gmbh.
Beethoven, L.v. Diabelli Variationen. Pollini. Deutsche Grammophon 459645-2
Beethoven, L.v. Klaviersonaten. Artur Schnabel. EMI CHS 7 63765 2 PM 936.
Beethoven, L.v. Symphonie no. 9. Staatskapelle Dresden; Herbert Blomstedt.
Brilliant Classics 99927, Phillips 442275-2.

Gérard Grisey. Modulations (1978). Ensemble Intercontemporain; Pierre Boulez.
Erato We 810.
Händel. G.F. Messiah. The Academy of Ancient Music; Christopher Hogwood.
Editions de L’Oiseau – Lyre 430 488-2.
Janácek, L. String quartets. Skampa Quartet. Supraphon SU 3486-2 131.
Ligeti, G. Works for Piano. Pierre Laurent Aimard. Sony SK62308.
Liszt, F. Sonata in B minor. Maurizio Pollini. Great Pianists. Deutsche Grammophon
Ges. /Phillips Classics.
Liszt, F. Eine Faust-Symphonie. Vinson Cloe Staatskapelle Dresden; Giuseppe
Sinopoli. Deutsche Grammophon 449 137-2 GH DDD.
Lutoslawski, W. Paroles tissées. Polskie Nagrania. PNCD 042A.
Lutoslawski, W. Jeux vénitiens. Polish Radio National Symphony Orchestra; Witold
Lutoslawski. EMI Classics/double fforte, 2000.
Mendelssohn, F. String Quartets vol. 2. Eroica Quartet. Harmonia Mundi HMU
907287.
Mosolov, A. Zavod. Decca 436640-2
Mozart, W.A. Piano Sonatas. Liv Glaser. Simax PSC 1125.
Thoresen, L. Illuminations. Oslo Philharmonic Orchestra; Liv Opdal, Aage Kvalbein;
Marcello Viotti. Aurora ACD 5008.
Thoresen, L. Løp, Lokk og Linjar. BIT20, Berit Opheim; Jeffrey Milarsky. Aurora
(forthcoming).
Stockhausen, K. Gruppen. Berliner Philharmoniker; Claudio Abbado. Deutsche
Grammophon 447 761-2.
Walton, W. Symphony no.2. The Cleveland Orchestra; George Szell. Sony Classical
01-046732-10.
Xenakis, I. Persephassa. Les Percussions du Strasbourg. Philips 442 218-2.
1 The term “music as heard” is the apt title of an important book on the
phenomenology of music. (Clifton, 1983)

2 “Le processus, plus qu’un procédé, est un matériau. A un niveau plus abstrait, le
fait que le processus soit dérivé d’un ‘matériau sonore’ implique qu’il contient
suffisamment de ce matériau même. Le matériau musical n’est plus l’objet de
départ, mais le mouvement que l’on imprime à l’objet: le processus généré par cet
objet. Cette évolution, qui tend à virtualiser l’objet sonore et à le substituer à
l’action que l’on effectue sur lui correspond à la différence entre les deux
générations que j’ai présentées. Le passage de l’objet au modèle, puis du modèle
au formel se caractérise par l’attitude qui tend à privilégier l’écriture et sa
dynamique par rapport à la contemplation statique du matériau sonore” (Dalbavie,
1991, p. 333).
3 Our perspectives on phenomenological philosophy is based on secondary sources
and interpretations on Husserl’s and Heidegger’s writings, such as Robert
Sokolowsky (1974, 2000), Itzchak Miller (1984), Dreyfus (1991), Henri Bortoft
(1996).
4 The semiological tripartition has been an important feature of the semiological
(or semiotic) approach to music, as worked out by Molino and Nattiez:
(a) The poïetic dimension: even when it is empty of all intended meaning, . .
. the symbolic form results from a process of creation that may be described
or reconstituted.
(b) The esthesic dimension: “receivers”, when confronted by a symbolic
form, assign one or many meanings to the form; the term “receiver” is,
however, a bit misleading. Clearly in our test case we do not “receive” a
“message’s” meaning (since the producer intended none) but rather
construct meaning, in the course of an active perceptual process.
(c) The trace: the symbolic form is embodied physically and materially in the
form of a trace accessible to the five senses. We employ the word trace
because the poetic process cannot immediately be read within its
lineaments, since the esthesic process (if it is in part determined by the
trace) is heavily dependent upon the lived experience of the “receiver”.
Molino proposed the name niveau neutre [neutral level] or niveau matériel
[material level] for this trace. An objective description of the neutral level
can always be proposed - in other words an analysis of its immanent and
recurrent properties. This is referred to throughout this volume as “analysis
of the neutral level.” (Nattiez, 1990, pp. 11-12)
5 Monelle’s criticism of Nattiez’ definition of the “neutral level” in Fondements
d’une sémiologie de la musique (Nattiez, 1975) is justified, particularly with regard
to the fact that his approach does not incorporate criteria for what makes sense
musically according to “native speakers” of the musical language.
Structural linguistics depends on the concept of pertinence, the native
speaker’s distinction between what is significant, and what is not, in the
phonetic continuum of the language. The pattern of equivalences that
results is called a phonemics; without the input of a pertinence, linguistics is
nothing more than phonetics. Yet in Nattiez’s “description of the neutral
level”, his programme for music analysis, it is clear that he is not concerned
to interrogate informants. On the contrary, the music – which is to say the
score - is examined according to rational criteria only. (Monelle, 2000, pp. 4-
5)

However, rather than discarding the semiotic tripartition entirely, it seems to me
more reasonable to reorganize it in the way shown. Music certainly has to make
sense; however, as any composer will know, it is also necessary to experiment with
sonic materials and their organization in their neutral aspect, i.e. before their
function in the music or for the listener is completely clear. This aspect of musical
reality would, however, belong to the neutral side of the poïetic domain; thus even
here, the analyst would need an informant: the composer himself, or, at least, the
material traces left from his compositional process.
6 What we call reductive listening consists in simply listening to the sound as
sound. The intention to listen to the sound as sound – not as an indication of its
cause, not as a result of communicative intention, not as a component in a
syntactic unit – constitutes a specific type of object that we shall call the sound
object. In the words of Michel Chion:
On appelle objet sonore tout phénomène et événement sonore perçue
comme un ensemble, comme un tout cohérent, et entendu dans une écoute
réduite qui le vise pour lui-même, indépendamment de sa provenance ou de
sa signification.
L’objet sonore est défini comme le corrélat de l’écoute réduite: il n’existe
pas ‘en soi’, mais à travers une intention constitutive spécifique. Il est une
unité sonore perçue dans sa matière, sa texture propre, ses qualités et ses
dimensions perceptives propres. Par ailleurs, il représente une perception
globale, qui se donne comme identique à travers différents écoutes; un
ensemble organisé, qu’on peut assimiler à une “gestalt” au sens de la
psychologie de la forme. (Chion, 1983, p. 34)
7 See e.g. Monelle (2000, pp. 10-19), Tarasti (1994, pp. 11-15), Hatten (2004, pp. 4-
18)
8 The following defines what I refer to as operational structuralism:
Or, par-delà les schémas d’association atomistique et ceux des totalités
émergents, il existe une troisième position, qui est celle des structuralismes
opératoires: c’est celle qui adopte dès le départ une attitude relationnelle,
selon laquelle ce qui compte n’est ni l’élément ni un tout s’imposant comme
tel sans que l’on puisse préciser comment, mais les relations entre les
éléments, autrement dit les procédés ou processus de composition (…), le
tout n’étant que la résultante de ces relations ou compositions dont les lois
sont celles du système. (Piaget, 1968, pp. 8-9)
9 Every method of musical analysis sets its particular foci, and would give a
complementary idea of another aspect of the musical object. Ferrara (1984, 1991)
has taken the full consequence of this and launched a method based on an eclectic
model. The idea to combine different methodologies with complementary functions
seems a reasonable step; however, since the analytical methods of Aural Sonology
are still developing, this step is not yet taken.
10 “A. J. Greimas has borrowed the term isotopy from the domain of physical
chemistry and has translated it to semantic analysis by conferring on it a specific
signification in the context of its new field of application. In its operational
character, the concept of isotopy first of all designated iterativity throughout a
syntagmatic chain of classemes which assure a discursive utterance [discourse =
énoncé] its homogeneity. From this definition, it is clear that the syntagm joining

at least two semic figures can be considered the minimal context allowing the
establishment of an isotopy. Thus, regarding the semic category which subsumes
two contradictory terms: the four terms of the semiotic square [carré semiotique],
when we take into account the trajectories to which they can give rise, would be
called isotopies” (Greimas, 1979, Ronald Schleifer’s introduction).
Tarasti defines musical isotopies in the following way: “In music, isotopies mean
the principles that articulate musical discourse into coherent sections” (Tarasti,
1994, p. 6).
11 We emphasize general, since the listed isotopies may be accorded a certain a
priori existence. Any relevant analysis, however, will have to start with a given
piece of music, and the open-minded analyst, bracketing her preconceptions to the
extent possible, should, initially at least, let the experienced music itself set its
foci. Thus a particular piece may suggest a particular, perhaps thematic isotopy,
one that possibly may be described as a focus on particular elements and functions
described in our general isotopies, or one that could best be described using a
combination of these, or one that might elude any description suggested by the
general isotopies. In the latter case, one will have to ask whether one has found an
isotopy with a potential for generalization. However, it is worthwhile noticing that
not all music has got a pertinent isotopy on the level of form (level 3). In Thoresen
(1987) actual thematized musical isotopies are discussed in connection with an
analysis of a piano sonata by F. Schubert. These determine the narrative form of
the sonata (whose thematic form is the traditional sonata form), and can be
interpreted as the signifiers (or tertium comparationis) of iconic signs, with extramusical
meanings as their signifiers.
12 The dynamic aspect of form opened for a non-reversible view of musical time.
Thus, the restatement of the principal theme after the development section has
got another formal function than its first statement. This change of function of the
principal theme when it occurs in the recapitulation is e.g. clearly composed out
e.g. in van Beethoven’s Apassionata and the first movement of the 9 th Symphony.
We see interference between two formal principles, one based on thematic
recurrence, the other on dynamic principles. The consequence of this is clearly
spelled out in Wagner’s Tristan prelude, the form of which is not primarily based
on contrasting different sections of thematic differences, but on waves of tension
and relaxation, moving towards a climax.
Une des propriétés fondamentales du processus symphonique est sa
téléologie et son irréversibilité: les composantes formelles ne sont pas
interchangeables, et il n’y a pas de répétitions symétrique et tautologique
en musique, même dans les formes bi- et tripartites simples et complexes,
dans la mesure ou le devenir en musique, du fait de sa nature temporelle,
est un processus cumulative. (Stoïanova, 2000, p. 11)
13 Schoenberg’s distinction between Loose and firm Gestalts owes undoubtedly
much to A. B. Marx distinction between Satz and Periode on the one hand, and
Gang. Whereas the two former terms refer to musical elements based on 4 and 8
bars with and clearly delineated borders, Gang refers to transitional sections, often
based on harmonic sequences, and without clearly marked boundaries. “Nun muss
es aber auch Tongebilde geben können, die eines Abschlusses, wie Sätze und
Perioden haben, entbehren (...) Ein solches Tongebilde nennen wir Gang” (Marx,

vol I:30). “Ein Gang ist eine Melodie ohne bestimmten Abschluss. Er entsteht aus
der Fortführung eines Motivs auf eine beliebige Strecke hin” (Marx, vol. I, p. 35).
(Marx’s Kompositionslehre came in several improved versions. The present
references are taken from Nielsen’s (1971) book on formal analysis; Nielsen seems
to quote the seventh edition (1868); I have not been able to identify his quotations
against the original, as this particular edition is not available to me.)
14 See Thoresen (1996, p. 153).
15 The contrast between textures can also be given form-building function that is as
important as the contrasting of themes in classical music. With F. J. Haydn, the
secondary theme of his sonatas and symphonies is not infrequently the same as the
principal one, the difference being that it is presented with a different texture and
tonal center. See e.g. Piano Sonata no 60, Hob. XVI/50.
16 A conclusion that can be drawn from this is, of course, that it will be harder to
obtain distinctive elements in compositions having a very complex musical texture;
the same will apply to compositions that only use very simple elements.
17 This sign is also useful when it comes to characterizing formal processes (giving
further nuances to the established categories of recurrence, variation, and contrast
as proposed by Bent (1998, pp. 5 and 88), and we will discuss this in greater detail
in forthcoming work.
18 Explaining the difference between a theme and a melody, Schoenberg writes:
Every succession of tones produces unrest, conflict, problems. One single
tone is not problematic because the ear defines it as a tonic, a point of
repose. Every added tone makes this determination questionable. Every
musical form can be considered as an attempt to treat this unrest either by
halting or limiting it, or by solving the problem. A melody re-establishes
repose through balance. A theme solves the problem by carrying out its
consequences. The unrest in a melody need not reach below the surface,
while the problem of a theme may penetrate the profoundest depths.
(Schoenberg, 1977, p. 102)
19 While Schoenberg (1977) describes liquidation, he does not treat the inverse
transformation. We have called it crystallization, the logical inverse of making
something liquid. Schoenberg’s ideas on classical forms have been brilliantly
developed by Caplin (1998).