Using ISO3382 measures to evaluate acoustical conditions in concert halls

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Using ISO3382 measures to evaluate acoustical conditions in concert halls

Bradley, J. S.

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U sing I SO 3 3 8 2 m e a sure s, a nd t he ir

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c ondit ions in c onc e r t ha lls

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B r a d l e y , J . S .

A version of this document is published in / Une version de ce document se trouve dans: Acoustical Science and Technology, v. 26, no. 2, 2005, pp. 170-178. doi:10.1250/ast.26.170

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Using ISO3382 measures, and their extensions, to evaluate acoustical

conditions in concert halls

Author: John S. Bradley

Affiliation:

Institute for Research in Construction, National Research Council 1200 Montreal Rd., Ottawa, Canada, K1A 0R6

Email address: john.bradley@nrc-cnrc.gc.ca

Keywords: concert halls, ISO3382, measurements, acoustical evaluation

PACS: 43.55.Gx

Short running title: Using ISO3382 measures

Submitted as: Paper

Address:

Building M27,

Institute for Research in Construction, National Research Council

1200 Montreal Rd., Ottawa, Canada, K1A 0R6 Pages of text: Pages of tables: Pages of figures:

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ABSTRACT

Application of the ISO3382 standard can lead to the acquisition of large amounts of data describing conditions in a hall. The data could include the values of a number of measures at 6 or more octave band frequencies and for many combinations of source and receiver location. This paper discusses and gives examples of using this data to find important acoustical features. The amount of data can be reduced by calculating average values over the entire data set or for each sub-area of the hall. Various important spatial variations can often be better understood from plots of values versus source-receiver distance. The analysis approach will depend on the purpose of the study, which could be for comparisons with various criteria, for investigations of problems, or to better understand the acoustical properties of the hall. The significance of new measurements can be determined by comparing values: with proposed ideal criteria, with values in well-known halls, or with theoretical predictions. The importance of differences between two values should be considered in terms of published just noticeable differences for particular measures. Separately examining early- and late-arriving sound levels can be a useful diagnostic tool for better understanding the acoustical properties of halls.

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INTRODUCTION

The ISO3382 standard [1] specifies how to measure a number of well-accepted room acoustics parameters and includes guidance concerning, the numbers of source and receiver positions to be used and the calculation details for each parameter. The combination of many different acoustical measures, at many frequencies, and from many positions in a hall, can result in a large amount of data that may at first hide interesting acoustical features. This paper discusses and gives examples of how to focus on these more interesting, and often more important features. It also introduces early- and late-arriving relative sound levels, as useful extensions to the basic measures in ISO3382. These can help us to better understand acoustical conditions in halls.

Many Measures: ISO3382 includes a number of well-accepted room acoustics measures in the main body of the standard and in appendices. As newer measures become accepted, these too may be added in future revisions of the standard. However, it is advisable to first focus on the more basic and more generally important parameters. Table 1 lists some acoustical measures under 4 headings. The basic measures of level (G, Strength or relative level) and reverberance (EDT, early decay time and T30, reverberation time) along with the

balance between clarity and reverberance (C80, early-to-late arriving sound ratio) are usually

most important. The lateral energy fraction, LF, (of the early-arriving sound), and the inter-aural cross correlation measures of the early and late-arriving sound (IACCe and IACCl)

are measures of spatial effects.

This paper introduces the early-arriving relative sound level G80 and the late-arriving

relative sound level GL as useful diagnostic measures that can be derived from values of G and

C80 (see Appendix for definitions). By describing early- and late-arriving sound levels

separately, they give a more detailed look at components of sound fields that will relate to expected subjective impressions, but without providing too much less-significant detail. Although C80 values indicate how the ratio of early-to-late arriving sound levels vary, G80 and

GL values make these variations more understandable by assessing each component separately.

The early- and late-arriving lateral sound levels (GEL and GLL) are also useful indicators of

spatial effects that are not currently included in ISO3382. They conveniently combine the level and lateral-direction-of-arrival information into simple single measures of each aspect of spatial impression (i.e. apparent source width and listener envelopment [2]).

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4k Hz. There are good reasons to extend this range to include the octave bands from 63 Hz to 8k Hz because these frequencies certainly influence perceptions of concert hall sounds. We don’t yet have much knowledge concerning the preferred variation with frequency of the various acoustical measures, but we do know that strong low frequency levels, rather than long low-frequency T30 values, influence the perceived strength of bass sounds in halls [3,4]. A full

audio bandwidth is necessary for impulse response measurements if it is intended to listen to convolutions of speech and music with these impulse responses. Including the 63 Hz and 8k Hz octaves adds significantly to the requirements of the measurement system. It is particularly difficult to produce an omni-directional sound source that can produce sufficient sound levels over this entire frequency range. It also suggests that testing laboratories should consider measuring the acoustical properties of materials over this broader frequency range. However, this too presents some considerable technical problems.

Many positions: In a large hall one might typically measure at the 36 combinations of 3 source positions and 12 receiver positions. This usually gives enough information for an understanding of spatial variations in a large hall. In a hall with more complex geometry, more positions would be preferred. Movements of the source or receiver position by as little as 10 or 30 cm can lead to measurable differences as shown in Table 2 [5]. The differences over 30 cm are similar to the just noticeable difference (JND) values for these quantities [6,7]. However, JND values are derived from careful comparisons of nearly equal conditions in laboratory experiments in which only one aspect of the sound field is changed. Differences that can be detected by listeners in actual halls are probably much larger. This is partly because more than one aspect of the sound field will change when the listener moves in a concert hall, making it more difficult to identify the individual effects of each changing parameter. No laboratory experiments have considered subjectively detectable changes when more than one aspect of the sound field is changed. The variations over 30 cm in Table 2 probably represent, in practical terms, the accuracy with which conditions at a particular seat can be characterized.

Purpose of Measurements and Data Reduction Techniques: The purpose of room acoustics measurements might be: a) to compare with design criteria, b) to better understand acoustical phenomena, or c) to diagnose the cause of acoustical problems. The approach to the data reduction will depend on the purpose of the measurements. While hall-average values of acoustical measures may allow comparisons with design criteria, they may not reveal important variations within a hall. Plotting values versus source-receiver distance, or examining averages over small sub-areas of audience seating, may better describe within-hall

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variations of acoustical characteristics. The following examples illustrate various possible approaches.

EXAMPLE 1, SOUND LEVEL DETAILS IN A MULTI-PURPOSE HALL

Measurements of sound levels in Southam Hall of the National Arts Centre, Ottawa are used to examine the questions of how many measurement positions are required and to examine the details of level variations in this hall. Figure 1 illustrates 1 kHz G value contours from measurements at 145 positions on one side the main floor of this hall, plus duplicate values reflected about the centre line to represent the other half of the main floor seating. While there are strong variations of these sound levels from front to rear of this hall, the pattern of variations is not that complex and there is little justification to make such detailed measurements.

While Figure 1 gives a more global view of the characteristics, Figure 2 illustrates the details that can be found at an individual location. For seat O2 near the centre of the main floor seating, Figure 2 plots G values and their components versus frequency. While total G values do not vary greatly with frequency at this location, the dominant component does. At lower frequencies the late-arriving sound (GL) is dominant and the seat dip attenuation [8] has greatly

reduced the low frequencies of the early-arriving sound (G80). At higher frequencies G80 values

are the dominant component. If one goes into more detail and examines the lateral component of the early- and late-arriving sound (GEL and GLL respectively), we see that the lateral-arriving

energies are relatively small parts of the total early and late energy values. One would therefore expect a very low sense of spatial impression at this location.

Examining how the variations of sound levels with frequency change throughout the hall can give a more complete understanding of the acoustical characteristics. Figure 3 shows measured G values with early and late components at 3 other locations in the same hall. Figure 3(a) shows values at a seat very close to the stage where the combined direct plus early reflection energy (G80) is dominant at almost all frequencies. The results in Figure 2 showed,

that near the centre of the main floor seating, the balance of early- and late-arriving sound had changed considerably from the results in Figure 3(a). In the centre of the second balcony (Figure 3(b)), early-arriving sound (G80) dominates at mid- and high-frequencies and the seat

dip attenuation seems now to be greatest at 250 Hz. However, in the third balcony, the Figure 3(c) results show more similar early and late sound levels with strong late-arriving sound (GL)

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Clearly, the character of the sound must vary considerably from area to area in this hall. At most locations, and especially at mid-to-high frequencies, early arriving sound energy dominates, creating a dry sound. The exception is in the third balcony (Figure 3(c)) where the late-arriving sound is relatively stronger. At lower frequencies the seat dip attenuation reduces the level of the early-arriving sound at the measured seats. However, increasing low frequency sound levels by reducing the amount of low frequency sound absorbing material in the hall is not likely to compensate for the large reductions in low frequency early-arriving sound.

EXAMPLE 2, HALL AVERAGES AND WITHIN HALL VARIATIONS

Figure 4(a) plots hall average EDT and T30 values from the Northern Alberta Jubilee

Auditorium (NAJA) with the range of EDT values obtained from measurements in 31 large halls [4] as well as a possible design goal for concert hall EDT values. Average EDT values are smaller than T30 values as is commonly found, and the measured averages are less than the

proposed design criterion values. However, this is very much a multi-purpose hall and it is easily argued that somewhat shorter decay times than the ‘ideal’ would be appropriate. The large range of EDT values from the 31 halls shows that there are many halls with much larger or smaller values.

These results give no indication of the unusual characteristics of this hall that are seen when decay time values are plotted versus source-receiver distance as shown in Figure 4(b). While the 1 kHz T30 values are quite constant throughout the hall (as is almost always the case),

EDT values vary quite dramatically with distance. Presumably, the sense of reverberance would be very different at the rear of the hall compared with at seats near the stage. These results, as well as those for early sound levels, can be explained as due to the shape of the ceiling sending all reflections to the rear of the hall as illustrated in Figure 5.

In order to appreciate the significance of these within-hall variations, we can compare the results in Figure 4(b) with those from other halls. These comparisons in Figure 6 show that variations of EDT in this hall (NAJA) are greater than in the other halls shown. In some halls there is very little variation of EDT values. Sometimes this occurs because the hall is quite reverberant and diffuse such as in Boston Symphony Hall (BOS) [9]. In other halls the reduced variation of EDT with distance is because the shape of the hall concentrates reflected energy near the stage (SWP) as illustrated in Figure 7(b). The results for the Neuesfestspielhaus in Salzburg (SLZ) shown Figure 6 are an example of a hall that tends to direct early-arriving

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reflections to the rear of the hall. This creates a situation where EDT values reduce with increasing distance from the source but less dramatically than found in NAJA. The variation with distance of G values is often inversely related to the variation of EDT values with distance. This is especially true in directed sound halls that are shaped to direct strong early reflections to particular audience areas [10]. By plotting EDT and G values as a function of source-receiver distance, we can therefore better understand the effects of the shape of a hall on early-arriving reflections.

EXAMPLE 3, COMPARISON WITH THEORETICAL PREDICTIONS

It is often useful to compare measurements with theoretical predictions to determine if there are unusual features. Barron’s procedure [11] for predicting relative sound levels of the early, late, and total sound components is particularly valuable because sound levels are so critical to subjective impressions of halls. In well-accepted halls, measured levels tend to agree well with the predictions of Barron’s theory.

For example, the variation of 1 kHz G values with distance in Boston Symphony Hall (BOS) in Figure 7(a), agree well with predictions. At seats close to the stage, measured levels are a little higher than predicted, probably due to strong reflections from the stage enclosure. At seats under the balcony (solid symbols) levels are a little lower than predicted. Figure 7(b) gives an example where measured levels closer to the stage are much above predictions, probably due to the shape of the orchestra shell and to sound energy scattered back towards the stage from the ceiling in this hall. This results in large variations of levels from the front to the rear of this hall. Figure 7(c) shows a hall where measured values tend to fall systematically below predictions at most seats. This is again due to the ceiling shape of the NAJA hall tending to send early reflections to the rear of the hall (see Figure 5). In support of this explanation Figure 7(d) shows that early-arriving sound levels (G80) are indeed higher than predicted at

locations at the rear of this hall (far right-hand side of graph).

As in the previous section, plotting values versus source-receiver distance is seen to be useful for understanding the acoustical characteristics of halls. When these results are also compared with the predicted levels from Barron’s procedure, we get an indication of where conditions are atypical.

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EXAMPLE 4, DIAGNOSING ACOUSTICAL PROBLEMS

The Orpheum Theatre in Vancouver was originally built as a theatre and later converted to a dedicated concert hall. Acoustical measurements identified several significant acoustical problems [12]. Again, hall-average values do not reveal the problems, and a simple plot of levels versus source-receiver distance (Figure 8(a)) only shows a large amount of scatter. The causes of this scatter can be identified by separating the data into those obtained from positions at balcony seats and those from seats on the main floor of the hall including seats under the balcony. Figure 8(b) indicates that there are 2 separate trends for the two different groups of measurements. Sound levels tend to be lower at seats under the balcony, and values measured at seats in the balcony tend to agree reasonably well with predictions using Barron’s theory.

The situation can be more completely understood by examining how early and late sound levels each vary with distance. Figure 9(a) shows that most, but not all G80 values, agree

quite well with the predictions of Barron’s theory. There are 5 positions in the balcony where early sound levels significantly exceed these predictions (i.e. by more than 1 dB). However, there is no systematic difference in early levels depending on whether they are measured at seats in the balcony or under the balcony. On the other hand, Figure 9(b) shows that late-arriving levels are systematically different depending on whether measurements are made at locations in or under the balcony. Measured values at locations under the balcony do not agree well with predictions using Barron’s theory but at other locations there is quite good agreement.

There are two different acoustical problems illustrated in these results. First, the very large balcony overhang produces very obvious reductions in the late-arriving sound at locations under the balcony. This is seen, to a much lesser degree, in Figure 7(a) for BOS. However, there is no systematic reduction of early-arriving sound levels at seats under balconies. The other problem evident in these results, leads to increased early sound levels at particular locations in the balcony. These are due to various concave surfaces (mostly in the ceiling) that focus sound to specific locations in this hall and cause significant variations in early levels. Figure 10(a) shows the initial part of the impulse response at the location with the most extreme focussing effect and another (Figure 10(b)) with no obvious focussing effect. The two strong reflections in Figure 10(a) are stronger than the direct sound and are perceived as a localization of the source in the ceiling.

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Plotting results versus source-receiver distance was again helpful in understanding the acoustical problems in this hall. However, it was most helpful when the values of the diagnostic parameters G80 and GL were examined. While the focussing problems were isolated

in the early-arriving sound, the weak levels at seats under the balcony were shown to be due to a lack of late-arriving sound.

CONCLUSIONS

The level of detail required in measurements of concert halls depends on the purpose of the measurements. A typical set of measurements at the combinations of 3 on-stage source positions and 10 to 12 receiver positions in the audience area will usually be adequate to characterize acoustical conditions in a large hall. Measurements at a large number of positions usually indicate systematic gradual changes in values. Seat-to-seat variations in measured values tend to be no more than one just-noticeable-difference (JND). A laboratory obtained JND from tests where only one aspect of the sound field is varied, may not be indicative of detectable changes in a hall where several different characteristics of the hall may vary in different ways from one seat to the next.

The analysis approach will depend on the purpose of the study, which could be for comparisons with various criteria, for investigations of problems, or to better understand the acoustical properties of the hall. The significance of new measurements can be determined by comparing values: with proposed ideal criteria, with values in well-known halls, or with theoretical predictions. Because ideal values of the various parameters defined in ISO3382 are not well established, it is often useful to compare measurements with values from well-regarded halls. Of course, just because a hall is well liked, does not ensure that measured values of all parameters are near to ideal values.

Although hall-average values give a general overall picture of a concert hall, we can much better understand the unique acoustical characteristics of a hall by examining within hall variations of each important parameter. This can be done by plotting values versus source-receiver distance or by averaging over sub-areas of the audience seating. The shape of a hall may have the effect of directing more of the early-arriving energy to one particular area of the hall. Such effects can be more easily understood by separately considering early- and late-arriving sound levels (G80 and GL values). For example, a hall may direct more early

energy to a particular area, or a large balcony overhang may reduce late-arriving sound at seats under the balcony. Comparisons of measured early- and late-arriving levels with predictions

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based on Barron’s theory can further aid the understanding of acoustical conditions in a concert hall.

There is an obvious need for new research to develop a better understanding of the subjective importance of variations with frequency of the various room acoustics parameters and also to try to determine preferred spectral characteristics for each of them.

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Acknowledgments

The author would like to thank the management and staff of the halls that have cooperated in the various measurement studies. It is also important to point out that these results were obtained before renovations were made to the Orpheum Theatre and before the planned renovation to the Alberta Jubilee Auditoria.

REFERENCES

[1] ISO3382, Acoustics — Measurement of the reverberation time of rooms with reference to other acoustical parameters, International Organisation for Standardisation, Geneva, Switzerland. [2] Bradley, J.S. and Soulodre, G.A., Objective measures of listener envelopment, J. Acoust. Soc. Am.,

Vol. 98, No. 5, pp. 2590-2597, (1995).

[3] Bradley, J.S., Soulodre, G.A., and Norcross, S., Factors influencing the perception of bass, J. Acoust.

Soc. Am., 101 (5) Pt. 2, p.3135, (1997).

[4] Bradley, J.S. The sound field for listeners in concert halls and auditoria, Computational

Architectural Acoustics, Editor J.J. Sendra WIT, Press, UK. (1999).

[5] Bradley J.S., Halliwell R.E., Accuracy and reproducibility of auditorium acoustics measures,

Proceedings of British Institute of Acoustics, Spring '88 Meeting, Cambridge, U.K., 10, Part 1,

339-406, (1988).

[6] Cox, T.J., Davies, W.J., and Lam, Y.W., The sensitivity of listeners to early sound field changes in auditoria, Acustica, 79, pp. 27-41 (1993).

[7] Bradley, J.S., Reich, R., and Norcross, S.G., A just noticeable difference in C50 for speech, Applied

Acoustics, 58 (2) 99-108, (1999).

[8] Bradley J.S., Some further investigations of the seat dip effect, J. Acoust. Soc. Am., 90 (1) 324-333, (1991).

[9] Bradley J.S., A Comparison of three classical concert halls, J. Acoust. Soc. Am., 89, 1176-1192, (1991).

[10] Bradley, J.S., Hall average characteristics of 10 halls, Proceedings of the 13th International

Congress on Acoustics, Belgrade, 1989.

[11] Barron, M., and Lee, L.-J., Energy relations in concert auditoria, I, J. Acoust. Soc. Am. 84, 618-628, (1988).

[12] O’Keefe, J. and Bradley, J.S., Acoustical renovations to the Orpheum, Vancouver: I. Measurements prior to renovations, Canadian Acoustics, 28 (1) 21-33, (2000).

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APPENDIX. DEFINITIONS OF SOME ROOM ACOUSTICS MEASURES

This appendix defines the principal room acoustics measures discussed in the results of this paper, including some quantities not included in the ISO3382 standard.

The sound strength (or relative sound level) G is measured using a calibrated omni-directional sound source, and is calculated as follows,

dB dt p dt p log 10 = G 0 2 0 10 , t t 2 10 ⎪⎪ ⎭ ⎪ ⎪ ⎬ ⎫ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧

∫

∞ ∞ ) ( ) ( (A1)

where p(t) is the instantaneous pressure in the measured impulse response and p10(t) is the response to the same source at a distance of 10 m in a free field.

The strength of the direct and early-arriving sound over the first 80 ms, G80, can be

defined with an equation similar to equation A1, but with the upper integration limit of the upper integral set to 0.08 s. The sound strength of the late-arriving sound, GL, consisting of

sound energy arriving at the receiver more than 80 ms after the direct sound can again be defined with an equation similar to A1, but with the lower integration limit of the upper integral set to 0.08 s.

The relative level or strength of the early-arriving lateral sound, GEL, and the late-

arriving lateral sound, GLL, can be calculated similar to G80 and GL respectively but using the

impulse response obtained from a figure-of-eight pattern microphone in the upper integral of an equation similar to A1. For example, the late arriving lateral sound level GLL, which is

related to listener envelopment, is calculated as follows,

dB dt p dt p log 10 = G 0 L 0.08 10 LL , t t 2 10 2 ⎪ ⎪ ⎭ ⎪ ⎪ ⎬ ⎫ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧

∫

∞ ∞ ) ( ) ( , dB (A2)

where pL(t) is the instantaneous pressure in the measured impulse response using a

figure-of-eight pattern microphone with the null pointing toward the sound source and p10(t) is the response to the same source at a distance of 10 m in a free field with an omni-directional measurement microphone.

The balance between early and late-arriving sound energy can be measured using C80

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dB , dt dt log 10 0.08 0.08 0 80 ) C _⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛

∫

p (t) ∞ p (t = 2 2 (A3) also C80 = G80 – GL, dB (A4)

The lateral energy fraction is defined as follows,

(A5) dt dt 2 080 . 0 0 2 0.080 0.005 t p t p = LF

∫

_L( )

/

∫

( )

The early and late relative sound levels G80 and GL can be calculated from measured G

and C80 values as follows,

dB , 10 1 10 10 log 10 _/₁₀ /10 10 / 80 ₈₀ 80 ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ∗ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = G C C G (A6) dB , 10 1 10 1 log 10 _/₁₀ /10 80 ⎭⎬ ⎫ ⎩ ⎨ ⎧ ∗ ⎥⎦ ⎤ ⎢⎣ ⎡ + = G C L G (A7)

Similarly, the relative level or strength of the early-arriving lateral sound, GEL, can

calculated from LF, C80 and G values as follows,

dB , 10 1 10 10 * log 10 _/₁₀ /10 10 / 80 80 ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ∗ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = G C C EL LF G (A8)

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Table Titles

Table1. Room acoustics measures discussed in this text. (See Appendix and the ISO3382 standard [1] for definitions)

Table 2. Average variations of measured values for small movements of the source or receiver [5].

Figure Titles

Figure 1. Contour fit to measured 1 kHz G values.

Figure 2. Measured relative levels (G) and early (G80) and late (GL) components at a centre main floor seat. GEL is the early lateral relative level and GLL is late lateral relative level.

Figure 3. Measured relative levels (G) and early (G80) and late components (GL), (a) seat B2

close to the stage, (b) seat D2 in the second balcony, and (c) seat D2 in the third balcony. Figure 4. Measured values from NAJA, (a) hall average T30 and EDT values, and the range of

EDT values from 31 halls, (b) variation of 1 kHz EDT and T30 with source-receiver distance.

Figure 5. Longitudinal section showing ceiling reflections in NAJA.

Figure 6. Straight line fits to measured 1 kHz EDT values in 4 halls: BOS Boston Symphony Hall, SWP Salle Wilfrid Pelletier (Montreal), SLZ Neuesfestspielhaus (Salzburg), and NAJA, Northern Alberta Jubilee Auditorium (Edmonton).

Figure 7. Comparison of measured 1 kHz values and predictions using Barron’s theory [9], (a) G values in BOS, (b) G values in SWP, (c) G values in NAJA, and (d) G80 values in

NAJA.

Figure 8. Measured 1 kHz G values versus source-receiver distance in the Orpheum Theatre (a), and (b) same data separated by measurement location (Balcony seats, and main floor seats in front of, or under the balcony) compared with predicted levels using Barron’s theory (solid line).

Figure. 9. Measured values of (a) early levels (G80), and (b) late sound levels (GL) versus

source- receiver distance in the Orpheum Theatre. Solid lines are predictions using Barron’s theory [9]. Different symbols identify measurement locations in balcony seats or main floor seats in front of or under the balcony. Data corresponding to the impulse responses in Figures 10(a) and 10(b) are also identified in panel (a).

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Figure 10. Impulse responses from balcony seats in the Orpheum Theatre, (a) with strong focusing, and (b) without obvious focussing.

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Tables Level Reverberance/ Clarity Diagnostic Spatial Effects G T30 G₈₀ LF EDT GL IACCe C80 IACCl C50 GEL TS GLL

Table1. Room acoustics measures discussed in this text. (See Appendix and the ISO3382 standard [1] for definitions)

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Measure ±10 cm ±30 cm G 0.4 dB 0.8 dB C80 0.6 dB 0.9 dB T30 0.04 s 0.06 s EDT 0.07 s 0.15 s LF 0.05 0.06

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FIGURES B D F H K M O Q S U W Y 5 10 15 20 25 Length, (1 m/row) Wi d th, m -1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 G(1k), dB

Figure 1. Contour fit to measured 1 kHz G values.

Print as: full page width figure Author: John S. Bradley

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125 250 500 1000 2000 4000 -25 -20 -15 -10 -5 0 5 R e la ti ve l e ve l, d B Frequency, Hz G G₈₀ G_L G_EL G_LL

Figure 2. Measured relative levels (G) and early (G80) and late (GL) components at a centre

main floor seat. GEL is the early lateral relative level and GLL is late lateral relative level.

Print as: half page width figure Author: John S. Bradley

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125 250 500 1000 2000 4000 -10 -5 0 5 10 G G80 GL Re la ti ve l e v e l, d B Frequency, Hz (a) 125 250 500 1000 2000 4000 Frequency, Hz (b) 125 250 500 1000 2000 4000 (c) Frequency, Hz

Figure 3. Measured relative levels (G) and early (G80) and late components (GL), (a) seat

B2 close to the stage, (b) seat D2 in the second balcony, and (c) seat D2 in the third balcony.

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125 250 500 1000 2000 4000 0 1 2 3 4 Ideal T₃₀ EDT D ecay t im e, s Frequency, Hz (a) 10 15 20 25 30 35 40 45 50 0.0 0.5 1.0 1.5 2.0 2.5 T₃₀ EDT Distance, m (b)

Figure 4. Measured values from NAJA, (a) hall average T30 and EDT values, and the range of

EDT values from 31 halls, (b) variation of 1 kHz EDT and T30 with source-receiver distance.

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Figure 5. Longitudinal section showing ceiling reflections in NAJA.

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0 5 10 15 20 25 30 35 40 45 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ED T , s Distance, m BOS SWP SLZ NAJA

Figure 6. Straight line fits to measured 1 kHz EDT values in 4 halls: BOS Boston Symphony Hall, SWP Salle Wilfrid Pelletier (Montreal), SLZ Neuesfestspielhaus (Salzburg), and NAJA,

Northern Alberta Jubilee Auditorium (Edmonton).

Print as: half page width figure Author: John S. Bradley

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0 4 8 12 G, d B (a) 0 4 8 12 G, d B (b) 5 10 15 20 25 30 35 40 45 -4 0 4 8 12 G, d B DIstance, m (c) 5 10 15 20 25 30 35 40 45-8 -4 0 4 8 G 80 , d B DIstance, m (d)

Figure 7. Comparison of measured 1 kHz values and predictions using Barron’s theory [9], (a) G values in BOS, (b) G values in SWP, (C) G values in NAJA, and (d) G80 values in NAJA.

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5 10 15 20 25 30 35 40 -1 0 1 2 3 4 5 6 7 G( 1k) , dB Distance, m (a) 10 15 20 25 30 35 40 In balcony Barron Under balcony In front of balcony Distance, m (b)

Figure 8. Measured 1 kHz G values versus source-receiver distance in the Orpheum Theatre (a), and (b) same data separated by measurement location (Balcony seats and main floor seats in

front of, or under the balcony) with predicted levels using Barron’s theory (solid line).

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5 10 15 20 25 30 35 40 -4 -2 0 2 4 6 GL (1 k), dB G80 (1k), dB Distance, m (a) Fig. 10(a) Fig. 10(b) 10 15 20 25 30 35 40 -8 -6 -4 -2 0 2 Main floor Balcony Barron Distance, m (b)

Figure. 9. Measured values of (a) early levels (G80), and (b) late sound levels (GL) versus

source- receiver distance in the Orpheum Theatre. Solid lines are predictions using Barron’s theory [9]. Different symbols identify measurement locations in balcony seats or main floor seats in front of under the balcony. Data corresponding to the impulse responses in Figures

10(a) and 10(b) are also identified in panel (a).

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0.0 0.1 0.2 0.3 -6000 -4000 -2000 0 2000 4000 6000 Re la ti ve p re ssu re TIme, s (a) 0.0 0.1 0.2 0.3 Time, s (b)

Figure 10 Impulse responses from balcony seats in the Orpheum Theatre, (a) with strong focusing, and (b) without obvious focussing.