ARCHIVES OF ACOUSTICS
Vol. 37, No. 4, pp. 529–547 (2012)
Copy igh c
2012 by PAN – IPPT
DOI: 10.2478/ 10168-012-0063-y
Objec i e Measu es o Spa ial E ec s in Spanish Conce Halls
Sa a GIRÓN(1), Teófilo ZAMARRE˜
NO(1), Ped o BUSTAMANTE(2)
(1) Depa amen o de F´ısica Aplicada II Uni e sidad de Se illa, E.T.S. A qui ec u a (IUACC)
A . Reina Me cedes 2, 41012-Se illa, Spain; e-mail: {sgi on, eofilo}@us.es
(2) Depa amen o de Cons ucciones A qui ec ónicas I, Uni e sidad de Se illa, E.T.S. A qui ec u a (IUACC)
A . Reina Me cedes 2, 41012-Se illa, Spain; e-mail: bus aman[email p o ec ed]
( ecei ed Ap il 9, 2012; accep ed Oc obe 22, 2012)
The p esen wo k consis s o a s a is ical s udy o he monau al (la e al- eflec ion ac ions and le el)
and binau al acous ic pa ame e s (in e -au al c oss-co ela ion coefficien s) ha e alua e he amoun o
ea ly and la e la e al acous ic ene gy encoun e ed in 9 pe o mance halls in Andalusia (sou he n Spain).
Hall olumes ange be ween 6,163 m3and 34,594 m3and all enclosu es a e used o p esen a ions o
symphonic conce s and o he music pe o mances. The majo i y o hese enues a e loca ed in p o incial
capi als o he communi y and o en cons i u e he only p emises in he ci y whe e symphonic conce s
can be held. The acous ic pa ame e s unde s udy he e we e de i ed om impulse esponses analyses
using a sine-sweep signals which we e gene a ed and p ocessed by WinMLS 2004 so wa e in he oc a e-
band equency cen ed om 125 o 4 kHz, and all pa ame e s we e spec ally a e aged acco ding o he
ISO 3382-1 s anda d. A compa ison is p esen ed o monau al expe imen al esul s as a unc ion o sou ce-
ecei e dis ance wi h he p edic ion o Ba on’s e ised heo y o conce halls, and he analyses o he
acous ic pa ame e esul s a e ca ied ou in e ms o hei espec i e jus no iceable diffe ences: a he
many mic ophone posi ions o he wo sou ce posi ions on s age, o he spa ial dis ibu ion o sea s in he
audience zone ela i e o he cen al axis ( o le - and igh -hand sides) o he ooms, and o he p esence
o he o ches a shell on s age. Resul s e eal ha he o ches a shell p opi ia es a pe cep ible dec emen
in he alues o he ea ly la e al ene gy ac ion and an inc emen in he la e la e al le el a he audience
sea s. In addi ion, a eg ession s udy e eals ha he wo kinds o measu es o la e ali y, monau al and
binau al, a e co ela ed when he hall-a e age da a is conside ed, bu hey emain unco ela ed when all
indi idual posi ions a e used. Likewise, he anges o a ia ion o he acous ic pa ame e s ound in hese
halls a e na owe han hose specified in he ISO 3382-1. The pape concludes wi h a discussion on he
ela ionships o hall-a e age da a o he fi e pa ame e s wi h eigh geome ic and acous ic a iables.
Keywo ds: conce hall acous ics, di ec ional ene gy pa ame e s, binau al pa ame e s, spa ial imp es-
sion, spa ial effec s.
1. In oduc ion
A e he commencemen o he science o a chi ec-
u al acous ics wi h W. C. Sabine’s con ibu ions in
1895 (Sabine, 1993), b eak h oughs and apid de el-
opmen o elec oacous ics in he fi s hal o he wen-
ie h cen u y p opi ia ed a g ea ad ance in gene al
acous ics. Howe e , i is om he las hi d o he las
cen u y ha he science o oom acous ics expe ienced
a esu gence p opelled by he eme gen compu e and
signal science. As a consequence o esea ch in ha new
age, conside a ions o he han hose in he monau al
empo al ac o s came in o play beyond he scope o e-
e be a ion ime o de e mine op imal configu a ions
o lis ening spaces (Be anek, 1962). In he 1960s,
he fi s e e ences appea ed (Sch oede e al., 1966;
Ma shall, 1967) ha conside ed he significance o
spa ial effec s in he acous ics o conce halls. This
pe cep ion e e s o how he acous ical imp ession in
a oom diffe s om ha which lacks many delayed e-
flec ions a i ing om all di ec ions. Soon a e , wo k
by Ma shall (1968), and Ba on (1971) confi med
ha his imp ession is p oduced by he ea ly la e al
eflec ions, and his unde s anding has since had a sig-
nifican impac on conce hall design (C eme , 1989;
Be anek, 1992). As a ypical spa ial ac o o he
sound field, Damaske and Ando (1972) defined he
in e au al c oss-co ela ion coefficien , and in a efined
530 A chi es o Acous ics – Volume 37, Numbe 4, 2012
app oach, Ando (2007) de eloped a heo y o subjec-
i e p e e ences in ela ion o empo al and spa ial ac-
o s o he sound fields based on he modelling o he
human audi o y-b ain sys em (Soe a e al., 2002).
Rooms o music a e he mos isible and in e es -
ing spaces in a chi ec u al acous ics whe e he h ee
disciplines, o acous ics, a chi ec u e and music a e
blended. Howe e , a ing he acous ic quali y o a hall
o musical pe o mances is a non i ial and mul idi-
mensional opic due o he lack o an unequi ocal c i-
e ion o lis ene s’ music app ecia ion, in con as o
ha o he one-dimensional comp ehension o speech
(Peu z, 1971).
Spa ial imp ession phenomenon is a gene al e m
which co e s wo subjec i e pe cep ual ca ego ies: ap-
pa en sou ce wid h (ASW), and lis ene en elopmen
(LEV). ASW is he appa en audi o y wid h o he
sound field c ea ed by a pe o ming en i y as pe cei ed
by a lis ene in he audience a ea o a conce hall,
and expe imen s ha e concluded ha i is mainly e-
la ed o he ea ly la e al eflec ions eaching he lis-
ene (Ba on, 1971). LEV is conside ed as he sub-
jec i e imp ession by a lis ene o being en eloped by
he sound field: a condi ion ha is, acco ding o ex-
pe imen s, p ima ily ela ed o he la e la e al sound
field (B adley e al., 2000).
Two ypes o measu emen s o la e al eflec ions
om he impulse esponse in a oom ha e eme ged:
he monau al la e al ene gy ac ions (J) ela ed o he
ene gy o ea ly o la e la e al eflec ions in he o me
case, and he in e au al c oss-co ela ion coefficien
(IACC) in he la e , which is a measu e o he diffe -
ence in sound a he wo ea s and hence o la e ali y.
To assess ASW, he ea ly la e al ene gy ac-
ion JLF (Ba on, Ma shall, 1981), (o al e na-
i ely, he ea ly la e al ene gy ac ion cosine JLFC
(Kleine , 1989), is accep ed as a monau al di ec ion-
ally influenced measu e. Likewise, he no malised in-
e au al c oss-co ela ion unc ion IACF (Damaske,
Ando, 1972) is a measu e o he dissimila i y be ween
he a i als o he wa e a he wo ea s. F om his unc-
ion he in e au al c oss-co ela ion coefficien s, IACC,
a e hen gi en by:
IACC 1, 2= max IACF 1, 2 o −1ms < τ < +1 ms.
In which 1= 0 and 2= 80 ms (subsc ip E) a e cho-
sen o he ea ly in e au al c oss-co ela ion coefficien
IACCEwhich assesses he ASW pe cep ual a ibu e
(Hidaka e al., 1995; Okano e al., 1998).
In he same way, he la e la e al sound le el LJis
p oposed as a s anda d (B adley, Soulod e, 1995a;
1995b) in he monau al impulse esponse measu emen
in o de o p o ide a p ac ical indica o o he amoun
o lis ene en elopmen in conce halls o sound a -
i ing om all di ec ions (E jen e al., 2001), and
he la e in e au al c oss-co ela ion coefficien IACCL
(co ela ion calcula ed om 1= 80 ms o infini y
(subsc ip L)) in he binau al measu emen , is p o-
posed by Hidaka e al. (1995), and Okano e al.,
(1998).
Al e na i ely, a u he pa ame e which in ol es a
a io, he la e la e al ene gy ac ion JLLF, (Ba on,
2001) defined by he same a io as JLF bu o he la e
in e al, o s udy lis ene in ol emen is also consid-
e ed he e. Bo h monau al la e la e al pa ame e s a e
ela ed o omnidi ec ional sound s eng h Gand cla -
i y pa ame e C80 h ough:
JLLF = 10(LJ−G)/10 1 + 10C80/10.(1)
Due o he con amina ion o he esul s wi h back-
g ound noise unde ce ain equencies, his pa ame e
canno be ob ained di ec ly om WinMLS, and hence
i s calcula ion in his wo k is as defined abo e.
Acco ding o se e al expe imen s, he spec al con-
en o la e al eflec ions ha con ibu e owa ds he
ASW and LEV and la e al le els in he monau al pa-
ame e s a e in he ou oc a e bands wi h cen e e-
quencies 125, 250, 500, and 1000 Hz (Hidaka e al.,
1995), espec i ely. This measu e a ou s he equency
egion whe e he wa eleng hs a e mos ly longe han
he acous ical dis ance be ween he le - and igh -
hand sides o a head. In he case o he IACC pa-
ame e , no widesp ead ag eemen ye exis s on how
o calcula e a e ages o e a ious oc a e bands: in
ac ISO 3382-1:2009(E) (2009) does no speci y his
poin . Th oughou his wo k he spec al a e age o
he IACC pa ame e is de e mined ollowing Hidaka’s
ins uc ions (Hidaka e al., 1995; Okano e al., 1998),
which a e based on p e ious expe imen s o Blaue
and Lindemann (1986a, 1986b) and which concludes
ha 500, 1 k, and 2 kHz a e he oc a e bands o equal
and p incipal impo ance o he ASW a ibu e co -
e ing he effec on spa ial imp ession ca ego ies o he
en i e oc a e band equency ange (Okano e al.,
1998). Hence o wa d, hese expe imen al measu es ob-
ained by a i hme ically a e aging wi hin hese e-
spec i e a o emen ioned equencies a e named JLFm,
JLFCm,JLLFm, IACCEm, and IACCLm, espec i ely.
Acco ding o in e na ional s anda ds (ISO, 2009) he
equency-a e aged la e la e al sound ene gy le el,
LJm mus be a e aged in ene gy.
Al hough De V ies e al. (2001) sugges ed a de-
composi ion o he measu es o supp ess in e e ence
effec s o which he human ea is appa en ly insensi-
i e, he e ised ISO s anda d (ISO, 2009) has p o-
posed JLFm,JLFCm as objec i e measu emen s o he
pe cep ual lis ene aspec ASW, a jus -no iceable di -
e ence o 0.05, and a ypical ange o alues om 0.05
up o 0.35 ( equency-a e aged alues in single posi-
ions in non-occupied conce and mul i-pu pose halls
up o 25,000 m3). Fo LJm, i s jus -no iceable di -
e ence emains unknown and o IACC acco ding o
Cox e al. (1993) a jus -no iceable diffe ence o 0.075
is assumed.
S. Gi ón, T. Zama e˜no, P. Bus aman e – Objec i e Measu es o Spa ial Effec s in Spanish Conce Halls 531
Wi hin his field, o he pieces o wo k (Mo imo o
e al., 2008) ha e p oposed expe imen s o cla i y he
essen ials o ASW and LEV om he poin o iew
o audi o y beha iou by sugges ing ha he acous-
ic componen s o he eflec ions o e and beyond he
uppe limi o he p ecedence effec con ibu e owa ds
ASW and LEV, espec i ely. Fu he mo e, he compo-
nen s om behind he lis ene gene a e g ea e LEV
(Mo imo o e al., 2001). Abdou and Guy (1996)
also poin ed ou he necessi y o spa ial in o ma ion
on he sound fields o he e alua ion o he acous ics
o ooms and he diagnosis and co ec ion o he causes
o acous ic de ec s.
This pape aims o in e p e and discuss he esul s
o monau al and binau al measu es o spa ial imp es-
sion in 9 pe o mance spaces o sou he n Spain which
a e used as conce halls and o o he musical pe o -
mances. Analyses a e ca ied ou in e ms o sea posi-
ions and hall-a e age alues wi h significan physical
a iables o he acous ic field. The spa ial dis ibu ion
o he a ious pa ame e s, he diffe ences ound due
o he wo sou ce posi ions on he s age, and o he
o ches a shell a e analysed in e ms o hei espec-
i e jus -no iceable diffe ences (JND). These analyses
could p o ide a s a ing poin o u he s udies o
co ela ion be ween objec i e pa ame e s and spa ial
imp ession.
2. Expe imen al me hod
2.1. Measu emen echnique
The p ocedu es employed he e a e hose es ab-
lished in he ISO 3382-1 s anda d (ISO, 2009), whe eby
measu emen s we e ca ied ou in unoccupied ooms
and on unoccupied s ages (no public, no musicians),
sa e y cu ains we e always d awn open, and, in ce -
ain cases wi h he o ches a shell configu a ion in he
s age, chai s and music s ands we e p esen . Tempe a-
u e and ela i e humidi y we e moni o ed du ing he
measu emen s which e ealed a ange o a ia ion o
he en i onmen al condi ions du ing measu emen s in
all enclosu es o 16.8–25.2◦C o he empe a u e, and
38–60% o he ela i e humidi y, espec i ely, wi h he
excep ion o Falla G and Thea e which was measu ed
in win e , whose minimum empe a u e was 14.1◦C.
The a ia ions be ween he en i onmen al condi ions
o he halls ha ha e been measu ed wi h and wi h-
ou an o ches a shell in he s ages ne e exceeded 1◦C
in empe a u e and 8.5% in ela i e humidi y espec-
i ely, excep o Falla G and Thea e whose measu e-
men s we e ca ied ou in win e and sp ing wi h a
diffe ence o 9◦C in empe a u e and 12% in ela i e
humidi y, espec i ely.
Monau al and binau al impulse esponses (IRs)
we e measu ed o de e mine, among o he s, he ol-
lowing pa ame e s o each equency band be ween
125 Hz o 4000 Hz and in all ecei e posi ions: he
ea ly la e al ene gy ac ion (JLF )and ea ly la e al
ene gy ac ion cosine (JLFC), he la e la e al ac ion
(JLLF), he la e la e al le el (LJ), and he binau al in-
e au al c oss-co ela ion coefficien s (IACC), o s udy
he spa ial imp ession phenomena in he ooms.
The IR has been ob ained a each ecep ion poin
using sine sweep signals which we e gene a ed and
analysed by WinMLS 2004 so wa e ia he VX Pocke
2 sound ca d om Digig am. The omnidi ec ional
dodecahed al sou ce DO12 wi h i s In e M-1000 am-
plifie , is placed a he mos usual poin o loca ion
o he na u al sou ce (S) on he o ches a pla o m
(none in he o ches a pi which was always co e ed
wi h wooden panels o hea y cu ains) a a heigh o
1.50 m om he floo . Whe e e possible, measu e-
men s in wo sou ce posi ions on he s age ha e been
ca ied ou (see Table 1 and Fig. 1). In all cases he S1
posi ion coincides wi h he cen al sou ce posi ion on
he s age; and hese wo sou ce loca ions coincide o
he configu a ions wi h and wi hou an o ches a shell.
Two mic ophones ha e been used: mul ipa e n config-
u able Audio-Technica AT4050/CM5 (wi h an app o-
p ia e signal-condi ioning Ea hwo ks LAB1 amplifie )
o measu e la e al ene gy ac ions and le els; and a
o so ype HSU III simula o (Code 1323) om Head
Acous ic (wi h OPUS amplifie ) o eco d binau al IR.
They a e all loca ed a he app oxima e heigh o he
head o a sea ed pe son, ∼1.20 m om he floo , in
a p ede e mined numbe o sea s wi hin he a ious
audience zones ( hese sea s a e coinciden o he mea-
su emen s ca ied ou wi h and wi hou he o ches a
shell on he s age in ce ain halls).
2.2. The halls esea ched
In his sec ion, da a o he 9 conce halls unde
esea ch is p esen ed: Co doba G and Thea e (CGT),
loca ed in Co doba; Falla G and Thea e (FGT), lo-
ca ed in Cadiz; Huel a G and Thea e (HGT), loca ed
in Huel a; Isabel la Ca ólica Thea e (ICT), loca ed
in G anada; Lope de Vega Thea e (LVT), loca ed
in Se ille; Miguel de Ce an es Thea e (MCT), lo-
ca ed in Malaga; Manuel de Falla Audi o ium (MFA),
loca ed in G anada; Maes anza Thea e (MT), lo-
ca ed in Se ille; and Villama a Thea e (VT), lo-
ca ed in Je ez de la F on e a (Cadiz). They appea
in alphabe ical o de in acco dance wi h he ac onyms
assigned om hei names on he MIREM web si e
(digi al scenic and musical enclosu e map o Spain),
whe e u he in o ma ion on he enclosu es is a ail-
able (MIREM, 2012). De ails on he s age shell o hese
spaces and s age suppo pa ame e s ha e been pub-
lished elsewhe e (Gi ón e al., 2010).
In all hese buildings, se e al ypes o cul u al ac-
i i ies, such as ope a, hea e, dancing, cinema and
conce s, may be pe o med, excep in he Manuel de
Falla Audi o ium whe e only conce s and eci als a e
p esen ed. These a e pe o mance spaces wi h a fixed
532 A chi es o Acous ics – Volume 37, Numbe 4, 2012
public-s age ela ionship and a on al desc ip ion, ex-
cep he Manuel de Falla Audi o ium which p esen s
a bi- on al desc ip ion, (i consis s o wo ooms A
and B, see Fig. 1). I is also pe inen o add ha
all 7 p oscenium hea es we e e u bished by he e-
gional go e nmen du ing he 1980s and 1990s, and
ha acous ic measu es ha e been ca ied ou a e
hese e u bishmen s.
In Table 1, he yea o comple ion o inaugu a ion,
a chi ec u al ype, he numbe o floo s, he numbe
o poin s o ecep ion o he mic ophones, and he
sea capaci y a e all summa ized in alphabe ical o -
de , oge he wi h he mos ele an a chi ec u al and
acous ical dimensions (León e al., 2007), whose cal-
cula ions a e desc ibed below.
Mean wid h W: o ho seshoe-shaped halls his is
he maximum wid h on he g ound floo excluding
boxes; i i is ec angula bu i egula , hen a mean
alue is aken as in ICT; in he case o MFA, his geo-
Fig. 1. G ound plan and longi udinal sec ion o 4 halls o he o al spaces analysed. The posi ions o he sou ce
and he ecep ion poin s on each floo a e also shown.
me ical ac o excludes boxes a bo h sides o oom A;
and in MT his is i s ans e se diame e .
Mean heigh H: calcula ed as he a e age o he
heigh o he oom in he mou h o he s age, in he
middle, and a he ea o he hall.
Mean dep h D: he a e age o he ho izon al mea-
su e ha exis s om he s age o he back o he oom
on all floo s. (In he case o MFA, i is he leng h o
oom A).
Audience su ace SA: he a ea occupied by all sea s
in he hall.
To al olume V: hall and s age olume (in he wo
configu a ions i i exis s wi h and wi hou he o ches-
a shell).
Re e be a ion ime T: he e e be a ion ime mea-
su ed in he unoccupied halls and a e aged spa ially
and spec ally in he 500 and 1000 Hz oc a e bands.
Abso p ion A: he abso p ion ob ained using he
e e be a ion ime in Sabine’s o mula.
S. Gi ón, T. Zama e˜no, P. Bus aman e – Objec i e Measu es o Spa ial Effec s in Spanish Conce Halls 533
Table 1. Rele an da a o he conce halls s udied.
Hall CGT FGT HGT ICT LVT MCT MFA MT VT
Yea o comple ion 1873 1910 1923 1952 1929 1870 1978 1991 1928
TypologyaHP HP SP SP HP HP RA CA SP
Numbe o sea s N946 1038 601 689 733 1058 A: 890
B: 413 1800 1200
Hall olume [m3] 6071 8114 4800 5035 5902 6594 A: 4274
B: 1536 20321 7988
Numbe o loo s 4 4 4 3 4 4 1 1 3
S age olume no shell [m3] 4631 5556 1963 1742 3363 4907 3421 14273 3703
S age olume wi h shell [m3] 872 1728 – – – 945 – 1850 574+405
To al olumeb[m3] no shell V′10702 13670 6763 6777 9265 13873 9231c34594 11691
To al olumeb[m3] wi h shell V6943 9842 – – – 9911 – 22171 8562
Hall mean wid h, W[m] 17.0 17.7 10.4 18.0 16.6 17.7 A+B: 19.7 37.0 22.8
Hall max dep h, D[m] 25.3 25.6 17.4 21.9 27.1 23.3 A+B: 24.4 36.3 24.9
Hall mean heigh , H[m] 12.4 14.9 16.7 17.3 18.9 19.9 A+B: 11.1 14.3 14.9
Sea su ace, SA[m2] 536 687 354 449 411 699 A+B: 786 1156 555
R. poin s no shell 22 15 16 12/12 14/14 15 22/22 – 18/18
wi h shell 17 15/15 – – – 15/15 – 15/15 17
T[s] no shell 1.17 1.89 1.41 1.26 1.44 1.26 2.33 – 1.85
wi h shell 1.19 1.86 – – – 1.14 – 2.51 1.70
A[m2]no shell 1473 1165 772 866 1036 1773 638 – 1017
wi h shell 939 852 – – – 1400 – 1422 811
aHP – Ho seshoe p oscenium loo plan. SP – Shoebox p oscenium loo plan. RA – Rec angula audi o ium loo plan.
CA – Cylind ical audi o ium loo plan. bHall and s age olumes. cHalls A and B plus s age.
To comple e his in o ma ion and o a oid excessi e
leng h, Fig. 1 shows he plo ed g aphs o he g ound
plans and longi udinal sec ion o only he CGT, MFA,
MT, and VT, espec i ely. The plans include he poin s
o ecep ion on each floo in he hea es wi h diffe en
Fig. 2. Views om he s age o he in e io s o he halls; o MFA he iew is om oom B.
symbols, and he wo posi ions o he sou ce on he
s age. In addi ion, Fig. 2 shows a se o pho og aphs
o he in e io s o each hall aken om hei s age, and
om oom B in he case o MFA.

534 A chi es o Acous ics – Volume 37, Numbe 4, 2012
3. Analyses o expe imen al esul s
and discussions
This sec ion co e s, in i s a ious subsec ions, he
analyses o monau al and binau al pa ame e s s udied
in he 9 conce enues, bo h in e ms o hei spa-
ial alues in he spaces as well as in e ms o he
ela ionships be ween he diffe en ypes o pa ame-
e s ha e alua e he same pe cep ual a ibu es o
spa ial imp ession. The co ela ions be ween he hall-
a e age pa ame e s wi h he geome ic and acous ic
pa ame e s o he halls a e also ca ied ou . In all cases,
he analyses p esen ed e e o he esul s o he spec-
al a e ages o he pa ame e s as s a ed a he end o
Sec. 1. These esul s can be used o u he s udies o
co ela ion be ween objec i e pa ame e s and spa ial
imp ession.
As a s a ing poin , a compa ison by eg ession o
he expe imen al alues o he wo monau al ea ly la -
e al ac ions, JLFm and JLFCm, is ca ied ou . Re-
g ession analysis shows ha he wo pa ame e s a e
linea ly ela ed when he esul s a e compa ed o each
hall and include he esul s o he wo s age configu a-
ions, and when he esul s a e s udied in all indi idual
posi ions in all he halls oge he . In he o me case
he weakes co ela ion is, o FGT wi hou he o ches-
a shell:
JLFCm = 0.569 JLFm + 0.132,
R2= 0.6144, P = 0.0005,
(2)
and he s onges linea co ela ion also o FGT, bu
wi h he shell:
JLFCm = 0.785 JLFm + 0.104,
R2= 0.9560, P < 0.0001.
(3)
By conside ing he esul s in all indi idual posi ions o
all halls (321 pai s o alues, o he wo configu a ions
o he s age and he wo sou ce posi ions) he bes fi
co esponds o a s aigh line:
JLFCm = 0.837JLFm + 0.091,
R2= 0.8554, P < 0.0001.
(4)
The good esul s o s a is ical analysis indica e ha
hese wo pa ame e s a e e y simila and ha he
expe imen al p ocedu e is co ec and can he e o e
be used al e na ely o ei he di ec ional pa ame e o
ea ly la e al ene gy. Simila esul s ha e been ob ained
wi h diffe en equipmen in wo ship spaces o a com-
mon ypology (Gi ón e al., 2008). Hence o wa d, he
esul s o JLFm a e used since his pa ame e p esen s
he bes acili ies o measu ing and has expe ienced
he wides use in o he expe imen al wo k, he eby a-
cili a ing compa ison.
3.1. Spa ial dis ibu ion o he la e al acous ic
pa ame e s. E ec o he o ches a shell
As a fi s s ep o his analysis, all he pa ame e s
we e s udied as a unc ion o sou ce- ecei e dis ance.
In gene al, he empi ical da a se appea s as a cloud o
poin s and ails o indica e any p edic able beha iou
in e ms o sou ce- ecei e dis ance. Fu he mo e, o
he wo possible s age configu a ions, hese expe imen-
al esul s we e also compa ed wi h he heo e ical al-
ues de e mined by Ba on’s e ised heo y o sound
p opaga ion in halls (Ba on, Lee, 1988), whe e e-
e be a ion ime T, (measu ed in he unoccupied halls
and a e aged spa ially and spec ally in he 500 and
1000 Hz oc a e bands), and he o al olume V, a e
he only magni udes in ol ed in hei calcula ions.
In o de o a oid excessi e leng h, he de ailed e-
sul s o his s udy a e no shown. Howe e , i s main
conclusions can be summa ized as: A) The e is con-
side able sca e om he heo e ical p edic ions and
he u hes de ia ions gene ally occu in he la e la -
e al le el LJm ega dless o he ype o hall and o
he sou ce- ecei e dis ance. B) The influence o he
o ches al shell on he s age in he heo e ical p edic-
ions is e y small. In he expe imen al esul s he di -
e ences a e small, simila o he findings ob ained by
B adley (1996), bu pe cep ible (in e ms o JND),
as will be analysed la e . C) Ba on’s e ised heo y o
sound p opaga ion in halls indica es ha la e la e al
sound le els a e mo e sensi i e o changes in e e be a-
ion ime and oom olume han ea ly la e al ac ions
(Ba on, 2001), and hence he effec o adding an o -
ches a shell may be he g ea es on he la e la e al
a i ing sound le els a audience sea loca ions.
In he absence o p edic able beha iou when
s udying he esul s o hese fi e pa ame e s e sus dis-
ance o he sou ce on he s age, i was decided o con-
duc a s udy o hei spa ial dis ibu ion by ollowing a
common me hodology o he fi e pa ame e s s udied.
This consis s o e alua ing he pa ame e s acco ding
o dis ances om he poin s o ecep ion o he cen al
axis o he oom, x( o le - and igh -hand sides), and
by no malizing hese dis ances wi h espec o hal he
a e age wid h o each oom, w, hen hese ela i e dis-
ances a e p esen ed as (x/w). This me hod o e alu-
a ion is jus ified by he ac ha spa ial imp ession is
ela ed o he p esence o ea ly and la e la e al eflec-
ions, and ha he close he walls, he highe in ensi y
should be.
Fo he analysis o his comp ehensi e spa ial dis-
ibu ion in all ooms, he alues o he acous ic pa-
ame e s ela ed o spa ial imp ession a e g ouped in o
disc e e in e als o he a o emen ioned ela i e dis-
ances (x/w). The magni ude o hese in e als is se
a 0.25, whe e posi ions x/w > 1exp ess he posi ions
o he mic ophone e y close o he side walls, which in
all cases co espond o posi ions in a eas o boxes and
S. Gi ón, T. Zama e˜no, P. Bus aman e – Objec i e Measu es o Spa ial Effec s in Spanish Conce Halls 535
side e aces on he g ound o uppe floo s and he e-
o e usually unde an o e hang, (e.g. in CGT, FGT,
HGT, LVT, MCT and MFA). I should be bo ne in
mind ha all he pa ame e s s udied a each posi ion
ha e been a e aged in equency a he oc a e bands,
wi h he p ocedu es es ablished by ISO 3382-1 (ISO,
2009), lis ed in Sec. 1.
On he o he hand, in small ci ies, i is e y com-
mon o adap pe o mance halls o he needs o o ches-
al music by means o o ches a shells. Despi e hei
widesp ead use, e y li le published in o ma ion exis s
on hei acous ical p ope ies and hei influence in he
acous ic field o he hall. This sec ion also analyses he
influence o shells on he pa ame e s conside ed in he
diffe en a eas.
3.1.1. Ea ly la e al ene gy ac ion JLFm
In Fig. 3a, he ea ly la e al ene gy monau al pa-
ame e JLFm is plo ed in o dina es and scaled a in-
e als o 1 JND. In abscissa, he ela i e dis ance o
he cen al axis o he oom is gi en o all he halls
s udied wi hou he o ches a shell and wi h esul s
o he wo posi ions o he sound sou ce (S1 and S2
on he s age, in he d awings o Fig. 1). The numbe
o measu emen poin s in each disc e e posi ional zone
is also specified a he op o he g aph. The ypical
ange o his pa ame e (exp essed in Fig. 3a as ISO)
acco ding o ISO 3382-1 (ISO, 2009), is (0.05, 0.35)
o non-occupied conce halls and mul i-pu pose halls
wi h a olume o less han 25,000 m3. Figu e 3a also
indica es ano he na owe ange ound in hese pe o -
mance spaces (0.10, 0.30) which means a cu o 1 JND
in bo h he uppe and lowe limi s o he ange wi h
espec o hose specified in ISO 3382-1. I can be ob-
se ed ha his ange includes, in each case, he as
majo i y o expe imen al esul s. The c i e ion used
in hei specific de e mina ion acco ding o Fig. 3b, is
discussed la e .
The filled symbols linked by lines show he a e age
alues o he JLFm pa ame e in each posi ional in e -
al, and he deg ee o spa ial dispe sion in each in e -
al is cha ac e ized by he s anda d de ia ion ( e ical
ba s). The spa ial dispe sion ends o inc ease sligh ly
o posi ions close o he side walls x/w >1 and he
analysis o he esul s indica es ha , o x/w be ween
0.25 and 0.75, he a e age alues o he pa ame e a e
e y cons an and only o he a ea nea he cen e o
he halls, x/w < 0.25, does JLFm educe i s alues by
0.5 JND.
As a complemen o Fig. 3a, and in o de o no mal-
ize he expe imen al da a wi h espec o he spa ial
dis ibu ion in he a eas conce ned, Fig. 3b exp esses
in o dina es he pe cen age o he expe imen al da a in
each in e al o 1 JND (n) o alues o JLFm in each
posi ional a ea (x/w) in ela ion o he o al da a in
he same a ea, named n∆(x/w)(see op o Fig. 3a).
a)
b)
Fig. 3. a) Ea ly la e al ene gy ac ions in he ela i e dis-
ance in e als o he cen al axis o he halls, o all halls,
o he wo sou ce posi ions and o he wi hou shell on
he s age. The mean alues and hei s anda d de ia ions
o each in e al a e also shown. The ypical ange o alues
in his wo k and in ISO 3382-1 a e p esen ed; b) ac ion
o da a o alues o JLFm in s eps o 1 JND in he diffe en
in e als o x/w ela i e o he o al numbe o da a in each
in e al co esponding o he esul s shown in pa (a).
I can be seen ha o each in e al he o al sum
ails o each 100%, he eason being ha only hose
alues o he acous ic pa ame e o which he da a lies
mos ly abo e 10% in he whole ange a ia ion we e
conside ed as significan in he wo figu es. Residual
alues co espond o he ange o a ia ion o JLFm be-
ween (0.00, 0.10) in he lowe ange and (0.30, 0.45) in
he op ange. This de e mines he ypical ange o pa-
ame e a ia ion in hese ooms. In his dis ibu ion,
i can be obse ed how he pe cen age o he wo ma-
jo anges (black and da k g ey ba s) inc emen s when
app oaching he la e al walls.
In o de o disce n he effec o he o ches al shell
on he beha iou o he pa ame e , Fig. 4a shows a sim-
ila s udy o JLFm bu conside ing only he ou pe -
o mance halls (CGT, FGT, MCT, and VT) which
536 A chi es o Acous ics – Volume 37, Numbe 4, 2012
a)
b) c)
Fig. 4. a) Ea ly la e al ene gy ac ions in e ms o he di -
e en in e als o ela i e dis ance o he cen al axis o 4
halls, a S1 sou ce posi ion and o he wo s age configu-
a ions. The mean alues and hei s anda d de ia ions o
each in e al and he ypical ange o alues in his wo k
(wi h shell and no shell) and in ISO 3382-1, a e also shown;
b) ac ion o da a o alues o JLFm in s eps o 1 JND in
diffe en in e als o x/w ela i e o he o al amoun o
da a in he same in e al, o 4 halls wi hou he o ches a
shell; c) idem wi h he o ches a shell on he s age.
ha e been s udied wi h he wo configu a ions o he
s age and solely a he sou ce posi ion S1, o ensu e
compa ible da a in he wo configu a ions. The s udy
hus shows he possible effec when he amendmen o
only one a iable is in ol ed ( he shell). (Al hough he
amoun o da a should coincide, he e emains a sligh
diffe ence due o echnical p oblems ha a ose in one
space (CGT), see he op o Fig. 4a).
Resul s confi m he end ob ained o he wi hou -
shell configu a ions ha we e s udied o all halls in
Fig. 3a, and he main enance o he ange es ablished
(0.10, 0.30) o bo h s a is ical popula ions o da a
( he eby alida ing s a is ical esul s o he wi h-shell
configu a ion), and also show ha shells lead o a sig-
nifican dec ease in he a e age alues o he pa ame e
JLFm in all audience zones. Specifically, in he cen e o
he s alls, x/w ∈(0.00, 0.25), while be ween 0.50 and
0.75, he dec ease is abou 0.5 JND. Fo he zone o
boxes and uppe balconies unde o e hangs, he o de
o he dec ease is 1 JND. This sugges s, a leas ini-
ially, ha shells ocus sound by dec easing he ini ial
la e al eflec ions, especially in he a eas unde bal-
conies.
In addi ion, spa ial dispe sion p esen s simila be-
ha iou emaining e y simila in he o he a eas and
eaches i s highes alue, a x/w >1, he a ea nea he
side walls.
Resul s also confi m he na owe ange deduced
be o e o he no-shell configu a ion in his pa ame e
(0.10, 0.30), and ano he e en na owe ange in he
uppe limi (0.10, 0.25) o he wi h-shell configu a-
ion. The effec o he p esence o he o ches a shell
on his ea ly la e al ene gy pa ame e in he audience
sea s al hough small is audible, as seen in B adley’s
wo k on a se o Ame ican halls (B adley, 1996).
Complemen a y o hese s a emen s, Figs. 4b
and 4c include he esul s o he pe cen age o da a
in each posi ional in e al o his pa ame e , in s eps
o 1 JND in each in e al, whe eby only hose esul s
o he pa ame e o which he e a e significan alues
abo e 10% in all a eas a e included. These esul s co -
espond o he ange om 0.10 o 0.30 o he s age
wi hou he o ches al shell and a e simila o he con-
clusion d awn om Fig. 3b, and om 0.10 o 0.25 o
he shell configu a ion. I is also wo h no ing ha he
black ba does no appea i he shell is p esen .
3.1.2. La e la e al le el LJm
A simila analysis was pe o med wi h he o he
monau al pa ame e associa ed wi h he subjec i e
pe cep ion, known as he en elopmen o sound o
he subjec , LJm. Thus Fig. 5a shows he expe imen-
al esul s ob ained a he wo sou ce posi ions in all
halls wi hou he shell, and he a e aged alues o he
pa ame e in he diffe en posi ional a eas. Mean al-
ues a e e y simila in all posi ional zones, and lowe
spa ial dispe sion is p esen a he cen e o he s alls
and in he icini y o he side walls. Fu he mo e, i is
wo h no ing ha he ange o a ia ion o he pa am-
e e s udied in all he ooms can be se om −6dB o
0 dB which is a na owe ange o a ia ion om he
ypical ange specified in ISO 3382-1 o conce halls
and mul ipu pose ooms wi h a olume <25,000 m3.
Fo he comple ion o his s udy, and in o de o
no malize he dis ibu ion o da a, Fig. 5b p esen s
he pe cen age o he amoun o da a, in s eps o
2 dB, ela i e o he o al amoun o da a in each
posi ional in e al agains hese spa ial in e als. I
is wo h no ing ha o he highes in e al (−2dB,
0 dB) he e is an inc emen o ecep ion poin s om
he cen e o he halls o he la e al walls (black ba ),
excep o he x/w > 1posi ions. Since he JND o
his pa ame e emains unknown, he alue o 2 dB
S. Gi ón, T. Zama e˜no, P. Bus aman e – Objec i e Measu es o Spa ial Effec s in Spanish Conce Halls 537
a)
b)
Fig. 5. a) A e aged la e la e al le el in he diffe en in e -
als o no malized dis ance o he cen al axis o he halls:
o all halls, he wo sou ce posi ions and wi hou o ches-
a shell. The means and hei s anda d de ia ion alues
a e also shown, oge he wi h he ypical ange o alues in
his wo k and he ypical ange in ISO 3382-1; b) ac ion
o da a o alues o LJm in s eps o 2 dB in he diffe en
in e als o x/w ela i e o he o al amoun o da a in he
same in e al, o all halls wi hou he o ches a shell on
he s age.
has been chosen due o he wide ange o he a ia ion:
om −8.57 dB o +8.15 dB. In his ep esen a ion,
he esul s o he alues o his pa ame e ha ail o
p esen a significan amoun o da a (abo e 10%) in
all posi ional zones a e igno ed.
By es ic ing he s udy o he 4 ooms in which
acous ic measu emen s we e aken in he wo config-
u a ions, wi h and wi hou he o ches a shell on he
s age, se o Figs. 6, he a e aged alues emain con-
s an in all posi ional a eas and confi m he beha iou
o he pa ame e alues in all ooms s udied in Fig. 5a,
al hough sligh ly highe alues a e encoun e ed. Bo h
Figs. 5a and 6a, main ain he uppe alue o he ange
o a ia ion o he pa ame e in hese spaces (0 dB) de-
spi e he significan numbe o poin s ha a e igno ed
abo e 0 dB, because hey a e less han 10% in each
2 dB jump. Fu he mo e, hese esul s ela e mos ly o
ecep o s o MFA ( his space has no o ches al shell)
and a e he e o e no shown in Fig. 6a. In ac , he
dis ibu ion o mean alues is app oxima ely −2dB
when he shell is p esen and app oxima ely −4dB in
i s absence (Fig. 6a). The gap be ween he wo con-
figu a ions ends o dec ease o he a eas closes o
he side walls (x/w > 0.75). Rega ding he spa ial dis-
pe sion as assessed by he s anda d de ia ion, his is
gene ally in he same o de o magni ude o he wo
configu a ions o he s age, in all posi ional zones o
he audience a ea.
a)
b) c)
Fig. 6. a) La e la e al le el esul s in he diffe en in e als
o no malized dis ance o he cen al axis o he halls o
4 halls, a S1 sou ce posi ion and o he wo s age config-
u a ions. The mean alues and hei s anda d de ia ions
o each in e al a e also shown, oge he wi h he ypi-
cal ange o alues in his wo k and he ISO 3382-1 ange;
b) ac ion o da a o alues o LJm in s eps o 2 dB in he
diffe en in e als o x/w, ela i e o he o al amoun o
da a in he same in e al, o 4 halls wi hou he o ches a
shell; c) idem wi h he o ches a shell on he s age.
As o he complemen a y s udy conduc ed h ough
Figs. 6b and 6c, he da ase wi h alues o n/n∆xabo e
he 10% limi sugges s sho ening he LJm ypical al-
ues o be ween −8dB and 0 dB o he wi hou -shell
configu a ion, in Fig. 5b he ange is na owe (−6dB,
0 dB), and be ween −6dB and +2 dB o he configu-
a ion wi h he shell. The shell he e o e inc eases he
544 A chi es o Acous ics – Volume 37, Numbe 4, 2012
In all cases, he linea fi s s udied show e y weak
co ela ions. Taking in o accoun he a o emen ioned
assump ions, he only eliable co ela ions a e hose
o (1-IACCEm)wi h A(wi h nega i e slope), (1-
IACCLm)wi h T, whe eby he pa ame e inc eases
when e e be a ion ime inc eases, and ha o LJm
wi h V/N which also has a posi i e slope Eqs. (10)–
(12). The alues and linea eg essions co esponding
o he binau al pa ame e s a e plo ed in Figs. 11a
and b, espec i ely.
LJm =−0.763(V/N) + 5.159,
R2= 0.4861, P = 0.0081,(10)
(1 −IACCEm) = −0.0001A+ 0.668,
R2= 0.5538, P = 0.0035,(11)
(1 −IACCLm) = 0.044T+ 0.759,
R2= 0.5828, P = 0.0024.(12)
In he same way as he simple image model indi-
ca es in conce halls and ope a houses, he mean hall
ea ly la e al ene gy ac ions a e influenced by he hall
wid h. O he pieces o wo k ha e ound his co ela-
ion, o ins ance Gade (1989) concludes ha JLFm
has no meaning ul connec ion o diffuse field heo y
a)
b)
Fig. 11. a) Hall-a e age alues o (1-IACCEm) e sus A;
b) (1-IACCLm) alues e sus T, in he wo configu a ions
o he s ages and hei linea fi s.
bu shows a highly significan ela ionship wi h hall
wid h. Based on he da a om all 32 halls, he co e-
la ion is R2= 0.43 and nega i e. Howe e , i he anal-
ysis is es ic ed o 16 ec angula halls, i inc eases o
R2= 0.67. In addi ion, he a io 2H/W which de e -
mines he ela i e a i al ime o ea ly la e al and e -
ical eflec ions, as Wes (1966) sugges ed o conce
halls, seems o be a geome ical measu e in connec ion
wi h ea ly la e al ac ion measu es. In he halls s ud-
ied in his wo k, he wo geome ical magni udes W,
and 2H/W p esen a e y poo ela ionship wi h he
monau al ac ion JLFm and wi h he binau al mea-
su e (1-IACCEm). Pe haps he low co ela ion in his
wo k is due o he ac ha o ches a shells p o oke au-
dible a ia ions in he acous ic pa ame e s, while he
associa ed geome ical quan i ies emain unchanged.
To sum up, unde he la ge olume o da a ana-
lyzed in his wo k and he many a iables included i
would be desi able o ollow B adley’s e y ecen sug-
ges ions (B adley, 2011) in connec ion wi h ca ying
ou expe imen al wo k o a mo e ocused na u e.
3.4. Summa y and discussion
In his sec ion, a synopsis o he s udy is un-
de aken and he esul s a e p esen ed o he objec-
i e acous ic pa ame e s, (spec ally a e aged in acco -
dance wi h he ISO 3382-1 s anda d (ISO, 2009)) ha
quali y he spa ial imp ession in 9 pe o mance halls in
sou he n Spain (Andalusia) in he a ious app oaches.
The dependence o monau al and binau al pa am-
e e s on sou ce- ecei e dis ance shows no p edic able
beha iou and expe imen al esul s ha e been com-
pa ed wi h he heo e ical calcula ions o Ba on’s e-
ised heo y, which needs only he mean e e be a ion
ime and o al hall olume o each hall (Subsec. 3.1,
(Ba on, Lee, 1988)).
The s udy o spa ial dis ibu ion o acous ic pa-
ame e s in he ooms was join ly ca ied ou by scal-
ing he esul s a in e als o 1 JND (0.05 o JLFm
and JLLFm, 0.075 o (1-IACCm)measu es, and 2 dB
o LJm, whose JND is no known) depending on he
ela i e posi ions o he poin s o ecep ion o he cen-
al axis o each oom ( o le and igh -hand sides),
which we e no malized ela i e o hal hei espec i e
mean wid h, (Subsec. 3.1). The o ches a shell com-
monly p oduces a small bu pe cep ible effec on hese
pa ame e s measu ed in he audience a ea, since o
JLFm, Fig. 4a, he change may each a alue o 1 JND,
especially in he a eas closes o he side walls. In ad-
di ion, he ange o a ia ion o JLFm in he se o
alues o all ooms is (0.10, 0.30) in he configu a ion
wi hou shell (Figs. 3a and 4a), and (0.10, 0.25) wi h
he o ches al shell, Fig. 4a, which sugges s ha he
shell a ou s a edis ibu ion o he acous ic ene gy in
he audience a ea in hese pe o mance spaces. Fu -
he mo e, he a e age alues o JLFm in all posi ional

S. Gi ón, T. Zama e˜no, P. Bus aman e – Objec i e Measu es o Spa ial Effec s in Spanish Conce Halls 545
in e als a e lowe when he shell is p esen on s age
han when i is absen . Fo he la e la e al le el LJm,
howe e , he shell seems o a ou an inc ease o he
pa ame e , and in bo h configu a ions o he s age he
ange o a ia ion is also much na owe han he yp-
ical ange s a ed in ISO 3382-1 (ISO, 2009), (−8, 0)
dB o he no-shell configu a ion, and (−6, 2) dB o
he wi h shell, see se o Figs. 6.
As o he binau al pa ame e s, (Table 2), bo h
he ea ly la e al ene gy as well as he la e ene gy ex-
hibi simila spa ial dispe sion and a e lowe han he
monau al pa ame e s a he a ious posi ional in e -
als. Fo (1-IACCEm), he ypical ange in hese spaces
is (0.40, 0.70) o he wo configu a ions o he s age.
Pa ame e (1-IACCLm)exhibi s he same beha iou
in i s mean alues in each posi ional zone wi h a sligh
peak in he a ea be ween he cen al axis and side
walls o he oom (s alls zone). The s anda d de ia-
ions show ha he spa ial dispe sions a e no wide,
and a e sligh ly highe , gene ally, in he configu a ion
wi hou shell. The ypical ange o his pa ame e in
hese a eas is (0.75, 0.90) ega dless o whe he he e
is an o ches a shell on s age.
The effec on la e al ene gy pa ame e s measu ed
in he audience zone due o he change o sou ce po-
si ion on s age has been also s udied in e ms o he
absolu e alue o he diffe ences in hei alues, scaled
a in e als o 1 JND a each ecep ion poin o each
oom. No p edic able beha iou o hese diffe ences in
he pa ame e s associa ed wi h he a ia ion o sou ce-
ecei e dis ance, no o he diffe en la e ali y o he
sou ce sound posi ion has been de ec ed. In a s a is i-
cal su ey o all ecep ion poin s, classified acco ding
o how hey see he sou ce in all ooms oge he , mos
o he sea s ha e a ia ions ha a e in he ange 1–2
JND o he ea ly la e al ene gy pa ame e s, whils o
he la e la e al ene gy, mos poin s lie wi hin diffe -
ences <1JND (Figs. 7 and Table 3).
Conside ing he beha iou o hese diffe ences o
each oom, JLFm p esen s e y homogeneous alues in
MCT and LVT halls, as shown in Fig. 8a, which bo h
ha e ho seshoe ypology. Gene ally o he la e la e al
le el, LJm, Fig. 8b, a g ea e change is ound in he
alues o hese diffe ences om place o place wi hin
all he halls s udied.
The esul s o he compa ison be ween alues o he
wo ypes o measu es o la e al ene gy (monau al and
binau al o he same empo al in e al) ob ained in
he 9 halls in all he indi idual posi ions show ha he
co ela ions a e e y weak and ha he ela ionships
a e no s a is ically significan , as shown in he se o
Figs. 9. Howe e , ela ionships imp o e when he da a
on each hall is conside ed exclusi ely, especially in ce -
ain halls, and when all hall-a e age da a is s udied o
a compa ison be ween JLFm and (1-IACCEm). In he
la e case, he inclusion in he s udy o he esul s o a
se o 15 halls om Okano’s wo k (Okano e al., 1998)
u he imp o es he co ela ion ound (Fig. 10a). Fo
he la e la e al ene gy pa ame e s, no simila da a is
a ailable in he li e a u e. Howe e , by aking in o ac-
coun he alues o he 9 halls s udied in his wo k o
he wo configu a ions o he s age, he ela ionship be-
ween (1-IACCLm)and LJm pa ame e s becomes sim-
ila o ha ob ained p e iously o he ea ly la e al
ene gy pa ame e s as shown in Fig. 10b.
Finally, he s udy in Subsec. 3.3.2 o he dependen-
cies o hese hall-a e age pa ame e s wi h eigh acous-
ic and geome ical pa ame e s, (namely, mean wid h
W, mean heigh - o-wid h a io H/W, mean heigh - o-
dep h a io H/D, mean dep h- o-wid h a io D/W ,
o al- olume- o-numbe -o -sea s a io V/N, audience-
su ace- o-numbe -o -sea s a io SA/N, e e be a ion
ime T, and abso p ion A), enables he conclusion
ha he s a is ically significan ela ionships a e he
ollowing linea eg essions be ween he a iables:
(1-IACCEm)wi h A, Fig. 11a, wi h nega i e slope;
(1-IACCLm)wi h T, Fig. 11b, wi h posi i e slope; and
ha o LJm wi h V/N, also wi h nega i e slope. I
can be obse ed ha , in all cases, he independen
a iable is ela ed o he e e be a ion cha ac e is ic
o he oom (i mus be aken in o accoun ha he
majo abso ben su ace in hese spaces is he audi-
ence zone, which is closely ela ed o he V/N a io).
In his analysis, no o he geome ical o acous ic a i-
ables ha e shown hei po en ial influence on he alues
o he pa ame e s ela ed o spa ial imp ession.
4. Conclusions
O he a ious aspec s s udied in his wo k on he
monau al di ec ional and binau al pa ame e s (spec-
ally a e aged in acco dance wi h he ISO 3382-1
s anda d) o e alua e he spa ial effec s o he sound
fields in 9 pe o mance spaces in Andalusia (sou he n
Spain), i is fi s wo h emphasising ha he depen-
dence o he pa ame e s on sou ce- ecei e dis ance in
each hall has e ealed ha la e al acous ic ene gy is
no dis ibu ed acco ding o he heo e ical p edic ions
o he diffuse e ised heo y by Ba on. As a esul , a
common me hodology has been used o all a eas and
pa ame e s unde s udy. In his me hodology he po-
si ion o he ecei ing poin s a e exp essed in ela ion
o hei dis ance om he symme y axis o he oom
(le - and igh -hand sides) no malized wi h espec o
hal he a e age wid h o he oom, and he acous-
ic pa ame e s a e scaled a in e als o hei espec-
i e JND.
The s a is ical ea men is he same o he pa-
ame e s, da a om all ooms wi h sou ce in S1 and
S2 wi hou shell, and hen he 4 ooms in which hey
a e measu ed wi h he wo configu a ions on he s age.
The main enance o conclusions when ea ing a wide
s a is ical ensemble wi h he second case (smalle )
gi es alidi y o he esul s and conclusions when shells
546 A chi es o Acous ics – Volume 37, Numbe 4, 2012
a e on he s ages. S a is ical esul s show ha he spa-
ial dis ibu ion o ea ly la e al ene gy ac ions p o-
ides highe alues o posi ions close o he side walls
(mean alues o x/w > 1exceed hose o he cen al
a ea o e 1 JND), whe eas hose pa ame e s associ-
a ed wi h la e la e al ene gy and binau al pa ame e s
p esen a mo e uni o m s a is ical dis ibu ion in he
posi ional zones.
The applied me hodology has allowed, o each pa-
ame e s udied, he sys ema ic es ablishmen o hei
cha ac e is ic anges o he dis ibu ion o hei al-
ues o he wo shell configu a ions on he s age. These
anges a e gene ally smalle han hose sugges ed in
ISO 3382-1.
S a is ical esul s ha e shown ha he o ches al
shell p omo es a edis ibu ion o acous ic ene gy in o
he audience a ea and p oduces a no iceable dec ease
o he ea ly la e al ene gy ac ion: his dec ease is
g ea e o posi ions close o he side walls. Howe e ,
o he la e la e al le el he p esence o he shell on
s age leads o an inc ease in i s alues and a simila i y
in magni ude in all posi ional in e als. This sugges s,
a leas ini ially, ha shells ocus sound by dec eas-
ing he ini ial la e al eflec ions, especially in he a eas
unde balconies. This is eflec ed in he alues o he
limi s o he anges men ioned in he p e ious pa a-
g aph.
The change in he wo posi ions o he sound sou ce
on s age also influences hese pa ame e s; i s influence
is g ea e on he ea ly la e al ene gy pa ame e s, and
he diffe ences ound due o he change a e mo e ho-
mogeneous o he ho seshoe ypology. Fo he la e
la e al ene gy pa ame e s, he e is a lowe incidence
o change in posi ion o he sound sou ce and esul s
p esen mo e uni o mi y in audi o ium ypologies. The
analysis has no shown ha he ela i e posi ion o he
ecei e in on o he sou ce (le / igh ) has a signi -
ican effec in any o he pa ame e s analyzed. The
change in posi ion o he sou ce implies ha , o all
he pa ame e s analysed, mo e han 80% o ecei e s o
he en i e enclosu es expe ience a ia ions lowe han
2 JND. Fo he (1-IACCLm)pa ame e , his pe cen -
age eaches 100% o ecei e s.
Monau al and binau al pa ame e s desc ibe e y
diffe en physical cha ac e is ics o he sound field, and
hus co ela ions a e e y weak when s udying pai s o
esul s a each posi ion o signal ecep ion. Exclusi ely
when each hall is desc ibed by a single alue ( he spa-
ial a e age) an accep able ela ionship be ween he
pa ame e s is ound bo h o he ea ly and la e ime-
in e al pa ame e s.
Finally, in o de o d aw conclusions in ela ion o
design a iables, monau al and binau al pa ame e s
ha e been compa ed wi h he mean alues o geome i-
cal and acous ical a iables o he pe o mance spaces.
Reg essions show ha nei he he mean wid h, no he
mean-heigh /mean-wid h a io is significan and ha
in all cases, pa ame e s ela ed o e e be a ion a e he
key (abso p ion, e e be a ion ime, and V/N a io).
Acknowledgmen
The au ho s wish o exp ess hei g a i ude o he
s aff and managemen o each hall o hei coope a ion
in allowing he measu emen s o be ca ied ou . This
wo k has been sponso ed by FEDER unds and he
Spanish Minis y o Science and Technology (MCYT)
wi hin he p ojec s wi h e e ences BIA2003-09306-
CO4-02, and BIA2010-20523.
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