MEASURING SENSORY DISSONANCE IN MULTI-TRACK
MUSIC RECORDINGS: A CASE STUDY WITH WIND QUARTETS
Simon Schwä S e an Balke Meina d Mülle
In e na ional Audio Labo a o ies E langen, Ge many
{simon.schwae , s e an.balke, meina d.muelle }@audiolabs-e langen.de
ABSTRACT
Senso y dissonance (SD) quan i ies he in e e ence be-
ween pa ials in a mix u e o simul aneously sounding
ones and co ela es wi h he pe cei ed dissonance o un-
pleasan ness o his mix u e. While i is mainly s udied in
music pe cep ion, o en using syn he ic signals o symbolic
inpu s, in his pape , we ocus on a p ac ical applica ion
and in es iga e SD as a ool o analyzing he in e ac ions
be ween oices in mul i- ack music eco dings. Using i-
sualiza ion and s a is ical analysis on an exis ing da ase o
ou -pa cho ales eco ded wi h a ious wind ins umen s,
we examine how imb e, uning, and sco e in luences SD.
To do his, we in oduce he no ion o ela i e SD, which
quan i ies how indi idual oices in a mul i- ack eco ding
con ibu e o o e all SD o hei polyphonic mix u e. In ad-
di ion o discussing p ac ical aspec s o measu ing SD be-
ween and wi hin eal music signals, ou case s udy shows
po en ial bene i s and limi a ions o using SD as an anal-
ysis ool in music p oduc ion, o example, o in o m o
au oma e asks like ake selec ion o equaliza ion.
1. INTRODUCTION
In music p oduc ion, he c ea i e p ocess o edi ing and
mixing can o en be aided by objec i e measu es o sound
p ope ies, such as displaying loudness di e ences wi h a
le el me e o isualizing phase di e ences be ween s e eo
channels wi h a goniome e . To ou knowledge, a p ope y
ha has no ye been conside ed in his con ex is he disso-
nance in a ack o eco ding. Wi h he in e play be ween
consonance and dissonance being conside ed a co e com-
ponen o musical exp ession [1], such a measu e could
gi e insigh s in o musical p ope ies o a mix, bo h o el-
a i e compa isons (e.g., o e alua e in ona ion and oice
blending be ween di e en acks) and as an absolu e quan-
i y (e.g., o e ie ing sec ions wi h high dissonance).
The musical concep o dissonance is a mul i- ace ed is-
sue [3] wi h s ong cul u al in luences [4]. While acous i-
cally measu able e ec s [5,6] ha e been ound o co ela e
wi h subjec i e dissonance a ings in isola ed in e als and
© S. Schwä , S. Balke, and M. Mülle . Licensed unde a
C ea i e Commons A ibu ion 4.0 In e na ional License (CC BY 4.0).
A ibu ion: S. Schwä , S. Balke, and M. Mülle , “Measu ing Senso y
Dissonance In Mul i-T ack Music Reco dings: A Case S udy wi h Wind
Qua e s”, in P oc. o he 26 h In . Socie y o Music In o ma ion Re-
ie al Con ., Daejeon, Sou h Ko ea, 2025.
Figu e 1. Exce p om he cho ale GE1 in Cho aleB icks
[2]. (a) Spec og ams o indi idual oices played wi h
umpe (S), cla ine (A), ba i one (T) and ba i one sax
(B). (b) Peak ep esen a ion P (m) o ame mand each
oice . Do ed lines illus a e he ampli ude-weigh ed dis-
sonance ke nels. (c) O e all dissonance Do he exce p .
(d) Rela i e SD by oice (ligh : D , , da k: D , ).
cho ds [7, 8], hey can only se e as indi ec p oxies o
musical dissonance. In his pape , we explo e senso y dis-
sonance (SD) [9], a measu e o he in e ac ions be ween
onal componen s in a complex sound [10, 11], as a way
o quan i y dissonance in eco ded music pe o mances di-
ec ly om audio. Simila o he goniome e ha does no
measu e he subjec i e imp ession o he s e eo image, he
goal is no o analyze pe cep ual p ope ies o SD, bu o
be e unde s and i s beha io in a ealis ic musical sce-
na io, explo ing wha i can e eal abou he ela ions be-
ween indi idual oices in a mul i- ack eco ding.
We app oach his ques ion wi h an explo a o y case
s udy using he Cho aleB icks da ase [2]. I comp ises
117
pe o mances o en Ba oque cho ales, each wi h ou
oices—sop ano (S), al o (A), eno (T), and bass (B)—
ha a e eco ded in isola ion and played on se e al di -
e en wind ins umen s. This way, he da ase p o ides
a con olled scena io o disce ning he in luence o di -
e en musical aspec s, including imb e (ins umen cha -
ac e is ics), uning (pi ch de ia ions), and sco e (cho ds
and oicings). As an ini ial example, we conside an ex-
ce p om he cho ale “Be iehl Du Deine Wege” (GE1 in
Cho aleB icks) in Fig. 1, played wi h umpe (S, o ange),
cla ine (A, ed), ba i one ho n (T, g een), and ba i one
saxophone (B, blue). A e es ima ing onal componen s
(in his case, he ha monics) o e ime om each o he
ou acks (Fig. 1a and b), we can calcula e he o e all SD
(shown in Fig. 1c) and spli i in o he ela i e con ibu ions
o each oice (shown in Fig. 1d). This isualiza ion—
inspi ed by Se ha es’ dissonance sco e [9]— e eals se -
e al aspec s abou SD. Fo ins ance, we can obse e di -
e ences be ween cho ds (Fig. 1d shows he no e onse s o
each oice as e ical lines o o ien a ion), a ia ions in
he con ibu ions o indi idual oices, and local luc ua-
ions wi hin cho ds (e.g., a ound 38 seconds). Explo ing
hese e ec s in de ail is a main objec i e o his pape .
In his con ex , we make h ee main con ibu ions. Fi s ,
we o malize he no ion o ela i e SD (Sec ion 2.1), mea-
su ing he con ibu ion o indi idual acks o he o e all
SD in a music pe o mance, and conside p ac ical aspec s
o calcula ing SD om eal signals (Sec ion 2.2). Sec-
ond, we examine he in luence o imb e, uning, and sco e
on ela i e SD by in oducing new isualiza ions and con-
duc ing sys ema ic expe imen s wi h Cho aleB icks (Sec-
ion 3). Thi d, we ou line possible applica ions o SD o
asks in music p oduc ion, including ake selec ion and
equaliza ion (Sec ion 4), and discuss limi a ions and am-
bigui ies ha a ise when measu ing SD. A Py hon lib a y
wi h all ools used in he expe imen s and ou new cho d
anno a ions o Cho aleB icks a e a ailable online. 1
2. SENSORY DISSONANCE
The concep o senso y dissonance (SD) plays a signi ican
ole in music esea ch, whe e i has been employed in pe -
cep ual models [8, 12–14], o he bo om-up cons uc ion
o scales and music heo ies [9,15], and o analyze in ona-
ion and uning [16, 17]. In hese con ex s, se e al models
ha e been p oposed o quan i y SD [8, 12–15], all based
on he summa ion o a (weigh ed) pu e- one dissonance
ac oss all pai s o onal componen s ha comp ise a com-
plex sound, i.e., all (ha monic and non-ha monic) pa ials
o all simul aneous ones combined.
Fo mally, gi en a se P=( 1, a1), ..., ( K, aK)o
Kpai s o onal componen s wi h equency in Hz and
ampli ude a, SD can be calcula ed wi h
D(P) := X
( i,ai)∈P
( j,aj)∈P
w(ai, aj)d( i, j),(1)
1h ps://audiolabs-e langen.de/ esou ces/MIR/
2025-ISMIR-SD
Figu e 2. Dissonance ke nels d( i, j) o i= 200 Hz.
Blue shaded a eas indica e 0.25 and 1ERB a ound i.
whe e w:R+×R+→R+is an ampli ude-dependen
weigh ing ac o and d:R+×R+→[0,1] is a model o
he pe cei ed dissonance be ween wo pu e ones. In he
ollowing, we p o ide an in ui i e explana ion o hese wo
e ms. Fu he de ails can be ound on ou supplemen al
websi e 1and in [9].
The dissonance ke nel dis based on pe cep ual expe i-
men s wi h sinusoids [11] and i should a ain a high alue
when he equency dis ance is small bu no oo small.
Fig. 2 shows possible ealiza ions o dissonance ke nels
[13–15] a ound i= 200 Hz. While hese ke nels sha e a
simila shape, hey di e in he posi ion o he dissonance
maximum. Fo example, o he equency ange consid-
e ed in Fig. 2, he ke nel by Vassilakis e al. [14] (do ed
line) leads o much wide in e als wi h high dissonance
compa ed o he na ow ke nel used by Be ezo sky [15]
(solid line). The expe imen s in [11] sugges a maximum
o pe cei ed dissonance a a ound 0.25 c i ical bands, a
measu e o he esolu ion o audi o y pe cep ion, o en ap-
p oxima ed in e ms o equi alen ec angula bandwid h
(ERB, e.g., [18]). The e o e, we explici ly se he maxi-
mum o 0.25 ERB, using he mean equency ( i+ j)/2
o he pai ing o de e mine his bandwid h. The esul ing
ke nel is shown as a ed cu e in Fig. 2 and also isual-
ized wi h do ed lines a ound each ha monic in Fig. 1c.
He e, he dependency o he ke nel shape on equency is
also isible, wi h wide ke nels o highe ha monics on
he linea equency axis.
The weigh ing ac o wensu es ha pai ings wi h high
ampli udes con ibu e mo e o D(P). We use he mini-
mum o he wo ampli udes as in [15], which is p opo -
ional o he ampli ude luc ua ion o he bea ing ha oc-
cu s be ween he wo sinusoids [9]. Addi ionally, many
models include an exponen <1 o accoun o he non-
linea i y o loudness pe cep ion [8, 9, 15]. Howe e , since
he beha io o exponen ial comp ession changes when all
ampli udes a e scaled by a cons an ac o , we use log-
a i hmic comp ession, esul ing in he weigh ing ac o
w(ai, aj) = log 1 + min(ai, aj), whe e adding 1en-
su es posi i e alues o w[19]. Finally, i is common o
also include some kind o no maliza ion ha makes D(P)
independen o he o e all loudness o he sound. We omi
his s ep he e and conside loudness no maliza ion an op-
ional p ep ocessing s ep in Sec ion 2.2.
While Eq. 1 allows o a wide ange o possible con-
igu a ions, he concep ual app oach o measu ing SD in
music eco dings emains he same. In he ollowing, we
ocus on he speci ic pa ame iza ion desc ibed abo e as
one illus a i e example.
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
118
Figu e 3. Illus a ion o conside ed subse s o ela i e SD.
2.1 Rela i e Senso y Dissonance
Ex ending ideas om [9] and [17], we can decompose
D(P)in o con ibu ions om di e en componen s o a
sound. In a mul i- ack polyphonic music scena io, his
may gi e addi ional insigh s in o how indi idual sou ces o
oices con ibu e o dissonance. To o malize he decom-
posi ion, we de ine subse s o Pco esponding o di e en
oices in a sound, so ha o an index se V,
P=[
∈V
P .(2)
Fu he mo e, o ∈ V, we de ine he complemen a y se
P =[
′∈V { }
P ′(3)
con aining he onal componen s o all o he oices. Ex-
ending Eq. 1, we compu e he SD be ween he onal com-
ponen s om wo sepa a e se s P1and P2wi h
D(P1,P2) := X
( i,ai)∈P1
( j,aj)∈P2
w(ai, aj)d( i, j),(4)
which we also deno e by D1,2in he ollowing o b e i y,
along wi h Dwi hou subsc ip s o he o e all dissonance
D(P,P). Eq. 4 allows us o decompose D o any oice
∈ V as shown in Fig. 3 on he le . He e, D , ep esen s
he in insic SD wi hin a single oice, D , is he SD inde-
penden o , and D , is he ela i e SD be ween a oice
and i s accompanimen . This esul s in a inal decomposi-
ion D=D , + 2D , +D , .
As a conc e e example, conside he ou -pa cho ale
case, whe e V={S, A, T, B}. The igh side o Fig. 3 il-
lus a es he possible ela i e SD pai ings in his scena io.
Pa icula ly ele an a e he in insic dissonances DS,S,
DA,A,DT,T , and DB,B, as well as he ela i e dissonances
DS,S(depic ed in o ange), DA,A ( ed), DT,T (g een), and
DB,B(blue). I becomes e iden om he igh side o
Fig. 3 ha he indi idual D , a e no independen , since a
change in any P in luences he ela i e SD measu emen s
o all o he oices due o he symme y o he ma ix. Ye ,
Fig. 1d shows how D , can s ill be used o clea ly iden i y
he di e en con ibu ions o o e all SD.
2.2 Tonal Componen s in Reco dings
So a , we ha e only conside ed he case whe e P ep e-
sen s a sound wi h cons an cha ac e is ics. To accoun o
ime- a ying music signals, le P(m) ep esen he onal
Figu e 4. Illus a ion o ha monic peak picking o a sin-
gle ame o a bass cla ine signal, showing he o iginal
DFT spec um (black do s), he cubic spline in e pola ion
(black line), ex emal poin s o he in e pola ion unc ion
( ed c osses), sea ch ange (ligh blue a eas) a ound F0
mul iples (blue icks), and he local h eshold ( ed line).
componen s (equi alen o ha monics in he monophonic
case) a a ime index m∈Z. In a mul i- ack scena io,
we u he equi e a me hod o ob ain obus es ima es o
P (m) om a ime-domain signal x o ∈ V. The e-
quency esolu ion o a disc e e Fou ie ans o m (DFT)
wi h any easonable window size would no be su icien
o his pu pose. P io me hods ha e used a peak pick-
ing algo i hm on he magni ude spec um, e ined wi h
pa abolic in e pola ion [20] o by ze o-padding [9], which
equi es in ica e ine- uning o pa ame e s o obus de-
ec ion o ha monics. Ins ead, we p opose a a ge ed peak
picking app oach ha le e ages undamen al equency
( 0) es ima es, assuming a quasi-ha monic o e one s uc-
u es. 0es ima es can be ob ained obus ly using mono-
phonic algo i hms (e.g., [21]), o wi h p edominan [22] o
polyphonic [23] 0es ima ion algo i hms o mo e com-
plex inpu signals. Since many musical ins umen s p o-
duce nea -ha monic spec a, his me hod is applicable o a
wide a ie y o eco dings.
The equency and ampli ude o each ha monic is ob-
ained in h ee s eps, as illus a ed in Fig. 4. Fi s , we
cons uc a cubic in e pola ing spline ep esen a ion (black
cu e) o he magni ude spec um (black do s) and com-
pu e i s de i a i e, a piecewise quad a ic unc ion. Second,
we ind he oo s o he spline de i a i e, iden i ying he
ex emal poin s o he o iginal cubic splines ( ed c osses).
The la ges ex emum in he icini y o n 0(blue ec an-
gles) is hen assumed o be he spec al peak co esponding
o he n h ha monic. To e ine hese es ima es (e.g., when
he e en ha monics o a cla ine a e below backg ound
noise le el), we inally apply local h esholding, emo ing
any peaks whose o al magni ude is below a ce ain alue.
The local h eshold ( ed cu e) is calcula ed using a sliding
Hann window wi h an adap i e wid h depending on 0, so
ha he a e aging spans Nw=⌈1.2· 0N/ s⌉ equency
bins. This way, a single ha monic wi h la ge magni ude
does no in luence he h eshold a he neighbo ing ha -
monics. Wi h his me hod, i is possible o accu a ely ack
ha monics ac oss mul iple ames o an STFT wi hou ex-
plici ly modeling con inui y be ween ames. Fo STFT
ames whe e he 0es ima e indica es an un oiced ame,
we se P (m) = ∅.
When using loga i hmic comp ession o win Eq. 1,
he scale o he ampli udes aiin P (m)can be a bi a y,
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
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as long as i is consis en ac oss all oices. I can u he
be desi able o emo e he in luence o loudness (and also
ela i e le el di e ences be ween he indi idual oices),
which can be achie ed by no malizing all ampli udes in
P (m) o sum o one. In he pa icula case o Cho ale-
B icks oices a e eco ded in isola ion and no in a musi-
cally meaning ul loudness balance anyway. The e o e, we
di ide each aiby a cons an
C= max c, X
( i,ai)∈P
ai,(5)
whe e limi ing C o no become smalle han c= 0.1
a oids a i icially in la ing he in luence o ames wi h
e y low o e all le el.
3. SENSORY DISSONANCE IN CHORALEBRICKS
A main goal o his pape is o s udy he beha io o SD
in a ealis ic musical scena io. Speci ically, we wan o
disen angle he in luence o di e en musical p ope ies—
imb e, uning, and sco e—o indi idual oices in a mul i-
ack eco ding on he SD alues, and o which ex en
his measu e enables compa isons be ween di e en in-
s umen s, akes, o composi ions.
Fo his explo a o y analysis, we use he Cho aleB icks
da ase [2], which p o ides eco dings o en Ba oque ou -
pa cho ales. Thei composi ion s yle is homophonic, i.e.,
oices ollow a synch onized hy hm while o ming cho ds
wi h a main melody (usually in he sop ano), using ela-
i ely simple cho ds and oicings. Fu he mo e, he da ase
con ains isola ed eco dings o each oice played on se -
e al di e en wind ins umen s, allowing o a compa ison
o a ious ou -ins umen combina ions (ensembles) play-
ing he same cho ale. To simpli y he no a ion o ensem-
bles, we in oduce sho hands. The ensemble used in mos
expe imen s and isualiza ions (e.g., Fig. 1) is deno ed by
E= ( p,cl,ba ,bs), using a uple o ins umen IDs
as shown in Table 1 in he o de o S,A,T, and B. To
deno e a single ins umen being eplaced in E, we use
a subsc ip , o example, ES= l = ( l,cl,ba ,bs).
In addi ion o E(wi h wo woodwinds and wo b ass
ins umen s), we assemble a pu e woodwinds ensemble
Ewood = (ob,cl,bs,bcl)and a pu e b ass ensemble
Eb ass = ( p, h,ba ,ba ), always choosing he in-
s umen wi h he highes numbe o a ailable eco dings
o he espec i e oice. Finally, as a syn he ic baseline
o compa ison, we c ea e an ensemble Esaw, whe e each
oice is syn hesized using a saw oo h wa e o m wi h 20
ha monics and he espec i e 12- one equal empe amen
(12-TET) equency o each no e as F0. Using hese en-
sembles and he exce p om Fig. 1 as a unning example,
we can y o disen angle he in luences o imb e, uning
and sco e on SD.
3.1 The In luence o Timb e
In Fig. 1e, la ge di e ences be ween ins umen s in ela-
i e (ligh e colo ) and in insic SD (da ke colo ) can be
obse ed, mos p ominen ly o he Tand B oice, played
Figu e 5. Ampli ude dis ibu ion ac oss he i s 20 ha -
monics in P o each ins umen (a e aged o e he en i e
da se , no showing alues below −60 dB). The saw oo h
imb e saw is shown o compa ison.
Ins umen ID # No es D , D , HC
Flu e l 449 0.03 1.85 1.55 ±0.3
Oboe ob 449 0.60 3.65 3.67 ±0.7
English Ho n eh 460 0.74 3.70 3.78 ±0.8
Cla ine cl 909 0.53 3.43 2.94 ±0.7
Bass Cla ine bcl 545 4.60 6.08 6.98 ±2.0
Al o Sax as 103 0.94 4.38 3.06 ±0.9
Ba i one Sax bs 816 1.92 4.68 3.99 ±1.4
All Woodwinds 3731 1.34 3.97 3.71
T umpe p 909 0.22 3.35 3.00 ±0.8
Fluegelho n h 909 0.12 2.75 2.25 ±0.6
T ombone b 372 0.45 2.83 3.69 ±1.3
Ba i one ba 963 0.16 1.90 2.43 ±0.8
Tuba ba 464 1.12 2.59 4.50 ±1.3
All B ass 3668 0.41 2.68 3.17
Saw oo h S 449 1.37 5.76 5.56 ±0.0
Saw oo h A 460 1.43 7.01 5.56 ±0.0
Saw oo h T 456 1.50 7.02 5.56 ±0.0
Saw oo h B 464 1.71 4.92 5.56 ±0.0
All Saw oo h 1829 1.50 6.18 5.56
Table 1. SD s a is ics by ins umen , showing in insic SD
D , , ela i e SD D , , and he ha monic cen oid (HC,
mean ±s anda d de ia ion). Values o he syn he ic saw-
oo h ensemble Esaw shown o compa ison.
on ba and bs. To e eal he cause o hese di e ences,
we i s cha ac e ize he imb e o he di e en ins umen s.
While he ull phenomenon o imb e encompasses many
p ope ies o a sound [24], we ocus on he he mos el-
e an aspec o SD, namely he dis ibu ion o ampli ude
ac oss ha monics independen o he o e all loudness o
he sound, as exp essed by he no malized P . Fig. 5
shows he a e age ampli ude dis ibu ion in he i s 20 ha -
monics o each ins umen in Cho aleB icks. Woodwinds
(excep o he lu e) end o ha e highe alues in he up-
pe ha monics (a b igh e imb e), while lu e, luegelho n
and ba i one ho n on a e age ha e mos sound ene gy con-
cen a ed in he low ha monics. We can quan i y his di -
e ence wi h he ha monic cen oid (HC), desc ibing he
mean ha monic index weigh ed by a e age ampli ude, sim-
ila o he spec al cen oid, which is o en used as a imb e
desc ip o [25]. The HC o each ins umen is gi en in Ta-
ble 1, and we can obse e ha o example he bass cla ine
(bcl) has i s ene gy cen e ed a ound he se en h ha monic
(HC o 6.98), while o he lu e ( l), he HC indica es ha
he mos ene gy is in he undamen al (HC o 1.55).
These di e ences in imb e na u ally also a ec bo h
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
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Figu e 6. Two di e en akes o Bplayed wi h bs (pe -
o med no mally and loudly) o he exce p om Fig. 1.
No e ha bo h P a e loudness-no malized, so ha di e -
ences in Donly s em om changes in imb e and uning.
in insic SD D , and ela i e SD D , . Table 1 also lis s
he a e age D , and D , o each ins umen , which a e
calcula ed ela i e o E, i.e., by eplacing he espec i e
oice in Ewi h his speci ic ins umen . Fo example,
when he ombone played bo h Tand B, we conside
ET= b and EB= b o each cho ale whe e he espec i e
eco ding is a ailable. We can obse e ha HC and he
SD alues a e highly co ela ed. Fu he mo e, he ins u-
men choice accoun s o 49% o he a ia ion in D , o e
he en i e da ase and 78% o he a ia ion in D , , as in-
dica ed by he e ec size (η2) o he K uskal-Wallis non-
pa ame ic s a is ical es [26]. This makes he ins umen ’s
ha monic ampli ude dis ibu ion he la ges p edic o o a
oice’s con ibu ion o SD.
In addi ion, he e a e also conside able imb e a ia ions
wi hin each ins umen , e lec ed o example in he s an-
da d de ia ion o HC epo ed in Table 1. As an illus a-
i e example, Fig. 6 shows wo di e en akes o he B
oice played on bs. In he second ake (“loud”), he playe
was ins uc ed o play as loud as possible. No ably, despi e
he loudness no maliza ion o P , bo h D , and D , a e
la ge by almos a ac o o wo o he loud ake, which
also shows s onge luc ua ions o ela i e SD wi hin he
indi idual cho ds. The possibili y o in luence SD h ough
a ia ions in an ins umen ’s imb al quali ies may also ex-
plain he educ ion in SD owa ds he end o he example
in Fig. 1, an e ec ha is no p esen o he loud ake.
3.2 The In luence o Tuning
SD has p e iously been shown o be a con ex -sensi i e
measu e o uning ela ed o jus in ona ion (JI) [16, 17].
In his sec ion, we aim o quan i y how la ge he e ec
o uning is on SD compa ed o o he in luences like im-
b e. To isualize his in ou unning example, we i ually
pi ch-shi each oice by a ce ain amoun p∈[−50,50]
in cen s by mul iplying all equencies in P (m)wi h a
ac o 2p/1200. We hen calcula e o each alue o p he
new ela i e dissonance D , agains he unmodi ied o he
oices o he ensemble (D , emains mos ly una ec ed by
a small pi ch shi ). In o he wo ds, we measu e how much
ela i e SD changes when a pe o me would change hei
Figu e 7. In luence o de uning each oice in Eby ±50
cen s (exce p om GE1, as in Fig. 1). Cho d labels and
shee music a e shown ime-aligned o e e ence.
in ona ion while he es o he ensemble plays no mally.
The esul is shown in Fig. 7. D , and D , is plo -
ed o each oice sepa a ely, and he lines om ligh blue
(p=−50 cen s) o ligh ed (p= 50 cen s) indica e he
change in D , wi h a iable uning. No ably, he uning
sensi i i y o D , (i.e, he ange be ween he maximum
and minimum D , wi hin a no e when pis a ied by ±50
cen s) changes be ween no es and cho ds. In pa icula , o
mos majo and mino hi ds in he exce p , SD inc eases
only sligh ly e en o he la ges pi ch shi s. Conside -
ing he s a is ics o e he en i e da ase , we ind ha o
he ensemble E, he oo no e has an a e age uning sen-
si i i y o 2.71, he mino hi d o 1.09, he majo hi d o
1.01, and he i h o 1.70 (only conside ing cho d deg ees
wi h equen occu ences). We mus howe e accoun o
he ac ha he oo no e o each cho d is o en doubled
(in he same o a di e en oc a e) in he ou -pa oicings
o cho ales. I we conside only cases whe e he espec i e
no e is no doubled, we eco d an a e age uning sensi i i y
o 1.13 ( oo ), 0.75 (mino hi d), 0.87 (majo hi d), and
1.62 ( i h). This sugges s ha SD is mo e sensi i e o he
uning o he oo and i h han o ha o he hi ds. Fu -
he mo e, in compa ison o he mean ela i e SD by ins u-
men in Table 1, uning sensi i i y in gene al is ela i ely
small, so ha measu ing uning (e.g., 12-TET and JI, which
o en di e only by a ew cen s) wi h SD is only meaning-
ul in condi ions whe e imb e emains unchanged.
The e a e wo cases in he exce p whe e he isualiza-
ion shows ha a change in uning would signi ican ly e-
duce ela i e SD. Fi s , he oo no e o he C:maj cho d
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
121
Cho d Type # D
E Ewood Eb ass Esaw
maj 229 15.21 31.74 7.90 29.73
min 119 15.99 34.14 9.02 31.96
maj/3 55 17.65 36.16 10.50 31.65
sus4 16 16.64 34.75 8.72 30.02
min/3 12 19.17 36.52 7.83 27.78
o he s 32 17.00 33.11 10.25 31.20
Table 2. SD s a is ics by di e en cho d ypes. Cho d sym-
bols ollow he no a ion scheme om [28].
in he T oice ( ed box ain Fig. 7) would con ibu e less o
Di i was played a ound 25 cen s highe . In ac , acco d-
ing o he anno a ed F0, he T oice is on a e age 17 cen s
la ela i e o he oc a e o med wi h B. In e es ingly, his
does no a ec he “op imal uning” (w. . . SD) o B, in-
dica ing ha he in e als o med wi h Sand Aa e s able.
Second, o he mino hi d o he D:min(2) cho d in S
( ed box bin Fig. 7), SD would be educed i he no e was
played up o 50 cen s lowe . Gi en ha his no e o ms
he musically dissonan in e al o a mino second wi h A,
his is an indica ion o a case whe e SD does no exhibi
a local minimum nea he in e al p esc ibed by he sco e.
This can become a p oblem o app oaches whe e SD is
used as a measu e o “op imize” uning [16,17].
3.3 The In luence o Sco e
Finally, we conside he in luence o sco e on SD, in
pa icula by analyzing di e ences be ween cho ds. In
Fig. 7, a p ominen example o he sco e in luence is he
D:min(2) cho d ha has he highes o e all SD in he
exce p . The ela i e SD o S,A, and B, as well as he
o e all SD signi ican ly d ops when he musically disso-
nan suspended second is esol ed in oice A.
Since he cho d ocabula y o he composi ions is el-
a i ely limi ed (majo and mino cho ds in oo posi ion
accoun o 75% o all cho ds), we can s a is ically ana-
lyze di e ences be ween cho d ypes by g ouping hem as
shown in Table 2, using he cho d labels wi hou oo . In
pa icula , we compa e how he cho d ype in luences he
o e all SD o E,Ewood,Eb ass, and Esaw by compu ing
he mean Do e he en i e da ase . In ac , he a ia ions
in mean SD by cho d ype a e mos ly consis en ac oss
ensembles. Fo example, he mean SD o maj cho ds is
lowe han ha o min cho ds. /3 cho ds wi h he hi d in
Ba e mo e dissonan , excep o min/3 in Eb ass. These
ends pa ly esemble a anking based on subjec i e disso-
nance a ings o iads and e ads [27], eplica ing a p e-
ious esul wi h syn he ic da a [7]. Howe e , e en wi hin
one ensemble, we ind ha he cho d ype only accoun s
o be ween 6% (Ewood) and 11% (Eb ass) o he a ia ion
in D(acco ding o he K uskal-Wallis es as abo e).
Ano he sco e- ela ed p ope y o each cho d is i s oic-
ing, i.e., he assignmen o no es o he indi idual oices.
Two e ec s can be obse ed in he s a is ics o indi id-
ual oices o Esaw in Table 1. Fi s , he a e age D ,
inc eases owa ds lowe oices. This ollows om mo e
ha monics alling in o he c i ical bands a ound neighbo -
ing ha monics, as can be obse ed in Fig. 1b. Second, he
a e age D , is highe o middle oices, indica ing ha
hese oices end o con ibu e mo e o he o e all SD, in-
dependen o imb e and uning, which is ixed in Esaw.
4. DISCUSSION & APPLICATION EXAMPLES
F om his analysis, we can d aw h ee main conclusions
o using SD as an in o ma i e measu e in music p oduc-
ion. Fi s , he ela i e SD o indi idual acks p o ides
insigh s in o hei musical in e ac ion, e.g., in e ms o un-
ing and he musical dissonance o in e als. Howe e , as
an absolu e measu e, SD is mainly de e mined by ins u-
men imb e, p ohibi ing di ec compa isons ac oss ins u-
men classes. Second, SD may o e an ad an age o e
F0-based uning analysis because i is con ex -sensi i e,
accoun ing o in e als be ween all oices. The sensi-
i i y o uning di e ences depends on he cho d deg ee
and oicing, whe e e en s ongly de uning a hi d by ±50
cen s may in some cho ds only sligh ly a ec he SD mea-
su e. Thi d, while sys ema ic sco e in luences a e p esen ,
hey a e compa a i ely small, which makes applica ions
like musicological analysis as ou lined in [9] only easi-
ble wi hin con olled scena ios. This sugges s a numbe o
p ac ical applica ions o SD measu es, wo o which we
b ie ly wan o ou line in he ollowing.
Take Selec ion: Compa ing he ela i e SD be ween
mul iple akes o he same exce p played wi h he same
ins umen , like in Fig. 6, can indica e di e ences in e ms
o imb e and/o uning in ela ion o a speci ic accompa-
nimen . Toge he wi h o he musically mo i a ed quali y
measu es (e.g., [29]), his could se e as he basis o sug-
ges ing an edi sequence ha aligns bes wi h he desi ed
p ope ies o he ack. As an example, he i h no e o he
T oice in he exce p om Fig. 1 could be eplaced wi h a
e sion om a di e en ake ha is mo e in une compa ed
o he o he oices. Since in classical music p oduc ion,
sound enginee s some imes ha e o deal wi h dozens o
akes o a single passage, e en so ing he akes by SD in
a ce ain cho d could aid he selec ion p ocess.
Equaliza ion: Since imb e is he p ima y con ibu -
ing ac o o ela i e SD, we can aim o modi y i h ough
equaliza ion o dec ease (o inc ease) SD while s ill p e-
se ing he ins umen ’s cha ac e is ic sound. As an ex-
ample, applying a il e o he B oice in he exce p om
Fig. 1, educing magni udes by only 6 dB be ween 2 and 4
kHz, leads o a educ ion o he mean D , by 11% ( om
3.53 o 3.15) wi hin he exce p . This adap a ion could also
be made con ex -dependen , e.g., by educing he ampli-
ude o ha monics ha con ibu e s ongly o SD only when
in e e ing oices a e p esen in he mix.
Finally, i should be emphasized again ha SD is no
measu ing he ac ual pe cei ed dissonance and ha a i-
a ions in he model assump ions o SD, as well as o he
acous ic measu es like hose based on ha monici y (e.g.,
[6, 30]), could yield signi ican ly di e en , bu equally
alid esul s. Unde s anding he p ope ies o di e en dis-
sonance measu es in ealis ic musical scena ios will be key
o es ablishing hem as a music p oduc ion ool.
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
122
5. ACKNOWLEDGEMENTS
This wo k was unded by he Deu sche Fo schungsge-
meinscha (DFG, Ge man Resea ch Founda ion) unde
G an No. 401198673 (MU 2686/13-2) and 555525569
(MU 2686/18-1). The In e na ional Audio Labo a o ies
E langen a e a join ins i u ion o he F ied ich-Alexande -
Uni e si ä E langen-Nü nbe g (FAU) and F aunho e In-
s i u e o In eg a ed Ci cui s IIS.
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