Doty Recital Hall Acoustics Preliminary Report

DOTY RECITAL HALL ACOUSTICS PRELIMINARY REPORT Gregory Palermo, David Meisel State University of New York, College at Geneseo Dept. of Physics & Astronomy December 16, 2014 ABSTRACT

features in its “standard” configuration or prescribing panel settings for different types of performances. The “live-ness” of a performance space corresponds to the length of its decay time. A recording made of an impulse in a closed environment features reflections from the different surfaces in the space that decay in amplitude as they propagate and are absorbed by the room’s surfaces; each of these reflections has its own corresponding reverberation time. The International Standards for the Measurement of room acoustic parameters reverberation time as a “significant parameter,” if not “the predominant indicator of [a room’s] acoustical properties.” While shorter reverberation times improve the intelligibility of speech, which is muddied in more reverberant spaces, a liver space is usually desired in musical contexts. Indeed, the reverberation time of sound in a space is discernable by musical audiences and influences their perception of its quality; in a limited psychoacoustics study, we determined that a 16-64 millisecond range of delay between a musical source signal and its reflections was most pleasurable to listeners (See Appendix A). The ISO Standards suggest other possible features that shape a performance space’s acoustics, but primarily are a guide for calculating reverberation times from a room’s impulse response: a brief source signal is sounded, is mediated by the space, and then recorded using an omnidirectional microphone. These recordings are then analyzed. This analysis of decay time, or of the frequency spectrum of the impulse response, has been traditionally performed using the Fourier transform. Because of the uncertainty principle between frequency and time, however, it is cumbersome if not impossible to use Fourier analysis as a technique to measure the decay time over a range of

The SUNY Geneseo Music department has not yet determined the acoustical function of the retractable panels in the newly renovated Doty Hall’s recital space. We use a 2D discrete Haar wavelet transform on two recordings of clapped wooden blocks, one made with and one made without the panels deployed, to plot a scalogram of the hall’s impulse response. From this timefrequency representation, we quantify the panels’ effect on the hall’s reverberation time, which suggests that the panels are designed to limit reverb when used. In addition, the reverb times are consistent with calculations based on the hall’s dimensions, so they legitimize our methodology for future analysis of additionally collected recordings made in Doty with different panel arrangements. These methods may be applied to study the acoustical properties of other venues, both on campus and beyond Geneseo. INTRODUCTION Performers and audience members alike have deemed the newly renovated Doty Hall’s recital space to be acoustically extraordinary. They cite, for instance, crisp and articulate vocals and a rich sound. Geneseo’s Music department, however, has not rigorously determined the acoustical function of the hall’s motorized retractable felt panels, which are dispersed along the walls throughout the house and behind the stage. Members of the department have noticed that the space sounds “liver” or “deader” with or without the panels deployed respectively, but no study has yet been performed to corroborate these anecdotal observations, quantifying the hall’s acoustical

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frequencies. Frequency and time are complementary variables; if the Fourier transform of a signal is taken, one can compute the average amplitudes of frequencies in the signal, but any information about when those frequencies occur in the signal is lost. The windowed discrete Fourier Transform can be used to plot a spectrogram with both variables, but the process involves a number of tradeoffs depending on one’s choice of window size. A viable method to circumvent this problem in time-frequency analysis is to instead apply the discrete Wavelet Transform. Loosely, wavelets are “little waves” that have a “start and stop;” Strang has noted the likeness between wavelets and musical notes themselves, which are wave pulses sustained for a duration of time [1]. When a signal is convolved with discrete wavelets of different scales, the wavelets can be localized in both time (smaller scales) and frequency (larger scales). While it is still impossible to achieve a point-by-point model of a signal’s amplitude over time and for all frequencies, its wavelet transform will yield its amplitude over ranges of frequencies and times. Gang, Bocko, and Headlam of the University of Rochester have used the 2D discrete Haar Wavelet Transform to plot the reverberation spectrum of musical recordings made in enclosed spaces [2]. Using edge-detection algorithms to recognize the features of this time-frequency representation, known as a “scalogram,” Gang, et al. are able to identify and quantify these features. While they cite possible applications of their signal-processing method ranging from audio forensics to music genre characterization to the deliberate removal of reverberation from speech recordings, we focus on its application to musical spaces and employ a similar approach in our assessment of Doty Recital Hall.

Appendix B) when identifying reflections from the hall’s back, side, and stage walls. These recordings were made using a Blue Snowball microphone hanging in a mesh bag below a tripod (Figure 1), set approximately in the geometric center of the hall, including the stage. The microphone was switched to its third and omnidirectional setting, which also had the flattest frequency response.

Figure 1: Recording Microphone From five different positions on the stage, two differently sized sets of wooden blocks were each clapped together to produce an impulse. This source signal was mediated by the hall and recorded for different panel arrangements, including no panels deployed, only the stage panels deployed, only the house panels deployed, and all them deployed. The resulting number of recordings is quite large, so in this report we will discuss only two situations, a subset of the data we collected: the results below are made from the recordings of the smaller wooden blocks sounded from center stage, both in the bare hall and with all of the panels in action. This focus will allow for an appraisal of the hall’s standard properties and how they are altered by the panels, rather than an investigation of different panel arrangements.

APPROACH Rather than using edge-detection to analyze the scalograms representing the transformed impulse response recordings, we are guided instead by rough measurements of the hall’s dimensions (see

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RESULTS

Note from this plot that the bulk of the reverb occurs within about 100ms of the pulse’s start and consists mostly of the lower frequencies. The “wrap around” of the lowest frequencies to the right edge of the plot is an artifact of the transform, apparent since it is a mirror image of the lower left-hand side.

The recordings for both of these two situations were imported as lists of amplitudes into Wolfram Mathematica. Plots of each pulse’s waveform are shown in Figure 2. Note that the decay time of the pulse with the panels deployed is much shorter. This suggests that the panels are acoustical absorption panels, intended to impede sound’s reflection and reduce reverberation when used.

Figure 3: Scalogram of Features Removed by Full Panel Deployment

Figure 2: Waveform of recorded signal for no panels (above) and all panels (below) Relative Power

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Because it is difficult to distinguish between the reverberation from the hall’s surfaces and from the source blocks, it is sensible to subtract the recording with all of the panels deployed from the recording with none deployed in order to isolate the effect of only the panels themselves. A scalogram of the resulting approximately 1 second spectrum, which shows relative sonic power, is below in Figure 3. The entire range of frequencies perceivable to humans is plotted in octaves on the vertical axis.

2.5 2. 1.5 1. 0.5 0.

20 481 10 241

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Time, sep. by Frequency (Hz)

Figure 4: Wavelet List Plots of Features Removed by Full Panel Deployment

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Also accompanying are two wavelet list plots (Fig. 4): the first is a time-frequency diagram of the first tenth of this transformed signal, which shows the relative power at each octave and which is useful for isolating the time at which different reflections occurred and in what octave; the second (3c) is a plot of the transformed signal’s decay at each octave, useful for comparing its relative overall contribution. From the first list plot, the primary and secondary reverberation patterns are apparent. The first reverb signal happens between 18 and 48ms. The strongest relative amplitude is at the end of this range, which is consistent with the reflection from the back stage panels. In other words, the bulk of the hall’s primary reverberation is coming from behind the performers. The second reverb signal happens at approximately 72ms, which is consistent with a reflection from the front of the stage following a reflection off the back wall. The relatively strong long-wavelength, low frequency component of the reverb throughout is likely produced by the hall’s catwalk, which is the largest structure in the hall exposed to sound. From the second list plot, note again the large component of the reverb in the bass frequencies. This frequency decomposition explains Doty’s pleasurable qualities: the relative lack of reverberation in the high end of the spectrum makes for crisp and un-muddied vocals with articulate consonants, which are generally sounded in that range; meanwhile, the bass reverb contributes to the hall’s rich quality. The distribution of relative amplitudes of among frequencies is also consistent with the ISO Equal-loudness contours, which plot the human perception of sound intensity versus frequency (Appended); bass frequencies have a higher threshold than treble frequencies, and there is a small spike at between 5 and 10 KHz. CONCLUSIONS

summed over an octave and arrived at from many angles, for a preliminary study such as this the manufacturer’s microphone specifications were sufficiently uniform that no corrections were deemed necessary at this stage. The details of the computerized wavelet processing for this situation have been refined and have been found to be sufficient for preliminary modeling of the hall, and perhaps also for other halls as well. The reverberation properties of the “bare” hall are in good agreement with the small sample psychoacoustical tests on listening preferences and explain why the hall is so highly regarded by performers and audiences even without the panels in place. The effect of the acoustical panels on the hall’s acoustics has been established and should aid in making recommendations about panel deployment or other architectural alterations in future. Items for continued exploration include (1) translating our wavelet results into the ISO standards, which currently mainly uses windowed Fourier results, (2) extracting maximum information through further signal processing from the existing recordings we haven’t yet analyzed, possibly using wavelets other than the Haar Wavelet, and (3) using wavelet packets to increase the frequency resolution (by subdividing octaves) which will be needed if studies of individual panel behavior are desired. This assessment of individual panel behavior would accompany a study of the other panel situations not covered in this paper. Additional follow up recordings with a full audience, rather than empty chairs, will clarify the role of the top wooden stage panels in the hall’s acoustics. REFERENCES [1]

Strang, Wavelets, American Scientist 82, 1994, 250-255. [2] Gang, Bocko, and Headlam, Reverberation Features Identification from Music Recordings Using the Discrete Wavelet Transform, IEEE, 2010

Preliminary acoustical properties of SUNY Geneseo’s Doty Hall have been determined using fairly unsophisticated computer-aided recording equipment. Because the wavelets are power

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APPENDIX A: PSYCOACOUSTICS EXPERIMENT A limited psychoacoustics experiment was conducted on five subjects in which artificial reverb was applied using an ADC DD-4AX Stereo Digital Delay Processor. As the delay was increased from zero, the subjects were asked to indicate when the recording sounded like a “live performance.” The delay was then turned up to maximum levels, and the subjects were asked to indicate when the recording no longer sounded artificial. Finally, the subjects were given a randomly ordered set of delay times within the range they indicated and asked to identify which was the most pleasurable to them. Note that the mean of the maximum perceived delay time is less than the mean of the minimum perceived delay time. This can be attributed to hysteresis in how the brain processes delay when compared to a lack of delay. Most important to our study is that these distributions are normal about approximately 30-60 ms, and the mean most preferred delay falls within this range. Mean: 61.5 STDev: 35.1

Mean: 49.1 STDev: 28.1

Delay Time Reported Most Pleasurable

Mean: 38.7 STDev: 29.4

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Responses

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Delay time (ms)

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APPENDIX C: ISO Equal-loudness contours (taken from Wikipedia, 12/16/2014)

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