Modal representations—decomposing the resonances of objects into their vibrational modes has historically been a powerful tool for studying and synthesizing the sounds of physical objects, but it also provides a flexible framework for abstract sound synthesis. In this paper, we demonstrate a variety of musically relevant ways to modify the model upon resynthesis employing a carillon model as a case study. Using a set of audio recordings of the sixty bells of the Robert and Ann Lurie Carillon recorded at the University of Michigan, we present a modal analysis of these recordings, in which we decompose the sound of each bell into a sum of decaying sinusoids. Each sinusoid is characterized by a modal frequency, exponential decay rate, and initial complex amplitude. This analysis yields insight into the timbre of each individual bell as well as the entire carillon as an ensemble. It also yields a powerful parametric synthesis model for reproducing bell sounds and bell-based audio effects.

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When measuring room impulse responses using swept sinusoids, it often occurs that the sine sweep room response recording is terminated soon after either the sine sweep ends or the long-lasting low-frequency modes fully decay. In the presence of typical acoustic background noise levels, perceivable artifacts can emerge from the process of converting such a prematurely truncated sweep response into an impulse response. In particular, a low-pass noise process with a time-varying cutoff frequency will appear in the measured room impulse response, a result of the frequency-dependent time shift applied to the sweep response to form the impulse response. Here, we detail the artifact, describe methods for restoring the impulse response measurement, and present a case study using measurements from the Berkeley Art Museum shortly before its demolition. We show that while the difficulty may be avoided using circular convolution, nonlinearities typical of loudspeakers will corrupt the room impulse response. This problem can be alleviated by stitching synthesized noise onto the end of the sweep response before converting it into an impulse response. Two noise synthesis methods are described: the first uses a filter bank to estimate the frequency-dependent measurement noise power and then filter synthesized white Gaussian noise. The second uses a linearphase filter formed by smoothing the recorded noise across perceptual bands to filter Gaussian noise. In both cases, we demonstrate that by time-extending the recording with noise similar to the recorded background noise that we can push the problem out in time such that it no longer interferes with the measured room impulse response.

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