Fuzzy C ea i i y: Composing wi h Unce ain y in
Ince a
Rod igo F. Cádiz∗
Music Ins i u e and Depa men o Elec ical Enginee ing
Pon i icia Uni e sidad Ca ólica de Chile
San iago, Chile
[email p o ec ed]
Abs ac
Ince a is an elec oacous ic composi ion ha explo es he a is ic po en ial o
uzzy logic as a ool o c ea i e decision-making in music. Ra he han elying on
da a-d i en gene a i e models, he piece is s uc u ed a ound a ule-based uzzy
in e ence sys em designed by he compose , allowing o nuanced, in e p e able
con ol o e spa ial and empo al p ocesses. The sys em go e ns he ac i a ion
and di usion o 21 sound sou ces ac oss an eigh -channel se up, using dynamic
Gaussian unc ions whose pa ame e s e ol e acco ding o uzzy logic ules. By
adjus ing he beha io o hese unc ions, he compose can shape mul iple dis inc
pe o mances o he piece, each eme gen , ye bounded by aes he ic in en . This
pape si ua es Ince a wi hin he b oade discou se on algo i hmic composi ion
and c ea i i y, highligh ing how uzzy sys ems o e a compelling al e na i e o
black-box AI app oaches. Th ough an “a is -in- he-loop" me hodology, Ince a
o eg ounds unce ain y as a composi ional o ce, enabling complexi y, a ia ion,
and con ol o coexis wi hin a human-guided c ea i e p ocess.
1 In oduc ion o Fuzzy Logic
Fuzzy logic, a b anch o a i icial in elligence de eloped by Zadeh (1965), o e s a ma hema ical
amewo k o easoning unde unce ain y. Unlike adi ional bina y logic, which imposes s ic
ue/ alse alues, uzzy logic allows o deg ees o u h, making i ideal o in e p e ing ambiguous,
g adual, o imp ecise da a. In he con ex o music, uzzy sys ems can ansla e ague musical
concep s—such as mo ion, densi y, o a icula ion—in o conc e e composi ional pa ame e s.
1.1 Fuzzy Logic and C ea i i y in Music Composi ion
Fuzzy logic con ibu es o c ea i i y in music by enabling compose s o o malize unce ain y
and subjec i i y—quali ies cen al o a is ic exp ession. Ins ead o elying on igid ules o pu e
andomness, uzzy sys ems allow nuanced modeling o ague musical concep s such as “sligh ly
as ," “somewha dissonan ," o “mode a ely dense" (Sui e , 2010a,b; Guliye and Memmedo a,
2020). In music, uzzy logic enhances musical exp essi i y by enabling compu a ional models o
in e p e quali a i e desc ip ions like “sligh ly as " o “mode a ely loud." (Cádiz, 2020). These
cha ac e is ics make uzzy logic pa icula ly sui able o asks like ha moniza ion, ph ase shaping,
spa ial design, o ule-based cons ain s ha inco po a e chance e en s (Ga e , 2017).
In composi ion, uzzy logic suppo s p e e ence-based decisions, whe e s ylis ic inclina ions a e
encoded as weigh ed ules. This allows in ui i e con ol o e complex a iables such as imb e,
pi ch mo ion, o empo al ges u es (Guliye and Memmedo a, 2018; Mugica e al., 2015). Unlike
bina y logic, uzzy easoning accommoda es g adual ansi ions, main aining a dynamic equilib ium
be ween de e minacy and openness—an essen ial condi ion o c ea i e low.
∗h p:// od igocadiz.com
P oceedings o he 6 h Con e ence on AI Music C ea i i y (AIMC 2025),
B ussels, Belgium, Sep embe 10 h-12 h
Fuzzy sys ems also suppo exp essi e eal- ime en i onmen s, enabling sys ems o espond musically
o a ec i e o ges u al cues in pe o mance (Lucas e al., 2016; Cádiz and González-Inos oza, 2018).
In his way, uzzy logic is no me ely a con ol mechanism bu a composi ional pa ne —shaping
sonic ma e ial wi h in e p e i e nuance while embedding he compose ’s in en in o algo i hmic
p ocesses.
In Ince a, uzzy logic ac s as a “so decision-make ", allowing he sys em o in e p e musical
pa ame e s h ough shades o g ay a he han black and whi e. This allows he compose o
embed musical in en ions in o a amewo k ha e ol es con inuously, while s ill s aying wi hin
he bounda ies o a cohe en aes he ic ision. By ansla ing uzzy se s in o spa ial ges u es and
ac i a ion en elopes, he piece explo es how unce ain y and imp ecision can be a is ically aluable.
Ra he han iewing uzziness as a echnical limi a ion, he composi ion emb aces i as a me apho
o emo ional and pe cep ual complexi y.
This app oach con as s wi h adi ional gene a i e sys ems, such as hose used in ea ly algo i hmic
composi ion (e.g., Rowe 1993, Cope 2001), which o en s uggle wi h in eg a ing sub le o subjec i e
c i e ia. Fu he mo e, unlike cu en gene a i e AI sys ems ha ely hea ily on aining da a, pa e n
ecogni ion, and s a is ical modeling, he app oach p esen ed in Ince a is ule-based and does no
depend on lea ned da a ep esen a ions. Ins ead o gene a ing musical con en om la ge da ase s,
he sys em uses a uzzy in e ence engine o con ol spa ial and empo al p ocesses in eal ime. This
allows o a mo e in e p e able and in en ional o m o algo i hmic composi ion, whe e composi ional
beha io is go e ned by human-designed ules ha cap u e nuanced aes he ic p e e ences and
unce ain ies, a he han eme gen pa e ns om opaque models. In summa y, uzzy logic p o ides a
solu ion by ea ing ambigui y as a esou ce o c ea i e explo a ion, hus expanding he ocabula y
o AI-assis ed music composi ion.
2 O e iew o Ince a
Ince a is an 8-minu e acousma ic composi ion o 8-channel playback, buil en i ely wi hin he
Max/MSP en i onmen (Cycling ’74, 2025). The wo k was designed as a es bed o explo e how
uzzy logic could be used o con ol a ious aspec s o a musical wo k in eal ime, pa icula ly spa ial
di usion and s uc u al de elopmen .
The sound ma e ial consis s o 21 ixed audio acks, ca ego ized in o h ee g oups based on spec al
con en : low, medium, and high equencies. These acks a e igge ed and spa ialized dynamically
du ing pe o mance, using a eal- ime uzzy in e ence engine.
2.1 Fuzzy Logic Con ol Toolki (FLCTK)
The Max/MSP pa ch used in he piece inco po a es he Fuzzy Logic Con ol Toolki (FLCTK), a
se o ex e nals and abs ac ions de eloped by he au ho (Cádiz and González-Inos oza, 2018).
This oolki suppo s he design and execu ion o uzzy in e ence sys ems (FIS) and is op imized o
eal- ime con ol applica ions in music and mul imedia.
2.2 Sys em Inpu s and Ou pu s
The uzzy sys em in Ince a is s uc u ed a ound se en inpu a iables:
•
Th ee o a ion angles (
θ1, θ2, θ3
) co esponding o he posi ions o Gaussian unc ions
associa ed wi h low, mid, and high- equency sound sou ces.
•
Th ee s anda d de ia ions (
σ1, σ2, σ3
) con olling he sp ead (densi y and wid h) o he same
Gaussian unc ions.
• A global ime a iable, which p o ides a no malized imeline o he du a ion o he piece.
The ou pu o he uzzy sys em consis s o inc emen al adjus men s o each Gaussian’s angle and
s anda d de ia ion. These changes in luence bo h he selec ion o sound ma e ials and hei di usion
in space. As he Gaussians o a e a ound a concep ual sound ci cle ep esen ing he eigh loudspeake s,
hei o e lapping egions de e mine which samples a e ac i a ed and whe e hey a e p ojec ed.
2
2.3 Sound Di usion and Dynamics
Each audio ack is associa ed wi h a ixed spa ial loca ion on he ci cula layou o speake s. When a
Gaussian unc ion’s peak o sp ead o e laps wi h a sound’s assigned loca ion, ha sound is ac i a ed.
The uzzy sys em con inuously upda es hese Gaussian cu es based on e ol ing inpu condi ions,
esul ing in dynamic and o ganic ansi ions.
This mechanism p oduces a o m o ges u al spa ializa ion, whe e changes in he uzzy a iables
cause sub le o ab up shi s in spa ial beha io . Sounds may ade in o ou , mo e ac oss he speake
a ay, o eme ge in dense clus e s depending on he in e ac ion o a iables.
2.4 A is in he Loop
The composi ional me hod in Ince a exempli ies he “a is in he loop" pa adigm, whe e he
compose plays an ac i e ole in shaping and con igu ing he beha io o he sys em. The uzzy
in e ence ules, membe ship unc ions, and sound ma e ial mappings a e all designed and ine- uned
by he compose , no lea ned om da a. This p ese es au ho ial in en while le e aging algo i hmic
complexi y, posi ioning he a is no only as a c ea i e ini ia o bu as a con inual pa icipan in he
sys em’s ope a ion and i s mul iple ealiza ions.
2.5 Video Demons a ions
Th ee di e en pe o mances o Ince a we e p oduced, each using a dis inc con igu a ion o he
uzzy logic sys em, allowing he audience o see he sys em’s eal- ime esponses as he music un olds.
While he unde lying sound ma e ials and algo i hmic s uc u e emain he same, changes o he uzzy
model esul in di e en empo al and spa ial beha io s, o e ing a ied ealiza ions o he piece.
The esul ing e sions highligh how uzzy logic enables con olled a iabili y wi hin a consis en
composi ional amewo k. These ideos a e a ailable a h p:// od igocadiz.com/ince a.
3 Conclusion
Ince a is a composi ional expe imen in embedding a i icial in elligence ools wi hin he musical
c ea ion p ocess. By using uzzy logic o modula e spa ial and empo al beha io s, he piece
demons a es how non-bina y easoning sys ems can open new exp essi e possibili ies o compu e
music. The usage o a eal- ime en i onmen c ea ed by he compose allowed o bo h p ecomposed
s uc u e and pe o mance-based a iabili y, con ibu ing o a ichly ex u ed sonic expe ience.
Acknowledgmen s and Disclosu e o Funding
This esea ch was suppo ed by ANID Chile: Fondecy 1230926, Anillo ATE220041, and Na ional
Cen e o A i icial In elligence FB210017.
Re e ences
Cope, D. (2001). Vi ual Music: Compu e Syn hesis o Musical S yle. MIT P ess.
Cycling ’74 (2025). Max/MSP: Visual P og amming En i onmen o Music and Mul imedia. Cycling
’74, San F ancisco, CA. Ve sion 8.6, h ps://cycling74.com/p oduc s/max.
Cádiz, R. F. (2020). C ea ing music wi h uzzy logic. F on ie s in A i icial In elligence, 3:59.
Cádiz, R. F. and González-Inos oza, M. C. (2018). Fuzzy logic con ol oolki 2.0: composing and
syn hesis by uzzy ica ion. In New In e aces o Musical Exp ession, pages 398–402.
Ga e , R. (2017). Gene a i e Music om Fuzzy Logic and P obabili y: A Po olio o Elec oacous ic
Composi ions. Bango Uni e si y (Uni ed Kingdom).
Guliye , J. and Memmedo a, K. (2018). Fuzzy logic-based composi ional decision making in music.
In In e na ional Con e ence on Theo y and Applica ions o Fuzzy Sys ems and So Compu ing,
pages 741–745. Sp inge .
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Guliye , J. and Memmedo a, K. (2020). Fuzzy easoning in music. In In e na ional Con e ence on
Theo y and Applica ions o Fuzzy Sys ems and So Compu ing, pages 192–197. Sp inge .
Lucas, P., As udillo, E., and Peláez, E. (2016). Human–machine musical composi ion in eal- ime
based on emo ions h ough a uzzy logic app oach. In Designing wi h Compu a ional In elligence,
pages 143–159. Sp inge .
Mugica, F., Paz, I., Nebo , À., and Rome o, E. (2015). A uzzy induc i e app oach o ule-based
modelling o high le el s uc u es in algo i hmic composi ion sys ems. In 2015 IEEE In e na ional
Con e ence on Fuzzy Sys ems (FUZZ-IEEE), pages 1–8. IEEE.
Rowe, R. (1993). In e ac i e Music Sys ems: Machine Lis ening and Composing. MIT P ess.
Sui e , W. (2010a). The p omise o uzzy logic in gene alised music composi ion. In En e ainmen
Compu ing Symposium, pages 118–127. Sp inge .
Sui e , W. (2010b). Towa d algo i hmic composi ion o exp ession in music using uzzy logic. In
New In e aces o Musical Exp ession, pages 319–322.
Zadeh, L. A. (1965). Fuzzy se s. In o ma ion and Con ol, 8(3):338–353.
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