The acous ics o 16 h-cen u y Jesui chu ches in Andalusia: La in c oss
plans ollowing he model o Il Gesù
J. Le´
on
*
, E. Albe di , P. Bus aman e , M. Galindo
Ins i u o Uni e si a io de A qui ec u a Y Ciencias de La Cons ucci´
on (IUACC), Escuela T´
ecnica Supe io de A qui ec u a, Uni e sidad de Se illa. A , Reina Me cedes 2,
41012 Se ille, Spain
ARTICLE INFO
Keywo ds:
Wo ship acous ics
Acous ic simula ion
Acous ic he i age
Jesui a chi ec u e
ABSTRACT
Following he Council o T en , p o ound changes we e obse ed in ecclesias ical a chi ec u al space as a esul
o he new spi i in used in o he Ca holic Chu ch by he Coun e -Re o ma ion. The Jesui mo he chu ch, Il Gesù,
con ibu ed o he consolida ion o he model o he single na e chu ch, elimina ing he aisles and educing he
size o he ansep . This a chi ec u al model was dissemina ed in s ep wi h he expansion o he Socie y. The
chu ches o San a Ca alina (Co doba), La Anunciaci´
on (Se ille), and La Enca naci´
on (Ma chena, Se ille) p o ide
emblema ic examples o he model adop ed by he Socie y o Jesus in he second hal o he 16 h cen u y in
Andalusia. The ypological, geome ic, and ma e ial simila i ies displayed by hese chu ches enable a common
analysis o he sound ield, o be ca ied ou h ough in-si u acous ic measu emen s and simula ions. The s udy o
di e en sou ce posi ions in simila models enables he de e mina ion o he op imal sou ce and ecei e con-
igu a ions. I was ound ha he posi ion on he main al a , coinciding wi h he posi ion o he p ies in he
T iden ine i e, does no acili a e he pe cep ion o he sound ield, excep in he posi ions in he high ibunes.
When he sou ce is unde he dome o he ansep , he sound ield e alua ion is mo e a ou able. Con e sely, a
compa a i e analysis o chu ches conside ed o be ’ wins’, S Ca alina and La Anunciaci´
on, has shown he impac
ha he in e io cladding o hese spaces has on he pe cep ion o hei sound ield.
1. In oduc ion
Following he Council o T en (1545–1563) he impo ance o
p eaching in he Ca holic Chu ch was made e iden h ough he o -
malisa ion o a Coun e -Re o ma ion ecclesias ical model. The single-
na e plan was es ablished as he mos sui able model, di e ging om
composi ional p inciples based on aes he ic conside a ions. In his book
Ins uc iones Fab icae e Supellec ilis Ecclesias icae (1577) S Cha les Bo -
omeo, A chbishop o Milan [1], applied he T iden ine dec ee o he
p oblem o a chi ec u e, deeming chu ches wi h a La in c oss plan and a
single na e o be he mos sui able, in con as o he cen alised plans o
Renaissance a chi ec s, iewed by Bo omeo as ypical o pagan emples.
The chu ch o San Fedele (Tibaldi, 1569–1579), buil in Milan o he
Jesui s a he eques o Bo omeo, was adap ed o he needs o he
T iden ine li u gical i e and applied he p inciples se ou by Bo omeo.
The mo he chu ch o Il Gesù in Rome (Vignola, 1568–1584) consoli-
da es his model. In his case, he la ge single na e is lanked by side
chapels, elimina ing he side aisles and educing he size o he ansep ,
acco ding o he T iden ine li u gical i e. In addi ion, he aising o he
p esby e y u he imp o ed he isibili y o he high al a o he
ai h ul. Valle y-Rado [2] p oduced an in en o y o mo e han 300
plans o Jesui buildings om 1580 o 1690. This ypology is iden i ied
in mo e han hal o he plans analysed.
Following i s ounda ion in 1569, he Jesui o de expanded apidly
in Eu ope and Ame ica du ing he 16 h and 17 h cen u ies. As a esul o
his expansion, many chu ches we e buil acco ding o he Jesui Modo
Nos o, ollowing he model o he chu ch o Il Gesù, bu adap ed o he
a chi ec u al cha ac e is ics o each egion. In he case o Spain [3], he
p edominan model was he La in c oss plan wi h side chapels and a
s aigh headwall, which we e adap ed o local building adi ions in
each case.
A e he Council o T en , he impo ance o p eaching led o an
in e es in he acous ic quali y o sac ed spaces. As Howa d highligh s
[4], unde s anding he knowledge o acous ics in he 16 h cen u y is
c ucial. Vi u ius adop ed he A is o elian heo ies o sound p opaga ion
as concen ic wa es, a concep ha pe sis ed h oughou he 16 h cen-
u y. In his con ex , p ominen Jesui s such as Biancani and Be ini
s udied acous ic phenomena. Biancani [5] analysed he phenomenon o
* Co esponding au ho .
E-mail add esses: [email p o ec ed] (J. Le´
on), [email p o ec ed] (E. Albe di), [email p o ec ed] (P. Bus aman e), [email p o ec ed] (M. Galindo).
Con en s lis s a ailable a ScienceDi ec
Applied Acous ics
jou nal homepage: www.else ie .com/loca e/apacous
h ps://doi.o g/10.1016/j.apacous .2025.110774
Recei ed 16 Janua y 2025; Recei ed in e ised o m 24 Ma ch 2025; Accep ed 23 Ap il 2025
Applied Acous ics 238 (2025) 110774
A ailable online 8 May 2025
0003-682X/© 2025 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license ( h p://c ea i ecommons.o g/licenses/by-
nc-nd/4.0/ ).
he echo, demons a ing he in e es o Jesui ma hema icians in he
s udy o acous ic phenomena, also highligh ed by B ia o e [6].
The conce n abou he mos sui able me hod o co e ing chu ches,
ei he wi h aul s o wi h wooden ceilings, was deba ed in I aly du ing
he Renaissance. Howa d [4] and Ba bie i [7] poin ou ha , in he
memo andum o he chu ch o San F ancesco della Vigna, F ancesco
Zo zi p oposed aul s o he choi and a wooden ceiling o he main
na e, conside ing he aul ed ceiling o be mo e app op ia e o singing.
Widesp ead p eoccupa ion o he acous ic aspec s o chu ches led he
Jesui s o e lec on he mos app op ia e way o co e hem. Na a o
[8] analyses h ee Jesui documen s which show he conce ns exp essed
by he Jesui o de ega ding his issue. In he speci ic case o he i s
Jesui chu ch in Mad id (Spain) dedica ed o he Holy Name o Jesus and
designed by Fa he Bus aman e, now disappea ed, documen s show ha
i was esol ed wi h a wooden oo , e lec ing he documen ed opinions
in he excellen acous ic condi ions o he chu ch by hose who knew he
building.
While he ad an ages o wooden ceilings we e p aised, as seen in
Ceballos [9], Fa nese and Vignola de ended he use o he ba el aul o
co e he chu ch o Il Gesù, which was unde cons uc ion. This wen
agains he c i e ion de ended by he Jesui s, suppo ed by Fa he
T is ´
an, who a ou ed he use o wooden ceilings o allow p eaching o
be hea d wi h pe ec cla i y. On his issue, he analysis by Ma ello a
[10], based on he da a o he ini ial acous ic s udy o he chu ch o Il
Gesù [11], e alua es he acous ics o he di e en p oposals o he
chu ch ceiling. A model wi h a la wooden ceiling a di e en heigh s,
wi h and wi hou a dome, was s udied agains he model buil wi h a
ba el aul . Ma ello a concluded ha he wooden ceiling was mo e
sui able han he ba el aul . Howe e , he a ia ions ob ained we e
no as signi ican as migh be expec ed. The esul s show ha he chosen
ceiling heigh had a g ea e in luence on he acous ics o he chu ch han
he cons uc ion ypology selec ed.
In ela ion o he acous ics o Jesui chu ches ha co espond o he
ypology o Il Gesù, esea ch has been ca ied ou on se e al chu ches,
albei wi hin la ge s udy samples, oge he wi h chu ches o o he
his o ical pe iods and/o ypologies [12]. Among he chu ches s udied
by di e en esea che s is he chu ch o S. Roque (Lisbon, Po ugal
(16 h-17 h c.)) s udied by Ca alho [13] alongside a g oup o 41 Po -
uguese chu ches o di e en s yles. Engel [14] includes he chu ch o S .
Pe e and S . Paul (K akow, Poland (16 h-17 h c.)) in a g oup o 14
Polish chu ches while Diand e as [15] analyses h ee Jesui chu ches
om a la ge sample o Pe u ian colonial chu ches - he Socie y in A e-
quipa, Ayacucho and Cusco (Pe u, 17 h c.) - which ollow he model o Il
Gesù (52).
The s udies by Abadía [16] analyse and e alua e he acous ics o
Jesui chu ches in he ci y o Co doba (A gen ina). Th ee o hese
chu ches (S a. Ca alina, S. Isid o Lab ado and La Compa˜
nía (17 h-18 h
cen u y)), ollow Jesui a chi ec u al models de i ing om he Spanish
ones, bu mainly in luenced by local deco a i e and cons uc i e as-
pec s, ea u ing unique elemen s like he wooden aul ed ceiling o he
chu ch o La Compa˜
nía [17]. The chu ches o S a. Ca alina and San
Isid o Lab ado , despi e hei ela i ely modes olume (2991.3 and
4434.2 m
3
), display e e be a ion imes a medium equencies (3.32,
6.17s) which exceed he op imum, as documen ed by Abadía. In he case
o he chu ch o La Compa˜
nía, which has a la ge olume (8236.5 m
3
),
he alues ob ained o T
30m
a e lowe (3.14s) due o he p esence o he
wooden ceiling in he na e o he chu ch.
The esea ch in oduces a no el y s udy o he sound ield in a g oup
o chu ches ha adhe e o he p inciples p oclaimed by he Council o
T en applied by he Jesui O de . The selec ed sample comp ises
chu ches wi h common ea u es in e ms o geog aphical loca ion
(Andalusia (Spain)), cons uc ion da es (second hal o he 16 cen u y),
dimensions, cons uc ion sys ems, ma e ials and e en he same Jesui
a chi ec s and supe iso s. These h ee chu ches ollow he model
es ablished by he Jesui s o hei mo he chu ch, Il Gesù, ea u ing a
La in c oss plan. These simila i ies allow us o ca y ou a join analysis
o he cha ac e isa ion o he sound ield o h ee sou ce posi ions, he
main al a , unde he ansep dome, and he choi .
The analysis, based on in si u measu emen s and acous ic models,
demons a es how a g ea e p opo ion o al a piece su aces and u -
nishings ha e a signi ican impac on he pe cep ion o he sound ield,
pa icula ly in e ms o e e be a ion, musical cla i y and speech
in elligibili y. Al hough he Jesui s we e awa e ha wooden ceilings
imp o ed he acous ics o hei enclosu es, o he ac o s led o he
p e e ence o aul s and domes as he main sys em. Compa ing hese
h ee chu ches wi h o he Jesui chu ches o he same pe iod, olume
and La in c oss plan ypology, i becomes clea how he choice o
wooden oo s would ha e mean a educ ion in e e be a ion imes and
enhanced cla i y.
Finally, he analysis allows us o es ablish ha he posi ion o he
speake on he main al a , as p esc ibed by he T iden ine i e, is
acous ically less a ou able compa ed o posi ioning he speake unde
he ansep dome. Fu he mo e, his s udy aims o analyse di e en
posi ions o sou ces and ecei e s inside he chu ches in o de o
de e mine how hese posi ions a ec he acous ics o hese enclosu es
and also s a ing he loca ions o he pa icipan s in eligious e en s and
conce s o which hese spaces a e also used.
2. Compa a i e analysis o he sample
The Jesui p o ince o Hispania was ounded in 1547 and di ided
in o ou p o inces in 1554 (A agon, Cas illa, Toledo and Andalucía). In
he p o ince o Andalusia, Fa he Ba olom´
e de Bus aman e, who du ing
he Second Gene al Cong ega ion (Rome 1565) had helped d a b ie
ules on how o cons uc Jesui buildings and chu ches, was commis-
sioned by F ancisco de Bo ja o d aw up he plans o he buildings being
ounded in he p o ince [18].
The h ee chu ches selec ed a e some o he colleges es ablished by
he Jesui s in he second hal o he 16 h cen u y (Fig. 1). Thei designs,
supe ised by Bus aman e, ollow he La in c oss plan and o e simila
cons uc ion cha ac e is ics. The chu ch o he college o San a Ca alina
(SC) (1564–1589) in Co doba belongs o he i s ounda ion o he So-
cie y in Andalusia and became he p o o ype o he ollowing con-
s uc ions. The Chu ch o La Anunciaci´
on (AN) (Se ille, 1565–1579)
was cons uc ed o he Jesui s’ Casa P o esa in Se ille and is ega ded as
a “ win” o SC, gi en i s a chi ec u al plan and dimensions. Once Bus-
aman e’s plans had been d awn up, hey we e adap ed and buil by
He n´
an Ruiz el Jo en. Bo h chu ches, wi h a single na e wi hou side
chapels, a e co e ed wi h aul ed ceilings in he na e, ansep and main
chapel, and a hemisphe ical dome in he ansep . Al hough he
chu ches ollow he same cons uc ion pa e n, SC has wo bays in he
na e, while AN has h ee. As Ceballos [9] poin s ou , he p opo ions o
AN a e mo e ha monious. In SC, he al a piece o San Ignacio, di ec ly
connec ing he na e o he o iginal chu ch wi h he chapel o he
Sag a io was elimina ed in 1853. As Fig. 1 shows, a seconda y olume
(567 m
3
) was added o he ini ial olume o he chu ch, esul ing in a
inal olume o 11,926 m
3
(Table 1).
The hi d chu ch selec ed o he exhibi ion is he Colegio de la
Enca naci´
on (EN) (1566–1588) in Ma chena (Se ille). As wi h he wo
p e ious chu ches, i s ini ial designs we e he wo k o Bus aman e,
assis ed in his case by Ma ín de Gainza, mas e builde o Se ille
Ca hed al. A a la e s age, He n´
an Ruiz El Jo en ook o e and pa ic-
ipa ed in he cons uc ion o he chu ch [9]. The plan o he chu ch, wi h
a single na e and h ee aul ed bays be o e he ansep , ollows a
simila layou o hose o AN and SC. Howe e , in EN he e a e side
chapels on ei he side o he main na e. These chapels, o he same dep h
as he ansep a ms, ollow he same pa e n as ha used by he Socie y.
Following he expulsion o he Jesui s in 1767, he chapels we e closed
o , as e idenced by he plan by F ay An onio Ramí ez o 1780. This
emained in place un il he ecen eno a ion o he chu ch
(1998–2002). In his las in e en ion, he pla o m o he main al a was
expanded, and is loca ed u he o wa d han in he o iginal design. In
J. Le´
on e al.
Applied Acous ics 238 (2025) 110774
2
Fig. 1. Sample chu ches. Geome ical pa ame e s. Posi ion o sou ces and ecei e s in-si u measu emen .
J. Le´
on e al.
Applied Acous ics 238 (2025) 110774
3
addi ion, his chu ch has a balcony on he igh a m o he ansep ha
was used as a ibune by he Dukes o A cos, o e ing a p i ileged an-
age poin o he e en s ha ook place in he chu ch. Al hough he
h ee chu ches a e con empo aneous and o simila concep ion, EN,
while main aining a simila longi udinal axis dimension o AN and SC,
has a smalle olume, due o he lowe heigh s o he na es and he
lan e n (Table 1). F om ma e ials pe spec i e, he h ee chu ches exhibi
no able simila i ies. Pain ed mo a is p edominan , co e ing he la ges
a eas o cladding in all h ee cases (39.2–59.7 %), as well as ma ble,
mainly p esen in he loo s (13.4–17.6 %) o he wooden benches and
he al a pieces (Table 6).
As Ceballos [9] poin s ou , hese h ee chu ches (AN, SC, EN) a e he
pu es examples o he Jesui chu ch ypology in Spain in he i s hal o
he 16 h cen u y, epea ing he same cons uc ion pa e n and app o-
p ia ing a Manne is -T en o s yle, e lec ing he sobe spi i o he ea ly
Socie y o Jesus.
3. Me hods
The s udy o he sound ield o he sample chu ches combines in-si u
acous ic measu emen s o he enclosu es and simula ions co esponding
o he di e en posi ions o sou ces and ecei e s commonly used in he
enclosu es. The h ee-dimensional acous ic models o he chu ches ha e
been analysed wi h CATT-Acous ic so wa e [19], ea u ing wo
di e en calcula ion engines, CATT-Acous ic .9.1b and CATT TUCT
2.0b (The Uni e sal Cone T ace ). The so wa e applica ion used is
sui able o bo h p edic ing he acous ic pa ame e alues and gene -
a ing he binau al impulse esponses [20,21], p o iding an accu a e
ep esen a ion o he acous ic beha iou in hese spaces. G aphic design
and modelling so wa e Ske chUp .14, which allows he geome y o be
expo ed o CATT-Acous ic has been used o ep oduce he 3D model o
he in e io o he h ee chu ches. No de ails smalle han 0.50 m we e
conside ed gi en he simpli ica ion equi ed by he complex in e io
geome y o hese spaces [21]. The models we e subsequen ly calib a ed
in o de o ep oduce he sound ield inside he chu ches wi h he s ic
applica ion o he pa ame e s ob ained om in-si u measu emen s. The
acous ic cha ac e is ics o he ma e ials, such as he abso p ion and
di usion o he di e en in e io su aces, play a decisi e ole in his
p ocess, o e and abo e any p e ious geome ic simpli ica ions [22].
Di e en sou ce and ecei e posi ions ha e been analysed based on he
ini ial calib a ed models, and conside ing di e en scena ios wi h emp y
and occupied chu ches and a ying he posi ions o he exis ing u ni-
u e, pa icula ly he pews used o sea he public, ollowing con igu-
a ions commonly used in he sample chu ches.
3.1. Acous ic pa ame e s
The sound ield o chu ches has been e alua ed on he basis o he
objec i e pa ame e s de ined in ISO 3382-1 [23]. The pa ame e T
30
(s)
has been conside ed in he analysis o he physical e e be a ion o hese
spaces. Howe e , when e alua ing he pe cei ed e e be a ion, EDT (s)
(Ea ly Decay Time) was analysed o p o ide in o ma ion on he ini ial
speed o he decay cu e. T
30
was used, oge he wi h all o he pa am-
e e s, o adjus he ini ial models ha ep oduce he sound ield o
chu ches. Sound s engh , pa ame e G (dB), allows us o e alua e he
subjec i e sound le el and uni o mi y o he sound ield. The assessmen
o pe cei ed sound cla i y is based on h ee pa ame e s, C
80
(dB) Musical
Cla i y Index, T
S
(ms) Cen e Time, and D
50
De ini ion, which measu e he
a io be ween he ini ial and la e ene gy eaching he lis ene . The
appa en sou ce wid h om J
LF
(Jus No iceable Le el Fluc ua ion) and
IACC
E
(Ea ly In e au al C oss-Co ela ion Index) co esponds o he i s
pa o he impulse esponse. The esul s a e ep esen ed in wo ways:
i s ly, by equency a e aging in oc a e bands (125–4000 Hz) and hen
by single numbe a e aged alues o e he equency ange indica ed in
Table A.1 o Annex A o ISO 3382-1. In addi ion o he abo e pa ame e s,
he STI (Speech T ansmission Index) pa ame e acco ding o IEC 60268-
16 [24], is used o e alua e speech in elligibili y, classi ying he e-
sul s ob ained on a s anda dised scale.
3.2. In-si u measu emen
The acous ic pa ame e s ha de ine he sound ield we e calcula ed
om he impulse esponses (IR) o he ooms. Fo his pu pose, in-si u
measu emen s we e ca ied ou ollowing he c i e ia indica ed in he
s anda ds [23,24] wi h he chu ches emp y o public. The sou ces we e
placed in he usual posi ions o he speake s in S1 (main al a ), S4 (side
al a ), and o he music, S2 (dome o he ansep ) and S3 (choi ). The
ecei e s dis ibu ed in he audience a ea included di e en posi ions
acco ding o he mos equen uses o each o he chu ches. The acous ic
pa ame e s we e ob ained a each poin whe e a ecei e was placed
h ough sweeps o sinusoidal signals, whe e he equency inc eases
exponen ially wi h ime. The en i onmen al condi ions o he chu ches
we e measu ed and aken in o accoun o he calcula ion, ob aining he
empe a u e, wi h an accu acy ange o ±0.1 ◦C and he ela i e hu-
midi y wi h a ange o ±0.5 %, a ecei e posi ion 1. Table 2 shows he
en i onmen al pa ame e s o each chu ch, as well as he numbe o
ecei e s s udied o each sou ce, as numbe ed in Fig. 1.
IRIS [25], as in eg a ed ha dwa e and so wa e sys em o measu ing
en i onmen al acous ics, was used o he in-si u measu emen s. IRIS so -
wa e [25] was used o gene a e he signal, eco d he esponse, and
analyse he esul s, connec ing he p ocesso compu e o he es o he
measu emen chain ia he MOTU 4PREHYBRID hyb id audio in e ace.
The Omnipowe 4292 Type 4292-L dodecahed al sound sou ce, loca ed
1.50 m abo e g ound le el, ep oduces he exci a ion signal, which is
ampli ied by a B&K 2734 powe ampli ie . The Co e Sound Te aMic
mic ophone, 1.20 m abo e he g ound and aligned in he sou ce- ecei e
di ec ion, cap u es he 3D impulse esponses. I u ilizes a e ahed al
mic ophone a ay, comp ising ou capsules a anged in he shape o a
e ahed on. This con igu a ion enables he cap u e o he sound ield
om all di ec ions. Once he measu emen s we e aken, in he pos -
p ocessing phase, IRIS placed mic ophones in a igu e o 8 o analyse
he i s 2 ms o he impulse esponse ob ained in he measu emen in
o de o de e mine he di ec ional pa ame e s (J
LF
). The so wa e used
iden i ies he di ec sound and aligns he null posi ion o he i ual side
mic ophone in he same di ec ion as ha o he analysis o he ini ial 2
ms o he eco ded impulse esponse. Acco ding o he so wa e manual
ins uc ions, he pa ame e s pe aining o sound in ensi y (G) a e ob-
ained by calib a ing he sound in ensi y wi hin a semi-anechoic
chambe . The equency ange and du a ion o he sweep a e designed
o ensu e ha he signal- o-noise a io exceeds 45 dB in all oc a e bands
subjec ed o analysis, spanning a ange om 125 o 4000 Hz. Head
Acous ic’s HMS III o so simula o was used o e alua e he signals wi h
he EASERA so wa e [26]. Backg ound noise was measu ed wi h a PCE-
430-Class I sound le el me e , a e aged o e 5 min. The esul s we e
ob ained o all equencies in he ange o 8 o 16000 Hz, exp essing he
BNC (Balance Noise C i e ion) alue aken as a ep esen a i e alue in
Table 2.
Table 1
Geome ical Cha ac e is ics.
SC AN EN
MAIN DIMENSIONS (m)
Longi udinal axis 45.28 47.25 45.28
T ans e se axis 24.25 26.06 19.67
Main na e heigh 19.51 19.82 15.81
Heigh unde lan e n 32.07 34.25 20.64
Dome diame e 11.59 14.09 10.17
SURFACES (m
2
)
Su ace. G ound loo 653.05 760.27 669.81
Su ace. Choi loo 125.83 166.39 113.06
VOLUME (m
3
)11,926 13,681 7,674
J. Le´
on e al.
Applied Acous ics 238 (2025) 110774
4
3.3. Model calib a ion
As indica ed abo e, he acous ic models which ep oduce he in e io
o he chu ches, made wi h Ske chUp .14 and impo ed in o CATT-
Acous ic .9.1b, equi ed calib a ion in o de o adjus hei sound
beha iou o he esul s ob ained in he in-si u measu emen .
TUCT algo i hm 1 is used o closed ooms acili a ing sho calcu-
la ion and basic au alisa ion wi h ‘max spli -up o de 0
′
. The numbe o
beams and he unca ion ime o each model a e se manually, and he
esul s ob ained we e e i ied o be accep able (Table 4). The ini ial
models a e calib a ed using a simpli ied i e a i e p ocedu e ha allows
T
30
o be calcula ed and compa ed wi h he T
30
alues ob ained om in-
si u measu emen s. To pe o m his p ocess, i is necessa y o assign
abso p ion and sca e ing coe icien s o he ma e ials o he inne en-
elope, based on li e a u e sou ces (Table 6). The i e a i e calcula ion
p ocedu e is epea ed o adjus hose abso p ion and sca e ing co-
e icien s alues ha p esen a g ea e unce ain y and o which
bibliog aphic da a is una ailable. Table 6 shows he ma e ial consid-
e ed. Once he model has been adjus ed using his simpli ied p ocess,
ano he calcula ion is ca ied ou using algo i hm 2, which imp o es he
s abilisa ion o he simula ed esul s. The esul s ob ained o all selec ed
acous ic pa ame e s a e compa ed wi h hose ob ained om he acous ic
measu emen s, conside ing he ini ial models’ condi ions o humidi y,
empe a u e, backg ound noise and occupa ion simila o hose exis ing
du ing in-si u measu emen s [21,27].
Acco ding o Bo k [28] simula ions a e conside ed adequa e when
he di e ences be ween measu ed and simula ed alues a e be ween one
and wo imes he Jus No i iable Di e ence (JND) alue o each
pa ame e , applying he JND alues seen in ISO 3382-1 [23]. The
coincidence be ween in-si u and simula ed alues wi h di e ences o less
han 1 JND o he T
30
pa ame e (less han 5 % o he measu ed alues
o each oc a e band) is conside ed a sui able calib a ion c i e ion [29].
Fo he es o he pa ame e s, he calib a ion o he model o alues
below 2 JND was conside ed adequa e [30]. Ma ello a [31] sugges s
ha , o musical cla i y and sha pness in chu ch spaces, deno ed by he
pa ame e s C
80
and T
s
, in pa icula ly e e be an spaces, he alue o 1
JND indica ed in he ISO 3382-1 [23] s anda d can be modi ied,
conside ing 1.5 dB o C
80
and 8.5 % o he e e ence alue o T
s
. The
compa ison o he esul s ob ained in-si u and om he ini ial model
(emp y chu ches) is g aphically ep esen ed in e ms o acous ic pa-
ame e s in oc a e bands.
3.4. Spa ial con igu a ions
Based on he alida ed models o each chu ch, he di e en sou ce
posi ions, ecei e posi ions and audience dis ibu ions we e ep o-
duced, conside ing bo h he emp y and occupied chu ch hypo heses. In
o al, 22 models we e p oduced: 6 models each o SC and EN (3 sou ce
posi ions) and 10 o AN (4 sou ce posi ions). The posi ions o sou ces
and ecei e s co espond o hose shown in Fig. 1 o SC and EN. In he
case o AN, by keeping he s ai s leading up o he main al a a he head
o he chu ch, as o iginally designed, a la ge space was eed up unde
he dome o he ansep , allowing a aised pla o m o be in oduced o
conce s and he side al a o be used o small li u gical e en s. Fig. 2
shows he audience a angemen s in AN o S2 and S4, in oducing new
ecei e posi ions and audience a eas in he aised pla o m a ange-
men . In he case o AN, Rico e al. [32] p esen ed a p oposal o he
acous ic ehabili a ion o he chu ch, analysing wo sou ce posi ions,
Table 2
In-si u measu emen s. Sou ces and ecei e s analysed pe .
R S1 S2 S3 S4 T (◦C), H
(%) BNC (dBA)
SC 21 1–17, 19–21 1–18 1,2,13,15,19 –26.0, 46.3 20.7
AN 25 1–25 1–22, 24–25 1–12, 23–25 1–12, 16, 18, 22–25 18.0, 59.6 32.1
EN 23 1–21, 23 1–13,15–18,20,21,23 1–7,19–22 –15.6, 52.7 21.6
Sou ce. R: o al model ecei e s. X-Y: all numbe ed ecei e s in he ange a e conside ed. En i onmen al pa ame e s
Fig. 2. Di e en con igu a ions o sou ces and ecei e s in La Anunciaci´
on chu ch (AN). a) Pho og aph o he S2 posi ion wi hou he pla o m, and b) S2 posi ion
wi h he pla o m.
J. Le´
on e al.
Applied Acous ics 238 (2025) 110774
5
one in he ansep unde he dome, coinciding wi h S2, and he o he
unde he choi . Howe e , he in e en ion p oposed an al e a ion o he
inishes on he side walls o he chu ch, and ins alling panels o o m an
acous ic shell on he pla o m, obs uc ing he di ec iew o he main
al a . These sugges ions we e no aken in o accoun in his s udy.
Table 3 shows he o al numbe o ecei e s o he acous ic models
(R) and hose conside ed o he di e en sou ce posi ions (S1 o S4). Fo
he AN case wi h he sou ce unde he dome (S2), he ecei e s analysed
in he model in oduced by he pla o m a e highligh ed in ed.
Table 4 de ails he calcula ion condi ions o he h ee chu ches in
he sample. The en i onmen al pa ame e s ( empe a u e, humidi y and
backg ound noise) ob ained in in-si u measu emen s we e conside ed in
he models and he abso p ion coe icien s o he pews we e modi ied in
he scena ios wi h he chu ch occupied (0.23, 0.37, 0.83, 0.99, 0.98,
0.98) ollowing he model es ablished by Ma ello a e al. [31].
The models made wi h CATT Acous ic ep esen he in e io o he
h ee chu ches (Fig. 3) in a simpli ied way (SC (1834 planes), AN (1144
planes), EN (2288 planes)) so ha he numbe o planes used in he
models depends on he deg ee o complexi y o he en elope o he in-
doo space.
4. Resul s and discussion
4.1. In-si u measu emen
Table 5 shows he esul s o he in-si u measu emen s, spec ally and
spa ially a e aged o each acous ic pa ame e . The esul s a e ca ego-
ized by chu ch classi ica ion (SC, AN, EN) and sou ce posi ions (S1 o
S4). Fo each acous ic pa ame e , he lowes alue is highligh ed in ed
and he highes alue in blue. In he case o EN, he esul s ob ained wi h
he sou ce loca ed a he main al a (S1) and unde he ansep dome
(S2) a e gi en o he ecei e R23, loca ed on a high os um (see
Fig. 1). This posi ion, known as he coun ’s balcony, is analysed sepa-
a ely. The esul s ob ained om his loca ion a e indica ed in g ey in
he able.
Fig. 4 illus a es he single-numbe a e aged alues o e e be a ion
imes (T
30m
) and musical cla i y (C
80m
) e sus olume o a g oup o
Jesui La in c oss chu ches s udied by o he esea che s
[13,14,15,16,17] and including SC, AN and EN in he g aphs. All alues
co espond o in-si u measu emen s laid down in ISO 3382 [23] a
a ious imes, excep o Ca alho (SR), whose esea ch p eda es he
s anda d.
In he olume ange o be ween 5,000 and 15,000 m
3
, SC p esen s
T
30m
alues close o he chu ches in i s ange. Fo AN and EN he
e e be a ion imes we e 1.5–2.0s abo e he mos ep esen a i e g oup.
The C
80m
esul s o SC, AN and EN we e in he cen al zone o he alues
seen in simila chu ches. The esul s ob ained o CPC show low T
30m
and high C
80m
wi h espec o he sample. This chu ch is he only one in
he sample wi h a aul ed wooden ceiling. As Abadía [17] s a es,
especially a low equencies, he wood o he aul su ace, gi en i s
la ge size, abso bs a hese equencies, conside ably dec easing he
e e be a ion ime, emphasising he ole o cladding in acous ically
quali ying hese spaces. Mo eo e , Albe di [33] analyses a g oup o 27
chu ches om he same his o ical pe iod wi h a La in c oss plan,
including Jesui chu ches and chu ches o o he eligious o de s. The
alues o T
30m
a e in line wi h he a e age o his ypology. In he case
o EN, he alues o C
80
a e in line wi h he a e age alue o his sample,
while SC and AN yield mo e a ou able alues, as can also be seen in he
g aph in Fig. 4.
As expec ed, he compa a i e analysis o he h ee chu ches (SC, AN,
EN) shows simila e e be a ion imes (T
30m
), ega dless o sou ce po-
si ion. In Fig. 5, in he g aphs showing he esul s o e e be a ion (T
30
and EDT) exp essed by equency in oc a e band, i is obse ed ha SC
and AN, wi h e y simila dimensions ( olume a ia ion 14.7 %, g ound
loo a ea 16.4 %, and leng h 4.3 %) p esen di e ences o a ound 1.25s
a all equencies, wi h he excep ion o 4000 Hz (0.5s) o T
30
. When
conside ing he ma e iali y o he h ee chu ches, pain ed mo a ep-
esen s he la ges p opo ion o su ace a ea in he in e io inishes in all
h ee cases, while o he ma e ials such as ma ble, al a pieces and
wooden pews can be ound in signi ican p opo ions, accoun ing o
mo e han 70 % o he o al (75.6 % SC, 80.6 % AN, 73.3 % EN)
(Table 6), highligh ing he simila i y be ween geome ies and inishes.
The p opo ions o hese ou ma e ials show di e ences o be ween 5
and 7.3 % when assessed join ly, al hough i is obse ed ha o ma ble
he di e ences a e small, wi h a ia ions o be ween 3–4.2 %. Fu he -
mo e, when al a pieces and pews, wooden elemen s wi h simila ab-
so p ion coe icien s a low and medium equencies, a e e alua ed
oge he hey show g ea e a ia ions (4.5–9.1 %), especially when
compa ing SC and AN. In sho , al hough hei geome ies a e e y
simila , pa icula ly in he case o SC and AN, he p opo ion o he
ma e ials which o m pa o he u ni u e show no able di e ences.
The signi icance o he ma e ials cons i u ing he in e io o chu ches
is highligh ed by an examina ion o he e e be a ion phenomenon as
elucida ed by he Sabine [34] equa ion.
T60 =0.161*V
A(1)
Conside ing he mean abso p ions a equencies o 500 and 1000 Hz,
calcula ed om he CATT Acous ic models, he alue o he abso p ion
coe icien
α
is 0.0890, 0.0870, and 0.0605 in SC, AN, and EN, espec-
i ely. In u n, he alue o he sound abso p ion a ea (A) depends on he
abso p ion coe icien (
α
) and he in e io cladding on he su aces o
each chu ch. I should hus be no ed ha SC, wi h a lowe olume, has a
highe alue o A (521.7 m
2
) han AN (484.3 m
2
), which, applying
Sabine, esul s in lowe e e be a ion imes in SC, as con i med wi h in-
si u es s. In EN, he ela ionship be ween olume and sound abso p ion
a ea (A) (285.4 m
2
) b ings he e e be a ion ime esul s close o AN.
The EDT analysis in all chu ches shows no a ia ions o mo e han 1
JND ega dless o he posi ion o he sou ce (S1 o S4) (Table 5). How-
e e , when analysing he sample as a whole, al hough his pa ame e
depends on he i s e lec ions whe e he posi ion o he sou ce can ha e
some impac , he di e ences in he JND alues o SC and AN o he
sou ces a e below 1 JND. In he case o EN, he di e ences a e mo e
Table 3
Sou ce posi ions analysed in he simula ions. Recep o s analysed pe sou ce. R:
o al model ecei e s. X-Y: all numbe ed ecei e s in he ange a e conside ed.
The ecei e s wi h he sou ce on he aised pla o m model a e unde lined.
R S1 S2 S3 S4
SC 21 1–21 1–17, 20, 21 1–10,
13–15,
19–21
–
AN 37 1–25 1, 3, 5, 7, 9,
10–20,21,22,
24–29
9–18, 24,
25, 30–37
1–14,
19–25
1–8,
19, 20,
23
EN 23 1–21,
23
1–18, 20, 21, 23 1–8, 13,
15–22
–
Table 4
Calcula ion condi ions.
Backg ound noise
(dBA)
125 250 500 1000 2000 4000
SC 10.4 18.2 21.8 24.1 22.9 16.1
AN 36.8 42.7 47.2 57.0 63.2 70.3
EN 11.9 17.8 16.8 22.2 25.4 17.2
Calcula ion
condi ions
Calcula ion algo i hm 2
Numbe o ays 130,000 (SC-AN);
100,000 (EN)
Echog am / impulse
esponse (ms)
6000 (SC, AN); 5500
(EN)
Ai densi y 1.20 kg/m
3
Ai abso p ion Ac i a ed
Di ac ion Ac i a ed
J. Le´
on e al.
Applied Acous ics 238 (2025) 110774
6
app eciable, especially when compa ing S2 and S3 (1.79 JND), while he
esul s could be expec ed o be mo e simila be ween S1 and S2, which
a e placed close oge he (Table 5 and Fig. 5). In con as , when he
sou ce is unde he dome (S2), he pe cep ion o he sound le el is highe
in SC and AN. In EN his occu s when he sou ce is posi ioned in he
choi (S3) (Table 5). In all hypo heses he esul s ob ained a e ela ed o
he sou ce- ecei e dis ance. In he case o SC and AN, he a e age
sou ce- ecei e dis ances a e lowe when he sou ce is unde he dome,
while he same is ue o EN when he sou ce is in he choi , aking in o
accoun he ecei e s conside ed in each scena io as shown in Table 2.
Sound cla i y, e alua ed om he C
80
plo s in Fig. 5 and he esul s
exp essed in Table 5 (C
80
, D
50
, T
s
), indica es be e alues in SC and AN
wi h he sou ce loca ed unde he dome (S2) han in he choi posi ion
(S3). In he case o AN, he alues ob ained o C
80
a e e y simila o
S1, S2, and S3, wi h di e ences o below 1 JND. Howe e , o he side-
al a sou ce posi ion (S4), he esul s o all he cla i y pa ame e s
wo sen, al hough hese alues a e close o 1 JND. When conside ing he
posi ioning o he sou ce (S4), i is essen ial o acknowledge ha as he
ecei e s unde s udy a e si ua ed below he dome (Table 2, Fig. 2) hey
do no co e all o he chu ch na e. Addi ionally, he dis ance be ween
sou ce and ecei e is smalle han ha obse ed in he o he models. In
SC, he di e ences in sound cla i y a e mo e no iceable be ween he
di e en sou ce posi ions, wi h di e ences abo e 1 JND (1.8 JND S2-
S3). Howe e , in EN he beha iou o sound cla i y is disc epan , as
he sou ce posi ion in he choi (S3) is mo e a ou able, wi h di e ences
o abo e 2 JND compa ed o o he posi ions. In EN, he heigh o he
main na e o he chu ch is lowe han ha o SC and AN (4 m lowe ), and
so is ha o he choi (2.4 m lowe ), which b ings he sou ce (S3) close
Fig. 3. CATT Acous ic 3D models. SC (San a Ca alina), AN (La Anunciaci´
on), EN (La Enca naci´
on).
Table 5
In-si u measu emen . Single numbe o spa ially a e aged alues o di e en sou ce posi ions. JND alue o each acous ic pa ame e . (*): lowes alue o he acous ic
pa ame e . (**): highes alue o he acous ic pa ame e . Unde lined: esul s R23 (EN).
Sou ce EDT
m
(s) T
30m
(s) T
sm
(ms) G
m
(dB) C
80m
(dB) D
50m
J
LFm
STI IACC
E
SC S1 3.95 3.89 297.18 8.85 −5.65 0.15 0.15 0.33 0.33
S2 3.93* 3.88* 257.06* 10.14 −3.61** 0.28 0.18 0.39** 0.37**
S3 4.11 3.90 318.21 8.73* −6.34 0.11* 0.09* 0.29 0.29*
AN S1 5.25** 5.15 370.71 10.25 −5.97 0.19 0.17 0.28* 0.36
S2 5.17 5.17** 339.65 11.21 −4.85 0.26** 0.17 0.33 0.37**
S3 5.07 5.15 334.96 10.74 −4.98 0.17 0.17 0.28* 0.24
S4 5.23 4.89 373.70 10.47 −6.45 0.18 0.18 0.29 0.31
EN S1 4.78 4.93 374.38** 12.24 −7.31* 0.12 0.19** 0.30 0.30
S2 4.93 4.95 364.73 12.62 −6.75 0.14 0.20** 0.31 0.33
S3 4.50 4.88 312.22 13.88** −4.61 0.22 0.18 0.37 0.31
EN_R23 S1 3.94 4.93 256.39 11.17 −3.07 0.23 0.30 0.38 0.22
S2 4.05 4.93 277.03 11.10 −3.57 0.16 0.27 0.38 0.35
JND –5 % 5 % 10 1.00 1.50 0.05 0.05 –0.075
Fig. 4. Jesui Chu ches La in c oss plan. Re e be a ion (T
30m
) and cla i y (C
80m
). Single numbe alues. Main sou ce al a .
J. Le´
on e al.
Applied Acous ics 238 (2025) 110774
7
o he plane o he audience, imp o ing he cla i y pa ame e s ob ained.
The musical cla i y esul s a e condi ioned by he sou ce- ecei e dis-
ance. Acco ding o his c i e ion, he bes esul s a e ob ained wi h
lowe a e age dis ances. In he cases o SC and AN, he a e age dis ances
wi h he sou ce unde he dome (S2) a e 13.58 and 12.80 m, espec-
i ely, whe eas when he sou ce is placed in he choi (S3) hese dis-
ances a e 26.75 and 20.73 m. In EN, he a e age dis ance o S2 is
17.09 m, while in he choi (S3) i is 13.96 m, which in his case yields
be e musical cla i y esul s wi h he sou ce loca ed in he choi .
In chu ches, he p esence o elemen s such as chapels, columns, apses
and la e al na es can con ibu e o a enua e he ea ly e lec ed ene gy
and inc ease i wi h sou ce- ecei e dis ance [35,36,37,38,39]. In he
sample chu ches, s udying he spa ial dis ibu ion o sound s eng h (G)
in ela ion o sou ce- ecei e dis ance, alues wi hin 1 o 2 JND a e
ob ained wi h espec o he Ba on and Lee model [40] (Fig. 6), bu wi h
g ea e a enua ions han p edic ed by his model, as expec ed. In o de
o quan i y hem, he alue o he
μ
pa ame e has been calcula ed based
on he
μ
-model [41]. The alue o he
μ
pa ame e ob ained o he
chu ches a e 0.14 (SC), 0.22 (AN) and 0.20 (EN), highe alues han
hose indica ed by Zama e˜
no e al. [41] o Go hic-Mudeja Spanish
s yle chu ches (0.09–0.16, a e age 0.13). These chu ches, in addi ion o
ha ing a smalle a e age olume, ea u e a wooden oo . Among he
h ee chu ches s udied, only SC ob ains a
μ
alue wi hin he ange o he
Go hic-Mudeja chu ches, as well as a T
30
alue close o hem, coin-
ciding wi h a highe pe cen age o wooden elemen s (al a pieces and
pews), as e alua ed in he e e be a ion imes analysis. Fu he mo e, we
can obse e ha o he h ee chu ches he poin s closes o he al a
show possible sound concen a ions caused by he domes, wi h esul s
exceeding hose o he heo e ical models.
The en eloping sensa ion, e alua ed om J
LF
, shows ma kedly ho-
mogeneous beha iou o AN and EN. In SC, he esul s ob ained o he
posi ion o he sou ce in he choi (S3) show lowe alues, wi h a di -
e ence o 1.80 JND compa ed o S2. The ecei e s analysed o his
sou ce posi ion (S2, SC) a e all loca ed unde he dome o he ansep
and no in he main na e, so ha he ac ion o la e al ene gy ecei ed is
lowe han o he ecei e s loca ed in he na e. In AN and EN, he
numbe o ecei e s included in he measu emen o his sou ce posi-
ion co e s he en i e na e (Fig. 1, Table 2).
In EN, he esul s ob ained o he posi ion o he Dukes o A cos
ibune (R23, S1, S2) show a lowe pe cei ed e e be a ion, wi h EDT
di e ences o a ound 3.5 JND compa ed o he a e age o all he e-
cei e s analysed (Table 5). Be e cla i y is obse ed wi h di e ences o
mo e han 8 JND o T
s
, while be e cla i y and de ini ion wi h di e -
ences o mo e han 2 JND a e ound o C
80
and D
50
. A sepa a e com-
pa ison o he esul s o R23 and he o he g ound loo ecei e s shows
ha only R18 and R19, posi ioned hal way om he sou ce, show
simila esul s. Compa ed o he g ound loo ecei e s loca ed a a
simila dis ance (R3), he esul s o he ansep os um posi ion (R23)
a e much mo e a ou able, as seen in he assessmen o musical cla i y,
whe e C
80
ob ains a e age alues o −7.32 dB o R3. The e o e, as
Albe di [41] poin s ou , ecei e posi ions in ibunes abo e he plane o
he audience yield a be e subjec i e acous ic sensa ion, especially wi h
he sou ce on he main al a .
In SC, placing he sou ce unde he dome (S2) esul s in imp o ed
speech in elligibili y and musical cla i y. This is accompanied by lowe
alues o T
s
and highe alues o C
80
, D
50
and STI. In he case o AN,
Fig. 5. T
30
, EDT, C
80
and J
LF
spa ially a e aged e sus equency oc a e band and e o s ba s (s anda d e o ).
J. Le´
on e al.
Applied Acous ics 238 (2025) 110774
8
while i can be a gued ha he op imal esul s a e achie ed when he
sou ce is posi ioned below he dome, hese a e no signi ican ly supe io
o hose ob ained when he sou ce is si ua ed in he choi (S3) o he
main al a (S1). Fo EN, which is smalle and ea u es side chapels o he
main na e, he op imal posi ion is ha o he choi (S3).
4.2. Calib a ion assessmen
To alida e he models, he emp y chu ch has been conside ed aking
in o accoun he condi ions o he on-si e measu emen and he posi ion
o he sou ce in he main al a (S1), which is he mos ep esen a i e o
Table 6
Main su aces used in he simula ion: Ma e ials, su ace (%), abso p ion (up) and sca e ing (down) coe icien s.
Ma e ial Chu ch A ea (%) 125 Hz 250 Hz 500 Hz 1 kHz 2 kHz 4 kHz
Pain ed mo a (A) * SC 40.0 0.130 0.090 0.055 0.043 0.050 0.043
AN 59.7 0.083 0.073 0.055 0.050 0.050 0.020
EN 39.2 0.080 0.070 0.050 0.030 0.010 0.010
Plas e (A) [42] SC/AN/EN 17.4/3.2/2.7 0.02 0.02 0.03 0.03 0.04 0.05
Facing b ick (B) [42] EN 14.5 0.03 0.03 0.03 0.04 0.05 0.07
Limes one (B) [42] EN 3.2 0.02 0.02 0.03 0.04 0.05 0.05
Limes one-mo a (A) [42] EN 2.4 0.02 0.03 0.03 0.04 0.05 0.06
Ma ble (A) [42] SC/AN/EN 14.6/13.4/17.6 0.01 0.01 0.01 0.02 0.02 0.02
Ce amic iles (A) [42] EN 0.6 0.02 0.02 0.03 0.03 0.04 0.05
Wooden decking (A) [42] AN 3.1 0.18 0.12 0.10 0.09 0.08 0.07
Al a pieces (C) [21] SC/AN/EN 12.3/7.2/5.5 0.12 0.12 0.15 0.15 0.18 0.18
Can as (A) [43] AN 1.6 0.01 0.01 0.01 0.10 0.20 0.45
Glass (A) [42] SC/AN/EN 0.8/1.8/0.3 0.1 0.05 0.04 0.03 0.03 0.03
Wooden pews (C) [44] SC/AN/EN 8.7/4.7/11.0 0.04 0.12 0.17 0.22 0.23 0.24
Ligh ly uphols e ed chai (C) [42] AN 0.5 0.44 0.56 0.67 0.74 0.83 0.87
Wooden doo (B) [42] SC/AN/EN 2.5/2.4/1.6 0.14 0.10 0.06 0.08 0.10 0.10
Ca pe (B) [42] SC/AN 1.3/8.5 0.07 0.31 0.49 0.81 0.66 0.54
Co on cu ain (C) [42] SC/AN 0.8/2.0 0.30 0.45 0.65 0.56 0.59 0.71
Vel e cu ain (C) [42] EN 0.4 0.05 0.12 0.35 0.45 0.38 0.36
Ai condi ioning duc (C) [45] SC 1.5 0.16 0.39 0.91 1.01 1.01 1.01
O gan (C) [46] AN 0.30 0.12 0.14 0.16 0.16 0.16 0.16
Wooden la ice (C) [42]
(semi anspa en )
EN 0.7 0.27 0.23 0.22 0.15 0.10 0.07
* Adap ed om he expe imen al esul s in he uning p ocess.
Sca e ing coe icien s by equency in oc a e bands (125–4000 Hz) [30].
A (Smoo h: 0.12/0.13/0.14/0.15/0.16/0.17).
B (Mode a ely i egula : 0.20/0.25/0.360/0.35/0.40/0.45).
C (I egula : 0.30/0.40/0.50/0.60/0.70/0.80).
4.3. Acous ic e alua ion o models.
Fig. 6. Sound s eng h (G). Main al a sou ce (S1). Values a e aged o a single numbe o he di e en models. Ba on and Lees model and
μ
-model, s sou ce-
ecei e dis ance.
J. Le´
on e al.
Applied Acous ics 238 (2025) 110774
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