Music is a temporal art. It takes place in time and as it does it seems to reveal something essential about time. One way time is revealed to us through music is by way of a spatial metaphor. We perceive a sequence of sounds unfolding in time as moving through an imaginary space. Our hearing music as movement in turn is bound up with our hearing it as changing or staying constant—musical change seems to embody movement, while musical constancy or stasis seems to stand still. In Metodologie dell’improvvisazione musicale, Italian composer, improviser and music theoretician Mirio Cosottini formulates a methodology of improvisation that takes change and constancy as its basic categories.
Cosottini’s methodology casts improvisation in terms of a dialectic of linearity and nonlinearity. These latter two concepts, which trace back to Jonathan Kramer’s book, The Time of Music, provide the foundation not only for Cosottini’s methodology, but for the set of exercises he presents as a means for improvisers to expand their horizons of musical possibility.
Briefly, linearity is the quality of development and change over time; nonlinearity is the quality of invariance over time. Linear music is music that appears to move from one point towards another, in a more-or-less unbroken progression; nonlinear music appears to stay in one place or to reside in discontinuous, autonomous events—to exist outside of or against the inexorable flow of time. The paradigm of linear music is the melody or cyclical chord progression; the paradigm of nonlinear music is the unchanging drone or discrete sound events of a pointillist work. In linear music “before” and “after” are explicitly traced in a succession of sounds; in nonlinear music succession appears to break down entirely into a set of non-contingent moments giving the impression of an eternal “now.” (For those with a taste for metaphysics, the difference between linear and nonlinear can be captured metaphorically by the difference between becoming and being, respectively.)
Cosottini’s appreciation for the potential importance of the nonlinear in music grew out of a personal experience. When asked to compose a contrapuntal exercise over a C major foundation, he wrote a melody based on C melodic minor. After repeated playing, he felt that the dissonance of the minor third within the context of the major modality revealed itself to be of interest as an alternative, if unconventional, way of combining pitches simultaneously rather than an error. Consequently, he began to understand nonlinearity as a way to analyze and organize improvisation.
The exercises, which make up the bulk of the book, are useful not only as ways of getting to know the heft and shape of improvisation’s constituent elements, but as a means of sharpening and directing musical awareness. Some of the exercises address attentiveness and the ability to hear nonlinearity. For example, one listening exercise asks us to hear a set of simultaneously played long tones as a “totality as if it were a sphere.” As the exercise shows, Cosottini presents linearity and nonlinearity are perceptual categories that are applied through judgments that take place within certain contexts; determining whether or not an element is linear or nonlinear may in many cases be the product of a perspective brought to the work. Cosottini describes this perspective in terms of cumulative listening, through which one can discern those pitches, timbres, rhythmic figures, dynamics or other elements that seem detached from the temporal flow of the music
When specifically addressed to active play, the exercises provide practical examples of how to use nonlinearity as a strategy for improvisation. For instance, some of the exercises call for using only five pitches, timbres, sounds or dynamics. Each of these closed sets can serve as the invariant kernel around which an improvisation—its other parameters being allowed to vary—can be built. Paradoxically, the use of relatively small, limited sets of musical material can lend a sense of larger-scale cohesion underlying and tying together individual musical events. When these sets function as constants providing points of reference for development of the improvisation as a whole, the closed set simply becomes an organizing structure for an open performance.
Cosottini’s methodology opens up clear possibilities for leveraging nonlinear forms of organization as alternatives to linear forms of organization. The former are particularly useful for music that eschews tonality; an improvisation based on textural rather than tonal structures, for instance, would offer one such kind of organization. To the extent that it is a purely vertical structure, texture by nature lacks directionality—textural movement doesn’t point toward a goal of resolution as does functional harmonic movement, nor does it imply a kind of musical entailment, as does melodic development. Instead, texture can serve as the basis of an organizational logic embodied in the relative densities, voice combinations and durations of sound complexes or other simultaneous aggregates of musical elements. Organization by textural synchrony, in other words, offers a nonlinear alternative to organization by harmonic or melodic diachrony.
A concern with texture is a concern with architecture in its vertical dimension; it’s a short step from recognizing this to a grasp of the possibilities arising from the use of nonlinear elements as formal substructures upon which to build improvisational superstructures. To take an example from outside the world of improvisation, we can discern in many of Morton Feldman’s compositions a dynamic element which stays at an unchangingly low level. In such cases we could speak of a nonlinear dynamic that serves as a structural anchor, one which remains static while pitches or timbres undergo variations. These changing pitches and timbres would then appear to belong to a linear surface floating over the constant dynamic. Cosottini similarly includes exercises that define musical parameters as constants; it isn’t hard to imagine these constants serving as structural elements on which to build a superstructure of linear events.
In a seeming reversal of meaning, nonlinear elements can serve to define horizontal relationships as well. Some nonlinear strategies—such as the imposition of sudden silences to introduce discontinuity into the flow of an improvisation—could serve as structural boundaries dividing a performance into discrete sections. The pointillism of local discontinuities, by regulating the development of collective sound densities, would then foster organization at the textural level. Recurring yet invariant tones or timbres, such as are suggested in some of Cosottini’s exercises could, when played during structurally separate passages, set up cross-sectional relationships through thematic coherence. An improvisation made up of autonomous events not explicitly related to what precedes or succeeds them—the kind of piece Cosottini refers to as “without memory [senza memoria]”—would nevertheless cohere through a unity of repetition and recollection. This would seem to present the paradox of having locally nonlinear elements work together to create a global sense of linearity, or continuity, but it is through such paradoxes that the musical dialectic of linearity and nonlinearity works in practice.