ISSN: 1795-6889
www.human echnology.jyu. i Volume 13(1), May 2017,109–141
109
DESIGNING A COMPUTER MODEL OF DRUMMING:
THE BIOMECHANICS OF PERCUSSIVE PERFORMANCE
Abs ac :
Becoming a compe en musician equi es signi ican p ac ice, including
ehea sal o a ious musical pieces. Complex sequences o musical no es and he
associa ed bodily mo emen s mus be cho eog aphed and memo ized so ha he human
body can ep oduce hese sequences consis en ly. Such bodily mo emen occu s wi hin
he ins umen al pe o mance space, wi h some ins umen s, no ably he d um se ,
equi ing mo e bodily mo emen han mos . Cho eog aphed bodily mo emen in
d umming is undamen al o p oducing he imb al and iming a ia ions c ucial in
delinea ing human s. compu e pe cussi e pe o mance. Cu en compu e models
designed o simula e pe cussi e pe o mance ocus on he cogni i e aspec s o
pe o mance o he musical s uc u e o de e mine he simula ion, while o he sys ems
ocus on ep oducing he physics o musical ins umen s. The ocus o his pape is on he
complexi ies o human mo emen in d umming, wi h a iew owa d p oposing, as pa o
a la ge esea ch p ojec , a backg ound unde s anding and me hodology o ex ac ing
empi ical da a om human pe o mance o in e ac i e compu e -based pe cussi e
pe o mance modeling applica ions.
Keywo ds:
pe cussion, pe o mance, modeling, d ums, biomechanics, compu e music.
© 2017 John R. Taylo and he Open Science Cen e, Uni e si y o Jy äskylä
DOI: h p://dx.doi.o g/10.17011/h /u n.201705272520
This wo k is licensed unde a C ea i e Commons A ibu ion-NonComme cial 4.0 In e na ional License.
John R. Taylo
MARCS Ins i u e
Wes e n Sydney Uni e si y
Aus alia
and
Sydney Conse a o ium o Music
Uni e si y o Sydney
Aus alia
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110
INTRODUCTION
Conside able li e a u e exis s conce ning he ield o compu a ional modeling o exp essi e
music pe o mance (Gab ielsson, 1999, 2003). This esea ch includes a di e se a ay o
app oaches, owing o he complexi y o human pe o mance (Widme & Goebl, 2004).
A guably, one o he mo e complex ins umen s o compu a ionally model is he d um se
because o he complexi y in ol ed in playing he ins umen . In pe cussi e pe o mance, he
in e ac ion be ween he playe and ins umen is pe haps he mos signi ican a iable in imb e
p oduc ion. This in e ac ion is mani es ed in di e en echniques, skill le els, musical
knowledge and expe iences, and he physical a ibu es o he pe o me s hemsel es (e.g.,
heigh , body mass, i ness, e c.). The ac o musical pe o mance encompasses a a ie y o
con ibu o y aspec s (Gab ielsson, 1999, 2003; Palme , 1997), speci ic examples o which
include he physiological (Fujii, Kudo, Oh suki, & Oda, 2009; Lee, 2010), cogni i e (Dahl &
F ibe g, 2004; Laukka & Gab ielsson, 2000; Repp, 1999), echnical (Dahl, G oßbach, &
Al enmülle , 2011), and musical (Repp, 1997), as well as bo h heo e ical and empi ical
pe spec i es (Sho e & Repp, 1995).
Se e al aims o music pe o mance modeling ha e been iden i ied in he li e a u e,
encompassing he design o in e ac i e music pe o mance sys ems, i ual music en i onmen s,
and composi ional so wa e ools. One aim o pe o mance modeling seeks o gene a e human-
like compu e pe o mance; he e o e, i is use ul o conside how human pe o mance is dis inc
om compu e pe o mance. In his esea ch, he analysis ega ding human and compu e
pe o mance add esses pa icula ly he con ex o modeling pe cussi e pe o mance on a nine-
piece d um se comp ising bass d um, sna e d um, hi-ha , loo om, low om, medium om, high
om, and ide and c ash cymbals. Such a d um se con igu a ion is ypically used in ock, jazz,
and pop music gen es. Fi s ly, he empi ical esea ch in o he physics o pe cussion ins umen s
shows ha a numbe o physical ac o s a e in ol ed in imb al a ia ion, such as s ike loca ion,
cons uc ion, ma e ial, and so o h (Fle che & Rossing, 1998; Rossing, 2000; Taylo , 2015).
Secondly, imb al a ia ions in d um sounds a e impo an o lis ene s’ o e all pe cep ion o
music (Ra h & Wäl e mann, 2008). Because playing he d ums is a ime-sensi i e endea o , he
human mo emen in ol ed in pe cussi e pe o mance can be conside ed o be “ch onemic
mo emen ” (Su il, 2015), in which he quali a i e de e mina ions o speed, sus ain, a ack, o
delay (Su il, 2015, pp. 35–37) in musical and imb al quali ies a e di ec ly ela ed o ins umen al
in e ac ion and ajec o y con ol. This a icle p esen s pa o a wide esea ch in es iga ion in o
he compu a ional simula ion o human pe cussi e pe o mance and p esen s discussion o
ele an li e a u e as a p equel o u he empi ical wo k.
Why Is Modeling Human Pe o mance on a D um Se So Di icul ?
D umming comp ises a a ie y o se d um pa e ns and echniques ha a e lea ned and pe o med
in di e en hy hmical and musical con ex s, o en in an imp o isa o y manne . To pe o m hese
d um pa e ns and echniques, he d umme mus cho eog aph he human mo emen o he
pa e ns wi hin he biomechanical cons ain s o his/he abili ies in o de o execu e hem wi hin
he hy hmic and ime cons ain s o he music. Each d um mus be played op imally a all imes,
wi h he pe o me able o add nuances, such as ges u al embellishmen s o imb al a ia ions ha
could a ec ei he he imb e o he iming, in each s ike. Consequen ly, a d um pe o mance can
Designing Compu e Models o D umming Pe o mance
111
be ega ded as mul iple pa e ns con aining cho eog aphed sequences o human mo emen . A
compu e model o d umming he e o e encapsula es he cho eog aphed mo emen s con ained
wi hin a pe o mance and he ansi ional mo emen s be ween cho eog aphies.
The main aim o his a icle is o decons uc and discuss he key aspec s o human mo emen
ha lead o iming and imb al impe ec ions in pe cussi e pe o mance on a nine-piece d um se .
This analysis enables he iden i ica ion o a me hodology ha can be used o analyze human
pe cussi e pe o mance wi h he goal o c ea ing a compu e model ha ep esen s, musically, he
con inuum o pe cussi e pe o mance mo emen in he physical wo ld. Mo e speci ically, his
analysis iden i ies ways in which eal-wo ld d umming in e ac ions can be cap u ed and how a
human migh in e ac wi h a sys em ha models ha in e ac ion. Such a compu e model could be
used in in e ac i e sys ems, i ual music en i onmen s, and in composi ional so wa e ools. This
a icle e alua es me hodologies o measu ing human mo emen in o de o c ea e a amewo k
ha u ilizes in e ac i e compu e algo i hms o simula e pe cussi e pe o mance.
This pape begins wi h a desc ip ion o d um udimen s and d umme s’ de elopmen
goals ha a e undamen al o lea ning op imal mo emen and o m in d umming. The pape
hen p esen s an analy ical amewo k, based upon in o ma ion p ocessing sys ems and
human mo o con ol, wi h which o unde s and he unde lying causes o pe o mance
a ia ion, pa icula ly ega ding ins umen al in e ac ion and physical con ol. This will
in ol e a summa y e iew o he li e a u e in he discipline o biomechanics and he
subsequen applica ion o hese p inciples in ela ion o pe cussi e pe o mance o a nine-
piece d um se . This a icle does no add ess he di e en op ions and imb al and acous ical
e ec s o s iking implemen s (see Halm as , Gue le , Bade , & Godøy, 2010, pp. 204–207),
no is i in ended o be an exhaus i e discussion. Many speci ic aspec s ha e been omi ed,
including he e ec o ba e head models on imb e (Henzie, 1960; Lewis & Beck o d,
2000); he e ec o disuni o m ension; po en ial onal e olu ion due o he age (and usage) o
he head; empo (Desain & Honing, 1993); eedback condi ions (B andmeye , Timme s,
Sadaka a, & Desain, 2011; Dahl & B esin, 2001; P o d eshe & Palme , 2002), and empo al
independence (Goebl, 2011). In addi ion, aspec s such as s yle and gen e which, wi h hei
ob ious con ex ual pe o mance di e ences, will no be discussed in de ail.
D um Rudimen s and De elopmen Goals
D umme s de elop hei echnique by lea ning d um udimen s es ablished by he
in e na ional d um udimen commi ee, pa o he Pe cussi e A s Socie y. The udimen s
cu en ly consis o 40 echniques (Pe cussi e A s Socie y, 20141) ha o en a e
cho eog aphed independen ly and ha e been de i ed om a ious musical s yles o o m a
pedagogical me hod o lea ning pe cussion. This me hod is designed o p o ide an “o de ly
p og ession o he de elopmen o physical con ol, coo dina ion, and endu ance” (Ca son &
Wanamake , 1984, p. 3). Al hough no explici ly de ined, hese de elopmen goals can be
in e p e ed and summa ized as ollows:
 Physical con ol, e e ing o he pe o me s’ managemen o s ick and ins umen
in e ac ion, which comp ises w is and hand mo emen and a m con ol;
 Coo dina ion, e e ing o he s ike accu acy and he pe o me ’s abili y o exe
physical con ol o e sequences o s ikes in di e en loca ions; and,
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 Endu ance, e e ing o pe o me a ibu es, ins umen al con igu a ion, and he
complexi y o piece being pe o med.
Al hough hese de elopmen goals can be conside ed independen o each o he , he e is
conside able in e dependence among he h ee. One example o his is whe e a pe o me has
good s ick and ins umen managemen bu poo coo dina ion. The esul is a d umme who
could play hy hmic sequences and imb es co ec ly bu no necessa ily hi he d um in ime.
Cho eog aphically, his could be a ibu ed o a disconnec be ween he sequence design and
poo mo ion con ol o o m. Ano he example o independen de elopmen goals can be
obse ed in a pe o me ’s abili y o main ain a m con ol and coo dina ion du ing p olonged
mo emen s in complex pe cussi e sequences. Con ol and coo dina ion will de e io a e a
a ying a es depending on he endu ance le els o he pe o me . Essen ially hese
de elopmen goals a e indi idually impo an o he success ul execu ion o a cho eog aphed
mo emen and con ibu e owa ds he o e all o m o he mo emen and he sound o he
pe o mance. The ela ionship be ween he de elopmen goals is desc ibed in Figu e 1.
The e is no “magic spo ” among hese de elopmen goals because each d um udimen
equi es a unique mix o he h ee componen s, depending on he pe cussionis ’s cu en
de elopmen al s age and he demands o he cho eog aphical con ex . Al hough hese goals
a e undamen al o he de elopmen o a pe cussionis ’s skill, ob aining an unde s anding o
pe cussi e pe o mance by way o decons uc ing p inciples o human mo emen om hese
goals is di icul due o he e ec o en i onmen al ac o s on skilled mo emen s (Dahl,
2005). Such ac o s could include, among o he s, he e ec o empe a u e and al i ude on
endu ance, audi o y eedback on coo dina ion, and s ick hickness on physical con ol. As a
esul , i is bo h di icul and imp ac ical o accoun o all hese independen a iables.
Figu e 1.
A diag am ou lining he in e dependency among he h ee de elopmen goals in d umming.
Indi idually and collec i ely, he de elopmen al goals impac pe o mance.
Adap ed om Ca son & Wanamake (1984).
Designing Compu e Models o D umming Pe o mance
113
The educ ion o independen a iables in he analysis o human mo emen , ex ending o
en i onmen al a iables, is no new. In ac he dimensionali y o a iables in unde s anding
human mo emen has been he subjec o in es iga ion since Nikolai Be ns ein i s p oposed
he heo y o he deg ees o eedom (DOF) in 1967. He heo ized ha because he e a e an
almos in ini e numbe o ways a mo emen could be execu ed h ough he la ge ne wo k o
muscles, join s, and cells in he human body, he e a e an in ini e numbe o ways ha
muscles can achie e he di e en mo emen s.
The con ol o he ne ous sys em on he musculoskele al sys em is highly complex: Fo
any gi en mo emen , he e a e a high numbe o DOF. This complexi y is illus a ed du ing
he ac i a ion o a single muscula elemen ei he in isola ion o in any pa icula sequence
(Be ns ein, 1967). Thus, i he ne ous sys em con ols mo emen by con olling syne gis ic
g oups a he han indi idual muscles and join s, he numbe o DOF (and he e o e he
dimensionali y o a iables) is educed (Tu ey, 1990). Be ns ein (1967) also sugges ed ha
senso y eedback om he en i onmen in e ac s wi h he ne ous sys em o educe he
numbe o DOF. Tu ey (1990) subs an ia ed he omission o en i onmen al ac o s wi hin
he con ex o Ca son and Wanamake ’s (1984) de elopmen goals o his amewo k by
a guing ha , “I he en i onmen o which he mo emen sys em ela es is in e p e ed as jus
ano he la ge se o a iables, hen he jux aposi ion o an animal and i s en i onmen would
ampli y he p oblem o deg ees o eedom” (Tu ey, 1990, p. 940).
Jux aposing en i onmen al ac o s on o pe cussi e pe o mance would no only conce n
human mo emen and he numbe o DOF bu would necessi a e ex ending en i onmen al
a iables o he ib a ional beha io o each o he nine d ums unde in es iga ion as well.
Because he speed o sound inc eases wi h ai empe a u e (Fle che & Rossing, 1998, p. 70),
a bigge pic u e eme ges ega ding he inhe en di icul y in adequa ely applying se e al
en i onmen al ac o s as a iables ac oss he di e en hemes no ed in his a icle. In ligh o
his, Tu ey’s (1990) posi ion will be conside ed o be he mos app op ia e iew and,
consequen ly, en i onmen al ac o s will be conside ed ou side he scope o his discussion.
THE ANALYSIS OF HUMAN MOVEMENT: A THEORETICAL FRAMEWORK
In 1982, neu oscien is Da id Ma p esen ed a i-le el hypo hesis by which in o ma ion
p ocessing sys ems could be analyzed. These le els o analysis can be summa ized as ollows
(Ma , 1982, p. 25):
 Compu a ional le el: Wha does he sys em do?
 Algo i hmic/Rep esen a ional le el: How does he sys em do wha i does?
 Physical le el: How is he sys em physically ealized?
Ma (1982) desc ibed how hese h ee le els o analysis a e no in insically dependen
upon one ano he and ha , in some ci cums ances, analysis can be achie ed by using only
one o wo le els. The choice o analy ical le el is c i ical in co ec ly unde s anding ce ain
sys ems. Mo e impo an ly, Ma desc ibed how he compu a ional le el o analysis is
essen ial in unde s anding ce ain phenomena, pa icula ly whe e he e a e signi ican le els
o abs ac ion be ween he unde s anding o a sys em and he compu a ional ep esen a ion.
Examples o his include a p io i unde s anding o he na u e o biological o pe cep ual

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p ocesses p io o compu a ional ep esen a ion, a he han by analyzing he compu a ional
ep esen a ion o such p ocess in a gi en compu a ional en i onmen (Ma , 1982, p. 27).
Da id Rosenbaum (2010), in his book on mo o con ol, desc ibed how Ma ’s h ee
analy ical le els o in o ma ion p ocessing sys ems also ep esen “ he s udy o human mo o
con ol” (p. 4). A he compu a ional le el o analysis, Rosenbaum desc ibed how, du ing
physical ac i i y, animals and humans plan hei mo emen s using wha he desc ibed as “implici
equa ions” (p. 5). These implici equa ions a e de i ed om Ma ’s (1982) compu a ional le el,
whe e a sys em mus achie e a unc ion whose ep esen a ion is o en desc ibed ma hema ically.
Howe e , o humans and animals, his e e s o he men al ep esen a ion o ask o be
pe o med. One example o his is he men al ep esen a ion a ock climbe has o a “dyno” (a
jump o leap) o he nex posi ion. In he con ex o pe cussi e pe o mance, his can be a men al
ep esen a ion o an impending d um ill and he d um s iking sequence ollowing om he
“cu en posi ion.” C i ically, he cu en posi ion is spa io empo ally unique, hus equi ing
ansi ional o linkage mo emen s be ween sequences. Rosenbaum (2010) no ed ha he
compu a ional le el o analysis does no include he execu ion o he ac ion, which is unsu p ising
conside ing he numbe o DOF.
In applying Ma ’s (1982) second le el, he algo i hmic/ ep esen a ional le el, Rosenbaum
(2010) no ed ha a compu e ’s algo i hms a e designed o enable a sys em o unde ake hei
unc ions wi h gua an eed success. In he na u al wo ld, mo emen s ope a e in eal ime
(analogous o un ime algo i hms) wi hou gua an eed success. As examples, a ock climbe migh
no jump high enough o g ab he nex hold (and hus all o he sa e y ne below) and he d umme
can hi he w ong ins umen o s ike he shell o he d um by acciden . As Rosenbaum poin ed
ou , each o hese eal ime mo emen s elies upon a p ocedu e, and he pe son execu ing he
ac ion will d aw upon beha io and cogni ion in o de o execu e and e i y he mo emen , hence
Rosenbaum’s ex ension o his e m as he “p ocedu al le el” (Rosenbaum, 2010, p. 5).
Rosenbaum (2010) desc ibed he inal le el o Ma ’s (1982) analysis, he implemen a ion
le el, as he physical aspec s o he mo emen . These biological elemen s a e desc ibed by
Rosenbaum (2010) as muscle ope a ion and b ain ac i i y (e.g., a ock climbe will use leg muscles
o jump, s e ched a ms o g ab he hold, and inge s and o ea ms o g ip and main ain he hold).
Fo he d umme playing a sna e d um ollowed by a ide cymbal, muscle ope a ion can include he
inge s and hand o g ipping he s ick, adduc ion o he lowe a m o he s ike, ollowed by a
la e al o a ion and abduc ion o he a m o each cymbal heigh . Such mo emen can be conside ed
ei he a cho eog aphed pa e n o a ansi ional o linkage mo emen . These examples a e highly
simpli ied, as i is in his analy ical le el ha he DOF p oblem is encoun e ed.
Rosenbaum’s (2010) biological adap a ion o Ma ’s (1982) i-le el analysis p o ides a
solid app oach o unde s anding he mo emen p ocess. I his h ee-s age analysis is
unde aken in he con ex o Ca son and Wanamake ’s (1984) de elopmen goals, i is possible
o objec i ely e alua e exis ing esea ch and li e a u e on human mo emen , speci ically o
pe cussion. Fu he mo e, he bo om-up na u e o he h ee analy ical le els in ela ion o
pe o ming a d umming ac ion allows o a mo e comp ehensi e and s uc u ed discussion.
This econ ex ualiza ion is desc ibed in Table 1.
Unde s anding he na u e o pe cussi e pe o mance a ia ion equi es only he compu a ional
le el o analysis o gain an unde s anding o he ele ance o human pe o mance on imb e and
iming and o unco e c i ical aspec s o human mo emen in physical pe o mance. Al hough
o he addi ional aspec s in he o he le els con ibu e o pe o mance a ia ion, his a icle p esen s
Designing Compu e Models o D umming Pe o mance
115
Table 1. Th ee Analy ical Le els Applied o a D umme ’s De elopmen Goals.
Adap ed om Ca son and Wanamake (1984) and Rosenbaum (2010).
Le el/Goal Physical Coo dina ion Endu ance
Compu a ional Planning he con ol o
 The physical
mo emen
 Ins umen al
in e ac ion
Planning coo dina ed
mo emen s
 Coo dina ing
simul aneous mul iple
physical e en s
 Mul iple ins umen al
in e ac ions
Planning mo emen o
imp o ing endu ance
 Economy o mo emen
P ocedu al The beha io al and
cogni i e aspec s o
ca ying ou a physical
mo emen , ela ing o
 Timb e
 Timing
The beha io al and
cogni i e mechanisms
o
 Measu ing cu en
posi ion
 Ve i ying nex
mo emen
 An icipa ing nex
imb e/ iming
The beha io al and
cogni i e aspec s o
imp o ing endu ance
 Pe o mance
psychology
Implemen a ion The physical aspec s o
ca ying ou a
mo emen
 Muscle ac i i y
 B ain unc ion
The physical aspec s o
coo dina ing mul iple
ins umen s
 In e limb coo dina ion
 Muscle ac i i y
 B ain unc ion
Physical ways o
imp o ing endu ance
 T aining
 Wa m up p o ocols
 Pe o me impai men s
a ionales ega ding why he majo i y o hese a e ou side o he scope o his in es iga ion due
o hei highly indi idual and highly subjec i e na u es, as well as he challenges in adequa ely
p o ing hese.
The i s aspec o he amewo k ou side o he scope o his in es iga ion is he
beha io al and cogni i e aspec s o ca ying ou a physical mo emen (physical/p ocedu al).
This is because beha io and cogni ion a e highly indi idual, as well as highly dependen on
he con ex o he pe o mance (e.g., gen e). An impo an cogni i e elemen o his analy ical
le el and con ex includes senso imo o synch oniza ion (SMS), which is he hy hmic
coo dina ion o an ac ion wi h a egula ex e nal e en (Repp, 2005). As a esul , he
compu a ional ep esen a ion o SMS would be di icul o ealize, and he empi ical es ing
equi ed o such a model is ou side he scope o his in es iga ion. Fo u he eading on his
subjec , conside Fujii e al. (2010), Ho e, Kelle , and K umhansl (2007), Repp (2005, 2006),
Wing, Chu ch, and Gen ne (1989), and Wing and K is offe son (1973a, 1973b).
Ano he a ea o he amewo k ou side o in es iga i e scope is he physical aspec o
ca ying ou a mo emen (physical/implemen a ion), pa icula ly ega ding muscle and b ain
ac i i y. This pa icula a ea p esen s wo sepa a e p oblems. In e ms o muscle ac i i y, he
mos signi ican modeling challenge lies wi h he DOF p oblem and de e mining which
classi ie s and ep esen a i e o ganiza ional sys ems o muscle ac i a ion o model. One such
solu ion would be o use a single DOF as a ep esen a i e o all simila mo emen s in he
model. In he case o a d umme , mo e han one DOF would need o be modeled o co e all
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limbs. In addi ion, de e mining he mos app op ia e DOF o he mo emen , and e en he
p ocess o making such assump ions, will p oduce heo e ical sho comings (pa icula ly o
neu ophysiologis s). Modeling muscle ac i a ions also p esen s p oblems ega ding he
ela ionship be ween abs ac ed models o muscle mo emen and imb e p oduc ion—a
p oblem ha also is ound in modeling b ain ac i i y. Fu he eading on muscle ac i a ion and
b ain ac i i y du ing pe o mance is a ailable in Fujii e al. (2009), Fujii and Mo i ani (2012a,
2012b), Gab ielsson (2003), and Todo o and Jo dan (2002).
The beha io al and cogni i e mechanisms associa ed wi h pe o mance eedback
(coo dina ion/p ocedu al) encompass a ange o me hods o eedback acquisi ion. These
include audi o y, isual, ac ile, hap ic, and kines he ic, and combina ions o one o mo e. Each
o hese indi idual ypes o eedback has di e en e ec s on cogni i e and beha io al
mechanisms and a ies depending on he pe o mance condi ions. Wi h so many combina ions
o eedback condi ions and en i onmen al a iables, inding an app op ia e ep esen a i e
model is di icul . Addi ionally, modeling speci ic e ec s o ce ain eedback condi ions would
ha e limi ed p ac ical applica ion. The e o e, aspec s o pe o mance a e ou side he scope o
his esea ch and he eade is di ec ed o B andmeye e al. (2011), Dahl and B esin (2001),
Fujii e al. (2010), Gab ielsson (2003), Pe ini e al. (2009), P o d eshe and Palme (2002), and
P o d eshe and Beni ez (2007).
I was no ed abo e ha modeling muscle ac i i y was challenging gi en he DOF p oblem,
he high le el o abs ac ion om imb e p oduc ion, he iming o bo h muscle ac i i y and
b ain unc ion, and he selec ion o sui able o ganiza ional sys ems o modeling con ol and
muscle ac i a ion. This p oblem is compounded when conside ing in e limb coo dina ion as a
physical aspec o coo dina ing he s ikes o mul iple d ums (coo dina ion/implemen a ion),
pa icula ly in complex asks such as hy hm p oduc ion. In c ea ing complex hy hms
bimanually, ask complexi y be ween he hands (which include coope a i e and disjoin ed
asks) oge he wi h he dex e i y le els and handedness o he indi idual will a ec he b ain’s
o ganiza ional con ol o he wo hands. In he case o d umming, i is mo e likely o include
leg con ol o ope a ing he bass d um and hi-ha . This would esul in a highly complex s udy
wi h oo many a iables o allow o meaning ul conclusions ele an o pe o mance
modeling. Fu he eading on his subjec , howe e , is a ailable om Be ns ein (1967), Cal in,
Huys, and Ji sa (2010), Ianna illi, Vannozzi, Iosa, Pesce, and Cap anica (2013), and Kelso,
Sou ha d, and Goodman (1979).
Endu ance is unique o indi iduals and can be inc eased wi h co ec aining. Howe e ,
du ing pe o mance, endu ance can be a ec ed by an indi idual’s le el o physical exe ion,
which can be mi iga ed by designing sequences o mo emen ha equi e less mo emen o
ha inc ease hei economy o mo emen . O he beha io al and cogni i e aspec s o imp o ing
le els o endu ance i i mly wi hin he ealms o pe o mance psychology, which a e di icul
o ep esen in a compu a ional pe o mance model. Simila ly, he modeling o aining and
wa m up p o ocols also is ou side o he scope o his in es iga ion in ha hey do no b ing any
di ec bene i o he modeled sys em. No bene i would be gained by modeling a pe o me wi h
an impai men , such as modeling a d umme wi h low le els o endu ance, because he sys em
would be designed wi h a le el o pe o me obsolescence, esul ing in poo playing a e a
pe iod o ime. The e o e compu a ional, p ocedu al, and implemen a ion le els o analysis
ela ing o endu ance a e ou side he scope o his in es iga ion. Howe e , u he eading is
Designing Compu e Models o D umming Pe o mance
117
a ailable om Abe ne hy, Han ahan, Kippe s, Mackinnon, and Pandy (2005), Gab ielsson
(1999, 2003), and Sha e (1989).
Thus in he ollowing sec ions, discussion will ocus on physical mo emen , ins umen al
in e ac ion, and bodily mo emen in he con ex o human mo emen in he physical wo ld. The
aim o his esea ch is o iden i y a me hod o analyzing he c i ical elemen s o music
pe o mance mo emen o elec onic ep esen a ion in ei he an in e ac i e music o a i ual
sys em. I is wo h no ing ha , al hough some aspec s o he amewo k a e speci ically
iden i ied as being ou side he scope o in es iga ion, he e a e o e laps be ween some o he
a iables men ioned and aspec s o pe o mance ha will be discussed in he ollowing sec ions.
Thei inclusion wi hin he discussion se es o highligh he complexi y o pe cussi e
pe o mance and demons a es he wide eaching implica ions and impo ance o he discussion.
CONTROLLING INSTRUMENTAL INTERACTION
Why is physical con ol so impo an ? S iking an objec wi h ano he objec has wo
epe cussions. Fi s ly, when he s uck objec p oduces sound, ib a ion in he s ick a els
h ough he inge s o he hand. In some ins ances, and depending on he o ce o he s ike and
he ma e ials in ol ed, his can ex end in o he a m. In se e e cases, his can cause discom o
(e.g., using a me al ba o s ike a la ge mass o solid me al wi h ex eme o ce). Secondly,
s iking an objec can cause he s iking ool o be de lec ed away om he su ace and,
depending on he elas ici y o s uck ma e ials, he le el o de lec ion will be ei he minimal
(e.g., a ha d me al su ace) o mo e signi ican (e.g., a memb ane unde ension). Because
playing he d ums equi es s iking many objec s consis ing o di e en ma e ials, and s iking
hem a di e en s eng hs, he amoun o ib a ion expe ienced in he playe ’s body a ies
among he ins umen s and which, du ing d um se pe o mance, is exace ba ed by de lec ions
o he s iking implemen caused by di e en elas ici ies in he s uck su aces, he angles o he
ini ial s ikes, and he s ike o ces ac oss he indi idual componen s o he d um se . S ike
loca ion plays a signi ican ole in modal equency exci a ion, subsequen ly a ec ing he
imb e o he d um. Mo eo e , because playing he d ums o en equi es mul iple s ikes, i is
impo an o imb al consis ency ha he d umme main ains physical con ol o he s iking
implemen ac oss a di e si y o po en ial s ike in e ac ions.
Unde s anding how a pe o me main ains physical con ol o a s iking implemen is
impo an in con ex ualizing how iming and imb al a ia ions occu in a d umming
pe o mance. This in o ma ion also is use ul o de eloping a pe o mance on ology in which
he sys em ei he simula es he elemen s o he esul s o physical con ol o ansi ions in o
new s a es as a esul o iden i ying embodimen s o physical con ol as inpu pa ame e s.
This sec ion p o ides a bo om-up app oach o discussing and e iewing he li e a u e
conce ning ins umen al in e ac ion, s a ing wi h s ick con ac and g ip, s ick ebounds, and
p epa a o y s ike mo emen s, o coo dina ing bodily mo emen and d um s ike ajec o ies
ac oss mul iple d ums. This app oach acili a es a de ailed discussion o he complex na u e
o pe cussi e pe o mance and helps in iden i ying eme gen hemes in human pe cussi e
pe o mance mo emen and biomechanics.
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The o e iding goals o hese componen s d aw pa allels o Sha e ’s (1989) desc ip ion o he
mo o geome y in piano pe o mance:
Ge ing he inge s o he igh loca ions on an ins umen is impo an bu only pa o
he mo o ask in playing. The pe o me can lea n o shape he ajec o ies o mo emen
so as o achie e iming o hy hm and a ia ion o dynamic and one quali y wi h an
economy o mo o e o . (Sha e , 1989, p. 383)
I is e iden om bo h Dahl (1997b) and Sha e ’s (1989) desc ip ion o musical pe o mance
ha d ums ick managemen comp ises echnical elemen s o playing he d ums, pa icula ly he
con ol o ebounds and he con ol o s ick a he heigh o he s ike mo ions. Technical elemen s
in d umming con ibu e owa d accu acy in imb e p oduc ion and iming con ol. Al hough Dahl
(1997b) desc ibed a ia ions in he o e all mo ion among he pa icipan s (especially a a ying
skill le els), he cu ilinea ajec o y ollowed he indings by Kelso e al. (1991).
Bodily Coo dina ion
One impo an concep o cho eog aphy ha con ibu es owa d mo ion and o m is ha o
balance a angemen , pa icula ly whe he he body is symme ical o asymme ical, which is
indica i e o s abili y and equilib ium o i egula i y and imbalance. Playing he d ums equi es
bo h bila e al mo emen (bo h limbs mo ing in unison) and unila e al mo emen (one limb
mo ing a a ime). Al hough d umming can be conside ed symme ical (mi o ed) o
asymme ical, depending on he combina ion o indi idual d ums being played (i.e., he
con ex ), he p ocess is inhe en ly asymme ical owing o he con igu a ion o he componen s
o he d um se . This a icle discusses he e ec s o he inhe en ly asymme ic en i onmen and
how a d umme esponds o and uses asymme y in designing d umming sequences.
A uin and La ash (1995) in es iga ed he e ec o opposing bila e al as mo emen s on
he shoulde s (wi h and wi hou load) o subjec s s anding on a o ce pla o m. They ound ha
an icipa o y pos u al muscle adjus men s (APAs) in he unk and leg muscles we e made by
he subjec s o main ain balance, wi h adjus men s inc easing o a maximum when a ms we e
mo ed in a o wa d o backwa d mo ion and dec easing o no APAs when mo ing he a m
along he sides (i.e., he co onal plane). Fu he mo e, he au ho s ound no signi ican di e ence
in muscle adjus men as a esul o addi ional load on he a ms. These APAs we e e iden by
changes in he subjec s’ an e io , pos e io , and e ical cen e s o p essu e and g a i y on he
o ce pla e p io o he mo emen .
In he case o d umming, i is qui e common o he d umme o be in a sea ed posi ion
wi h much o he playe ’s weigh suppo ed by he sea . Consequen ly, he leg muscles play a
lesse ole in edis ibu ing cen e s o o ce and g a i y o an APA. The edis ibu ion o
weigh using he legs is u he complica ed by hei use in applying independen p essu e o he
hi-ha and bass d um pedals. Consequen ly, uppe body s abiliza ion is ca ied ou by he unk,
speci ically he e ec o spinae (ES) and ec us abdominis (RA), i espec i e o he ypes le els
o suppo in he legs (A uin & Shi a o i, 2003). These indings we e suppo ed by San os and
A uin (2008), who also ound ha he la e al muscles con ibu ed o up igh pos u e con ol in
eed- o wa d mo emen s (i.e., mo emen s elying on an icipa o y co ec ion), akin o eed-
o wa d mo emen s in d umming and whe e he le el o muscle ac i a ion being is di ec ionally
speci ic. Wi h bo h legs in a ixed posi ion o ope a ing he hi-ha and bass d um, a d umme ’s

Designing Compu e Models o D umming Pe o mance
125
di ec ional pos u e con ol is o g ea impo ance, pa icula ly in con olling mo emen s
equi ing axial o a ion o he uppe body.
Thus APAs in compound mul ijoin mo emen s—especially hose in ol ing changes in
di ec ion (Holmes, 1939, pp. 17–19) such as bila e al as mo emen s o shoulde s coupled wi h
poin - o-poin axial o a ion—a e c i ical in main aining pos u al s abili y. Howe e , in addi ion
o bila e al mo emen s, a d umme ’s a m mo emen s o en a e unila e al, a e no di ec ly
opposing, and a e execu ed a di e en s eng hs and speeds ela i e o he loca ion and dis ance
be ween subsequen d ums o be s uck. Whe e a d umme has di e en maximum a m heigh s
ela i e o he ho izon al plane, as well as di e en maximum dis ances in a m each equi ed
om he cen e o he o so be ween s ikes, hen pos u al con ol and s abili y also a ec s
mo emen on he e ical (i.e., sagi al) plane. Thus, consequen ly, a hunched-o e posi ion is
no conduci e o playing s ikes a g ea e heigh s. Wi h his in mind, i is easy o imagine he
a ia ions in he cen e s o p essu e and g a i y on a playe du ing he cou se o a pe cussi e
pe o mance. In ac , Alén (1995) sugges ed simila links be ween mo emen and pe o mance
a ia ions. In his analysis o he Cuban music gen e umba ancesa, pa icula ly a ype o
pe o mance called a oque maco a, Alén desc ibed how he la ge size o a Cuban bulá d um
may ha e a ec ed he pe o me ’s s abiliza ion, equi ing o so mo emen s ha could con ibu e
owa ds iming de ia ions.
Al hough he e a e as di e ences be ween he d um se and he bulá, i is concei able ha
Alén’s (1995) links also apply o playing he d um se . One heo e ical iew is ha a pe o me
mi iga es hese e ec s by main aining a pos u al equilib ium, wi h ex eme changes in pos u al
s abili y coun e ed by APAs s emming om pe o mance planning and musical ead-ahead, bo h
o which can be linked o pe o mance skill and ha ing epe cussions on musical ges u e as a
lea ned de ia ion.3 In summa y, one gene al ule o d umming pe o mance a ia ion is ha he
g ea e he dis ance and angle o mo emen ( ela i e o he o so) p io o he s ike, he g ea e
he inequali y be ween he opposing each angle and dis ance o he o he hand, he g ea e he
synch ony/asynch ony o he a m mo emen s, he mo e complex he biomechanical and
neu ophysiological p ocess and he inc eased likelihood o pe o mance a ia ion.
D um S ike T ajec o y
The ajec o y o a d um s ike is impo an in d umming o such an ex en ha d um s ike
ajec o y was used as an impo an componen in he composi ional speci ica ion o Ka lheinz
S ockhausen’s composi ion Zyklus (1959). As desc ibed p e iously, ebound con ol can be
used o a ec he ajec o y o he subsequen s ike in a sequence o pe cussi e hi s. Be ween
ebounds, he playe mus mo e he s ick om one s ike loca ion o ano he a a speed
su icien o main aining co ec iming. The success o his aim is la gely dependen upon
ajec o y, de ined by Abend, Bizzi, and Mo asso (1982, p. 331) as “ he pa h aken by he hand
as i mo es o a new posi ion and he speed o he hand as i mo es along he pa h.”
In hei s udy o hand ajec o y o a ge , Abend e al. (1982) ound ha he majo i y o
subjec s who we e asked, wi h no ins uc ion, o mo e hei hand delibe a ely o a a ge , op ed
o a s aigh line. Wi h he sho es dis ance be ween wo poin s being a s aigh line, one
would expec mo emen s wi h s aigh ajec o ies o ha e a sho e du a ion han cu ed
ajec o ies o he same a ge . Al hough his was ound o be ue, mo emen du a ion also is
dependen on speed, which Abend e al. ound o be mo e i egula du ing cu ed ajec o ies.
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Howe e , in cases whe e he a e age speed was low, e en s aigh ajec o ies showed i egula
speed pa e ns, sugges ing g ea e di icul y in con olling he mo emen . In a pe o mance
con ex , a lowe mo emen speed and, he e o e, a lowe s ike eloci y, will p oduce weake
ebounds. Thus, he in e ac ion wi h he ins umen in e ms o ebound con ol and he
mo emen be ween he s ikes is ha de o he playe o con ol.
Rega ding he i egula speed p o iles o he cu ed ajec o ies in Abend e al. (1982), i
was no ed p e iously ha he mo emen o a d ums ick du ing a s ike has cu ilinea
esemblances due o he phasing o muscle mo emen s (Kelso e al., 1991). Howe e , a
connec ion be ween he wo canno be d awn because he e we e di e ences in plana
mo emen in hese s udies. The pa icipan s in Abend e al. (1982) ope a ed on a ho izon al
plane, compa ed o sagi al mo emen s in Kelso e al., (1991) and compa ed o bo h sagi al and
ho izon al mo emen s in Dahl (2000). Despi e his, he e was a co ela ion in he inc eased
i egula i y in hand speed ela i e o he an iphase na u e o he angula eloci y o he shoulde
and elbow—in o he wo ds, a join - ocused dicho omy wi h pa allels o Kelso e al.’s (1991)
muscle syne gies.
D umming in a iably uses mul iple join s, each wi h di e en o ques applied om he
muscles ha , in a mul ijoin mo emen , ex end o he in e ac ion o o he join s and o ques in
he mo emen . In he case o mul ijoin mo emen , each join will be subjec o di e en
eloci y in e ac ions a a ious poin s in he mo emen . Whe e a ajec o y is changed midai
and no using a ebound (e.g., a a highe p epa a o y s ick heigh , as in Dahl e al., 2011), he
join o ques will change depending on he new ajec o y. Such a mo emen is subjec o
in e ac ional o ces du ing he planning and con ol o he mo emen —such as he Co iolis,
cen ipe al, and eac ion o ques (Abend e al., 1982, p. 331)—al hough he e ec s o hese
o ces change dynamically o e he mo emen . Holle bach and Flash (1982) obse ed such
beha io in ela ion o a cu ed ajec o y whe e “ he eloci y in e ac ion o ques in ac
comple ely domina e he dynamics a he mo emen midpoin because he ine ial o ques go
h ough ze o as he mo emen swi ches om accele a ion o decele a ion and he a m is
mo ing he as es a his poin ” (Holle bach & Flash, 1982, p. 76).
In he case o a single s oke, as measu ed in Dahl e al. (2011), he midpoin would be he
a c a he peak o he p epa a o y mo emen . In some ins ances, a change in ajec o y a his
poin would ha e h ee bene i s. Fi s ly, his enables a g ea e p epa a o y s oke heigh o he
nex s ike. Secondly, he g ea e heigh enables highe maximum accele a ion and downwa d
eloci y. Thi dly, as a poin wi h he leas amoun o ine ial o que, he playe can p epa e o
he join o que o he nex mo emen . Such o que con ol can mi iga e iming a ia ion.
In e ms o accu acy, i has been ound ha he ajec o y o aimed mo emen can be
lea ned. These lea ned ajec o y mo emen s we e demons a ed by Geo gopoulos, Kalaska,
and Massey (1981) du ing a s udy o aimed mo emen s in Rhesus monkeys. They ound ha
p ac ice o e a pe iod o ime educed he mean a iabili y o he ajec o y owa ds a a ge ,
oge he wi h imp o ed accu acy, i espec i e o a ge loca ion. The implica ion he e is ha a
human d umme is likely o do he same using he d ums as a ge s. Howe e , as p e iously
no ed, d umming equi es bila e al and unila e al a m mo emen , and humans can be ei he le
handed o igh handed. Each o hese ha e been demons a ed o be con ibu ing ac o s
owa ds a ge accu acy (Ga y & F anks, 2000), wi h inc eases in eac ion ime o bila e al
s ikes wi h a ge ing aimed by he weake hand compa ed o unila e ally mi o ed a ge ing.
Designing Compu e Models o D umming Pe o mance
127
The e ec s o his can be minimized h ough d um se con igu a ion, wi h li le impac on
mul ijoin bila e al mo emen .
Al hough se e al ac o s can a ec ajec o y and con ol du ing pe cussi e pe o mance,
he mos signi ican ac o occu s du ing mul ijoin mo emen , whe e join o ques impac no
only he choice o ajec o y bu also he con ol and speed o he mo emen . In he case o
d umming, sequences in ol ing mul ijoin mo emen s can o en include mul iple simul aneous
planes o mo ion and axes o o a ion. Such an ac ion is illus a ed in Figu e 4, whe e a
d umme ’s mo emen is desc ibed be ween changes o s ike loca ion, om a s ike on a sna e
d um o a s ike on a c ash cymbal.
In he example in Figu e 4, du ing he mo emen o he igh hand om he s a ing
posi ion (sna e d um) o he c ash cymbal, he e is abduc ion and ex ension o he igh
shoulde on he on al plane wi h a pos e io axis o ex e nal o a ion. The e is also an elbow
and w is ex ension on he sagi al plane wi h a la e al axis o o a ion. Assuming no mo emen
o he le a m, hen he e is also a e ical axis o o a ion o he unk on he ho izon al plane
o allow he d umme o posi ion he body o eaching he new a ge . Kine ically, each o
hese axes o o a ion and mo emen in his mul ijoin sequence con ain o que o ces ha
a ec he mo emen .
I he d umme in he igu e had no included a s ike a he c ash cymbal bu a epea
s ike o he sna e d um, he e would ha e been minimal changes o he exis ing pa e ns o
join o que and muscle ac i a ion. Addi ionally, ano he d um loca ed a he same heigh as he
sna e d um, bu close o he c ash cymbal, would cause he d umme o make a unk and
shoulde o a ion. Howe e , because he d ums a e a a simila heigh , he e would be less
mo emen o e he h ee planes. The e o e, mo emen s spanning mul iple planes o mo ion
and axes o o a ion a e mos likely o a ec he mo emen o a d umme and, subsequen ly, he
imb e and iming a ia ions. Mul ijoin mo emen s, such as hose in Figu e 4, a e conside ably
Figu e 4. An illus a ion showing he ypical mo emen s associa ed wi h a change o s ike loca ion
by a d umme mo ing om a sna e d um s ike o a c ash cymbal s ike.
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128
p oblema ic o model because he e a e 17 DOFs in mo emen s o he shoulde , elbow, and
w is : 9 kinema ic ne momen s and 8 dynamic wi h op imized muscle o ces (Chadwick & an
de Helm, 2003, p. 15).
This discussion p esen s some clea di icul ies in modeling pe cussi e pe o mance om
body, mo emen , and spa ial pe spec i es. Fi s ly, s ick managemen plays an impo an ole in
he in e ac ion be ween he s ick and he d um in he way ha s ick con ac imes can be
in luenced o al e he ib a ion o he d um (and he subsequen imb e). Simila ly, s ick g ip
in luences he ebound o he s ick om he d um, which has wo e ec s on d umming: o ce
con ac dampening o a d um a e a s ike and posi i e and nega i e ebound use o
subsequen s ikes, pa icula ly in sequences o d ums ope a ing a di e en angles and
loca ions ela i e o he o so. Al hough in mos cases s ick con ol can be execu ed du ing he
s ike, due o ime cons ain s much o he ebound and s ike con ol is managed du ing
p epa a o y mo emen s.
Du ing he downwa d mo ion o a s ike, a cu ilinea ajec o y was obse ed in Dahl’s
s udy (1997b); his can be explained by he phasing o muscle ac i i y in he homologous
muscle g oups o he a m (Kelso e al., 1991). In-phase muscle ac i i y p oduced g ea e a m
s abili y and economy o mo emen , which is a con ibu o y ac o in s ick con ol. A he apex
o a s ike, a ish ail mo ion was desc ibed (Dahl, 1997b), which u he exploi s he exis ing
syne gy be ween muscle ac i i ies by aking ad an age o he ups oke o minimize addi ional
muscle ac i i y in he uppe a m. In bimanual and unila e al a m mo emen s, which a e
common occu ences du ing d umming, APAs we e obse ed as a means o main ain pos u al
s abili y. These in ol ed small muscle mo emen s ha compensa ed o changes in o ce (e.g.,
changes in he cen e o g a i y) esul ing om a m ex ension. The e ec o his, when in a
sea ed posi ion, is ha he unk is esponsible o pos u al s abili y in he uppe body. Wi h
mo e complex a m mo emen s in d umming sequences, compa ed o he simple a m
mo emen s as s udied in p e ious esea ch, he po en ial need o cons an pos u al an icipa ion
and con ol was highligh ed, pa icula ly in a hy hmic unila e al s ikes a nonopposing angles
and a a ious dis ances om he o so.
TOWARDS A TEMPORAL MOVEMENT CONTEXT
This s udy aimed o assess he cu en li e a u e ela ing o human pe cussi e pe o mance on a
nine-piece d um se . This was done in o de o unde s and human mo emen and ehea sal as
cho eog aphed mo ion. The no ion o cho eog aphy in he eal-wo ld con ex o d umming, as
ehea sed sequences o mo emen s, s ems om he in e na ionally ecognized d um udimen s
in ended o de elop pe cussionis s’ physical con ol, coo dina ion, and endu ance.
In he i ual wo ld con ex o in e ac i e compu e sys ems, a clea unde s anding o how
hese de elopmen goals ela e o ins umen al in e ac ion, biomechanics, and human
mo emen p o ides an oppo uni y o explo e he in e ac ion possibili ies be ween human and
machine. The i-le el Ma /Rosenbaum amewo k (Table 1) o analyzing in o ma ion sys ems
and mo o con ol, applied h ough he lens o he de elopmen goals, acili a ed a bo om-up
analysis o eal-wo ld human in e ac ion wi h d ums. The signi icance o his app oach om a
human- o-machine in e ac ion pe spec i e is ha eal-wo ld, bo om-le el in e ac ions (i.e., end
e ec o in e ac ions) can ha e a signi ican impac on any gene a ed simula ion (e.g., o ce
Designing Compu e Models o D umming Pe o mance
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con ac a ec ing he imb e o a d um by al e ing he d um’s ib a ional cha ac e is ics). Such
condi ions may be ei he oo di icul o ma hema ically ep esen o compu a ionally oo
expensi e, pa icula ly ac oss he nine indi idual componen s o a d um se . Unde s anding he
nuances o eal-wo ld in e ac ion p o ides o mo e in o med decision making when designing
in e ac i e i ual sys ems and human in e ac ion. Design op ions include subs i u ing
ma hema ical ep esen a ions (algo i hms o subsys ems) o some in e ac ions wi h simila le el
ep esen a ions (algo i hms o subsys ems) o o he in e ac ions. The measu emen o such
in e ac ions may allow design choices ha de e in e ac ion om a dynamic ma hema ical
ep esen a ion o a senso -based human in e ace (e.g., measu ing o ce con ac du a ion on a
compu e -enabled su ace), hus educing compu a ional o e head while simul aneously
main aining eal-wo ld in e ac i e au hen ici y.
The hie a chical na u e o a bo om-up analysis allows each eal-wo ld in e ac ion o be
con ex ualized wi hin a la ge se o mo emen s. In he i ual wo ld, his is equi alen o
me ging wo subsys ems o o m a la ge complex sys em ep esen a i e o a mo e abs ac
unc ion. F om an in e ac ion pe spec i e, his may mean de i ing a o ce con ac du a ion
om a se ies o assump ions abou he cu en s a e o he con ex o he sys em. Such an
abs ac ion could include he ep esen a ion ha s ick con ol is mo e di icul wi h weake
ebounds, hus weake s iking leads o longe du a ions o o ce con ac . Howe e , as each
in e ac ion is abs ac ed o a la ge se o mo emen s, human in e ac ion wi h he sys em
becomes mo e abs ac . Consequen ly, in designing an in e ac i e sys em ha simula es human
pe cussi e pe o mance, he e a e ade-o s in de e ing simula ion unc ions o ei he
ho izon ally in eg a ed subsys ems o abs ac laye s wi h ega ds o he le el o simila eal-
wo ld human in e ac ion wi h he sys em. This analy ical amewo k p o ides a unique way o
in es iga ing human pe cussi e pe o mance while concu en ly analyzing compu a ional
aspec s ele an o he sys em design. The con e gence o hese wo pa adigms mani es
hemsel es in sys em in e ac i i y and how he sys em ep esen s eal-wo ld mo emen s ha
a e inhe en ly bo h comp omised and unique, depending on he ision o he sys em.
Rep esen ing Human Mo emen
I is clea ha signi ican issues exis in using he biomechanical conside a ions o he human
body du ing pe cussi e pe o mance as a me hod o gene a ing bo h pe o mance con ex and in
algo i hmic con ol o ep esen a i e compu a ional musical ou pu . Fundamen ally, he main
p oblem in modeling d um se pe o mance is ha i is p edominan ly asymme ical: The
pe o me ’s a m mo emen s (e.g., each dis ance, heigh , and angle) a e o en unequal, and he
hy hmic s iking o hese can be i egula . The inequali y o a m loca ion and i egula i y in
d umming cons an ly changes he join o ques and he o ce in e ac ions ha a ec ajec o y
con ol, mo emen s abili y, and pos u al s abili y, which subsequen ly a ec s ike con ol, s ike
accu acy, ebound con ol, and s ick managemen , ul ima ely causing a ia ions in imb e and
iming. This p oblem is compounded by an almos in ini e numbe o combina ions o
mo emen s be ween Ca esian s ike coo dina es du ing d umming and, i one akes in o accoun
he DOF p oblem, he e is an ex eme abundance o po en ial sys em ep esen a ions. Such an
abundance o po en ial ep esen a ions would be ha d o implemen compu a ionally; ye , he
selec ion o a smalle numbe o ep esen a i es is di icul o jus i y heo e ically. As Abend e
al. (1982) no ed, he e would need o be an in e se kinema ic ans o ma ion o he Ca esian- o-

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join coo dina es and hen, using in e se dynamics, he join o ques would need o be calcula ed.
This has signi ican implica ions o bo h he selec ion o pa icula a iables ha would o m he
basis o any compu a ional model and on he way in which hese a iables a e ep esen ed.
One way o ep esen ing human body mo emen in pe cussi e pe o mance would be o
examine a speci ic mo emen and iden i y he mos likely used DOF in he join s ac i a ed du ing
ha mo emen , such as he me hods used by Bouëna d, Gibe e al., (2011). This would equi e
in es iga ing he e ec ha each indi idual join can ha e on he o e all mo emen , including he
selec ion o mul iple DOFs and subsequen join angles on he ou come o he mo emen . Such
an app oach would allow o an assessmen o whe he a a ia ion in DOF a a join close o he
ins umen has a g ea e impac in p oducing biomechanical e o s han a ia ions in DOF a
join s close o he o so. In addi ion, p e e ences and/o ends in plana mo emen o each join
o a gi en mo emen could be iden i ied, oge he wi h he impac o hese plana p e e ences on
biomechanical e o . One way o compu a ionally ep esen ing his app oach is o design an
algo i hm ha uses weigh ed p obabili y o calcula e he likelihood o a selec ed DOF o angula
mo emen in a gi en join . An example o a me hod o ep esen ing his compu a ionally would
be a Gaussian dis ibu ion o alues o ep esen a join angle (e.g., shoulde ) and a Ma ko chain
o de e mine he nex selec ed join angle (e.g., elbow), and so on un il a join angle alue is
de e mined o he w is . A his poin , a mo emen assigned a unique iden i ica ion numbe
could be used o igge a p ede e mined imb al o empo al a ia ion o ep esen he le el o
biomechanical e o in he mo emen (as compa ed o a heo e ical ideal).
De e mining he p obabili ies o join a ia ion wi hin mo emen s would equi e
signi ican analysis o mul ijoin , mul iplane mo emen and would equi e also measu ing a
quan i iable e o om he a ious mo emen s. Fu he mo e, deciding which mo emen s o
in es iga e can be p oblema ic in ha hei ela i e impo ance is highly subjec i e. In addi ion,
iden i ying p e e ences o ends in mo emen a join le el may equi e signi ican sample
sizes and may gene a e la ge quan i ies o da a, pa icula ly should he h ee axis plana
mo emen be measu ed a high equencies. Finally, a link be ween join a ia ion and
pe o mance a ia ion would need o be quan i ied and would equi e mul iple me hods o
analysis, o example, co ela ing da a om join mo emen wi h audio o iden i y he ends in
pe o mance a ia ions associa ed wi h combina ions join alues. Exac ly how he many
combina ions o join alues ep esen pe o mance a ia ion also is c i ical in ep oducing
human pe cussi e pe o mance in a compu e en i onmen , as i ela es o a me hod o
con olling one o mo e aspec o musical pa ame e s, such as imb e o iming.
Ano he po en ial me hod lies in he ep esen a ion o he d umming echniques by c ea ing
an algo i hm ha ep esen s he DOFs associa ed wi h a pa icula d um udimen . A skilled
d umme will ha e a s anda d epe oi e o d umming echniques a his/he disposal; so i may be
possible o assign a ious combina ions o mo emen o a gi en echnique ha hen gene a es a
musical ou pu ha closely esembles ha echnique. Howe e , he execu ion and applica ion o
hese echniques will di e ac oss pe o me s and pe o mances, no wi hs anding he s ylis ic
di e ences o he pe o med music. As a esul , he p ocess may p oduce disjoin ed sounding
pe o mances because he selec ed echniques a e inapp op ia e, unusual, o humanly impossible
o he gi en musical o pe o mance con ex . O cou se, i may be possible o conca ena e
algo i hmic ep esen a ions o echniques o o m a cohe en pe o mance, bu ha depends upon
whe he he echniques ha e unique muscle and join ac i a ions ha a e ep oducible and
ele an . The mos signi ican challenge in his app oach is iden i ying and empi ically measu ing
Designing Compu e Models o D umming Pe o mance
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hese mul iple echniques wi hin a pe o mance and de e mining a unique mo emen alue. The
di icul ies associa ed wi h collec ing join in o ma ion as desc ibed abo e a e suddenly
inc eased when mo e a iables a e in oduced in o he pe o mance con ex . I is clea ha , in
designing a sys em ha simula es human pe cussi e pe o mance, he shee numbe o
biomechanical and pe o mance conside a ions pose signi ican challenges in compu a ionally
ep esen ing any meaning ul o si ua ionally speci ic in e ac ion. The e o e, i is use ul o
conside he biomechanical conside a ions and pe o mance con ex a a lowe le el o de ail and
in he con ex o playing he d ums. So wha do we know a his poin ?
One b oade iew ha can be aken o he pu poses o modeling pe cussi e pe o mance is
ha la ge mul ijoin mo emen s ope a ing on mul iple planes o mo ion a e mo e likely o
gene a e pe o mance a ia ions o wo easons. Fi s ly, a pe cussi e pe o me playing he d um
se is inhe en ly cons ained by his/he numbe o limbs ega ding how many ins umen s can be
s uck simul aneously. Fo example, a nine-piece d um se has 64 po en ial combina ions o
simul aneous ins umen s ikes using only he wo hands. Wi h he ee ixed in posi ion, he
main a eas o mo emen lie in he uppe body and o so, which ela es o he complexi y and
equali y o bimanual d umming. Secondly, because he numbe o d ums limi s he combina ions
o a m mo emen s, he complexi y o he mo emen is la gely a ec ed by p io a m loca ion.
Collec ing Da a om Human Mo emen
The li e a u e discussed in his a icle p esen a ious me hods o ob aining obse a ional and
empi ical da a om human pe cussi e pe o mance. Despi e a ying esea ch aims, hese
s udies e eal impo an insigh s in o eal-wo ld human in e ac ion wi h d ums. In o de o
i ualize his human–d um in e ac ion, a ious me hods can be exploi ed o sys em design
and con ol. The ask hen is o de e mine whe he he sys em should be e en -d i en (i.e.,
so wa e ha changes beha io in line wi h an e en ), da a-d i en (i.e., so wa e whose
embedded da a con ols he low o he p og am), o a combina ion o he wo.
An e en -d i en sys em would espond o human in e ac ion, such as playing a ypical
comme cially a ailable elec onic d um machine in which elec onic d um pads measu e he
s ike o ce and play a sampled d um sound in esponse. One key conside a ion o his
app oach is o ensu e ha he in e ac ion be ween human and machine accu a ely simula es
eal-wo ld, s ick- o-d um in e ac ion. Howe e , mos mode n elec onic d um pads accoun o
his need. In ac , mos mode n elec onic d um se s ha e begun o inco po a e di e en zones
in o he d um pads in o de o igge di e en imb es, hus mi o ing he ac ion o physical
d ums. Ob aining a measu emen o con ac du a ion ubiqui ously om he d um pad may be
use ul o il e ing a igge ed sound o simula e memb ane dampening. P essu e senso s
moun ed in o below he d um s ool (simila o he o ce pla o m used by A uin & La ash,
1995) could be used o con ol addi ional imb al pa ame e s, al hough how he cen e o mass
ela es o meaning ul sys em ou pu would depend on sys em ep esen a ion. Consequen ly,
such unc ions would p oduce limi ed meaning ul addi ional in e ac ion. A comple ely e en -
d i en sys em such as an elec onic d um ki has wo d awbacks. Fi s ly, i elies on he human
use o in e ac wi h he sys em and will only p oduce sounds ela i e o he skill le el o he
use . Secondly, wi h music being a ime-sensi i e ask, sys em esponses om human
in e ac ion would need o be ex emely low la ency. This may no be possible, depending on
he speed o he pe o mance and he numbe o e en s ha need o be handled.
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A da a-d i en sys em could use da a cap u ed om ac ual human pe o mance in o de o
c ea e an embedded da abase o o use in eal- ime in e ac ion. One me hod o cap u ing
human pe o mance uses in a ed came as and senso s, as demons a ed by Dahl (2004), Dahl
e al. (2011), and Kelso e al. (1991). This app oach also was used by Bouëna d, Gibe e al.
(2008, 2011) o cap u e impani pe o mances o c ea e a mo ion da abase. Al hough his
app oach add essed some limi a ions in physics-based modeling o pe o me s, Bouëna d,
Gibe e al. no ed ha he ins umen could obs uc he in a ed ma ke s. In ela ion o a nine-
piece d um se , his is a signi ican limi a ion in ha a ypical d um se has componen s a
a ious poin s a ound he pe o me . In addi ion, Bouëna d, Wande ley, Gibe , and Ma andola
(2011) desc ibed limi a ions in cap u ing nuances in pe o mance, such as s ick g ip. Wi h his
in mind, eal- ime con ol o a pe cussi e sys em using in a ed came as and senso s would
need o ake place in an en i onmen de oid o obs uc ions because, om a human–machine
in e ac ion pe spec i e, a signi ican po ion o he s ick- o-d um in e ac ion is los , such as he
ebound and o ce con ac .
The desc ip ions abo e p o ide he pola exempla s o e en -d i en e sus da a-d i en
sys ems, wi h each ha ing comple ely dis inc aims and ou comes. The e en -d i en sys em
wi h he elec onic d um ki is ypical o a pe o mance sys em, while he da a-d i en sys em
wi h he mo ion cap u e is eminiscen o i ual cha ac e anima ion (Bouëna d, Gibe e al.,
2011). In e ac i e sys ems ha employ a combina ion o e en -d i en and da a-d i en me hods
include in e ac i e compu e -gene a ed pe o mance ools and elec onic composi ion ools ha
ende a pe o mance based on human in e ac ion. Such sys ems equi e a la ge amoun o
abs ac ion on he da a side complemen ed by human in e ac ion o igge e en s and compu e
s a e changes. In he case o abs ac ing da a, se e al me hods a e a ailable o c ea ing a
ep esen a ion o an aspec o pe o mance. One me hod o empi ical da a collec ion ha could
help o iden i y he le els o mo emen in a d umming pe o mance is he ideo cap u e o
mul iple pe o mances by di e en pe o me s wi h he compa a i e analysis o he mo emen
le el in he ideo ac oss he pe o me s. I also is possible o a ach accele ome e s o he
pe o me ’s hands o measu e he amoun and di ec ion o hei accele a ion.
In addi ion, audio da a could help o iden i y he ex en o pe o mance a ia ion by
enabling a empo al analysis o pe o mance e en s and compa ing hese wi h elemen s o he
ideo and senso da a. This could yield in o ma ion ega ding he empo al s abili y o
pe o mance. Al hough his me hodology would acili a e a mo e gene ic ep esen a ion o
pe cussi e pe o mance, much in o ma ion can be ob ained om his mul ime hod app oach.
Fi s ly, any empi ical pe o mance da a ob ained could be used in a da a-d i en model.
Secondly, i is possible o in e mo e gene ic ules su ounding he use o mul iple
combina ions o ins umen s and a oid he need o gene a ing mul iple a iables o ca e o he
DOF p oblem. Finally, his app oach is mo e p ac ical because b oade obse a ions can be
made om a ela i ely ewe numbe o pa icipan s han would be equi ed o calcula e he
median join angle a e ages o mul iple pe cussi e echniques. The e o e, by iden i ying
complex bodily mo emen in an ins umen al pe o mance space, algo i hmic logic can be
c ea ed ha can simula e he pe o mance con ex ha o ms he undamen al logic o a sys em
ha con ols he le els o a ia ions simula ed in a compu e model o d umming. This app oach
suppo s e hinking he cho eog aphy o pe o mance and i s ole in designing compu e -
simula ed human in e ac ion, as well as e hinking empi ical mo emen da a o con ibu e
owa ds new concep s o compu e gene a ed hy hm sys ems.
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Sound gene a ion and ins umen al ep esen a ion a e impo an componen s o any
pe o mance modeling sys em. Wi h a a ie y o echniques a ailable o sys em-modeling
conside a ion, he main conside a ions a e compu a ional o e head, exp essi i y o he
syn hesis, and accu acy o he ep esen a ion (Kah s & B andenbu g, 1998). The complexi y o
accu a ely syn hesizing a nine-piece d um ki comp ising memb anophones and idiophones
places some physical modeling syn hesis echniques i mly ou o scope, pa icula ly when
conside ing he compu a ional o e head and ime sensi i i y o he sys em. Consequen ly,
sound gene a ion is mo e e icien when he compu a ional o e head is ans e ed o decision
making, da abase ma ching, and sound playback, as opposed o calcula ing complex equa ions
and esy hesizing he sound a un ime. The e o e, using a comp ehensi e sample da abase o
sonically ep esen he ins umen s would augmen he ealism o he simula ion by allowing
imb al a ia ions o be linked o in e ed ep esen a ions o pe o mance.
Towa ds a Theo e ical Model
Adop ing a physical-based app oach p esen s wo le els o concep ual ep esen a ion o he
sys em. The i s ela es o Da id Ma ’s (1982) ep esen a ional le el, whe eby he ela ionships
be ween he samples in a da abase concep ually ep esen an ins umen . The second le el
u he abs ac s pe o mance and p esen s a mo e con ex ual unde s anding o he a iables
a ec ing he ela ionship be ween he samples by in e ing a ela ionship be ween he
ins umen al ep esen a ions hemsel es. This is desc ibed in Figu e 5, a simpli ied diag am
showing he con ex o wo ins umen al ep esen a ions.
Holis ically, he ins umen al ep esen a ions should be pa o a la ge concep ual cons uc
ela ed o pe o mance con ex . Wi h his in mind, a heo e ical model is p esen ed in Figu e 6
ha shows a pe o mance model de i ed om in o ma ion in he sample da a, augmen ed by
ep esen a ions o pe o mance con ex .
Figu e 5. In ains umen al pe o mance con ex . Pulse-code modula ion samples o s ikes on a single
ins umen ep esen only one occu ence o he pe o mance. The e o e, i is necessa y o use he sonic
con en o each sample o p o ide a con ex ual ep esen a ion o he ins umen , by in e ing a ela ionship
be ween he spec al ea u es o each sample.
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