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JMM 4, Winter 2007, section 3

Lasse Thoresen
(with the assistance of Andreas Hedman and Olav Anton Thommessen)

An Approach to the Aural Analysis of Emergent Musical Forms

3.1. 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.

3.1.1. 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.

3.1.2. 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 reference ... 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.

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 extra-temporal, 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.

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.

3.1.4. 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.

3.1.5. 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.

3.2. 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.

3.2.1. 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

3.2.2. Context Organization of Form-Elements

Form-building segments will be defined through the combination of form-elements (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 form-elements, 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 [recording]

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 [recording]

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 [recording]

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 [recording]

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 [recording]

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

3.2.3. 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 [recording]

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 [recording]

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 [recording]

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 [recording]

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 [ open in separate window ]

Figure 17 Partitioning: W. Walton, Symphony no 2 [ open in separate window ]

Figure 18 Integration: F. Liszt: Eine Faust Symphonie, first movement [recording]

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 [ open in separate window ]

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 [recording]

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 [recording]

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 [ open in separate window ]

Figure 23 Synthesis: L. Thoresen, Tradlarudl [ open in separate window ]

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 [ open in separate window ]

Figure 25 Proliferation: K. Stockhausen, Gruppen (1) [ open in separate window ]

Figure 26 Collection: W. Lutoslawski, Paroles Tissés [recording]

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 [ open in separate window ]

Figure 28 Fusion: K. Stockhausen, Gruppen (2 & 3) [recording]

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 [ open in separate window ]

Figure 30 Fission: W. Lutoslawski, Jeux Vénitiens [ open in separate window ]

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 20th 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.

3.2.4. 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 form-segment 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 [recording]
Figure 34b Sentence: Beethoven, Piano Sonata in C major op. 2:2 [recording]

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 [ open in separate window ]

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 long-range 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 [recording]

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.

3.2.5. 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 form-building 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 19th century, the musical forms that were more or less spontaneously created during the 18th 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 19th 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 20th 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.





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