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Distribution of Mode Frequencies

Another way in which current reverberation systems are ``artificial'' is the unnaturally uniform distribution of resonant modes with respect to frequency. Because Schroeder, FDN, and waveguide reverbs are all essentially a collection of $ N$ delay lines with feedback around them, the modes tend to be distributed as the superposition of the resonant modes of $ N$ feedback comb filters. Since a feedback comb filter has a nearly harmonic set of modes (see §2.6.2), aggregates of comb filters tend to provide a uniform modal density in the frequency domain. In real reverberant spaces, the mode density increases as frequency squared, so it should be verified that the uniform modes used in a reverberator are perceptually equivalent to the increasingly dense modes in nature. Another aspect of perception to consider is that frequency-domain perception of resonances actually decreases with frequency. To summarize, in nature the modes get denser with frequency, while in perception they are less resolved, and in current reverberation systems they stay more or less uniform with frequency; perhaps a uniform distribution is a good compromise between nature and perception?

At low frequencies, however, resonant modes are accurately perceived in reverberation as boosts, resonances, and cuts. They are analogous to early reflections in the time domain, and we could call them the ``early resonances.'' It is interesting that no system for artificial reverberation except waveguide mesh reverberation (of which the author is aware) explicitly attempts precise shaping of the low-frequency amplitude response of a desired reverberant space, at least not directly. The low-frequency response is shaped indirectly by the choice of early reflections, and the use of parallel comb-filter banks in Schroeder reverberators serves also to shape the low-frequency response significantly. However, it would be possible to add filters for shaping more carefully the low-frequency response. Perhaps a reason for this omission is that hall designers work very hard to eliminate any explicit resonances or antiresonances in the response of a room. If uneven resonance at low frequencies is always considered a defect, then designing for a maximally uniform mode distribution, as has been discussed for the high-frequency modes, would be ideal also at low frequencies. Quite the opposite situation exists when designing ``small-box reverberators'' to simulate musical instrument resonators [432,204]; there, the low-frequency modes impart a characteristic timbre on the low-frequency resonance of the instrument (see Fig.3.2).


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-10-15 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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