Formalizing musical thought, a personal model of musical articulation (2011)

In the following observations, I discuss the outlines of a general model of composing with sounds developed and used during the composition of my latest works. With respect to concepts and notions of measurement and proportion of structure that can be applied both in theory and in praxis of the process of composition, this model illustrates some general steps for articulating musical form as well as ways the overall architecture of a musical work can be developed out of smaller compositional units.

As self knowledge is something that usually comes out from the composer’s individual experiences and the experiences that he gathers in his research. My aim here, is to demonstrate a set of metacognitive tools that enable me to monitor and assess my degree of self knowledge with a certain or more processes, concerning the creation of musical morphologies. My main concern is with representational aspects, rather than with implementation. However a part of this idea implemented in order to serve my compositional needs during the construction of the different parts of my musical work “Wondering Around” (2011) and consequently of some parts of my work “Conspiracy of the Scapegoats” (2011) to be discussed in chapter III. Considering composition as the action of defining, articulating, and bringing into interaction a variety of levels I created a model of musical articulation, in which compositional dimensions are defined by fundamental assumptions about the generation of structure, referring to formalized notions of measurement and proportion as mentioned before. These formalized notions of measurement and proportion are generalizing the concept of structure in three deferent levels. Micro, meso and macro. They are considered as operational levels, without reference to any representation. They are are forming an abstract conceptual tool, which is applied on and developed during the composition of my musical work “Under the Sunlight” and expanded in composing the pieces “Wondering Around” and “Conspiracy of the Scapegoats”. (https://soundcloud.com/soph)

Conceptual Tools

The model of musical articulation provided here, is concerning musical relationships and a method that may be used from different perspectives. It is a set of metaphors that use musical information. These metaphors can be organized into units and mapped onto higher levels of musical articulation and of musical structure. Roads, (2001) projects a view of nine time scales of musical sound structure. He examines these time scales a hierarchy, from both aesthetic and technical viewpoints, as well as the particularities and the boundaries between these various time scales.

According to the concept of the various time scales, the model of musical articulation I developed, concerns the projection of different proportions of sound in time, articulated into various sound structures, used in the construction of one final structure. While we are working with sound material, we find ourselves confronted with different time levels. A variety of proportions of sound have to be organized into higher levels of time. Stockhausen, (1957) in his article “How time passes”, which is a unified view of the relationship between the various time scales of musical structure states that: "Music consists of order relationships in time”. Wishart, (et all. 1994) introduced the term “time-frame”. He states that: “in working with sound materials, we quickly become aware of the different time frames involved and their perceptual consequences”.
In analyzing the model of musical articulation used in the development of my compositions “Under the Sunlight”, “Wondering Around” and “Conspiracy of the Scapegoats”, deferent elements of various sizes are forming the overall architecture of each piece of music. This approach is been used from two deferent perspectives. From one perspective a structure can be developed in a hierarchical way. This means that the smallest elements have to be constructed first. Then these small elements have to organized into networks to form higher levels of structure.
According to this, sounds may be organized in a multidimensional fashion, into formal sections. Formal sections are considered as sets or groups of formal units in terms of different classes, qualities or properties of them forming a network of relationships, defined by the composer. Finally different formal sections are combined together in order to define the overall structure of the piece. The properties of the formal units, as well as, the form sections are represented by variants, assigned to parameters. These variants are gradually taking deferent values in the range of time perception. So the term form unit is representing something that has to be composed. From an other perspective, compositional elements, no matter their size, can be organized in fashion in which a multidimensional system is defined as a combination of individual stepped lines in different directions. In this way, any size of material can be the starting point and relationships between deferent sound materials and consequently musical form is established in a non hierarchal way, during and by the exploration of this multidimensional system.

Structure

According to the concept of measurement and proportion, the first notion of measurement and proportion is “Structure”. It is a word with latin roots “struere”. It means to built, to arrange and contains the notion of an organized thing. The term refers both to the arrangement and the establishment of relationships between the parts or the elements of something complex such as a sound or a musical composition. In a way, we can consider that there is no deference between sound material and structure, we are just confronting deferent operating levels to compose.

“I consider sound itself not as something already given, but as something to be composed. So the tiniest sound already has a structure on which we can operate, that is, articulate, projecting onto it our own musical desires. Consequently, I assume that there is no difference of nature between structure and sound materials; we are just confronting different operating levels, corresponding to different time scales to compose.”
(Budon O. & Vaggione H. 2000)

Time

Time is a part of a measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects. Relationships between sound materials concern the way in which materials are arranged in sequences, simultaneities or juxtapositions and occur in the range of time perception. Musical structure here is developed throw deferent levels of time. The term time in a certain model of musical articulation can be considered as the indefinite continued progress, of the existence and coexistence of sonic events in the past, present, and future, regarded as one unique entity. This existence and coexistence of sonic events is established in a fashion in which low level entities that are forming a high level one, are expressed in proportions.

Scale

Scale is a sort of rule determining the distances between points arranged on a line. Such as a mathematical function. The term scale, in compositional praxis, refers both to a graduated range of values forming a standard system for measuring, or to a series of points at regular intervals in a line used in measuring things. This things, might be durations or other parameters concerned with the composition of a particular sound or with the composition of larger scale forms. Not only sound but all kinds of musical aspects can be expressed as proportions. This makes possible to use the same proportions for different parameters or different parameters for the same proportions. In addition, a scale allows the composer to mediate between two extreme points that are establishing the scale
Time scales

Time scale is the time allowed for a sequence of sonic events. According to the concept of musical time scale, in the model of musical articulation I developed, I distinguish the following musical time scales:

Micro (time-scale)

“Microsound is ubiquitous in the natural world. Transient events unfold all around in the wild: a bird chirps, a twig breaks, a leaf crinkles...”
Roads, C. et all. (2001)

A term with historical roots in the work of Iannis Xenakis, and strongly associated with the work of Curtis Roads. The term refers on conceiving of and representing sound in terms of particles. In this particular model of musical articulation, by operating on the micro time scale we end up with individual sounds. These individual sounds, constructed from smaller components can be treated as audible objects. Therefore the composer's theory of composition in this particular stage, is defined by the creation of abstract classes of individual sounds treated as sound objects.

“The sound object is the result of composition, and therefore is wholly comprised in the world of the artificial, it represents no preexisting nature to be contemplated in its perfection, nor does it represent an aim that results from an exploitation of natural forces”.
Di Scipio et all. (1998)

The Individual sound treated as an object is the basic unit of musical structure, generalizing the traditional concept form unit, in order to include spectrally complex instances of sound. The range of the existence of an audible object is from a fraction of a second to several seconds. In addition an audible object is something that has to be found, generated, modified or composed. Considering the audible object as the basic unit of musical structure, the next step is to organize a variety of audible objects into hierarchies. According to this, the next time scale of this model of musical articulation is the meso time scale.

Meso (time-scale)

Divisions of form - form sections. Groupings of individual sounds. Audible objects into hierarchies of phrase structures, of various sizes, measured in minutes or seconds. The meso time scale is a unit of structure, made from other units. These form sections are individual sounds organized into structures. These structures can sustain an independed existence. By applying now to the result of the process of grouping into hierarchies different classes of audible objects, the same process we arrive to the next time scale which is the overall architecture of a composition.

Macro (time-scale)

The time scale of the general configuration of musical architecture or form, measured in minutes or hours. Level of sound structure composed of several events that are placed into a network. Forms of organization at this level, result from interactions among lower level processes. The macro level of musical time corresponds to the notion of form of an entire musical work, and encompasses the overall architecture of a composition.

Levels of structure

Sound composition is the outcome of technical development and scientific research, but it is only in most recent years that it has reached a stage at which it may be considered as part of the legitimate musical sphere. On the other hand, as Eimert, (1957) noted, there is an essential relationship between electronic music and the traditional world of sound. Not only the because of the fact that musical elements are defined by pitch or by their spectral identity, duration and intensity, but also because of the connection between the traditional world of sound and the most contemporary development of musical thought. The task of composers has always been the management of the interaction among structures on different levels, while musical practice offers ways to project low level processes into macrostructures.

“Smaller forms may be expanded by means of external repetitions, sequences, extensions, liquidations and broadening of connectives. The number of parts may be increased by supplying codettas, episodes, etc. In such situations, derivatives of the basic motive are formulated into new thematic units”.
(Schoenberg, 1967)

Sound composition differs from traditional composition in its emphasis on direct acoustic manipulations of sounds and subsequently of families of similar sounds that may derived from a single sound object. The concept of the notions of measurement and proportion in this particular model of musical articulation I developed, is reflected on the structure of sound at any level related to any time scale, while time scales interlink. According to Roads, (et all. 2001) a given level of structure encapsulates events on lower levels and is itself subsumed within higher time scales. Operating on one level, affects other levels. However the interaction between time scales is not a simple relation. Linear changes on a given time scale do not guarantee a perceptible effect on neighboring time scales.

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According to which time scale I operate, I distinguish the three levels of musical structure, analyzed below.
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Micro-level Structure

Micro - origin: from Greek: “μικρός” = small. In general, this term, concerns the construction or identification of micro level entities that are used to create the architecture of an individual sound. It can be considered as the fine structure of a sound material, that can not be made visible and examined with the “naked” ear. A “microscope” by means of a device which can give us valuable information about this sound, expressed in numbers or represented graphically is appropriate here. Di Scipio (et. all 1998) notes that if this fine structure of our desired sound material considered as a model, this model provides us with the operative description for composing this sound. The character of a “model” of sound material shows its features. This features are elements of the microstructure. Now, by organizing or by operating on the microstructure of a sound we end with individual sounds. In the case of this particular model of sound articulation these individual sounds are treated as form units. Several different classes of sound events on a short time scale. Each class is characterized by its spectral envelope. The next task concerns the creation of groups of audible objects, placed into a network in order to interact. Short structures that can be considered as form sections, characterized by a specific "personality” consisting of many different and connected classes of audible objects. They can ether be collections of groups of audible objects, or individual groups of audible objects, organized together, in order to create form units. This applies to all types of possible relationships between collections of groups of audible objects and individual groups of audible objects.
As micro-level structure is considered here as the fine structure of the material, audible objets are characterized by the operative description of composing a sound. For instance, each sound of our every day surrounding environment, already has a structure on which we can operate. The already existing structure of a spectrum, can be utilized to change the original sound (Whishart, 1994). In addition real world sounds are the references these sounds provide. If the fine structure of our desired sound considered as a model, this model provides us with the operative description for composing this sound. By organizing these form units into form sections, we move to the next level of structure. The meso level structure.

Meso-level Structure

Hierarchies of phrase structures, constructed by following the same strategy but in a larger time scale. This means that collections of form units are organized together in order to create form sections. These form sections are the final material for the construction of the next level of musical structure, the Macro-level Structure.

Macro-level Structure

A large scale line or network of collections of form sections. This term concerns the construction or identification of entities, larger than those at the level of form unit and form section. This level of structure defines the architecture of a musical work.

References

Roads, Curtis. (2001). Microsound. Cambridge, MA: MIT Press.

Budon O. & Vaggione HA. (2000). “Composing with Objects, Networks, and Time Scales: An Interview with Horacio Vaggione”. Computer Music Journal, Vol. 24, No. 3 (Autumn, 2000), pp. 9-22.

Stockhausen, Karlheinz. (1957). "... wie die Zeit vergeht .. ." In Die Reihe no.3. Vienna: Universal Edition, 1957. (English edition, titled ". .. How Time Passes . . . ," trans. Cornelius Cardew. Bryn Mawr: Theodore Presser Company, 1959. German text, annotated by Dr. Georg Heike, reprinted in Karlheinz Stockhausen, Textezur Musik 1 (Cologne: Verlag DuMont Schauberg, 1963), 99-139. English edition, trans. and ed. Jerome Kohl (Kiirten: Stockhausen Verlag, in preparation).) pp. 10

Di Scipio. (1998). “Compositional Models in Xenakis's Electroacoustic Music”. Perspectives of New Music, Vol. 36, No. 2 (Summer, 1998), pp. 201-243

Schoenberg A. (1967). Fundamentals of Music Composition. London: Faber and Faber.

Wishart, Trevor. et. all. (1994). “Audible design.” Orpheus the pantomime Ltd, 1994