## The mapping technique

The organisation principles of ChaOs intuitively suggest that it could be applied to control the production of larger acoustic particles which together form a complex sound event. To find an effective way to map the behaviour of ChaOs onto the parameters of a synthesis algorithm is not however a straightforward task. We have devised and tested several techniques; but only a few produced interesting sounds. We introduce below the technique which is currently implemented in Chaosynth.

Each sonic particle produced by Chaosynth is composed of several partials; each partial is a sinewave produced by an oscillator. An oscillator needs three parameters to function: frequency, amplitude and duration (in milliseconds) of the sinewave (Figure 3). ChaOs controls the frequency and duration values of a particle, but the amplitude values are set up by the user beforehand. The states of the nerve cells are associated to a frequency value and oscillators are associated to a number of nerve cells. The frequency values of the partials at time t are therefore established by the arithmetic mean of the frequencies associated with the states of the nerve cells of the oscillators. The user also specifies beforehand the dimension of the grid, the amount of oscilators, the allocation of nerve cells to oscillators and the parameters of ChaOs (that is, the number of states, the resistances of the potential divider, the capacitance of cells and the number of iterations).

Figure 3: An oscillator. Various oscillators are associated to different sets of nerve cells

Each particle is in fact the product of the additive synthesis [23] of sinewaves (Figure 4): at each iteration of ChaOs, all oscillators simultaneously produce sinewaves, whose frequencies are determined by the arithmetic mean over the frequency values of their corresponding nerve cells.

Figure 4: The additive synthesis of sinewaves

The duration of a whole sound event is determined by the number of iterations and the duration of the particles; for example, 100 iterations of 30 milliseconds particles result in a sound event of 3 seconds of duration.

An example of a grid of 400 cells allocated to 16 oscillators of 25 cells each is shown in Figure 5.

Figure 5: An example of a grid of nerve cells allocated to oscillators

This mapping method is interesting because it explores the behaviour of ChaOs in order to produce sounds in a way which resembles the functioning of some acoustic instruments (for example, the violin and the human voice). The random initialisation of states in the grid produces an initial wide distribution of frequency values, which tend to settle to an oscillatory cycle. This behaviour resembles the way in which the sounds produced by most acoustic instruments evolve during their production: their harmonics converge from a wide distribution (as in the noise attack time of a vocal sound, for example) to oscillatory patterns (the characteristic of a sustained tone).

We have synthesised sounds using up to 40 different ChaOs states (that is, up to 40 different frequency values) and up to 25 oscillators, on a grid of 1,000,000 nerve cells (1,000 x 1,000). The results resemble the sounds of flowing water, bird calls and insects. Chaosynth can produce a wide range of gurgling sounds in various flow speeds, by varying the speed of the clock. Variations in tone colour are achieved by varying the frequency values and the amount of nerve cells per oscillator. Different rates of transition, from noise to oscillatory patterns, are obtained by changing the values of r1, r2 and k.

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