- The PhISEM approach uses the results of ``off-line'' particle interaction simulations to derive statistical collision distributions.
- From a numerical simulation of a maraca, statistics were collected with respect to frequency, waiting time, and sound intensity of bean collisions with the outer gourd wall.
- In general, a short-term energy input produced an exponential decay in intensity of collisions.
- The likelihood of a significant sound-producing collision was found to be roughly constant, until all beans were nearly at rest.
- A process with constant event probability at any given time has an exponential distribution in time (i.e., the time duration between events decays away exponentially over time).
- The collected statistics could then be used to control a model in which events trigger distinct overlapping, decaying signals.
- However, a more efficient approach is found by noting the noise-like nature of the resulting sound from a maraca. This suggests the use of decaying noise to represent collision events and a single second-order digital filter to model the gourd resonance.
- Because the sum of exponentially decaying random noise is equal to a single noise source multiplied by a decaying value, only a single exponential decay and a single noise source are required to compute the total sound.
- The maraca synthesis algorithm requires only two random-number calculations (for collision-event likelihood and noise sound source), two exponential decay multiplications (for net system energy and sound level), and one biquad filter, as shown in Fig. 9.
- The Matlab script maraca.m
implements the Maraca PhISEM model of Cook (2002).
- More complex resonant structures can be incorporated with additional second-order filters.

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