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  • Stochos:Software for Real-Time Synthesis of Stochastic Music
  • Sinan Bokesoy and Gerard Pape

Stochos is a real-time stochastic, chaotic, and deterministic event generator implemented as a Max/MSP patch with a unique control interface for assigning stochastic, chaotic, or deterministic curves to different sound transformation and synthesis parameters. It provides a compositional environment with access to a wide range of time scales for these operations. As Stochos is still under development, we will present its current capabilities and our long-term goals for this program. Stochos was designed, programmed, and realized by Sinan Bokesoy in collaboration with Gerard Pape, who conceived and directed the project. The program currently runs on Macintosh computers.

Indeterminacy in the 20th-century music has been applied on different levels by composers like John Cage ("chance music"); Karlheinz Stockhausen, Pierre Boulez, and Luciano Berio ("aleatoric music"); and Iannis Xenakis ("stochastic music"). It is useful to begin our discussion with a definition of the term "stochastic music" taken from Trevor Wishart:

Stochastic music is based on a process in which the probabilities of proceeding from one state, or set of states, is [sic] defined. The temporal evolution of the process is therefore governed by a kind of weighted randomness, which can be chosen to give anything from an entirely determined outcome, to an entirely unpredictable one.

(Wishart 1994)

The idea of stochastically distributing sonic events in sound space was first realized by Iannis Xenakis, beginning with his work Achorripsis (1957), followed by his "ST" series of compositions. (See, for example, Pape 2002.) The approach of Xenakis in his "ST" series of compositions combined ideas of stochastic music with algorithmic event generation. He proposed the use of probability functions and invented the "Dynamic Stochastic Synthesis" concept that resulted in his program Gendyn (1991-1994). In his book Formalized Music, he described the mathematical background of these models and also provided examples of compositional applications.

The physicist Denis Gabor (1946, 1947) had the initial idea of a quantum representation for sound, and Iannis Xenakis was the first to develop a compositional theory for "sound quanta" or "grains." Out of those ideas was born the concept of "granular synthesis" whereby very short sound events that contain a synthetic or sampled waveform are seen as musical quanta. These quanta are distributed in sound space using parameters like density, grain size, and a windowing function to envelope the waveform. Changing the pitch and the amplitude of the original waveform along with those parameters brings secondary effects in the spectral domain. Here we can see granular synthesis as a possible consequence of stochastic music synthesis-possibilities that occur on the micro-time scale. We will provide examples of granular synthesis applications.

Composer/researchers Curtis Roads and Barry Truax have done extensive research on the musical applications of granular synthesis for composition. Roads (1996, 2001) proposed the terms synchronous granular synthesis (SGS) and asynchronous granular synthesis (AGS). De Poli and Piccialli have implemented pitch-synchronous granular synthesis (PSGS), which is an analysis-resynthesis technique applied on the granular boundaries of sound (De Poli and Piccialli 1991).

The real-time granulation of sampled sound was made possible in the 1980s with the DMX-1000 signal processor by Barry Truax (Truax 1987). Mr. Roads's Cloud Generator software, which is a non-real-time application, provides an example of how a user can control the event distribution process in AGS and SGS by selecting starting and ending states for granular synthesis parameters. The [End Page 33] result is clouds of grains that fill up a sound space changing in time. A more recent application by Mr. Roads, Pulsar Generator, works with very short waveforms. By controlling granular synthesis parameters, this program can simulate formant synthesis.

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Figure 1.

Basic structure of Stochos.

Stochos also allows manipulation of sound at the micro-time level; in addition, it provides multiple control sources working in parallel to manipulate the sonic parameters on any event time level. The main advantage is the flexible algorithm, which distributes the events by assigning different probability distributions for onset time and event duration. Furthermore, the density is controlled by probability distributions as in the Achorripsis model...


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