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Late lateral energy fractions and the envelopment question in concert halls
Applied Acoustics 62 (2001) 185±202 www.elsevier.com/locate/apacoust
Late lateral energy fractions and the envelopment question in concert halls M. Barron * Department of Architecture and Civil Engineering, University of Bath, Bath, Somerset BA2 7AY, UK Received 3 August 1999; received in revised form 11 October 1999; accepted 27 June 2000
Abstract In concert hall acoustics, spatial perception is a crucial element of the experience, yet several questions remain unresolved. In the 1960s, there was some work on what was then called `room impression' caused by diuse reverberation. The possible importance of early lateral re¯ections was proposed in 1967 by Marshall [Marshall AH. A note on the importance of room cross-section in concert halls. Journal of Sound and Vibration 1967;5:100±12] and until recently concern for the eect of early re¯ections has overshadowed study of the spatial eects linked to the later sound. Bradley and Soulodre [Bradley JS, Soulodre GA. The in¯uence of late arriving energy on spatial impression. Journal of the Acoustical Society of America 1995;97:2263±71; Bradley JS, Soulodre GA. Objective measures of listener envelopment. Journal of the Acoustical Society of America 1995;98;2590±7] have now suggested that early re¯ections are predominantly responsible for creating a sense of source broadening [and apparent source width (ASW)], whereas a sense of envelopment, which had on occasions been linked to ASW, is almost solely produced by later lateral re¯ections. Bradley and Soulodre have proposed the late lateral energy level as a measure of listener envelopment (LEV). This paper considers some of the history of spatial perception in concert halls and reports on measured results made in 17 halls of the late lateral energy fraction (LLF) and the late lateral energy level (GLL). The spread of measured values of LLF turned out to be small and GLL was found to be predominantly determined by the total acoustic absorption of halls. # 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Reverberation is perceived in two distinct ways Ð the temporal and the spatial. The temporal aspect, which can be called `liveness', can be isolated by monophonic recording or monaural listening. The decay of sound is responsible for creating an * Tel.: +44-1225-826826; fax: +44-1225-826691. E-mail address: [email protected] 0003-682X/01/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0003-682X(00)00055-4
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audible background against which the latest note in music or latest syllable in speech is heard. The optimum value for reverberation time is largely determined by the temporal situation. The spatial aspect of reverberation is more intractable. Hearing reverberation from all directions is clearly an important part of listening to music in large auditoria. Spatial reverberation is at its most extreme in highly reverberant spaces (particularly large church spaces and reverberation chambers), when direct sound is relatively weak or indeed absent. In this case the listener can be without clues as to the direction from which the sound originates. Some aspects of spatial sound with no temporal behaviour can be studied by using continuous noise signals. The strength of the early relative to the reverberant sound is conventionally measured by the Clarity Index, C80. As its name implies, the index is usually applied to the temporal response to reverberation. It may however also have a role to play regarding spatial response. The Clarity Index can also be considered as an inverse measure for perceived reverberation [4]. Some aspects of the perception of spatial reverberation were studied during the 1960s which will be reviewed below. But before several important issues of spatial hearing of reverberation were resolved, a second spatial eect was identi®ed which has dominated much of the subsequent discussion. Marshall in his original publication [1] was in fact less speci®c about the subjective eect that he felt was crucial to concert hall listening than many people probably imagine [5]. The eect of early lateral re¯ections was quickly termed `spatial impression', whereas Marshall had referred to `spatial responsiveness', a characteristic of the space in which the music is performed. Two measures of spatial impression due to early re¯ections have emerged, the early lateral energy fraction (LF) [6] and cross-correlation measures [7]. The early sound is generally taken as the ®rst 80ms after the direct. Sound level is also considered to in¯uence perceived spatial impression, though the relative importance of the spatial and level components is as yet unresolved [8]. In 1989, Morimoto and Maekawa [9] suggested that at least two subjective spatial eects occurred. They provided evidence that a sense of being enveloped by sound was independent of spaciousness (spatial impression caused by early re¯ections) and that envelopment was linked to incoherence (a low interaural cross-correlation) of the reverberant sound. Bradley and Soulodre [2,3] conducted further subjective experiments into spatial hearing. Their experiments were conducted in an anechoic chamber with a simulation system using ®ve (or three) loudspeakers arranged symmetrically in front or to the side of subjects. They found that sound from behind had no special in¯uence on the subjective eects being studied, and they therefore did not include loudspeakers behind the subjects. The simulations involved direct sound followed by four discrete re¯ections and then reverberation whose relative level from dierent directions was varied. Bradley and Soulodre basically agreed with Morimoto and Maekawa that there were two spatial eects which had in the past often been confused. Bradley and Soulodre called the two eects: source broadening and listener envelopment (LEV); this nomenclature will be used here. (The expression `spaciousness' has been used to mean dierent things by dierent authors and will only be used here in quotations.)
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Source broadening can be measured by the perceived apparent source width (ASW). Their experiments showed that ASW is predominantly determined by the early sound, whereas envelopment is governed by the late sound. Most earlier work had concentrated on source broadening, referring to it as spatial impression. Just as perceived source broadening is in¯uenced by sound level, so Bradley and Soulodre also found sound level to be signi®cant for LEV. Bradley and Soulodre [3] proposed as an objective measure for LEV the late lateral sound level, LG1 80 or more simply GLL: 1 1 1 2 2 pF t:dt= pA t:dt ; dB 1 LG80 GLL 10 log 0:08
0
where pF t is the pressure measured at a listener position with a ®gure-of-eight microphone with the null pointing at the source and pA t is the omni-directional response to the same source at a distance of 10 m in a free ®eld. Time t is measured relative to the arrival time of the direct sound. The late lateral sound level is measured at four octave frequencies (125±1000 Hz) and averaged. Sound direction in the horizontal plane can be simply divided into frontal, lateral left and right and from the rear. In the case of source broadening, experiments have shown that re¯ections from the rear produce the same eect as re¯ections which arrive from in front with the same angle to the axis through the listeners ears [6,10]; listeners cannot perceive the sound as coming from behind them. Bradley and Soulodre consider that for LEV listeners have the same insensitivity to whether sound arrives from in front or behind, but there is, of course, a subjective dierence here: source broadening is heard in front of the listener whereas listener envelopment involves feeling surrounded by sound, including the sense of receiving sound from behind. Some researchers are unhappy with the notion that sound can be perceived from behind when in reality no sound arrives at the listener from that direction. This paper ®rstly reconsiders some work on spatial perception of reverberation from the 1960s. The remaining discussion considers measured values of the late lateral energy fraction (LLF) and the late lateral level (GLL) and what design consequences result if the GLL is to be optimised. 2. Room impression as studied in the 1960s In the 1960s, German authors used the word `Raumeindruck' for the spatial aspect of reverberation. This seems best translated as `room impression' to distinguish it from spatial impression generally used for the eect of early re¯ections. Most experimental work in the 1960s involved simulations which produced diuse reverberant sound ®elds. It is thus reasonable to equate the room impression from these experiments with listener envelopment. A key experience in simulations of concert hall acoustics is to vary the ratio of direct to reverberant energy. Reichardt and Schmidt [11] quanti®ed the transition
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from maximum room impression to zero perceived spatial reverberation in a paper whose title can be translated as ``The audible steps of room impression with music''. Subjects were presented with direct sound and reverberation from a reverberation plate (reverberation time 2 s). Four incoherent reverberation signals were fed to four loudspeakers arranged at 45 and 135 in azimuth relative to straight ahead of the subject. The onset of reverberation was delayed 50 ms after the direct sound. The reverberant separation, H (Hallabstand), was varied while the total level was kept constant; H is the direct sound level relative to the reverberant. It is equivalent to C50 in this experiment. Subjects determined just noticeable dierences (jnd) which led to a 15 point scale of room impression (Fig. 1). However the range of room impression used in this experiment is much larger than encountered in concert halls. A proposed preferred range for C80 is between 2 dB [12], which is only three steps of room impression. Slightly larger ranges of C80 are found in actual halls so one can conclude that only four or ®ve steps are perceived in practice. Schmidt [13] subsequently extended the experiment using the same apparatus but varying both the reverberant separation H and the reverberation time. The experiment showed that H was not a unique measure of room impression. An attempt by Reichardt [14] to resolve the question of room impression for impulse responses containing both early re¯ections and reverberation did not prove entirely successful since two measures emerged, one more successful in reverberant ®elds and the other in unreverberant sound ®elds. In retrospect, one can interpret Reichardt's diculties to a lack of understanding of the role of early lateral re¯ections. Major experimental work relating to room impression was also conducted at GoÈttingen. Damaske [15] investigated what was required in order to simulate the
Fig. 1. Perceived room impression as a function of reverberant separation (direct relative to reverberant level) after Reichardt and Schmidt [11]. One unit of room impression corresponds to one just noticeable dierence.
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eect of a diuse reverberant ®eld, without the hundreds of interfering re¯ections which exist in real rooms. Most of his experiments were undertaken with continuous noise signals. Fig. 2 illustrates the results of two experiments using (a) two and (b) four incoherent noise signals; subjects were required to indicate the areas in the hemispherical space above them from which they heard sound. One can conclude from Fig. 2 that, except for sound arriving only in the median plane [last diagram in Fig. 2(a)], sound is perceived as arriving from the region between the various directions of the incident sound. The directional acuity of listeners is seen not to be large but, for a sense of subjective diuseness, sound must arrive from four principal directions. Unfortunately no result is presented for sound from the front, back and two sides. The importance of Damaske's work at the time is recorded by Kuttru ([16] p. 197): ``For a long time it was common belief among acousticians that spaciousness (i.e. a sense of subjective diuseness) was a direct function of the uniformity of the directional distribution in the sound ®eld: the higher the diusion, the higher the degree of spaciousness. This belief originated from the fact that many old and highly renowned concert halls are decorated with statuettes, pillars, coered ceilings and other projections which supposedly re¯ect the sound rather in a diuse manner than specularly. It was the introduction of synthetic sound ®elds as a research tool which led to the insight that the uniformity of the stationary directional distribution is not a primary cause of spaciousness''. In retrospect, one might question generalising from Damaske's result, which used noise signals, to the case of music in concert halls. But the design solution with all surfaces highly diusing (as in the Beethovenhalle, Bonn of 1959 [12]) has only rarely been used since. Neither of the studies from the 1960s is conclusive regarding room impression (envelopment) but, reviewing this work in 1970, one would have probably concluded that spatial reverberation depended on sound arriving from all four key directions and that the magnitude of perceived room impression was determined by the ratio of early to reverberant sound. 3. Measurement procedures in British concert halls Objective measurements have been made in 17 unoccupied British halls which are used for concert performance (Table 1). Detailed accounts of the individual halls are to be found in [12]. The survey used an omni-directional loudspeaker at a central position close to the front of the stage and a microphone of variable directivity placed at ear height in audience locations. On average, 11 microphone positions were used per hall. The source was placed 3 m from the stage front. The survey used single cycle sine pulses as signals with the impulse responses being recorded on analogue tape. The microphone used was an AKG C414EB; careful calibration of the relative sensitivities of the ®gure-of-eight and omni-directional characteristics is needed with this sort of microphone. The expressions for the early lateral energy fraction (LF) and late lateral energy fraction (LLF) are:
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Fig. 2. Perceived areas in the hemisphere above subjects listening to incoherent noise signals in an anechoic chamber after Damaske [15]. Arrows indicate the positions of loudspeakers with (a) two loudspeakers and (b) four loudspeakers.
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Table 1 Basic details of the 17 British concert spaces Hall
Label
Year of completion
Seating capacitya
Volume (m3)
Mean width (m)
Plan form
Royal Festival Hall, London Royal Albert Hall, London Queen Elizabeth Hall, London Barbican Concert Hall, London Wigmore Hall, London Fair®eld Hall, Croydon Wessex Hall, Poole Colston Hall, Bristol St. David's Hall, Cardi Assembly Hall, Watford Music School Auditorium, Cambridge Royal Concert Hall, Nottingham Free Trade Hall, Manchester Philharmonic Hall, Liverpool Usher Hall, Edinburgh Conference Centre, Wembley Butterworth Hall, Warwick University
F A Q R G C P B D W S
1951 1871 1967 1982 1901 1962 1978 1951 1982 1940 1977
2645+256 4670+419 1106 2026 544 1539+250 1473+120 1940+182 1687+270 1586 496
21 950 86 650 9600 17 750 2900 15 400 12 430 13 450 22 000 11 600 4100
32 47 23 34 13 26 30 22 34 22 20
Parallel-sided
N M L E Y K
1982 1951 1939 1914 1976 1981
2315+196 2529 1767+184 2217+333 2511 1152+177
17 510 15 400 13 560 16 000 24 000 12 100
26 22 27 29 50 30
a
Parallel-sided Parallel-sided Parallel-sided Parallel-sided Parallel-sided
Parallel-sided Fan-shape Parallel-sided
The second number refers to choir seating.
LF
0:08 0:005
p2F t:dt=
0:08 0
p2O t:dt LLF
T 0:08
T p2F t:dt= p2O t:dt; 0:08
2
where pF t is the pressure measured at the listener position with the ®gure-of-eight characteristic with the null pointing at the source and pO t is the pressure measured with the omni-directional characteristic. Time t 0 is the arrival time of the direct sound; the limiting time, T, for integration for the LLF was taken as 0.4 reverberation time to ensure sucient accuracy without contamination by background noise. The responses were analysed by computer to produce results in the four octaves between 125 and 1000 Hz. To calculate the late lateral level (GLL), a measurement is also required of the total relative sound level (G). The total sound level is measured with the same loudspeaker fed with calibrated octave noise signals, while the sound level in the same seat locations was measured with sound level meters. Further details about the measurement procedure are given in [17]. 4. Mean values and distributions of lateral energy fractions Table 2 lists the mean values and standard deviations for the 189 early and late lateral energy fractions measured in the 17 halls. The early lateral energy fraction
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Table 2 Means and standard deviations of measured early and late lateral energy fractionsa
Mean Standard deviation Distribution a
Early lateral energy fraction
Late lateral energy fraction
Diuse
0.19 0.085 Not normal
0.31 0.047 Highly normal
0.33 ± ±
Data set of 189 values.
results are discussed in more detail elsewhere [8]. One observes that the mean early fraction is signi®cantly lower than the late. A major reason for this is surely that the early sound contains the direct sound which by de®nition is not lateral. The mean value of the late lateral energy fraction at 0.31 is very close to the theoretical value for a diuse sound ®eld of 0.33. The scatter of measured values is small for the late lateral energy fraction. Fig. 3 shows the distributions of both the early and late lateral energy fractions. Tests on the statistical normality of each set of data using the 2 test show the early lateral energy fraction to be ``almost certainly not normal'' with a con®dence limit of over 0.1%. On the other hand the 2 test on the late lateral energy fraction shows that the data is ``highly normal'' (signi®cantly less than the P=10% value). Fig. 4 shows the means and standard deviations of measurements of the early and late lateral energy fractions as a function of frequency. Though the mean of the early
Fig. 3. Distributions of the early and late lateral energy fractions as measured at 189 receiver positions.
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fraction is constant with frequency, the late fraction has lower values at the lower frequencies. Since the measurement systems for both fractions were identical, and indeed the two fractions were derived from the same impulses responses, these lower values of the late fraction at low frequencies would seem to be either a feature of sound ®elds or a consequence of the measuring process. The second looks unlikely since consideration of the dierences between the character of early and late sound does not obviously lead to this conclusion. (This could be checked by rotating the ®gure-of-eight microphone through 90 degrees and measuring the late frontal energy fraction.) Nor is there an obvious reason why the directional character of the late sound ®eld should vary with frequency. For instance, a major in¯uence on low frequency sound is attenuation at grazing incidence, also known as the seat dip eect, but if the late sound ®eld is diuse, we would expect attenuation at grazing incidence to eect both frontal and lateral sound and thus have a neutral eect on the late lateral energy fraction. It is just possible that the low values of late fraction at low frequencies indicate less diuse sound ®elds at these frequencies. The other feature to note in Fig. 4 is that the scatter of measured values of both the early and late lateral fractions is smallest at mid-frequencies (500/1000 Hz) and largest at 125 Hz. Apart from unresolved details regarding frequency, the conclusion regarding the late lateral energy fraction is that it is randomly distributed with a small degree of scatter around a mean, which is close to the value expected in a diuse sound ®eld.
Fig. 4. Octave means 1 standard deviation for the measured early and late lateral energy fractions.
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5. Late lateral energy fractions averaged by hall When late lateral energy fractions are averaged by hall, the hall means only vary between 0.25 and 0.34, a range of 0.09 compared with a range of 0.20 for the early lateral energy fraction [8]. The hall mean values have been compared to various hall parameters by regression analysis. The following were considered but found to be unrelated to the mean late lateral energy fraction (LLF): auditorium volume, seat capacity and mid-frequency reverberation time. The only parameter found to correlate with mean LLF was hall width, with a correlation coecient of r ÿ0:55 signi®cant at the 5% level. (The corresponding coecient for the early lateral energy fraction is ÿ0.59, signi®cance level <2%.) Mean LLF is plotted in Fig. 5 against hall width. One observes in Fig. 5 that the narrowest hall (G, Wigmore Hall, London) is one of three halls with the highest measured LLF, whereas the widest (Y, Wembley Conference Centre) has the lowest LLF. The Wembley hall is semicircular in plan, which is an extreme form of fan-shape; one notes that it sits below the regression line in Fig. 5. On the other hand, the Royal Albert Hall, London (A) behaves well for its width with regard to LLF. In spite of its well-known faults [12], the Royal Albert Hall does have a particularly good dynamic response with extremely smooth transitions during crescendos. A good dynamic response is thought to be a characteristic of diuse sound ®elds and the result here regarding the mean hall LLF provides objective evidence to corroborate this subjective observation. Another outlier in Fig. 5 deserves comment: the Assembly Hall, Watford (W) has a low mean LLF value for its width. This rectangular-plan hall has six large windows along each side wall which are covered with curtains; this surely in¯uences lateral re¯ections and therefore lateral fractions.
Fig. 5. Hall mean late lateral energy fractions as a function of hall width. Hall labels according to second column of Table 1.
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6. Late lateral energy fractions within halls The standard deviation (S.D.) for LLF measurements within halls ranges from 0.02 to 0.06, with a mean S.D. of 0.04. Again this is smaller than the within hall mean standard deviation of 0.06 for the early lateral fraction. An interesting observation can be made on the halls with the lowest standard deviations for the LLF; there are four halls with a standard deviation of 0.03 or 0.02. Two of these halls are the smallest in volume and seating capacity of the 17 measured: Cambridge Music School and the Wigmore Hall, London. The other two halls with low scatter of LLF are St. David's Hall, Cardi and the Butterworth Hall, Warwick University. Both these halls have designs which are likely to promote a diuse sound ®eld [12]. In the case of St. David's Hall, the audience seating is arranged in ``vineyard terraces'' and the ceiling is highly diusing; both characteristics are good for diuse late sound. The Warwick University hall also has a highly diusing ceiling. Within each hall, the behaviour of the late lateral energy fraction has been compared with two distances: the source-receiver distance and the lateral distance, the distance of the measurement position from the axis of symmetry. In three (out of the 17 halls) there is a positive correlation (at the 10%) level between source-receiver distance and LLF, whereas there is one hall with a negative correlation at the 10% level. Three other halls exhibit positive correlations of LLF with lateral distance. None of this behaviour is very consistent nor is there any correlation between LLF values and either source-receiver distance or lateral distance for the whole data set. 7. Comparison between measured early and late lateral energy fractions Fig. 6 is a scatter diagram for the 189 measured values of the early and late lateral energy fractions. The correlation coecient is 0.45. Though this correlation is statistically signi®cant (at the 0.1% level), there is probably a considerable random element. We would not expect a good correlation since the early and late sound have dierent characters. The late sound consists of many interfering re¯ections with an approximately diuse directional distribution. The early sound is dominated by the direct sound and discrete early re¯ections; the relative level of the direct sound is a function of source±receiver distance and the early re¯ections are determined by the hall geometry. In the light of the above, it comes as a surprise to observe the relationship between hall mean early and late energy fractions (Fig. 7). With a correlation coecient of 0.80 signi®cant at the 0.1% level, one concludes that the hall average LLF is strongly determined by the average early lateral fraction. The regression equation is: Mean late lateral fraction=0.37 * Mean early lateral fraction+0.24 In view of the relationship between hall mean lateral fractions, the correlation between both hall mean fractions and hall width mentioned in Section 5 is expected. Regarding the relationship in Fig. 7, the surprise arises due to the dierent directional distributions of early and late sound incident on room surfaces. Late re¯ections
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arriving at listeners from the side have been incident on the side wall surfaces from all directions. The early sound is generally dominated by the ®rst-order re¯ections, which have originated from the source only. Thus, a small plane surface which provides ®rst-order early lateral re¯ections will only provide late lateral re¯ections
Fig. 6. Late versus early lateral energy fractions in 17 concert spaces.
Fig. 7. Mean hall late versus mean hall early lateral energy fractions. Hall labels according to second column of Table 1.
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for sound which originates from the stage area; the surface does not produce late lateral re¯ections for sound originating from elsewhere. In two situations, one can argue that hall design features would promote both early and late lateral re¯ections. If the side wall surfaces are highly diusing, then the angle of incidence on these surfaces is irrelevant and we could expect the strength of both early and late lateral sound to be similarly in¯uenced by the location of these surfaces. Likewise, a large side wall surface will provide lateral re¯ections to listeners both for sound originating at the source and sound from other directions ``visible'' from the side wall surface. Only a few of the 17 halls measured have particularly diusing side walls but many have large side wall surfaces. It can be concluded that design for good early lateral re¯ections is on average good for late lateral re¯ections. However, the dierences between the mean values of the late lateral fraction for halls are small. 8. Determinants of the late lateral level As discussed in Section 1, Bradley and Soulodre [3] have proposed the late lateral level (GLL) as a measure for perceived listener envelopment (LEV). In practice, the late lateral level is likely to be calculated from measured values of three quantities: the total relative sound level (G), the early-to-late sound index (C80) and the late lateral energy fraction (LLF). The calculation uses the logarithmic version of the late lateral energy fraction, which can be called the late lateral index [LLI=10. log(LLF)]. Late lateral level; GLL Late level 10: log LLF ÿ G ÿ 10: log 1 10C80 =10 10: log LLF
3
In other words, the late lateral level is the sum of a level term (the late level GL ) and a directional term based on the late lateral energy fraction. It is of interest to establish the relative importance of level and late re¯ection directivity for the late lateral level. With knowledge of their relative importance, it may be possible to establish the design implications to achieve a high late lateral level. As part of the original acoustic survey of British auditoria, both C80 and G were measured [17]. Octave results for each measure were combined into two frequency bands: a bass frequency (125 and 250 Hz octaves) and mid-frequency band (500, 1000 and 2000 Hz). From these the bass and mid-frequency late levels have been calculated. These two levels have been averaged by taking antilogs, averaging and taking logarithms to give a mean late level. The late lateral energy fraction is measured over the frequency range 125±1000 Hz. The minor discrepancy in frequency range for the late level is very unlikely to be of signi®cance. The measurements in halls were made in unoccupied auditoria and no corrections for occupancy have been made; the validity of the arguments below is not likely to be aected by this either. Levels are quoted relative to the level of the direct sound at 10 m from the omni-directional source.
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Table 3 lists the basic statistics of the measured components in Eq. (3). Bradley and Soulodre [3] quote a measured range from ÿ14.4 to +0.8 dB for GLL, which is in good agreement with the range in British halls. One notices in Table 3 that the standard deviation for the late lateral index is much smaller than that for the late level. The ratio of these two standard deviations can provide us with the information we are seeking: the relative importance of the late level, GL , and directivity, LLI, towards the late lateral level, GLL. However one condition needs to be ful®lled for this ratio to be used, it is necessary that the GL and LLI are independent of one another. The very low correlation coecient between them of 0.073 suggests that they are independent. A better check involves normalising GL , LLI and GLL by subtracting the relevant mean value in each case. The sums of squares for each normalised quantity is calculated, as is the sum of the cross-products between GL and LLI. The sum of squares for GLL is 2157 and the sum of cross-products is 30, which is considered small enough to indicate independence between GL and LLI. The relative importance of GL compared with LLI for the late lateral level is thus 3.27/0.68=4.8. In other words, the level GL contributes to 83% of the variation of the late lateral level and the late lateral index only contributes towards 17% of the variation. Inspection of the correlation coecients in ®nal row of Table 3 provides qualitative support for this conclusion. The late lateral level is thus in practice principally determined by the level of the late sound. Though the late lateral energy fraction was found to be related to hall width and the mean hall early lateral energy fraction, these variations have only a small in¯uence on the proposed measure, the late lateral level. The discussion now turns to the late level and what are the main determinants of the late level. Two theoretical values are considered for comparison with the measured late levels: the traditional re¯ected sound level and the late sound level according to revised theory [12]. For both theoretical values, linear regressions have been conducted with measured values. The results of the regression analysis are presented in Table 4. Details of revised theory are given in the Appendix. The comparison of measured with prediction according to revised theory is shown in Fig. 8. Agreement is good with a regression line with a slope of unity. The reasons for the level dierence of 0.9 dB have already been discussed in detail; they include such things as the eects
Table 3 Measured means, standard deviations and range of values for the components in Eq. (3)a
Mean (dB) Standard deviation (dB) Range (dB) Correlation coecient for regression with GLL a
Data set of 189 values.
Late level (GL)
Late lateral index (LLI)
Late lateral level (GLL)
0.3 3.27 ÿ8.4 to +8.2 0.98
ÿ5.2 0.68 ÿ7.2 toÿ3.4 0.27
ÿ4.8 3.39 ÿ14.1 to +3.4 (1.00)
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Table 4 Results of linear regression between measured and theoretical late levelsa
Correlation of measured with: Late sound according to revised theory Traditional re¯ected sound level a
Slope
Dierence of means (dB)
Correlation coecient, r
Standard error of estimate (dB)
0.99 1.04
ÿ0.9 ÿ5.8
0.89 0.82
1.5 1.9
Data set of 189 values.
Fig. 8. Measured late sound level relative to the theoretical late sound level according to Eq. (4), including line of best ®t.
of balcony overhangs [18], absorption in the stage area [17], a fan-shaped hall [12] and attenuation at grazing incidence in the bass [19]. Revised theory was developed in response to the observed reduction in sound level in concert halls as one moves away from the source. The theory matches measured behaviour well on average. The expression for the theoretical late sound according to revised theory contains three terms: 31200:T 482 0174:r ÿ 4 ÿ Theoretical GL 10: log V T T where T is the reverberation time, V the auditorium volume and r the source±receiver distance. The ®rst term is the traditional one for the re¯ected sound level (assuming
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Sabine's reverberation time equation is valid). The second term relates to it being the late sound arriving more than 80 ms after the direct sound. The third term takes account of the arrival time of the direct sound after it is emitted from the source; this term provides the variation in level with position. The theoretical late level according to Eq. (4) is used in Fig. 8. One question of interest in concert halls is whether the sense of envelopment varies with distance from the source. The variation in late level with distance in a typical hall is 2.6 dB (30 m range, RT=2 s). If the late lateral level is the relevant measure, then we expect the sense of envelopment to reduce as we move away from the source; the 2.6 dB range should be compared with the total measured range for the late lateral level of 17.5 dB. On this basis, the variation with distance may not be subjectively signi®cant. Eq. (4) contains three variables on the right hand side. Can we usefully reduce the correlation of measured late levels to a single objective measure? Table 4 also includes the correlation between the measured late level and the traditional expression for the re¯ected sound [the ®rst term in Eq. (4)]. The correlation between the measured value and traditional theory is still good with a standard error of 1.9 as opposed to 1.5 dB for revised theory. The conclusion therefore regarding the major in¯uence on the late lateral level has to be that it is the ratio of reverberation time to auditorium volume, in other words the total acoustic absorption. We would thus expect the sense of envelopment to be high in small halls and low in large halls. Sound level for the listener is also determined by the performance and ¯uctuates during a piece of music. For comparison between halls it is appropriate to compare halls when used with similar musical forces. We can expect on the basis of the late lateral level to experience the greatest sense of envelopment when a large orchestra plays in a small hall. 9. Conclusions The proposal by Bradley and Soulodre on spatial hearing in rooms is a major advance in our understanding of auditorium acoustics. They have clari®ed the distinction between the spatial eects created by early and late re¯ections. Their work led them to propose a speci®c measure, the late lateral sound level (GLL), as relating to listener envelopment (LEV). The aim of this paper was to determine what were the design implications of the late lateral level and to consider whether there was any evidence that the late lateral level might not be the ®nal answer to the envelopment question. The late lateral level can be considered as the sum of two components: a directional component based on the late lateral energy fraction (LLF) and a level component. Analysis of measured values collected from 17 British music spaces showed that the LLF does not vary much between or within halls. The late lateral level was discovered to be substantially determined by the late level. And the late level itself was found to be principally linked to the total acoustic absorption in halls. This leads one to the conclusion that listener envelopment should be high in small halls and low in large ones. Subjective studies at real concerts would be welcome to establish
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whether this simple conclusion is valid, and also to ®nd out whether there are signi®cant changes in perceived LEV within halls. It is possible that the late lateral level is biased too far towards the level component. Is the design criterion for good envelopment just to optimise sound level? Objective measures involving energy are either absolute or relative. Sound level is an absolute measure, as is the proposed late lateral level; other components of the sound excluded from the late lateral level are assumed not to in¯uence the subjective eect. A relative measure involves the balance between one component and another, as in the Clarity Index, C80. A relative measure takes into account the masking of one sound component by another. Using a very simple impulse response, Reichardt and Schmidt found that room impression, which is surely equivalent to envelopment, was determined by the balance between direct and reverberant sound. (They used a relative measure but in fact, because total level was kept constant in their experiment, an absolute measure of reverberant sound level would have worked as well!) Is listener envelopment really immune to the relative level of early sound, for instance? Bradley and Soulodre [2,3] provide evidence that variations in C80 have some in¯uence on perceived LEV, but reject it as a major in¯uence. The ®nal question concerns the role of sound from behind. To this author, the presence or absence of sound from behind can be perceived in concert halls. The proposal that sound from behind is irrelevant to the sense of feeling surrounded by sound is surprising. Acknowledgements I am grateful to the managements of the various halls for allowing access to make measurements in their halls. The measurement work was undertaken while the author was at the Martin Centre for Architectural and Urban Studies, Cambridge, with the assistance of Lee-Jong Lee. The measurement programme was supported by the Science and Engineering Research Council. Appendix. Revised theoretical level for late sound Energies are expressed relative to the direct sound at 10 m from the omni-directional source. The expression for the direct sound is the traditional one with the direct energy=100/r2, where r is the distance from the source. According to revised theory, the late sound energy, l, arriving later than 80ms after the direct sound is [17]: l 31200T=Veÿ1:11=T :eÿ0:04r=T : where V is the auditorium volume, T the reverberation time. Hence the late level is 31200:T 482 0174:r ÿ dB: ÿ Theoretical GL 10: log V T T
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References [1] Marshall AH. A note on the importance of room cross-section in concert halls. Journal of Sound and Vibration 1967;5:100±12. [2] Bradley JS, Soulodre GA. The in¯uence of late arriving energy on spatial impression. Journal of the Acoustical Society of America 1995;97:2263±71. [3] Bradley JS, Soulodre GA. Objective measures of listener envelopment. Journal of the Acoustical Society of America 1995;98:2590±7. [4] Barron M. The Gulbenkian Great Hall, Lisbon, II: an acoustic study of a concert hall with variable stage. Journal of Sound and Vibration 1978;59:481±502. [5] Marshall AH, Barron M. Spatial responsiveness in concert halls and the origins of spatial impression. Applied Acoustics, 2000;62(2):91±108. [6] Barron M, Marshall AH. Spatial impression due to early lateral re¯ections in concert halls: the derivation of a physical measure. Journal of Sound and Vibration 1981;77:211±32. [7] Keet W de V. The in¯uence of early lateral re¯ections on the spatial impression. Proc 6th International Congress on Acoustics, Tokyo, 1968, paper E-2-4. [8] Barron M. Measured early energy fractions in concert halls and opera houses. Journal of Sound and Vibration, 2000;232:79±100. [9] Morimoto M, Maekawa Z. Auditory spaciousness and envelopment. Proc 13th International Congress on Acoustics, Belgrade, 1989;2:215±8. [10] Morimoto M, Iida K, Sakagami K. The role of re¯ections from behind the listener in spatial impression. Applied Acoustics, 2000;62(2):109±24. [11] Reichardt W, Schmidt W. Die hoÈrbaren Stufen des Raumeindruckes bei Musik. Acustica 1966;17:175±8. [12] Barron M. Auditorium acoustics and architectural design. London: E & FN Spon, 1993. [13] Schmidt W. Zusammenhang zwischen Hallabstand und Nachhallzeit fuÈr den Raumeindruck (Halligkeit und RaÈumlichkeit bei Musik). Hochfrequenz und Electroakustik 1968;77:37±42. [14] Reichardt W. Der Impuls-Schalltest und seine raumakustische Beurteilung. In: Proc 6th International Congress on Acoustics, Tokyo, 1968, paper GP-2-2 p. GP11±20. [15] Damaske P. Subjektive Untersuchungen von Schallfeldern. Acustica 1967;19:199±213. [16] Kuttru H. Room acoustics. 3rd ed. London: Elsevier Applied Science, 1991. [17] Barron M, Lee L-J. Energy relations in concert auditoriums, I. Journal of the Acoustical Society of America 1988;84:618±28. [18] Barron M. Balcony overhangs in concert auditoria. Journal of the Acoustical Society of America 1995;98:2580±9. [19] Barron M. Bass sound in concert auditoria. Journal of the Acoustical Society of America 1995;97:1088±98.
Late lateral energy fractions and the envelopment question in concert halls M. Barron * Department of Architecture and Civil Engineering, University of Bath, Bath, Somerset BA2 7AY, UK Received 3 August 1999; received in revised form 11 October 1999; accepted 27 June 2000
Abstract In concert hall acoustics, spatial perception is a crucial element of the experience, yet several questions remain unresolved. In the 1960s, there was some work on what was then called `room impression' caused by diuse reverberation. The possible importance of early lateral re¯ections was proposed in 1967 by Marshall [Marshall AH. A note on the importance of room cross-section in concert halls. Journal of Sound and Vibration 1967;5:100±12] and until recently concern for the eect of early re¯ections has overshadowed study of the spatial eects linked to the later sound. Bradley and Soulodre [Bradley JS, Soulodre GA. The in¯uence of late arriving energy on spatial impression. Journal of the Acoustical Society of America 1995;97:2263±71; Bradley JS, Soulodre GA. Objective measures of listener envelopment. Journal of the Acoustical Society of America 1995;98;2590±7] have now suggested that early re¯ections are predominantly responsible for creating a sense of source broadening [and apparent source width (ASW)], whereas a sense of envelopment, which had on occasions been linked to ASW, is almost solely produced by later lateral re¯ections. Bradley and Soulodre have proposed the late lateral energy level as a measure of listener envelopment (LEV). This paper considers some of the history of spatial perception in concert halls and reports on measured results made in 17 halls of the late lateral energy fraction (LLF) and the late lateral energy level (GLL). The spread of measured values of LLF turned out to be small and GLL was found to be predominantly determined by the total acoustic absorption of halls. # 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Reverberation is perceived in two distinct ways Ð the temporal and the spatial. The temporal aspect, which can be called `liveness', can be isolated by monophonic recording or monaural listening. The decay of sound is responsible for creating an * Tel.: +44-1225-826826; fax: +44-1225-826691. E-mail address: [email protected] 0003-682X/01/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0003-682X(00)00055-4
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audible background against which the latest note in music or latest syllable in speech is heard. The optimum value for reverberation time is largely determined by the temporal situation. The spatial aspect of reverberation is more intractable. Hearing reverberation from all directions is clearly an important part of listening to music in large auditoria. Spatial reverberation is at its most extreme in highly reverberant spaces (particularly large church spaces and reverberation chambers), when direct sound is relatively weak or indeed absent. In this case the listener can be without clues as to the direction from which the sound originates. Some aspects of spatial sound with no temporal behaviour can be studied by using continuous noise signals. The strength of the early relative to the reverberant sound is conventionally measured by the Clarity Index, C80. As its name implies, the index is usually applied to the temporal response to reverberation. It may however also have a role to play regarding spatial response. The Clarity Index can also be considered as an inverse measure for perceived reverberation [4]. Some aspects of the perception of spatial reverberation were studied during the 1960s which will be reviewed below. But before several important issues of spatial hearing of reverberation were resolved, a second spatial eect was identi®ed which has dominated much of the subsequent discussion. Marshall in his original publication [1] was in fact less speci®c about the subjective eect that he felt was crucial to concert hall listening than many people probably imagine [5]. The eect of early lateral re¯ections was quickly termed `spatial impression', whereas Marshall had referred to `spatial responsiveness', a characteristic of the space in which the music is performed. Two measures of spatial impression due to early re¯ections have emerged, the early lateral energy fraction (LF) [6] and cross-correlation measures [7]. The early sound is generally taken as the ®rst 80ms after the direct. Sound level is also considered to in¯uence perceived spatial impression, though the relative importance of the spatial and level components is as yet unresolved [8]. In 1989, Morimoto and Maekawa [9] suggested that at least two subjective spatial eects occurred. They provided evidence that a sense of being enveloped by sound was independent of spaciousness (spatial impression caused by early re¯ections) and that envelopment was linked to incoherence (a low interaural cross-correlation) of the reverberant sound. Bradley and Soulodre [2,3] conducted further subjective experiments into spatial hearing. Their experiments were conducted in an anechoic chamber with a simulation system using ®ve (or three) loudspeakers arranged symmetrically in front or to the side of subjects. They found that sound from behind had no special in¯uence on the subjective eects being studied, and they therefore did not include loudspeakers behind the subjects. The simulations involved direct sound followed by four discrete re¯ections and then reverberation whose relative level from dierent directions was varied. Bradley and Soulodre basically agreed with Morimoto and Maekawa that there were two spatial eects which had in the past often been confused. Bradley and Soulodre called the two eects: source broadening and listener envelopment (LEV); this nomenclature will be used here. (The expression `spaciousness' has been used to mean dierent things by dierent authors and will only be used here in quotations.)
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Source broadening can be measured by the perceived apparent source width (ASW). Their experiments showed that ASW is predominantly determined by the early sound, whereas envelopment is governed by the late sound. Most earlier work had concentrated on source broadening, referring to it as spatial impression. Just as perceived source broadening is in¯uenced by sound level, so Bradley and Soulodre also found sound level to be signi®cant for LEV. Bradley and Soulodre [3] proposed as an objective measure for LEV the late lateral sound level, LG1 80 or more simply GLL: 1 1 1 2 2 pF t:dt= pA t:dt ; dB 1 LG80 GLL 10 log 0:08
0
where pF t is the pressure measured at a listener position with a ®gure-of-eight microphone with the null pointing at the source and pA t is the omni-directional response to the same source at a distance of 10 m in a free ®eld. Time t is measured relative to the arrival time of the direct sound. The late lateral sound level is measured at four octave frequencies (125±1000 Hz) and averaged. Sound direction in the horizontal plane can be simply divided into frontal, lateral left and right and from the rear. In the case of source broadening, experiments have shown that re¯ections from the rear produce the same eect as re¯ections which arrive from in front with the same angle to the axis through the listeners ears [6,10]; listeners cannot perceive the sound as coming from behind them. Bradley and Soulodre consider that for LEV listeners have the same insensitivity to whether sound arrives from in front or behind, but there is, of course, a subjective dierence here: source broadening is heard in front of the listener whereas listener envelopment involves feeling surrounded by sound, including the sense of receiving sound from behind. Some researchers are unhappy with the notion that sound can be perceived from behind when in reality no sound arrives at the listener from that direction. This paper ®rstly reconsiders some work on spatial perception of reverberation from the 1960s. The remaining discussion considers measured values of the late lateral energy fraction (LLF) and the late lateral level (GLL) and what design consequences result if the GLL is to be optimised. 2. Room impression as studied in the 1960s In the 1960s, German authors used the word `Raumeindruck' for the spatial aspect of reverberation. This seems best translated as `room impression' to distinguish it from spatial impression generally used for the eect of early re¯ections. Most experimental work in the 1960s involved simulations which produced diuse reverberant sound ®elds. It is thus reasonable to equate the room impression from these experiments with listener envelopment. A key experience in simulations of concert hall acoustics is to vary the ratio of direct to reverberant energy. Reichardt and Schmidt [11] quanti®ed the transition
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from maximum room impression to zero perceived spatial reverberation in a paper whose title can be translated as ``The audible steps of room impression with music''. Subjects were presented with direct sound and reverberation from a reverberation plate (reverberation time 2 s). Four incoherent reverberation signals were fed to four loudspeakers arranged at 45 and 135 in azimuth relative to straight ahead of the subject. The onset of reverberation was delayed 50 ms after the direct sound. The reverberant separation, H (Hallabstand), was varied while the total level was kept constant; H is the direct sound level relative to the reverberant. It is equivalent to C50 in this experiment. Subjects determined just noticeable dierences (jnd) which led to a 15 point scale of room impression (Fig. 1). However the range of room impression used in this experiment is much larger than encountered in concert halls. A proposed preferred range for C80 is between 2 dB [12], which is only three steps of room impression. Slightly larger ranges of C80 are found in actual halls so one can conclude that only four or ®ve steps are perceived in practice. Schmidt [13] subsequently extended the experiment using the same apparatus but varying both the reverberant separation H and the reverberation time. The experiment showed that H was not a unique measure of room impression. An attempt by Reichardt [14] to resolve the question of room impression for impulse responses containing both early re¯ections and reverberation did not prove entirely successful since two measures emerged, one more successful in reverberant ®elds and the other in unreverberant sound ®elds. In retrospect, one can interpret Reichardt's diculties to a lack of understanding of the role of early lateral re¯ections. Major experimental work relating to room impression was also conducted at GoÈttingen. Damaske [15] investigated what was required in order to simulate the
Fig. 1. Perceived room impression as a function of reverberant separation (direct relative to reverberant level) after Reichardt and Schmidt [11]. One unit of room impression corresponds to one just noticeable dierence.
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eect of a diuse reverberant ®eld, without the hundreds of interfering re¯ections which exist in real rooms. Most of his experiments were undertaken with continuous noise signals. Fig. 2 illustrates the results of two experiments using (a) two and (b) four incoherent noise signals; subjects were required to indicate the areas in the hemispherical space above them from which they heard sound. One can conclude from Fig. 2 that, except for sound arriving only in the median plane [last diagram in Fig. 2(a)], sound is perceived as arriving from the region between the various directions of the incident sound. The directional acuity of listeners is seen not to be large but, for a sense of subjective diuseness, sound must arrive from four principal directions. Unfortunately no result is presented for sound from the front, back and two sides. The importance of Damaske's work at the time is recorded by Kuttru ([16] p. 197): ``For a long time it was common belief among acousticians that spaciousness (i.e. a sense of subjective diuseness) was a direct function of the uniformity of the directional distribution in the sound ®eld: the higher the diusion, the higher the degree of spaciousness. This belief originated from the fact that many old and highly renowned concert halls are decorated with statuettes, pillars, coered ceilings and other projections which supposedly re¯ect the sound rather in a diuse manner than specularly. It was the introduction of synthetic sound ®elds as a research tool which led to the insight that the uniformity of the stationary directional distribution is not a primary cause of spaciousness''. In retrospect, one might question generalising from Damaske's result, which used noise signals, to the case of music in concert halls. But the design solution with all surfaces highly diusing (as in the Beethovenhalle, Bonn of 1959 [12]) has only rarely been used since. Neither of the studies from the 1960s is conclusive regarding room impression (envelopment) but, reviewing this work in 1970, one would have probably concluded that spatial reverberation depended on sound arriving from all four key directions and that the magnitude of perceived room impression was determined by the ratio of early to reverberant sound. 3. Measurement procedures in British concert halls Objective measurements have been made in 17 unoccupied British halls which are used for concert performance (Table 1). Detailed accounts of the individual halls are to be found in [12]. The survey used an omni-directional loudspeaker at a central position close to the front of the stage and a microphone of variable directivity placed at ear height in audience locations. On average, 11 microphone positions were used per hall. The source was placed 3 m from the stage front. The survey used single cycle sine pulses as signals with the impulse responses being recorded on analogue tape. The microphone used was an AKG C414EB; careful calibration of the relative sensitivities of the ®gure-of-eight and omni-directional characteristics is needed with this sort of microphone. The expressions for the early lateral energy fraction (LF) and late lateral energy fraction (LLF) are:
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Fig. 2. Perceived areas in the hemisphere above subjects listening to incoherent noise signals in an anechoic chamber after Damaske [15]. Arrows indicate the positions of loudspeakers with (a) two loudspeakers and (b) four loudspeakers.
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Table 1 Basic details of the 17 British concert spaces Hall
Label
Year of completion
Seating capacitya
Volume (m3)
Mean width (m)
Plan form
Royal Festival Hall, London Royal Albert Hall, London Queen Elizabeth Hall, London Barbican Concert Hall, London Wigmore Hall, London Fair®eld Hall, Croydon Wessex Hall, Poole Colston Hall, Bristol St. David's Hall, Cardi Assembly Hall, Watford Music School Auditorium, Cambridge Royal Concert Hall, Nottingham Free Trade Hall, Manchester Philharmonic Hall, Liverpool Usher Hall, Edinburgh Conference Centre, Wembley Butterworth Hall, Warwick University
F A Q R G C P B D W S
1951 1871 1967 1982 1901 1962 1978 1951 1982 1940 1977
2645+256 4670+419 1106 2026 544 1539+250 1473+120 1940+182 1687+270 1586 496
21 950 86 650 9600 17 750 2900 15 400 12 430 13 450 22 000 11 600 4100
32 47 23 34 13 26 30 22 34 22 20
Parallel-sided
N M L E Y K
1982 1951 1939 1914 1976 1981
2315+196 2529 1767+184 2217+333 2511 1152+177
17 510 15 400 13 560 16 000 24 000 12 100
26 22 27 29 50 30
a
Parallel-sided Parallel-sided Parallel-sided Parallel-sided Parallel-sided
Parallel-sided Fan-shape Parallel-sided
The second number refers to choir seating.
LF
0:08 0:005
p2F t:dt=
0:08 0
p2O t:dt LLF
T 0:08
T p2F t:dt= p2O t:dt; 0:08
2
where pF t is the pressure measured at the listener position with the ®gure-of-eight characteristic with the null pointing at the source and pO t is the pressure measured with the omni-directional characteristic. Time t 0 is the arrival time of the direct sound; the limiting time, T, for integration for the LLF was taken as 0.4 reverberation time to ensure sucient accuracy without contamination by background noise. The responses were analysed by computer to produce results in the four octaves between 125 and 1000 Hz. To calculate the late lateral level (GLL), a measurement is also required of the total relative sound level (G). The total sound level is measured with the same loudspeaker fed with calibrated octave noise signals, while the sound level in the same seat locations was measured with sound level meters. Further details about the measurement procedure are given in [17]. 4. Mean values and distributions of lateral energy fractions Table 2 lists the mean values and standard deviations for the 189 early and late lateral energy fractions measured in the 17 halls. The early lateral energy fraction
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Table 2 Means and standard deviations of measured early and late lateral energy fractionsa
Mean Standard deviation Distribution a
Early lateral energy fraction
Late lateral energy fraction
Diuse
0.19 0.085 Not normal
0.31 0.047 Highly normal
0.33 ± ±
Data set of 189 values.
results are discussed in more detail elsewhere [8]. One observes that the mean early fraction is signi®cantly lower than the late. A major reason for this is surely that the early sound contains the direct sound which by de®nition is not lateral. The mean value of the late lateral energy fraction at 0.31 is very close to the theoretical value for a diuse sound ®eld of 0.33. The scatter of measured values is small for the late lateral energy fraction. Fig. 3 shows the distributions of both the early and late lateral energy fractions. Tests on the statistical normality of each set of data using the 2 test show the early lateral energy fraction to be ``almost certainly not normal'' with a con®dence limit of over 0.1%. On the other hand the 2 test on the late lateral energy fraction shows that the data is ``highly normal'' (signi®cantly less than the P=10% value). Fig. 4 shows the means and standard deviations of measurements of the early and late lateral energy fractions as a function of frequency. Though the mean of the early
Fig. 3. Distributions of the early and late lateral energy fractions as measured at 189 receiver positions.
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fraction is constant with frequency, the late fraction has lower values at the lower frequencies. Since the measurement systems for both fractions were identical, and indeed the two fractions were derived from the same impulses responses, these lower values of the late fraction at low frequencies would seem to be either a feature of sound ®elds or a consequence of the measuring process. The second looks unlikely since consideration of the dierences between the character of early and late sound does not obviously lead to this conclusion. (This could be checked by rotating the ®gure-of-eight microphone through 90 degrees and measuring the late frontal energy fraction.) Nor is there an obvious reason why the directional character of the late sound ®eld should vary with frequency. For instance, a major in¯uence on low frequency sound is attenuation at grazing incidence, also known as the seat dip eect, but if the late sound ®eld is diuse, we would expect attenuation at grazing incidence to eect both frontal and lateral sound and thus have a neutral eect on the late lateral energy fraction. It is just possible that the low values of late fraction at low frequencies indicate less diuse sound ®elds at these frequencies. The other feature to note in Fig. 4 is that the scatter of measured values of both the early and late lateral fractions is smallest at mid-frequencies (500/1000 Hz) and largest at 125 Hz. Apart from unresolved details regarding frequency, the conclusion regarding the late lateral energy fraction is that it is randomly distributed with a small degree of scatter around a mean, which is close to the value expected in a diuse sound ®eld.
Fig. 4. Octave means 1 standard deviation for the measured early and late lateral energy fractions.
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5. Late lateral energy fractions averaged by hall When late lateral energy fractions are averaged by hall, the hall means only vary between 0.25 and 0.34, a range of 0.09 compared with a range of 0.20 for the early lateral energy fraction [8]. The hall mean values have been compared to various hall parameters by regression analysis. The following were considered but found to be unrelated to the mean late lateral energy fraction (LLF): auditorium volume, seat capacity and mid-frequency reverberation time. The only parameter found to correlate with mean LLF was hall width, with a correlation coecient of r ÿ0:55 signi®cant at the 5% level. (The corresponding coecient for the early lateral energy fraction is ÿ0.59, signi®cance level <2%.) Mean LLF is plotted in Fig. 5 against hall width. One observes in Fig. 5 that the narrowest hall (G, Wigmore Hall, London) is one of three halls with the highest measured LLF, whereas the widest (Y, Wembley Conference Centre) has the lowest LLF. The Wembley hall is semicircular in plan, which is an extreme form of fan-shape; one notes that it sits below the regression line in Fig. 5. On the other hand, the Royal Albert Hall, London (A) behaves well for its width with regard to LLF. In spite of its well-known faults [12], the Royal Albert Hall does have a particularly good dynamic response with extremely smooth transitions during crescendos. A good dynamic response is thought to be a characteristic of diuse sound ®elds and the result here regarding the mean hall LLF provides objective evidence to corroborate this subjective observation. Another outlier in Fig. 5 deserves comment: the Assembly Hall, Watford (W) has a low mean LLF value for its width. This rectangular-plan hall has six large windows along each side wall which are covered with curtains; this surely in¯uences lateral re¯ections and therefore lateral fractions.
Fig. 5. Hall mean late lateral energy fractions as a function of hall width. Hall labels according to second column of Table 1.
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6. Late lateral energy fractions within halls The standard deviation (S.D.) for LLF measurements within halls ranges from 0.02 to 0.06, with a mean S.D. of 0.04. Again this is smaller than the within hall mean standard deviation of 0.06 for the early lateral fraction. An interesting observation can be made on the halls with the lowest standard deviations for the LLF; there are four halls with a standard deviation of 0.03 or 0.02. Two of these halls are the smallest in volume and seating capacity of the 17 measured: Cambridge Music School and the Wigmore Hall, London. The other two halls with low scatter of LLF are St. David's Hall, Cardi and the Butterworth Hall, Warwick University. Both these halls have designs which are likely to promote a diuse sound ®eld [12]. In the case of St. David's Hall, the audience seating is arranged in ``vineyard terraces'' and the ceiling is highly diusing; both characteristics are good for diuse late sound. The Warwick University hall also has a highly diusing ceiling. Within each hall, the behaviour of the late lateral energy fraction has been compared with two distances: the source-receiver distance and the lateral distance, the distance of the measurement position from the axis of symmetry. In three (out of the 17 halls) there is a positive correlation (at the 10%) level between source-receiver distance and LLF, whereas there is one hall with a negative correlation at the 10% level. Three other halls exhibit positive correlations of LLF with lateral distance. None of this behaviour is very consistent nor is there any correlation between LLF values and either source-receiver distance or lateral distance for the whole data set. 7. Comparison between measured early and late lateral energy fractions Fig. 6 is a scatter diagram for the 189 measured values of the early and late lateral energy fractions. The correlation coecient is 0.45. Though this correlation is statistically signi®cant (at the 0.1% level), there is probably a considerable random element. We would not expect a good correlation since the early and late sound have dierent characters. The late sound consists of many interfering re¯ections with an approximately diuse directional distribution. The early sound is dominated by the direct sound and discrete early re¯ections; the relative level of the direct sound is a function of source±receiver distance and the early re¯ections are determined by the hall geometry. In the light of the above, it comes as a surprise to observe the relationship between hall mean early and late energy fractions (Fig. 7). With a correlation coecient of 0.80 signi®cant at the 0.1% level, one concludes that the hall average LLF is strongly determined by the average early lateral fraction. The regression equation is: Mean late lateral fraction=0.37 * Mean early lateral fraction+0.24 In view of the relationship between hall mean lateral fractions, the correlation between both hall mean fractions and hall width mentioned in Section 5 is expected. Regarding the relationship in Fig. 7, the surprise arises due to the dierent directional distributions of early and late sound incident on room surfaces. Late re¯ections
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arriving at listeners from the side have been incident on the side wall surfaces from all directions. The early sound is generally dominated by the ®rst-order re¯ections, which have originated from the source only. Thus, a small plane surface which provides ®rst-order early lateral re¯ections will only provide late lateral re¯ections
Fig. 6. Late versus early lateral energy fractions in 17 concert spaces.
Fig. 7. Mean hall late versus mean hall early lateral energy fractions. Hall labels according to second column of Table 1.
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for sound which originates from the stage area; the surface does not produce late lateral re¯ections for sound originating from elsewhere. In two situations, one can argue that hall design features would promote both early and late lateral re¯ections. If the side wall surfaces are highly diusing, then the angle of incidence on these surfaces is irrelevant and we could expect the strength of both early and late lateral sound to be similarly in¯uenced by the location of these surfaces. Likewise, a large side wall surface will provide lateral re¯ections to listeners both for sound originating at the source and sound from other directions ``visible'' from the side wall surface. Only a few of the 17 halls measured have particularly diusing side walls but many have large side wall surfaces. It can be concluded that design for good early lateral re¯ections is on average good for late lateral re¯ections. However, the dierences between the mean values of the late lateral fraction for halls are small. 8. Determinants of the late lateral level As discussed in Section 1, Bradley and Soulodre [3] have proposed the late lateral level (GLL) as a measure for perceived listener envelopment (LEV). In practice, the late lateral level is likely to be calculated from measured values of three quantities: the total relative sound level (G), the early-to-late sound index (C80) and the late lateral energy fraction (LLF). The calculation uses the logarithmic version of the late lateral energy fraction, which can be called the late lateral index [LLI=10. log(LLF)]. Late lateral level; GLL Late level 10: log LLF ÿ G ÿ 10: log 1 10C80 =10 10: log LLF
3
In other words, the late lateral level is the sum of a level term (the late level GL ) and a directional term based on the late lateral energy fraction. It is of interest to establish the relative importance of level and late re¯ection directivity for the late lateral level. With knowledge of their relative importance, it may be possible to establish the design implications to achieve a high late lateral level. As part of the original acoustic survey of British auditoria, both C80 and G were measured [17]. Octave results for each measure were combined into two frequency bands: a bass frequency (125 and 250 Hz octaves) and mid-frequency band (500, 1000 and 2000 Hz). From these the bass and mid-frequency late levels have been calculated. These two levels have been averaged by taking antilogs, averaging and taking logarithms to give a mean late level. The late lateral energy fraction is measured over the frequency range 125±1000 Hz. The minor discrepancy in frequency range for the late level is very unlikely to be of signi®cance. The measurements in halls were made in unoccupied auditoria and no corrections for occupancy have been made; the validity of the arguments below is not likely to be aected by this either. Levels are quoted relative to the level of the direct sound at 10 m from the omni-directional source.
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Table 3 lists the basic statistics of the measured components in Eq. (3). Bradley and Soulodre [3] quote a measured range from ÿ14.4 to +0.8 dB for GLL, which is in good agreement with the range in British halls. One notices in Table 3 that the standard deviation for the late lateral index is much smaller than that for the late level. The ratio of these two standard deviations can provide us with the information we are seeking: the relative importance of the late level, GL , and directivity, LLI, towards the late lateral level, GLL. However one condition needs to be ful®lled for this ratio to be used, it is necessary that the GL and LLI are independent of one another. The very low correlation coecient between them of 0.073 suggests that they are independent. A better check involves normalising GL , LLI and GLL by subtracting the relevant mean value in each case. The sums of squares for each normalised quantity is calculated, as is the sum of the cross-products between GL and LLI. The sum of squares for GLL is 2157 and the sum of cross-products is 30, which is considered small enough to indicate independence between GL and LLI. The relative importance of GL compared with LLI for the late lateral level is thus 3.27/0.68=4.8. In other words, the level GL contributes to 83% of the variation of the late lateral level and the late lateral index only contributes towards 17% of the variation. Inspection of the correlation coecients in ®nal row of Table 3 provides qualitative support for this conclusion. The late lateral level is thus in practice principally determined by the level of the late sound. Though the late lateral energy fraction was found to be related to hall width and the mean hall early lateral energy fraction, these variations have only a small in¯uence on the proposed measure, the late lateral level. The discussion now turns to the late level and what are the main determinants of the late level. Two theoretical values are considered for comparison with the measured late levels: the traditional re¯ected sound level and the late sound level according to revised theory [12]. For both theoretical values, linear regressions have been conducted with measured values. The results of the regression analysis are presented in Table 4. Details of revised theory are given in the Appendix. The comparison of measured with prediction according to revised theory is shown in Fig. 8. Agreement is good with a regression line with a slope of unity. The reasons for the level dierence of 0.9 dB have already been discussed in detail; they include such things as the eects
Table 3 Measured means, standard deviations and range of values for the components in Eq. (3)a
Mean (dB) Standard deviation (dB) Range (dB) Correlation coecient for regression with GLL a
Data set of 189 values.
Late level (GL)
Late lateral index (LLI)
Late lateral level (GLL)
0.3 3.27 ÿ8.4 to +8.2 0.98
ÿ5.2 0.68 ÿ7.2 toÿ3.4 0.27
ÿ4.8 3.39 ÿ14.1 to +3.4 (1.00)
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Table 4 Results of linear regression between measured and theoretical late levelsa
Correlation of measured with: Late sound according to revised theory Traditional re¯ected sound level a
Slope
Dierence of means (dB)
Correlation coecient, r
Standard error of estimate (dB)
0.99 1.04
ÿ0.9 ÿ5.8
0.89 0.82
1.5 1.9
Data set of 189 values.
Fig. 8. Measured late sound level relative to the theoretical late sound level according to Eq. (4), including line of best ®t.
of balcony overhangs [18], absorption in the stage area [17], a fan-shaped hall [12] and attenuation at grazing incidence in the bass [19]. Revised theory was developed in response to the observed reduction in sound level in concert halls as one moves away from the source. The theory matches measured behaviour well on average. The expression for the theoretical late sound according to revised theory contains three terms: 31200:T 482 0174:r ÿ 4 ÿ Theoretical GL 10: log V T T where T is the reverberation time, V the auditorium volume and r the source±receiver distance. The ®rst term is the traditional one for the re¯ected sound level (assuming
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Sabine's reverberation time equation is valid). The second term relates to it being the late sound arriving more than 80 ms after the direct sound. The third term takes account of the arrival time of the direct sound after it is emitted from the source; this term provides the variation in level with position. The theoretical late level according to Eq. (4) is used in Fig. 8. One question of interest in concert halls is whether the sense of envelopment varies with distance from the source. The variation in late level with distance in a typical hall is 2.6 dB (30 m range, RT=2 s). If the late lateral level is the relevant measure, then we expect the sense of envelopment to reduce as we move away from the source; the 2.6 dB range should be compared with the total measured range for the late lateral level of 17.5 dB. On this basis, the variation with distance may not be subjectively signi®cant. Eq. (4) contains three variables on the right hand side. Can we usefully reduce the correlation of measured late levels to a single objective measure? Table 4 also includes the correlation between the measured late level and the traditional expression for the re¯ected sound [the ®rst term in Eq. (4)]. The correlation between the measured value and traditional theory is still good with a standard error of 1.9 as opposed to 1.5 dB for revised theory. The conclusion therefore regarding the major in¯uence on the late lateral level has to be that it is the ratio of reverberation time to auditorium volume, in other words the total acoustic absorption. We would thus expect the sense of envelopment to be high in small halls and low in large halls. Sound level for the listener is also determined by the performance and ¯uctuates during a piece of music. For comparison between halls it is appropriate to compare halls when used with similar musical forces. We can expect on the basis of the late lateral level to experience the greatest sense of envelopment when a large orchestra plays in a small hall. 9. Conclusions The proposal by Bradley and Soulodre on spatial hearing in rooms is a major advance in our understanding of auditorium acoustics. They have clari®ed the distinction between the spatial eects created by early and late re¯ections. Their work led them to propose a speci®c measure, the late lateral sound level (GLL), as relating to listener envelopment (LEV). The aim of this paper was to determine what were the design implications of the late lateral level and to consider whether there was any evidence that the late lateral level might not be the ®nal answer to the envelopment question. The late lateral level can be considered as the sum of two components: a directional component based on the late lateral energy fraction (LLF) and a level component. Analysis of measured values collected from 17 British music spaces showed that the LLF does not vary much between or within halls. The late lateral level was discovered to be substantially determined by the late level. And the late level itself was found to be principally linked to the total acoustic absorption in halls. This leads one to the conclusion that listener envelopment should be high in small halls and low in large ones. Subjective studies at real concerts would be welcome to establish
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whether this simple conclusion is valid, and also to ®nd out whether there are signi®cant changes in perceived LEV within halls. It is possible that the late lateral level is biased too far towards the level component. Is the design criterion for good envelopment just to optimise sound level? Objective measures involving energy are either absolute or relative. Sound level is an absolute measure, as is the proposed late lateral level; other components of the sound excluded from the late lateral level are assumed not to in¯uence the subjective eect. A relative measure involves the balance between one component and another, as in the Clarity Index, C80. A relative measure takes into account the masking of one sound component by another. Using a very simple impulse response, Reichardt and Schmidt found that room impression, which is surely equivalent to envelopment, was determined by the balance between direct and reverberant sound. (They used a relative measure but in fact, because total level was kept constant in their experiment, an absolute measure of reverberant sound level would have worked as well!) Is listener envelopment really immune to the relative level of early sound, for instance? Bradley and Soulodre [2,3] provide evidence that variations in C80 have some in¯uence on perceived LEV, but reject it as a major in¯uence. The ®nal question concerns the role of sound from behind. To this author, the presence or absence of sound from behind can be perceived in concert halls. The proposal that sound from behind is irrelevant to the sense of feeling surrounded by sound is surprising. Acknowledgements I am grateful to the managements of the various halls for allowing access to make measurements in their halls. The measurement work was undertaken while the author was at the Martin Centre for Architectural and Urban Studies, Cambridge, with the assistance of Lee-Jong Lee. The measurement programme was supported by the Science and Engineering Research Council. Appendix. Revised theoretical level for late sound Energies are expressed relative to the direct sound at 10 m from the omni-directional source. The expression for the direct sound is the traditional one with the direct energy=100/r2, where r is the distance from the source. According to revised theory, the late sound energy, l, arriving later than 80ms after the direct sound is [17]: l 31200T=Veÿ1:11=T :eÿ0:04r=T : where V is the auditorium volume, T the reverberation time. Hence the late level is 31200:T 482 0174:r ÿ dB: ÿ Theoretical GL 10: log V T T
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References [1] Marshall AH. A note on the importance of room cross-section in concert halls. Journal of Sound and Vibration 1967;5:100±12. [2] Bradley JS, Soulodre GA. The in¯uence of late arriving energy on spatial impression. Journal of the Acoustical Society of America 1995;97:2263±71. [3] Bradley JS, Soulodre GA. Objective measures of listener envelopment. Journal of the Acoustical Society of America 1995;98:2590±7. [4] Barron M. The Gulbenkian Great Hall, Lisbon, II: an acoustic study of a concert hall with variable stage. Journal of Sound and Vibration 1978;59:481±502. [5] Marshall AH, Barron M. Spatial responsiveness in concert halls and the origins of spatial impression. Applied Acoustics, 2000;62(2):91±108. [6] Barron M, Marshall AH. Spatial impression due to early lateral re¯ections in concert halls: the derivation of a physical measure. Journal of Sound and Vibration 1981;77:211±32. [7] Keet W de V. The in¯uence of early lateral re¯ections on the spatial impression. Proc 6th International Congress on Acoustics, Tokyo, 1968, paper E-2-4. [8] Barron M. Measured early energy fractions in concert halls and opera houses. Journal of Sound and Vibration, 2000;232:79±100. [9] Morimoto M, Maekawa Z. Auditory spaciousness and envelopment. Proc 13th International Congress on Acoustics, Belgrade, 1989;2:215±8. [10] Morimoto M, Iida K, Sakagami K. The role of re¯ections from behind the listener in spatial impression. Applied Acoustics, 2000;62(2):109±24. [11] Reichardt W, Schmidt W. Die hoÈrbaren Stufen des Raumeindruckes bei Musik. Acustica 1966;17:175±8. [12] Barron M. Auditorium acoustics and architectural design. London: E & FN Spon, 1993. [13] Schmidt W. Zusammenhang zwischen Hallabstand und Nachhallzeit fuÈr den Raumeindruck (Halligkeit und RaÈumlichkeit bei Musik). Hochfrequenz und Electroakustik 1968;77:37±42. [14] Reichardt W. Der Impuls-Schalltest und seine raumakustische Beurteilung. In: Proc 6th International Congress on Acoustics, Tokyo, 1968, paper GP-2-2 p. GP11±20. [15] Damaske P. Subjektive Untersuchungen von Schallfeldern. Acustica 1967;19:199±213. [16] Kuttru H. Room acoustics. 3rd ed. London: Elsevier Applied Science, 1991. [17] Barron M, Lee L-J. Energy relations in concert auditoriums, I. Journal of the Acoustical Society of America 1988;84:618±28. [18] Barron M. Balcony overhangs in concert auditoria. Journal of the Acoustical Society of America 1995;98:2580±9. [19] Barron M. Bass sound in concert auditoria. Journal of the Acoustical Society of America 1995;97:1088±98.