/LMAR=0/XLINE=10/FONT#0=BASL30/FONT#1=BASI30/FONT#9=CLAR30/FONT#10=BASB30/FONT#11=BASI30
␈↓ α∧␈↓␈↓ ε,1␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓ ∧o␈↓	PROPOSED RESEARCH:
␈↓"∧␈↓ α∧␈↓	␈↓ αd␈↓ βXA MODEL FOR TIMBRE PERCEPTION
␈↓"∧␈↓ α∧␈↓	␈↓ αd␈↓ ∧,BASED ON DATA-REDUCTION


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓
A. Introduction

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈α∞issue␈α∞which␈α
we␈α∞plan␈α∞to␈α∞exhaustively␈α
investigate␈α∞in␈α∞our␈α∞furture␈α
research
␈↓ α∧␈↓␈↓ αdprogram␈α⊂is␈α∂that␈α⊂of␈α⊂data␈α∂reduction␈α⊂in␈α⊂the␈α∂physical␈α⊂representation␈α⊂of␈α∂timbre.
␈↓ α∧␈↓␈↓ αdThe␈α
main␈α
thrust␈α
of␈α
data␈α
reduction␈α
research␈α
in␈α
the␈α
past␈α
has␈α
been␈α
to␈α
measure
␈↓ α∧␈↓␈↓ αdthe␈α∪perceptual␈α∪effects␈α∪of␈α∪simplifications␈α∪(or␈α∪modifications)␈α∪of␈α∪the␈α∪physical
␈↓ α∧␈↓␈↓ αdparameters␈αfor␈α
computer-synthetized␈αsignals.␈α
 The␈αadditive␈αsynthesis␈α
technique
␈↓ α∧␈↓␈↓ αdhas␈α↔been␈α↔used␈α↔to␈α↔generate␈α_these␈α↔signals,␈α↔being␈α↔based␈α↔on␈α_the␈α↔physical
␈↓ α∧␈↓␈↓ αdparameters␈α∂derived␈α⊂for␈α∂actual␈α∂musical␈α⊂instrument␈α∂tones␈α∂by␈α⊂heterodyne␈α∂filter
␈↓ α∧␈↓␈↓ αdanalysis.␈α∪ Analyzed␈α∪tones␈α∪have␈α∀been␈α∪represented␈α∪by␈α∪pairs␈α∀of␈α∪time-variant
␈↓ α∧␈↓␈↓ αdamplitude␈α⊗and␈α∃frequency␈α⊗functions␈α∃for␈α⊗each␈α∃harmonic.␈α⊗ The␈α∃subsequent
␈↓ α∧␈↓␈↓ αdsimplifications␈α⊂(or␈α⊂modifications)␈α⊂have␈α⊂been␈α⊂performed␈α⊂on␈α⊂this␈α⊂set␈α⊃of␈α⊂time-
␈↓ α∧␈↓␈↓ αdvariant␈α⊂functions,␈α∂and␈α⊂the␈α∂resulting␈α⊂functions␈α∂have␈α⊂been␈α∂used␈α⊂to␈α∂synthesize
␈↓ α∧␈↓␈↓ αdnew signals.

␈↓"∧␈↓ α∧␈↓␈↓ αdIt␈α
should␈α
be␈α
noted␈αthat␈α
this␈α
research␈α
has␈α
only␈αbeen␈α
possible␈α
through␈α
the␈αuse␈α
of
␈↓ α∧␈↓␈↓ αda␈α␈↓↓digital␈αcomputer␈↓,␈αwhich␈αprovides␈αthe␈αaccuracy␈αand␈αstorage␈αnecessary␈αfor␈αthe
␈↓ α∧␈↓␈↓ αdanalysis␈α∂of␈α∂tones,␈α∞which␈α∂allows␈α∂the␈α∞interactive␈α∂flexibility␈α∂and␈α∂complexity␈α∞for
␈↓ α∧␈↓␈↓ αdthe␈αexperimental␈αmodification␈αalgorithms,␈αand␈αwhich␈αhas␈αthe␈αreplicability␈αand
␈↓ α∧␈↓␈↓ αdcontrol needed for synthesis.

␈↓"∧␈↓ α∧␈↓␈↓ αdIn␈α∪our␈α∀proposed␈α∪research,␈α∀the␈α∪systematic␈α∪approach␈α∀to␈α∪the␈α∀data␈α∪reduction
␈↓ α∧␈↓␈↓ αdprocess␈αwill␈αbe␈αoriented␈αtowards␈αthe␈αmodeling␈αof␈αtimbre␈αperception.␈α The␈αdata
␈↓ α∧␈↓␈↓ αdreduction␈α_technique␈α_provides␈α_the␈α_most␈α_powerful␈α_and␈α_direct␈α_means␈α↔for
␈↓ α∧␈↓␈↓ αduncovering␈α⊃both␈α∩the␈α⊃distinctive␈α∩features␈α⊃in␈α∩timbre␈α⊃identification␈α∩and␈α⊃their
␈↓ α∧␈↓␈↓ αdrelated physical properties.

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈α
perceptual␈α
measurements␈α
employed␈α
to␈α
date␈α
in␈α
conjunction␈α
with␈α
the␈αdata
␈↓ α∧␈↓␈↓ αdreduction␈α~scheme␈α→have␈α~included␈α→␈↓↓discrimination␈↓␈α~and␈α~subjective␈α→␈↓↓distance
␈↓ α∧␈↓↓␈↓ αdestimation␈↓.␈α⊂ Measurements␈α⊃have␈α⊂been␈α⊃made␈α⊂between␈α⊃a␈α⊂number␈α⊃of␈α⊂different
␈↓ α∧␈↓␈↓ αdconditions␈α
of␈α
data␈α
reduction␈αfor␈α
a␈α
number␈α
of␈αtimbres.␈α
 In␈α
future␈α
research␈αwe
␈↓ α∧␈↓␈↓ αdwill␈αalso␈αmeasure␈αthe␈αeffects␈α
of␈αparameter␈αmodifications␈αon␈α␈↓↓identification␈↓.␈α
This
␈↓ α∧␈↓␈↓ αdwill␈α∂point␈α∂more␈α⊂directly␈α∂at␈α∂the␈α⊂types␈α∂of␈α∂cues␈α⊂that␈α∂are␈α∂active␈α⊂in␈α∂perceptually
␈↓ α∧␈↓␈↓ αddetermining␈α
the␈α
source␈α
of␈α
a␈α
tone,␈α
and␈α
will␈α
systematically␈α
lead␈α
to␈α∞a␈α
distinctive
␈↓ α∧␈↓␈↓ αdfeatures model for timbre.
␈↓ α∧␈↓␈↓ ε,2␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdNote␈αthat␈αthe␈αgoal␈αof␈αthis␈αextension␈αof␈αthe␈αdata␈αreduction␈αscheme␈αis␈αto␈αspecify
␈↓ α∧␈↓␈↓ αdsuch␈αcues␈αfor␈αtimbre␈αidentification␈αand/or␈αtonal␈αquality,␈αrather␈αthan␈α
the␈αmore
␈↓ α∧␈↓␈↓ αdlimited␈α∩goal␈α∩pursued␈α∩in␈α∩our␈α∩past␈α⊃research,␈α∩which␈α∩was␈α∩merely␈α∩to␈α∩obtain␈α⊃a
␈↓ α∧␈↓␈↓ αdsimplified␈α
set␈α∞of␈α
tones␈α∞useful␈α
for␈α
other␈α∞types␈α
of␈α∞perceptual␈α
research.␈α∞ We␈α
are
␈↓ α∧␈↓␈↓ αdnow␈α
of␈α
the␈α
opinion␈αthat␈α
the␈α
data␈α
reduction␈αtechnique␈α
itself␈α
is␈α
the␈α
␈↓↓most␈αdirect
␈↓ α∧␈↓↓␈↓ αdmethod␈↓␈α
for␈α
perceptual␈α
modeling.␈α In␈α
view␈α
of␈α
the␈αabove,␈α
the␈α
sense␈α
of␈α
the␈αterm
␈↓ α∧␈↓␈↓ αd␈↓↓data␈α↔reduction␈↓␈α⊗has␈α↔been␈α⊗extended␈α↔from␈α⊗the␈α↔domain␈α⊗of␈α↔pure␈α⊗acoustical
␈↓ α∧␈↓␈↓ αdsimplification␈α⊃to␈α∩the␈α⊃area␈α⊃of␈α∩representational␈α⊃simplification␈α⊃with␈α∩respect␈α⊃to
␈↓ α∧␈↓␈↓ αdperception.  We will discuss this representational scheme below.

␈↓"∧␈↓ α∧␈↓␈↓ αdFinally,␈α⊂it␈α⊂is␈α⊂clear␈α⊂that␈α⊂data␈α⊂reduction␈α⊂will␈α⊂serve␈α⊂not␈α⊂only␈α⊂to␈α⊂point␈α⊂out␈α⊂the
␈↓ α∧␈↓␈↓ αdsalient␈α
qualities␈αof␈α
tones␈α-␈α
in␈αmodeling␈α
timbre␈αperception␈α
-␈αbut␈α
in␈α
the␈αprocess
␈↓ α∧␈↓␈↓ αdof␈αsimplifying␈αthe␈αphysical␈αproperties␈αof␈αsignals␈αwill␈αsimultaneously␈αreduce␈αthe
␈↓ α∧␈↓␈↓ αdcomplexities␈αinvolved␈α
in␈αtimbre␈αresearch␈α
on␈αall␈αfronts.␈α
The␈αsignificance␈αof␈α
this
␈↓ α∧␈↓␈↓ αdline of research cannot be overstated.


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓
B. Data Reduction Modeling as a Function of Perceptual Modeling

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈α∞most␈α
prominent␈α∞direction␈α
in␈α∞our␈α∞future␈α
research␈α∞is␈α
the␈α∞treatment␈α∞of␈α
the
␈↓ α∧␈↓␈↓ αddata␈α∞reduction␈α∞technique␈α∞with␈α∞respect␈α∞to␈α∞a␈α∞model␈α∞for␈α∞timbre␈α∂perception.␈α∞ As
␈↓ α∧␈↓␈↓ αdstated␈α
above,␈αthis␈α
technique␈αwill␈α
be␈α
pursued␈αfor␈α
the␈αpurpose␈α
of␈αuncovering␈α
the
␈↓ α∧␈↓␈↓ αdphysical␈α∂cues␈α⊂in␈α∂timbre␈α⊂identification␈α∂and␈α∂judgments␈α⊂of␈α∂tonal␈α⊂quality.␈α∂ The
␈↓ α∧␈↓␈↓ αdorientation␈α
of␈α
our␈α
research␈αwill␈α
be␈α
to␈α
cast␈α
a␈αdata␈α
reduction␈α
scheme␈α
in␈αthe␈α
terms
␈↓ α∧␈↓␈↓ αdof␈α⊂a␈α⊃model␈α⊂for␈α⊂timbre␈α⊃perception.␈α⊂ Here,␈α⊂instead␈α⊃of␈α⊂merely␈α⊃simplifying␈α⊂the
␈↓ α∧␈↓␈↓ αdshapes␈α"of␈α!time-variant␈α"functions␈α!and␈α"then␈α!checking␈α"the␈α!resulting
␈↓ α∧␈↓␈↓ αddiscriminability␈α⊂of␈α⊂the␈α⊂original␈α⊂tone␈α⊂with␈α⊂the␈α⊂modified␈α⊂signal,␈α⊂we␈α⊃desire␈α⊂to
␈↓ α∧␈↓␈↓ αddecompose␈α
the␈α
original␈α
tone␈α
into␈α
its␈α
perceptual␈α
components.␈α
 This␈α∞entails␈α
not
␈↓ α∧␈↓␈↓ αdonly␈α∀a␈α∀different␈α∀goal␈α∀for␈α∀perceptual␈α∀testing,␈α∀but␈α∀a␈α∀substantially␈α∀different
␈↓ α∧␈↓␈↓ αdapproach␈αin␈αmodeling␈α
data␈αreduction.␈α At␈αthe␈α
outset,␈αhowever,␈αthe␈α
model␈αwill
␈↓ α∧␈↓␈↓ αdbe␈α∞based␈α∞upon␈α
the␈α∞simplified␈α∞line-segment␈α
representation␈α∞of␈α∞the␈α
time-variant
␈↓ α∧␈↓␈↓ αdfunctions␈α
from␈α
our␈α
past␈α
research␈αwhich␈α
itself␈α
suggests␈α
modes␈α
of␈α
higher␈αorder
␈↓ α∧␈↓␈↓ αddata reduction.

␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Minimal Line-Segment Representations of Harmonic Activity␈↓

␈↓"∧␈↓ α∧␈↓␈↓ αdIt␈α∩has␈α∩been␈α∩found␈α⊃that␈α∩the␈α∩harmonic␈α∩activity␈α⊃of␈α∩tones␈α∩can␈α∩be␈α⊃adequately
␈↓ α∧␈↓␈↓ αdrepresented␈α
by␈α
minimal␈α
line-segment␈α
fits␈α
to␈α
the␈α
complex␈α
time-variant␈α
functions.
␈↓ α∧␈↓␈↓ αdUp␈α~until␈α~now,␈α≠these␈α~fittings␈α~have␈α≠been␈α~empirically␈α~specified␈α≠by␈α~the
␈↓ α∧␈↓␈↓ αdexperimenter.␈α⊂ A␈α⊂major␈α⊂thrust␈α⊂of␈α⊂our␈α⊂future␈α⊂research␈α⊂will␈α⊂be␈α⊂to␈α⊃design␈α⊂an
␈↓ α∧␈↓␈↓ αdimproved␈αalgorithm␈αfor␈αautomatic␈αminimal␈αline-segment␈αfitting.␈α
 As␈αdescribed
␈↓ α∧␈↓␈↓ ε,3␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdbelow,␈α⊃this␈α⊃will␈α⊃entail␈α∩the␈α⊃systematic␈α⊃decomposing␈α⊃of␈α⊃the␈α∩complex␈α⊃physical
␈↓ α∧␈↓␈↓ αdactivity␈α⊂of␈α⊂signals␈α⊂rather␈α⊂than␈α⊂trying␈α⊂to␈α⊂simplify␈α⊂all␈α⊂activity␈α⊂with␈α⊂the␈α⊂same
␈↓ α∧␈↓␈↓ αdalgorithm␈αas␈αdone␈αin␈αthe␈αpast.␈α An␈αadvantage␈αto␈αthis␈αapproach,␈αof␈αcourse,␈αwill
␈↓ α∧␈↓␈↓ αdbe␈α⊃the␈α⊃greater␈α⊂uniformity␈α⊃in␈α⊃minimal␈α⊂line-segment␈α⊃representations,␈α⊃and␈α⊂the
␈↓ α∧␈↓␈↓ αdincreased precision at specifying the nature of the data reduction.

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈α⊃minimal␈α⊂representation␈α⊃of␈α⊃the␈α⊂harmonic␈α⊃activity␈α⊃of␈α⊂the␈α⊃signal␈α⊃will␈α⊂be
␈↓ α∧␈↓␈↓ αdfurther␈αdecomposed␈αinto␈αperceptually␈αsalient␈αelements.␈α The␈αfreqeuncy␈αdomain
␈↓ α∧␈↓␈↓ αdwill␈αbe␈αinvestigated␈αas␈αa␈αproduct␈αof␈αa␈αfixed␈αharmonic␈αseries␈αwith␈αvarious␈αlow-
␈↓ α∧␈↓␈↓ αdfrequency␈α
modulations␈αin␈α
pitch,␈αsuch␈α
as␈α
vibrato␈αor␈α
the␈αalterations␈α
in␈α
pitch␈αat
␈↓ α∧␈↓␈↓ αdthe␈α∂boundaries␈α∂of␈α∂a␈α∂note.␈α⊂ The␈α∂simplification␈α∂hoped␈α∂for␈α∂is␈α∂to␈α⊂represent␈α∂the
␈↓ α∧␈↓␈↓ αdcomplex␈α∩frequency␈α⊃behavior␈α∩of␈α⊃the␈α∩harmonics␈α⊃by␈α∩a␈α⊃single␈α∩function␈α∩or␈α⊃by
␈↓ α∧␈↓␈↓ αdseveral functions which control subsets of harmonics as groups.

␈↓"∧␈↓ α∧␈↓␈↓ αdIn␈α
the␈α∞amplitude␈α
domain␈α
we␈α∞will␈α
also␈α
investigate␈α∞the␈α
perceptual␈α∞correlates␈α
to
␈↓ α∧␈↓␈↓ αdslower␈α∂modulations␈α∂found␈α∂in␈α∂many␈α∂signals.␈α∂ In␈α∂addition,␈α∂an␈α∂attempt␈α⊂will␈α∂be
␈↓ α∧␈↓␈↓ αdmade␈α∩to␈α∩simplify␈α∩the␈α∩spectral␈α∩representation␈α∩of␈α∩a␈α∩signal␈α∩by␈α∪exploring␈α∩the
␈↓ α∧␈↓␈↓ αdsalience␈α⊃of␈α⊂the␈α⊃amplitude␈α⊃functions␈α⊂for␈α⊃different␈α⊃harmonics␈α⊂of␈α⊃tones.␈α⊃ It␈α⊂is
␈↓ α∧␈↓␈↓ αdexpected␈α⊂that,␈α∂because␈α⊂of␈α∂their␈α⊂relative␈α∂unanalyzeability␈α⊂(as␈α∂shown␈α⊂in␈α∂other
␈↓ α∧␈↓␈↓ αdpsychoacoustical␈α∀research),␈α∀the␈α∀activities␈α∀of␈α∀the␈α∀higher␈α∀harmonics␈α∀will␈α∀be
␈↓ α∧␈↓␈↓ αdsubject␈αto␈αgroup␈αrepresentations,␈αleading␈α
to␈αsimplified␈αmodeling␈αin␈αthe␈α
spectral
␈↓ α∧␈↓␈↓ αddomain.␈α The␈αeffects␈αof␈αcritical␈αbandwidths␈αin␈αhearing␈αwould␈αstrongly␈αsuggest
␈↓ α∧␈↓␈↓ αdthat␈α∩individual␈α∩higher␈α∩harmonics␈α∩may␈α∪not␈α∩have␈α∩to␈α∩be␈α∩specified␈α∪with␈α∩the
␈↓ α∧␈↓␈↓ αddegree␈αof␈α
accuracy␈αused␈αto␈α
date.␈α Other␈αsimplifications␈α
may␈αbe␈α
achieved␈αwith
␈↓ α∧␈↓␈↓ αdrespect␈α
to␈α
the␈α
masking␈α
patterns␈α
of␈α
the␈α
harmonics.␈α
 Significant␈α∞data␈α
reduction
␈↓ α∧␈↓␈↓ αdmay␈α⊃be␈α⊃possible,␈α⊃then,␈α⊃basing␈α⊃synthesis␈α⊃upon␈α⊃simplified␈α⊃models␈α⊃of␈α⊂spectral
␈↓ α∧␈↓␈↓ αdevolution␈α~which␈α~approximate␈α→the␈α~actual␈α~physics␈α→of␈α~tones,␈α~and␈α→which
␈↓ α∧␈↓␈↓ αdapproximations would be evaluated through perceptual experimentation.

␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Inharmonicity and Colored Noise␈↓

␈↓"∧␈↓ α∧␈↓␈↓ αdImportant␈α⊃perceptual␈α⊃features␈α⊂discovered␈α⊃through␈α⊃the␈α⊃minimal␈α⊂line-segment
␈↓ α∧␈↓␈↓ αdrepresentations␈α⊃reside␈α∩in␈α⊃the␈α⊃attack␈α∩segments␈α⊃of␈α⊃signals.␈α∩ It␈α⊃is␈α∩therefore␈α⊃of
␈↓ α∧␈↓␈↓ αdinterest␈α∂that␈α⊂this␈α∂complex␈α∂activity␈α⊂be␈α∂directly␈α∂included␈α⊂in␈α∂the␈α∂␈↓↓model␈↓␈α⊂for␈α∂the
␈↓ α∧␈↓␈↓ αdreduction.␈α⊗ The␈α⊗reduction␈α⊗involved␈α↔is␈α⊗one␈α⊗of␈α⊗simplifying␈α⊗the␈α↔␈↓↓means␈α⊗of
␈↓ α∧␈↓↓␈↓ αdrepresenting␈↓␈αthis␈α
complex␈αphysical␈α
activity␈αwhich␈α
is␈αproven␈α
to␈αhave␈α
perceptual
␈↓ α∧␈↓␈↓ αdsignificance.

␈↓"∧␈↓ α∧␈↓␈↓ αdSuch␈α_activity␈α_is␈α_the␈α_inharmonicity␈α_or␈α_colored␈α_noise␈α_in␈α_the␈α_attacks␈α↔of
␈↓ α∧␈↓␈↓ αdinstruments␈αwhich␈αhas␈αbeen␈αshown␈αto␈αeffect␈αthe␈αperceived␈αquality␈αof␈αthe␈αtone,
␈↓ α∧␈↓␈↓ αdthe␈αperceived␈αstyle␈αof␈αplaying,␈αand␈αin␈αsome␈αcases,␈αeven␈αthe␈αbasic␈αidentification
␈↓ α∧␈↓␈↓ ε,4␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdof␈αthe␈αsource.␈α This␈αactivity␈αwill␈αbe␈αsubject␈αto␈αsimplified␈αrepresentations,␈αsuch
␈↓ α∧␈↓␈↓ αdas␈α
frequency␈α
or␈α
amplitude␈α
modulation,␈α
which␈α
can␈α
be␈α
systematically␈αcontroled.
␈↓ α∧␈↓␈↓ αdThe␈α
model␈α
for␈α
a␈α
tone,␈α
then,␈α
will␈α
include␈α
not␈α
only␈α
the␈α
minimal␈αrepresentation
␈↓ α∧␈↓␈↓ αdof␈α⊗harmonic␈α⊗activity,␈α⊗in␈α⊗a␈α⊗form␈α⊗discussed␈α⊗above,␈α⊗but␈α⊗also␈α⊗will␈α∃include
␈↓ α∧␈↓␈↓ αdcomponents of inharmonicity or noise.

␈↓"∧␈↓ α∧␈↓␈↓ αdTo␈α⊂sum␈α⊃up,␈α⊂the␈α⊂basic␈α⊃goal␈α⊂of␈α⊂data␈α⊃reduction␈α⊂modeling␈α⊃␈↓↓vis-a-vis␈↓␈α⊂perceptual
␈↓ α∧␈↓␈↓ αdmodeling␈α⊂is␈α⊃to␈α⊂decompose␈α⊃a␈α⊂timbre␈α⊃into␈α⊂basic␈α⊃features.␈α⊂ The␈α⊃simulation␈α⊂of
␈↓ α∧␈↓␈↓ αdsignals␈α⊃will␈α⊂be␈α⊃accomplished␈α⊃by␈α⊂means␈α⊃of␈α⊃additive␈α⊂synthesis␈α⊃based␈α⊃on␈α⊂this
␈↓ α∧␈↓␈↓ αdrepresentational␈αmodel.␈α The␈αprocess␈α
of␈αdata␈αreduction␈αwill␈αbe␈α
representational
␈↓ α∧␈↓␈↓ αdrather␈αthan,␈αas␈αin␈α
past␈αwork,␈αstrictly␈αacoustical.␈α
 Therefore,␈αthe␈αprocess␈αwill␈α
not
␈↓ α∧␈↓␈↓ αdresult␈α
in␈α
a␈αsimple␈α
succession␈α
of␈αattempts␈α
to␈α
simulate␈αthe␈α
original␈α
tone␈αwith␈α
ever
␈↓ α∧␈↓␈↓ αdgreater␈α
economy,␈α
which␈α
is␈α
the␈α∞limit␈α
of␈α
acoustical␈α
data␈α
reduction.␈α∞ Rather,␈α
the
␈↓ α∧␈↓␈↓ αdlimit␈α∂of␈α∂the␈α∂technique␈α∂will␈α∂be␈α∂in␈α∂the␈α∂decomposition␈α∂of␈α∂the␈α∂signal␈α∂into␈α∞basic
␈↓ α∧␈↓␈↓ αdperceptual␈α∪components␈α∪and␈α∪further␈α∪simplification␈α∪of␈α∪the␈α∪representation␈α∩of
␈↓ α∧␈↓␈↓ αdthese␈α∞components.␈α∞ ???????????␈α∞ The␈α∞result␈α∞will␈α∞be␈α∞a␈α∞parallel␈α∞model␈α∞for␈α
timbre
␈↓ α∧␈↓␈↓ αdperception.  ?????????????????


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓
C. Increasing the Data Base for the Perceptual Model

␈↓"∧␈↓ α∧␈↓
␈↓ αd␈↓An Extension of the Timbral Range and Cues for Identification

␈↓"∧␈↓ α∧␈↓␈↓ αdOne␈α⊂of␈α⊂the␈α⊂most␈α∂significant␈α⊂extensions␈α⊂of␈α⊂our␈α∂data␈α⊂reduction␈α⊂research␈α⊂-␈α∂in
␈↓ α∧␈↓␈↓ αdgetting␈α
at␈α
the␈α
cues␈α
in␈α
timbre␈αperception␈α
-␈α
will␈α
be␈α
to␈α
investigate␈α
a␈αbroader␈α
range
␈↓ α∧␈↓␈↓ αdof␈α
timbres.␈α
 The␈αextension␈α
of␈α
the␈α
timbre␈αdomain␈α
includes␈α
both␈α
a␈αlarger␈α
variety
␈↓ α∧␈↓␈↓ αdof␈αplaying␈αtechniques␈αfor␈αinitiating␈αtones␈αand␈αa␈αwider␈αrange␈αof␈αpitches␈αplayed
␈↓ α∧␈↓␈↓ αdby instruments.

␈↓"∧␈↓ α∧␈↓␈↓ αdIn␈αthis␈αbroadening␈αof␈αthe␈αdata␈αbase␈αfor␈αtimbres␈αunder␈αstudy,␈αour␈αresearch␈αwill
␈↓ α∧␈↓␈↓ αdaim␈α
to␈α
uncover␈α
the␈α␈↓↓invariant␈α
features␈↓,␈α
where␈α
they␈αexist,␈α
across␈α
a␈α
range␈αof␈α
notes
␈↓ α∧␈↓␈↓ αdidentified␈α∂as␈α∂originating␈α∂from␈α∂the␈α⊂same␈α∂source.␈α∂ This␈α∂will␈α∂be␈α∂critical␈α⊂in␈α∂the
␈↓ α∧␈↓␈↓ αdattempt␈α∞to␈α∞pinpoint␈α∂the␈α∞cues␈α∞for␈α∂timbre␈α∞␈↓↓identification␈↓.␈α∞ The␈α∂main␈α∞perceptual
␈↓ α∧␈↓␈↓ αdmeasurement␈αhere␈αwill␈αbe␈αthat␈αof␈αidentification␈αof␈αsignals␈αhaving␈α
various␈αsets
␈↓ α∧␈↓␈↓ αdof physical factors.


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Timbre Perception in Non-Isolated Tonal Contexts

␈↓"∧␈↓ α∧␈↓␈↓ αdJust␈αas␈αit␈αwas␈αnecessary␈αin␈αour␈αpast␈αresearch␈αto␈αmove␈αfrom␈αan␈αinvestigation␈αof
␈↓ α∧␈↓␈↓ αdsteady-state␈α∞tones␈α∞to␈α∞one␈α∂of␈α∞time-variant␈α∞musical␈α∞tones,␈α∂so␈α∞it␈α∞is␈α∞clear␈α∂that␈α∞we
␈↓ α∧␈↓␈↓ ε,5␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdnow␈α∞must␈α
move␈α∞toward␈α
an␈α∞examination␈α
of␈α∞timbre␈α
perception␈α∞in␈α
non-isolated
␈↓ α∧␈↓␈↓ αdtonal␈αcontexts.␈αA␈αmajor␈αconcern␈αin␈α
timbre␈αperception␈αresearch␈α-␈αwhich␈αhas␈α
not
␈↓ α∧␈↓␈↓ αdbeen␈α
met␈α∞to␈α
date␈α∞-␈α
is␈α∞that␈α
empirical␈α∞information␈α
derived␈α∞from␈α
studies␈α∞of␈α
the
␈↓ α∧␈↓␈↓ αdperception␈αof␈αisolated␈αtones␈αmay␈αnot␈αbe␈αrepresentative␈αof␈αmore␈αtypical␈αmusical
␈↓ α∧␈↓␈↓ αdperception.

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈α≠great␈α≠difficulty␈α≤found␈α≠with␈α≠several␈α≠musically-trained␈α≤listeners␈α≠in
␈↓ α∧␈↓␈↓ αdidentifying␈α⊃the␈α⊂sources␈α⊃of␈α⊃isolated␈α⊂instrumental␈α⊃tones␈α⊂testifies␈α⊃to␈α⊃the␈α⊂rather
␈↓ α∧␈↓␈↓ αdlimited␈α∞nature␈α∞of␈α
past␈α∞research.␈α∞It␈α
is␈α∞certain␈α∞that␈α
other␈α∞dimensions␈α∞of␈α
timbre
␈↓ α∧␈↓␈↓ αdperception␈α
come␈αinto␈α
play␈α
when␈αlistening␈α
to␈α
a␈αcontextual␈α
passage␈α
of␈αmusic.␈α
Not
␈↓ α∧␈↓␈↓ αdonly␈α∂do␈α⊂specific␈α∂idiomatic␈α⊂traits␈α∂of␈α⊂instruments␈α∂occur,␈α⊂but␈α∂more␈α⊂global␈α∂data
␈↓ α∧␈↓␈↓ αdbases for perception are presented.

␈↓"∧␈↓ α∧␈↓␈↓ αdOne␈α∃such␈α∃data␈α∃base␈α∃which␈α∃is␈α∃opened␈α∃to␈α∃the␈α∃listener␈α∃is␈α∃the␈α⊗pattern␈α∃of
␈↓ α∧␈↓␈↓ αdresonances␈αtraced␈α
as␈αthe␈α
instrument␈αis␈αplayed␈α
through␈αa␈α
register.␈αThis␈α
sort␈αof
␈↓ α∧␈↓␈↓ αdinformation␈αmust␈αbe␈αsignificant␈α
in␈αnormal␈αlistening␈αsituations.␈α
 The␈αincreased
␈↓ α∧␈↓␈↓ αddata␈α
base␈α
proposed␈α∞above␈α
with␈α
the␈α
extension␈α∞of␈α
the␈α
range␈α
of␈α∞timbre␈α
studied
␈↓ α∧␈↓␈↓ αdmust␈αbe␈αaccompanied␈αby␈αa␈αconcurrent␈αmove␈αtowards␈αthe␈αpresentation␈αof␈αtones
␈↓ α∧␈↓␈↓ αdin (at least) minimal musical contexts.

␈↓"∧␈↓ α∧␈↓␈↓ αdThrough␈α
the␈α
evaluation␈α
of␈αtimbre␈α
in␈α
a␈α
minimal␈αcontext,␈α
we␈α
may␈α
explore␈αnot
␈↓ α∧␈↓␈↓ αdonly␈α
the␈α
invariant␈α
cues␈α
involved␈α
with␈α
␈↓↓identification␈↓,␈α
but␈α
we␈α
may␈α
also␈α
look␈α
at
␈↓ α∧␈↓␈↓ αdthe␈αeffects␈αof␈αcontext␈αon␈αthe␈α
salience␈αof␈αfeatures␈αas␈αmeasured␈αby␈α
␈↓↓discrimination␈↓
␈↓ α∧␈↓␈↓ αdand␈α∪␈↓↓subjective␈α∪distance-estimation␈↓.␈α∩ Here,␈α∪the␈α∪effects␈α∩of␈α∪musical␈α∪context␈α∩on
␈↓ α∧␈↓␈↓ αdattention to timbral details will be investigated.

␈↓"∧␈↓ α∧␈↓␈↓ αdAs␈αthe␈αmusical␈αcontexts␈αbecome␈αless␈α
minimal␈α(i.e.␈αmore␈αcomplex),␈αtools␈αmust␈α
be
␈↓ α∧␈↓␈↓ αddeveloped␈α
for␈α
the␈α
simulation␈α∞of␈α
articulations␈α
and␈α
patterns␈α
of␈α∞phrasing.␈α
 New
␈↓ α∧␈↓␈↓ αdanalysis␈α
schemes␈α
are␈α
discussed␈α
below␈α
which␈α
may␈α
meet␈α
these␈α
needs.␈α
 This␈αwill
␈↓ α∧␈↓␈↓ αdbe␈α↔a␈α⊗growing␈α↔interest␈α⊗in␈α↔our␈α⊗research␈α↔program.␈α⊗ The␈α↔ability␈α↔to␈α⊗detect
␈↓ α∧␈↓␈↓ αddifferences␈α
in␈α
musical␈α
contexts␈α
ultimately␈αwill␈α
be␈α
a␈α
more␈α
meaningful␈αmeasure
␈↓ α∧␈↓␈↓ αdthan discrimination studies on isolated tones.


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓
D. The Development of Analytic Tools for Future Research

␈↓"∧␈↓ α∧␈↓
␈↓ αd␈↓The Use of New Analysis-Synthesis and Data Display Techniques

␈↓"∧␈↓ α∧␈↓␈↓ αdAn␈α_effort␈α↔to␈α_explore␈α↔the␈α_usefulness␈α↔of␈α_new␈α↔types␈α_of␈α↔analysis-synthesis
␈↓ α∧␈↓␈↓ αdtechniques␈αand␈α
related␈αgraphical␈αdisplays␈α
of␈αphysical␈α
information␈αwill␈αoccur␈α
in
␈↓ α∧␈↓␈↓ αda␈αlater␈αpart␈αof␈αour␈αresearch␈αprogram,␈αgrowing␈αout␈αof␈αvarious␈α
needs␈αexpressed
␈↓ α∧␈↓␈↓ ε,6␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdabove.␈α∀ One␈α∀scheme␈α∀which␈α∀may␈α∀be␈α∀of␈α∀future␈α∀use␈α∀is␈α∀that␈α∀of␈α∪subtractive
␈↓ α∧␈↓␈↓ αdsynthesis␈αbased␈αupon␈αan␈αanalysis␈αfor␈αthe␈αtonal␈αproperties␈αof␈αspectral␈αevolution.
␈↓ α∧␈↓␈↓ αdThis␈αapproach␈α
has␈αbeen␈αused␈α
with␈αgreat␈α
success␈αin␈αthe␈α
field␈αof␈αspeech␈α
analysis
␈↓ α∧␈↓␈↓ αdand␈α
synthesis,␈αand␈α
could␈αlead␈α
to␈α
new␈αinsights␈α
if␈αsuccessful␈α
with␈αmusical␈α
timbre.
␈↓ α∧␈↓␈↓ αdDisplays␈αof␈αinformation␈αwould␈α
be␈αoriented␈αtowards␈αthe␈α
time-variant␈αbehavior
␈↓ α∧␈↓␈↓ αdof␈α∂spectral␈α∞energy␈α∂distribution,␈α∂and␈α∞a␈α∂perspective␈α∞plot␈α∂of␈α∂time-slices␈α∞through
␈↓ α∧␈↓␈↓ αdformant␈αactivities␈αmay␈α
be␈αmost␈αinformative.␈α
In␈αsynthesis,␈αdata␈αreduction␈α
would
␈↓ α∧␈↓␈↓ αdoccur␈αin␈αthat␈αsmall␈αnumbers␈αof␈αtime-variant␈αfilters␈αmay␈αbe␈αadequate␈α
to␈αmodel
␈↓ α∧␈↓␈↓ αdthe perceptually salient aspects of tone.

␈↓"∧␈↓ α∧␈↓␈↓ αdThis␈α∂approach␈α∂may␈α∂broaden␈α∂the␈α∂domain␈α∂of␈α∂timbres␈α∂which␈α∂may␈α∂be␈α∂studied.
␈↓ α∧␈↓␈↓ αdRecall␈α∪that␈α∪the␈α∪analysis-based␈α∪additive␈α∪synthesis␈α∪technique␈α∪has␈α∪only␈α∪been
␈↓ α∧␈↓␈↓ αdapplicable␈α∞to␈α
tones␈α∞with␈α∞␈↓↓harmonic␈↓␈α
overtone␈α∞structures,␈α∞that␈α
is,␈α∞to␈α∞tones␈α
whose
␈↓ α∧␈↓␈↓ αdpartials␈α∞are␈α∞at␈α∞approximately␈α∞integer␈α∞multiples␈α∞in␈α∞the␈α∞frequency␈α∞domain.␈α
An
␈↓ α∧␈↓␈↓ αdimportant␈α∂step␈α⊂for␈α∂the␈α∂additive␈α⊂synthesis␈α∂approach␈α∂will␈α⊂be␈α∂to␈α∂seek␈α⊂out␈α∂new
␈↓ α∧␈↓␈↓ αdforms␈αof␈α
analysis␈αthat␈α
are␈αcapable␈α
of␈αdealing␈α
with␈αstrongly␈αinharmonic␈α
spectra.
␈↓ α∧␈↓␈↓ αdCurrent␈αplans␈αare␈αbeing␈αformulated␈αto␈αextend␈αthe␈αuse␈αof␈αdigital␈αfilters␈αfor␈αthe
␈↓ α∧␈↓␈↓ αdanalysis␈α∪of␈α∪inharmonic␈α∪spectra.␈α∪This␈α∩will␈α∪increase␈α∪the␈α∪domain␈α∪of␈α∩timbres
␈↓ α∧␈↓␈↓ αdcapable␈α⊂of␈α⊂exploration␈α⊂to␈α⊃include␈α⊂many␈α⊂other␈α⊂important␈α⊂subsets␈α⊃of␈α⊂musical
␈↓ α∧␈↓␈↓ αdsounds, thus leading to a more general model for timbre perception.


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Analysis and Synthesis of Melodic Contexts

␈↓"∧␈↓ α∧␈↓␈↓ αdAn␈αimportant␈αstep␈αwhich␈αmust␈αbe␈αtaken␈αin␈αmethodological␈αdevelopment␈αis␈αthe
␈↓ α∧␈↓␈↓ αdanalysis␈α⊗and␈α↔synthesis␈α⊗of␈α⊗connected␈α↔notes.␈α⊗This␈α⊗necessarily␈α↔will␈α⊗precede
␈↓ α∧␈↓␈↓ αdcarefully␈α∩controlled␈α∩work␈α∩on␈α∩the␈α∩perception␈α∩of␈α∩timbre␈α∩in␈α∩complex␈α∩musical
␈↓ α∧␈↓␈↓ αdcontexts.␈αRecall␈αthat␈αthe␈αanalysis␈αtechniques␈αemployed␈αto␈αdate␈αfor␈αtimbre␈αhave
␈↓ α∧␈↓␈↓ αdbeen␈α∂inherently␈α∂designed␈α∂for␈α∂and␈α∂applied␈α∂to␈α∂isolated␈α∂notes.␈α∂There␈α⊂exists␈α∂no
␈↓ α∧␈↓␈↓ αdanalytic scheme which is directly applicable to musical phrases.

␈↓"∧␈↓ α∧␈↓␈↓ αdSince␈α∃there␈α⊗are␈α∃no␈α∃analytic␈α⊗techniques␈α∃for␈α∃directly␈α⊗analysing␈α∃continuous
␈↓ α∧␈↓␈↓ αdwaveforms␈α
over␈α
articulation␈α
boundaries␈α
as␈α
exist␈α
for␈α
separated,␈α
stationary␈α
notes,
␈↓ α∧␈↓␈↓ αdwe␈α∃must␈α⊗approach␈α∃the␈α⊗problem␈α∃in␈α∃a␈α⊗somewhat␈α∃circuitous␈α⊗manner.␈α∃The
␈↓ α∧␈↓␈↓ αdheterodyne␈α∂filter␈α∂is␈α∂capable␈α∂of␈α∂tracking␈α∂strong␈α∂transients␈α∂if␈α∂the␈α∂frequency␈α∂is
␈↓ α∧␈↓␈↓ αdheld␈αnearly␈αconstant,␈αso␈αthat␈αmany␈αdifferent␈αinstruments␈αand␈αarticulations␈αmay
␈↓ α∧␈↓␈↓ αdbe␈α↔analysed␈α_just␈α↔by␈α_having␈α↔the␈α_player␈α↔hold␈α_the␈α↔pitch␈α_constant␈α↔while
␈↓ α∧␈↓␈↓ αdarticulating.␈α∂To␈α∂extend␈α∞this␈α∂to␈α∂articulation␈α∞at␈α∂different␈α∂frequencies,␈α∂we␈α∞must
␈↓ α∧␈↓␈↓ αdknow the following information about the behavior at the transition.
␈↓ α∧␈↓␈↓ ε,7␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdIs␈α
there␈α
a␈α
discontinuity␈α
at␈α∞the␈α
articulation␈α
point?␈α
If␈α
there␈α
is␈α∞no␈α
discontinuity,
␈↓ α∧␈↓␈↓ αdthen␈α⊂the␈α⊂frequency␈α⊂must␈α⊂change␈α∂smoothly␈α⊂between␈α⊂notes.␈α⊂ We␈α⊂may␈α⊂use␈α∂the
␈↓ α∧␈↓␈↓ αdlinear␈α
predictor␈α
to␈α
determine␈α
the␈α
spectral␈α
envelope␈α
during␈α
the␈α
transition␈α
period
␈↓ α∧␈↓␈↓ αdand␈αa␈αpitch␈αdetector␈αto␈αdetermine␈αthe␈αperiod␈αat␈αeach␈αpoint␈αin␈αtime.␈αThis␈αdoes
␈↓ α∧␈↓␈↓ αdnot␈α
give␈α∞us␈α
the␈α
inharmonicity␈α∞of␈α
the␈α
signal,␈α∞if␈α
there␈α
is␈α∞any.␈α
We␈α
will␈α∞have␈α
to
␈↓ α∧␈↓␈↓ αdgeneralize␈α∞on␈α∞the␈α∞basis␈α∞of␈α∞what␈α∞we␈α∞know␈α∞about␈α∞the␈α∞tones␈α∞when␈α∞the␈α∂pitch␈α∞is
␈↓ α∧␈↓␈↓ αdheld␈αconstant.␈α
If␈αthe␈α
instrument␈αis␈α
slightly␈αinharmonic,␈α
we␈αmust␈α
preserve␈αthat
␈↓ α∧␈↓␈↓ αdinharmonicity while the frequency is changing.

␈↓"∧␈↓ α∧␈↓␈↓ αdIf␈α∩there␈α∪is␈α∩a␈α∩discontinuity␈α∪at␈α∩the␈α∩articulation␈α∪point,␈α∩we␈α∩may␈α∪consider␈α∩the
␈↓ α∧␈↓␈↓ αdcomplex␈α⊗as␈α⊗two␈α⊗separate␈α⊗tones␈α∃and␈α⊗perform␈α⊗the␈α⊗analysis␈α⊗on␈α⊗each␈α∃tone
␈↓ α∧␈↓␈↓ αdindividually.␈αThis␈αrequires␈αthat␈αwe␈αdetermine␈αthe␈αposition␈αof␈αthe␈αdiscontinuity
␈↓ α∧␈↓␈↓ αdand␈αseparate␈αthe␈αnotes␈αby␈αhand.␈αWe␈αmay␈αdiscover␈αthe␈αdiscontinuity␈αand␈αlocate
␈↓ α∧␈↓␈↓ αdits␈α⊂position␈α⊃by␈α⊂examining␈α⊃the␈α⊂derivative␈α⊃of␈α⊂the␈α⊃sound␈α⊂waveform.␈α⊃We␈α⊂may
␈↓ α∧␈↓␈↓ αdobtain␈α∞the␈α∞derivative␈α∞of␈α∞the␈α∞sound␈α∞waveform␈α∞by␈α∞passing␈α∞it␈α∞through␈α∞a␈α∞wide-
␈↓ α∧␈↓␈↓ αdband digital differentiator.

␈↓"∧␈↓ α∧␈↓␈↓ αdDoes␈α∞the␈α∞amplitude␈α
go␈α∞to␈α∞zero,␈α∞or␈α
nearly␈α∞zero␈α∞at␈α
the␈α∞articulation␈α∞point?␈α∞If␈α
it
␈↓ α∧␈↓␈↓ αddoes,␈α⊃then␈α⊃we␈α⊃may␈α⊃separate␈α⊃the␈α⊃notes␈α⊃into␈α⊃isolated␈α⊃tones␈α⊃and␈α⊃perform␈α⊂the
␈↓ α∧␈↓␈↓ αdanalysis␈α_separately.␈α↔ If␈α_it␈α_does␈α↔not␈α_go␈α↔to␈α_zero,␈α_and␈α↔does␈α_not␈α_have␈α↔a
␈↓ α∧␈↓␈↓ αddiscontinuity,␈α⊂then␈α⊃we␈α⊂must␈α⊃analyse␈α⊂for␈α⊃spectral␈α⊂envelope␈α⊃and␈α⊂fundamental
␈↓ α∧␈↓␈↓ αdfrequency, as described above.

␈↓"∧␈↓ α∧␈↓␈↓ αdAlthough␈α∞it␈α∞may␈α∂turn␈α∞out␈α∞that␈α∂there␈α∞are␈α∞some␈α∂kinds␈α∞of␈α∞articulation␈α∂that␈α∞we
␈↓ α∧␈↓␈↓ αdcannot␈α_synthesize␈α_because␈α_of␈α_inadequate␈α_analysis␈α_techniques,␈α_there␈α_will
␈↓ α∧␈↓␈↓ αdcertainly␈αbe␈αa␈αgreat␈αvariety␈αof␈αarticulation␈αtypes␈αthat␈αare␈αamenable␈αto␈αanalysis.
␈↓ α∧␈↓␈↓ αdWe␈α⊃expect␈α⊃that␈α∩most␈α⊃tongued␈α⊃wind␈α∩instruments␈α⊃will␈α⊃accept␈α∩analysis␈α⊃easily.
␈↓ α∧␈↓␈↓ αdStrings␈α∞when␈α∞the␈α∞direction␈α∞of␈α∞bowing␈α∞is␈α∞reversed,␈α∞or␈α∞when␈α∞the␈α∞bow␈α∞is␈α∞lifted
␈↓ α∧␈↓␈↓ αdfrom␈α
the␈α
string␈α
should␈α
be␈α
analyzable.␈α∞The␈α
only␈α
case␈α
that␈α
will␈α
not␈α∞be␈α
directly
␈↓ α∧␈↓␈↓ αdanalyzable␈α~will␈α~be␈α~␈↓↓legato␈↓␈α~tones,␈α~where␈α~the␈α~pitch␈α~is␈α≠changed␈α~without
␈↓ α∧␈↓␈↓ αdarticulation.

␈↓"∧␈↓ α∧␈↓␈↓ αdIt␈αremains␈αpossible␈αthat␈αmany␈αof␈αthe␈αproperties␈αnecessary␈αfor␈αthe␈α␈↓↓simulation␈↓␈αof
␈↓ α∧␈↓␈↓ αdconnected␈αpassages␈αwill␈αbe␈αamenable␈αto␈αsimplification.␈αThis␈αwill␈αgreatly␈αreduce
␈↓ α∧␈↓␈↓ αdthe␈αprocess␈α
of␈αstimulus␈αspecification␈α
in␈αthe␈αphysical␈α
domain,␈αand␈α
lend␈αgreater
␈↓ α∧␈↓␈↓ αdcontrol␈αto␈αthe␈αsynthesis␈αmethod.␈αFurthermore,␈αit␈αmay␈αturn␈αout␈αthat␈α
empirically-
␈↓ α∧␈↓␈↓ αdbased␈α∂studies␈α∞on␈α∂the␈α∂perceptual␈α∞simulation␈α∂of␈α∂connected␈α∞phrases␈α∂will␈α∂be␈α∞the
␈↓ α∧␈↓␈↓ αdmajor approach to this whole issue.


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓
E. Perceptual Measurement Techniques
␈↓ α∧␈↓␈↓ ε,8␈↓ 
d

␈↓"∧␈↓ α∧␈↓
␈↓ αd␈↓Discrimination and Subjective Distance Estimation

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈α⊃measurement␈α⊃of␈α⊂perceptual␈α⊃discrimination␈α⊃will␈α⊂be␈α⊃used␈α⊃in␈α⊃attempts␈α⊂to
␈↓ α∧␈↓␈↓ αdevaluate␈α∂the␈α∂fidelity␈α∂of␈α∂data␈α∞reduction␈α∂models␈α∂with␈α∂respect␈α∂to␈α∂original␈α∞tones
␈↓ α∧␈↓␈↓ αdand/or␈α
other␈α
models␈α
for␈α
simulation.␈α
 It␈αmay␈α
at␈α
times␈α
be␈α
combined␈α
in␈αa␈α
multiple
␈↓ α∧␈↓␈↓ αdtask␈α∞with␈α∂subjective␈α∞distance␈α∂estimation.␈α∞ Both␈α∂measurements␈α∞will␈α∂follow␈α∞the
␈↓ α∧␈↓␈↓ αdparadigm␈α∂described␈α∂for␈α∂our␈α∂previous␈α∂research␈α∂(pp␈α∂37-39␈α∂of␈α∂the␈α⊂NSF␈α∂Grant
␈↓ α∧␈↓␈↓ αdProposal).

␈↓"∧␈↓ α∧␈↓␈↓ αdTo␈α_many␈α↔investigators,␈α_the␈α_multiple␈α↔task␈α_appears␈α_at␈α↔first␈α_sight␈α_to␈α↔be
␈↓ α∧␈↓␈↓ αdunnecessarily␈α⊂difficult.␈α⊂ However,␈α⊂with␈α⊂just␈α⊂a␈α⊂little␈α⊂practice,␈α⊂we␈α⊂have␈α∂found
␈↓ α∧␈↓␈↓ αdthat␈α⊗listeners␈α⊗are␈α⊗able␈α⊗to␈α↔perform␈α⊗without␈α⊗any␈α⊗difficulties␈α⊗at␈α↔all.␈α⊗ The
␈↓ α∧␈↓␈↓ αdcorrelation␈α⊃between␈α∩percent␈α⊃accuracy␈α⊃and␈α∩subjective␈α⊃distance␈α∩estimations␈α⊃is
␈↓ α∧␈↓␈↓ αdvery␈αgood␈α
(pg␈α44).␈α
 We␈αhave␈α
found␈αthat␈α
the␈αadditional␈αinformation␈α
obtainable
␈↓ α∧␈↓␈↓ αdwith␈αthe␈αdistance␈αestimation␈αwarrants␈αits␈αcollection␈αin␈αspecific␈αinstances␈α(see␈α
pp
␈↓ α∧␈↓␈↓ αd91; 96-97).

␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Multidimensional Scaling of Perceptual Distances␈↓

␈↓"∧␈↓ α∧␈↓␈↓ αdIn␈α↔collecting␈α↔distance␈α⊗estimations,␈α↔as␈α↔described␈α⊗above,␈α↔we␈α↔are␈α⊗implicitly
␈↓ α∧␈↓␈↓ αdderiving␈αa␈αproximity␈αmatrix␈αwhich␈αmay␈αbe␈αused␈αfor␈αmultidimensional␈αscaling.
␈↓ α∧␈↓␈↓ αdThis␈αform␈αof␈αdata␈αanalysis␈αhas␈αproven␈αto␈αbe␈αquite␈αuseful␈αin␈αconjunction␈αwith
␈↓ α∧␈↓␈↓ αdthe␈α↔discrimination␈α⊗work,␈α↔pointing␈α↔at␈α⊗specific␈α↔dimensions␈α↔underlying␈α⊗the
␈↓ α∧␈↓␈↓ αdperceived␈α∞differences␈α∞between␈α∞data␈α∂reduction␈α∞techniques␈α∞(see␈α∞pp␈α∂39-48).␈α∞ We
␈↓ α∧␈↓␈↓ αdwill continue to employ this measurement tool when appropriate.

␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Identification of Signal Sources␈↓

␈↓"∧␈↓ α∧␈↓␈↓ αdAnother␈αtask␈αwhich␈αwill␈αbecome␈αincreasingly␈αimportant␈αin␈αour␈αresearch␈αis␈αthe
␈↓ α∧␈↓␈↓ αdidentification␈α∂of␈α∂the␈α∂source␈α∂of␈α∂a␈α∞signal.␈α∂ Two␈α∂formats␈α∂may␈α∂be␈α∂used␈α∂for␈α∞this
␈↓ α∧␈↓␈↓ αdtask.␈α
 One␈α
of␈α
these␈α
(described␈α
on␈α
pg␈α
93)␈α
is␈α
a␈α
multiple␈α
choice␈αidentification␈α
task.
␈↓ α∧␈↓␈↓ αdThe␈αother␈αwould␈αbe␈αa␈αfree␈αchoice␈αidentification␈αtask.␈α We␈αfeel␈αthat␈αthe␈αformer
␈↓ α∧␈↓␈↓ αdtask␈α∩is␈α∩easier␈α∩for␈α∩the␈α∩listener,␈α∩and␈α∩may␈α∩be␈α∩more␈α∩convenient␈α∩in␈α⊃computer-
␈↓ α∧␈↓␈↓ αdinteractive␈α
situations.␈α
 Therefore,␈α
it␈α
will␈α
most␈α
likely␈α
be␈α
the␈α
dominant␈α
task␈αfor
␈↓ α∧␈↓␈↓ αdmeasuring identification functions.

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈αuses␈αof␈α
identification␈αfunctions␈αwill␈α
be␈αmore␈αsignificant␈α
in␈αour␈αattempts␈α
to
␈↓ α∧␈↓␈↓ αduncover␈αthe␈αcues␈αinvolved␈αon␈αthe␈αlevel␈αof␈αperceptually␈αdetermining␈αthe␈αsource
␈↓ α∧␈↓␈↓ αdof␈α⊂a␈α⊂sound.␈α∂ The␈α⊂more␈α⊂qualitative␈α⊂judgements␈α∂of␈α⊂tone␈α⊂may␈α⊂be␈α∂approached
␈↓ α∧␈↓␈↓ αdeither␈αby␈α
the␈αdiscrimination␈α
paradigm␈αdescribed␈α
above,␈αor␈α
perhaps,␈αby␈α
specific
␈↓ α∧␈↓␈↓ αdverbal measurements, discussed below.
␈↓ α∧␈↓␈↓ ε,9␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Verbal Measurements of Qualitative Aspects of Timbre␈↓

␈↓"∧␈↓ α∧␈↓␈↓ αdOur␈α∞opinion␈α∞concerning␈α∞verbal␈α∞measurement␈α∞techniques␈α∞is␈α∞that␈α∞they␈α∞are␈α
not
␈↓ α∧␈↓␈↓ αdgenerally␈α⊂useful␈α⊂in␈α⊂exploring␈α⊂the␈α⊂dimensions␈α⊂of␈α⊂timbre␈α⊂perception.␈α⊂ This␈α∂is
␈↓ α∧␈↓␈↓ αddiscussed␈α
in␈α
our␈α
review␈α
of␈α
timbre␈α
research␈α
(pp␈α
7-9).␈α
 However,␈α∞in␈α
examining
␈↓ α∧␈↓␈↓ αdthe␈αcues␈αfor␈α
playing␈αstyles␈αof␈αinstruments,␈α
we␈αmay␈αresort␈αto␈α
specific␈αmusically-
␈↓ α∧␈↓␈↓ αdrelated␈α∞verbal␈α∞measurement␈α∞scales,␈α∞such␈α
as␈α∞the␈α∞dimensions␈α∞of␈α∞␈↓↓muted␈α∞␈↓vs.␈↓↓␈α
non-
␈↓ α∧␈↓↓␈↓ αdmuted␈↓,␈α␈↓↓legato␈α␈↓vs.␈↓↓␈αstaccato␈↓,␈α␈↓↓tongue-stop␈α␈↓vs.␈↓↓␈αair-stop␈↓,␈αand␈αso␈αforth.␈α
 These␈αverbal
␈↓ α∧␈↓␈↓ αdscales␈α
would␈α∞be␈α
designed␈α
to␈α∞get␈α
at␈α
specific␈α∞evaluative␈α
judgments,␈α
and␈α∞not,␈α
as
␈↓ α∧␈↓␈↓ αdoften␈α⊂attempted␈α∂in␈α⊂the␈α⊂past,␈α∂to␈α⊂get␈α∂at␈α⊂the␈α⊂more␈α∂basic␈α⊂dimensions␈α⊂of␈α∂timbre
␈↓ α∧␈↓␈↓ αdperception via lengthy (if not but quasi-relevant) adjective lists.

␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Listeners and Musical Training␈↓

␈↓"∧␈↓ α∧␈↓␈↓ αdThere␈αare␈αseveral␈αadvantages␈αin␈αusing␈αmusically-trained␈αlisteners.␈α In␈αour␈αpast
␈↓ α∧␈↓␈↓ αdseven␈α↔years␈α↔of␈α↔research␈α↔on␈α↔various␈α↔psychoacoustical␈α↔aspects␈α_of␈α↔musical
␈↓ α∧␈↓␈↓ αdperception,␈α⊂we␈α∂have␈α⊂found␈α∂that␈α⊂those␈α∂listeners␈α⊂who␈α∂have␈α⊂moderate␈α⊂to␈α∂high
␈↓ α∧␈↓␈↓ αddegrees␈αof␈α
musical␈αtraining␈α
have␈αproven␈αto␈α
be␈αthe␈α
most␈αaccurate␈α
and␈αreliable
␈↓ α∧␈↓␈↓ αdsubjects.␈α⊃ Reports␈α⊃from␈α∩a␈α⊃majority␈α⊃of␈α⊃other␈α∩laboratories␈α⊃confirm␈α⊃this␈α∩as␈α⊃a
␈↓ α∧␈↓␈↓ αdgeneral rule.

␈↓"∧␈↓ α∧␈↓␈↓ αdMore␈αto␈αthe␈αpoint,␈αhowever,␈αis␈αthe␈αmusical␈αrelevance␈αof␈αour␈αresearch.␈α In␈αmost
␈↓ α∧␈↓␈↓ αdof␈α∂our␈α⊂tasks␈α∂we␈α⊂find␈α∂that␈α∂musical␈α⊂training␈α∂becomes␈α⊂essential.␈α∂ Identification
␈↓ α∧␈↓␈↓ αdcertainly␈α
necessitates␈α
a␈α
high␈α
degree␈α
of␈α
familiarity␈α
with␈α
the␈α
sources,␈α
as␈α
will␈α
other
␈↓ α∧␈↓␈↓ αdtypes␈α
of␈α∞verbal␈α
measurements.␈α∞ In␈α
the␈α∞discrimination␈α
and␈α∞distance␈α
estimation
␈↓ α∧␈↓␈↓ αdtasks,␈α∩musicians␈α∩have␈α∩the␈α∩years␈α∩of␈α∩previous␈α∩training␈α∩that␈α∩orients␈α∩them␈α∩to
␈↓ α∧␈↓␈↓ αdmaking␈αvery␈αfine␈αdistinctions␈αin␈αthe␈αproduction␈αof␈αmusical␈αsounds,␈αhence␈αsuch
␈↓ α∧␈↓␈↓ αdtasks are second-nature to these listeners.

␈↓"∧␈↓ α∧␈↓␈↓ αdIn␈α∞that␈α∞we␈α∂are␈α∞striving␈α∞to␈α∞construct␈α∂the␈α∞most␈α∞sophisticated␈α∞model␈α∂for␈α∞timbre
␈↓ α∧␈↓␈↓ αdperception,␈α⊃we␈α⊃will␈α∩necessarily␈α⊃use␈α⊃the␈α∩most␈α⊃sophisticated␈α⊃listeners␈α∩to␈α⊃these
␈↓ α∧␈↓␈↓ αdsounds.␈α
 Future␈α
research␈α
projects␈α
may␈α
be␈α
aimed␈α
at␈α
the␈α
individual␈αdifferences
␈↓ α∧␈↓␈↓ αdin␈αtimbre␈αperception␈αbrought␈αabout␈αby␈αdifferences␈αin␈αtraining,␈αat␈αwhich␈αpoint
␈↓ α∧␈↓␈↓ αdwe will be interested in testing a larger cross-section of listeners.

␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓Novel Tones as a Means of Ranking Distinctive Features␈↓

␈↓"∧␈↓ α∧␈↓␈↓ αdWe␈α∞propose␈α∞to␈α∂obtain␈α∞estimates␈α∞of␈α∞the␈α∂relative␈α∞importance␈α∞of␈α∂the␈α∞distinctive
␈↓ α∧␈↓␈↓ αdperceptual␈α
features␈α
of␈αinstrument␈α
tones␈α
through␈α
the␈αuse␈α
of␈α
novel␈α
tones␈αor␈α
tones
␈↓ α∧␈↓␈↓ αdwhich␈α∞fall␈α∞"in␈α∞between"␈α∞instrument␈α∞families␈α∞where␈α∞a␈α∞source␈α∞either␈α∞cannot␈α∞be
␈↓ α∧␈↓␈↓ αdidentified or is ambiguous.
␈↓ α∧␈↓␈↓ ε%10␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈α
one␈α
drawback␈α
in␈α
using␈α
highly␈αtrained␈α
musicians␈α
as␈α
subjects␈α
is␈α
that␈α
as␈αa
␈↓ α∧␈↓␈↓ αdgroup␈α↔they␈α↔have␈α↔such␈α↔well␈α↔formed␈α↔associations␈α↔of␈α↔tones␈α↔with␈α↔physical
␈↓ α∧␈↓␈↓ αdinstruments␈αthat␈αit␈αis␈αnot␈αknown␈αto␈αwhat␈αdegree␈αsimilarity␈αjudgements␈αof␈α
tones
␈↓ α∧␈↓␈↓ αdare␈α⊂influenced␈α∂by␈α⊂the␈α⊂similarity␈α∂of␈α⊂the␈α∂physical␈α⊂instruments␈α⊂associated␈α∂with
␈↓ α∧␈↓␈↓ αdthose␈α∀tones.␈α∪ As␈α∀an␈α∀example,␈α∪although␈α∀we␈α∪have␈α∀already␈α∀determined␈α∪that
␈↓ α∧␈↓␈↓ αdinharmonicity␈αduring␈αthe␈αattack␈αof␈αsome␈αwind␈αand␈αstring␈αtones␈αis␈αa␈αdominant
␈↓ α∧␈↓␈↓ αdperceptual␈α
feature,␈α
we␈α
do␈α
not␈α
know␈α
that␈α
the␈α
multi-dimensional␈α
scaling␈αresults
␈↓ α∧␈↓␈↓ αdof␈α
distance␈α
estimation␈α
between␈α
these␈α
tones␈α
is␈α
not␈α
significantly␈α
influenced␈α
by␈α
the
␈↓ α∧␈↓␈↓ αddissimilarity of the physical instruments themselves.

␈↓"∧␈↓ α∧␈↓␈↓ αdAn␈α∂unanticipated␈α∂bi-product␈α∂of␈α∂the␈α∂timbral␈α∂interpolation␈α∂algorithm␈α⊂was␈α∂the
␈↓ α∧␈↓␈↓ αdoccurence␈αof␈αtones␈αwhich␈αwere␈αeither␈αambiguous␈αor␈αdissociated␈αfrom␈αeither␈αof
␈↓ α∧␈↓␈↓ αdthe␈α
natural␈αend␈α
points␈αtones.␈α
 Such␈α
"in␈αbetween"␈α
tones␈αmay␈α
be␈αideal␈α
candidates
␈↓ α∧␈↓␈↓ αdfor␈α⊗estimation␈α⊗experiments␈α⊗where␈α∃perceptual␈α⊗features␈α⊗of␈α⊗interest␈α⊗can␈α∃be
␈↓ α∧␈↓␈↓ αdmanipulated␈α∂in␈α∂spectral␈α∂structures␈α∂which␈α∂are␈α∂without␈α∂strong␈α∂connotations␈α∂of
␈↓ α∧␈↓␈↓ αdphysical␈α∃instruments.␈α∃ Of␈α∀interest␈α∃is␈α∃whether␈α∀or␈α∃not␈α∃novel␈α∃tones␈α∀having
␈↓ α∧␈↓␈↓ αdcommon␈α∃features␈α∃such␈α∃as␈α∀inharmonicity␈α∃or␈α∃changing␈α∃bandwidth␈α∃tend␈α∀to
␈↓ α∧␈↓␈↓ αdcoalesce␈αto␈αa␈αgreater␈αdegree␈αin␈αa␈αthree-dimensional␈αprojection␈αthan␈αdo␈αthe␈αthe
␈↓ α∧␈↓␈↓ αdinstrument tones in the past experiment.


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓
F. Facilities for Research

␈↓"∧␈↓ α∧␈↓␈↓ αdOur␈α∪work␈α∪has␈α∪been␈α∪extensively␈α∪centered␈α∪around␈α∪the␈α∀powerful␈α∪computing
␈↓ α∧␈↓␈↓ αdfacility␈α!of␈α"the␈α!Stanford␈α!Artificial␈α"Intelligence␈α!Laboratory␈α"to␈α!date.
␈↓ α∧␈↓␈↓ αdUnfortunately,␈αthe␈αLaboratory␈αcan␈αno␈αlonger␈αsupport␈αus␈αat␈αthis␈αlevel.␈α For␈αthis
␈↓ α∧␈↓␈↓ αdreason,␈α⊃we␈α⊃are␈α⊃attempting␈α⊃to␈α⊃establish␈α⊃the␈α⊃kind␈α⊃of␈α⊃facility␈α⊃needed␈α∩for␈α⊃our
␈↓ α∧␈↓␈↓ αdresearch.␈αThis␈α
includes␈αa␈α
powerful␈αcomputer,␈α
a␈αgraphical␈α
display,␈αa␈α
high-speed
␈↓ α∧␈↓␈↓ αddisk,␈α∪a␈α∪real-time␈α∪signal␈α∀processor,␈α∪acoustically␈α∪treated␈α∪modules,␈α∀and␈α∪audio
␈↓ α∧␈↓␈↓ αdequipment.

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈α∩experiments␈α⊃we␈α∩have␈α⊃done␈α∩to␈α⊃date␈α∩almost␈α⊃entirely␈α∩have␈α∩used␈α⊃stimuli
␈↓ α∧␈↓␈↓ αdrecorded␈α∂on␈α∂audio␈α∂tape.␈α∂The␈α∂matching␈α∂experiment␈α∂(pp␈α∂48-65),␈α∂on␈α∂the␈α∂other
␈↓ α∧␈↓␈↓ αdhand,␈α≠was␈α≠an␈α≠interactive␈α≠computer-based␈α≠experiment,␈α≠and␈α≤had␈α≠many
␈↓ α∧␈↓␈↓ αdadvantages.␈αOur␈αexperience␈αwas␈αthat␈αthe␈αmedium␈αof␈αaudio␈αtape␈αis␈αnot␈αreliable
␈↓ α∧␈↓␈↓ αdand␈α∞does␈α∞not␈α∂record␈α∞truely.␈α∞There␈α∞are␈α∂problems␈α∞of␈α∞hiss,␈α∞dropout,␈α∂and␈α∞print-
␈↓ α∧␈↓␈↓ αdthrough␈α∩which␈α∪confound␈α∩experimental␈α∩stimuli.␈α∪Since␈α∩in␈α∩many␈α∪cases,␈α∩these
␈↓ α∧␈↓␈↓ αddistortions␈α⊃were␈α⊃of␈α⊃a␈α⊃magnitude␈α⊃comparable␈α⊃to␈α⊃that␈α⊃of␈α⊃the␈α⊃differences␈α⊂the
␈↓ α∧␈↓␈↓ αdsubjects␈αwere␈αdetecting,␈αwe␈αcannot␈αbe␈α
sure␈αthat␈αwe␈αhave␈αreached␈αthe␈α
limits␈αof
␈↓ α∧␈↓␈↓ αddiscrimination.␈α∃ We␈α∃feel␈α∀that␈α∃a␈α∃more␈α∀rigorous␈α∃experimental␈α∃setup␈α∀would
␈↓ α∧␈↓␈↓ ε%11␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdinvolve␈α∩bypassing␈α∩the␈α∪medium␈α∩of␈α∩audio␈α∪tape␈α∩and␈α∩reproducing␈α∪the␈α∩sound
␈↓ α∧␈↓␈↓ αddirectly out of the computer, as was done with the matching experiment.

␈↓"∧␈↓ α∧␈↓␈↓ αdUnfortunately,␈αhowever,␈αthe␈αmatching␈α
experiment␈αdid␈αrequire␈αa␈αgreat␈α
quantity
␈↓ α∧␈↓␈↓ αdof␈α⊗disk␈α⊗storage␈α∃space,␈α⊗because␈α⊗the␈α⊗sound␈α∃samples␈α⊗had␈α⊗to␈α⊗be␈α∃computed
␈↓ α∧␈↓␈↓ αdbeforehand␈αand␈αstored␈αin␈αdigital␈αform.␈αWe␈αfeel␈αthat␈αa␈αmuch␈αmore␈αsatisfactory
␈↓ α∧␈↓␈↓ αdarrangement␈α
would␈αbe␈α
to␈α
construct␈αspecial-purpose␈α
digital␈α
hardware␈αwhich␈α
can
␈↓ α∧␈↓␈↓ αdsynthesize␈α∪these␈α∀signals␈α∪in␈α∀real␈α∪time,␈α∀thus␈α∪eliminating␈α∀both␈α∪the␈α∀need␈α∪for
␈↓ α∧␈↓␈↓ αdextensive␈α⊃disk␈α∩storage␈α⊃of␈α∩sound␈α⊃samples␈α∩and␈α⊃for␈α∩recording␈α⊃the␈α∩stimuli␈α⊃on
␈↓ α∧␈↓␈↓ αdaudio tape.

␈↓"∧␈↓ α∧␈↓␈↓ αdA␈α∂real-time␈α∂digital␈α∂synthesizer␈α∂offers␈α∂far-reaching␈α∂possibilities␈α∂in␈α∂developing
␈↓ α∧␈↓␈↓ αdresearch␈α∂methodologies.␈α∂It␈α∂is␈α⊂now␈α∂the␈α∂case␈α∂that␈α∂several␈α⊂such␈α∂special-purpose
␈↓ α∧␈↓␈↓ αddigital␈α∞devices␈α∞are␈α∞being␈α∞built␈α∞in␈α∞this␈α∞country,␈α∞thus␈α∞offering␈α∞us␈α∞a␈α
reasonable
␈↓ α∧␈↓␈↓ αdselection␈αof␈α
prices␈αand␈α
available␈αfeatures.␈α With␈α
such␈αa␈α
device,␈αwe␈αcan␈α
imagine
␈↓ α∧␈↓␈↓ αdattaching␈α↔several␈α⊗synthesis␈α↔parameters␈α⊗directly␈α↔to␈α⊗knobs␈α↔that␈α↔either␈α⊗the
␈↓ α∧␈↓␈↓ αdexperimenter␈α⊂or␈α∂subject␈α⊂could␈α⊂control,␈α∂providing␈α⊂instant␈α∂feedback␈α⊂as␈α⊂to␈α∂the
␈↓ α∧␈↓␈↓ αdaural␈α
effect␈α
of␈α
the␈α
knob.␈α
To␈α
do␈α
this␈α
without␈α
the␈α
device␈α
would␈αrequire␈α
countless
␈↓ α∧␈↓␈↓ αdhours␈α⊃of␈α⊃computer␈α⊃time␈α⊃to␈α⊃synthesize␈α⊃tones␈α⊃corresponding␈α⊃to␈α⊃each␈α⊂possible
␈↓ α∧␈↓␈↓ αdvalue␈α∂of␈α∂the␈α∂parameter.␈α⊂With␈α∂several␈α∂simultaneous␈α∂parameters,␈α⊂the␈α∂problem
␈↓ α∧␈↓␈↓ αdsoon␈α↔becomes␈α↔unmanageable.␈α↔With␈α↔real-time␈α↔response␈α↔and␈α↔the␈α↔inherent
␈↓ α∧␈↓␈↓ αdprecision␈α∂of␈α∂control␈α∂made␈α∂possible␈α∂by␈α∂digital␈α∂synthesis␈α∂of␈α∂the␈α∂waveform,␈α∂we
␈↓ α∧␈↓␈↓ αdexpect␈α⊃significant␈α⊃developments␈α∩in␈α⊃methodological␈α⊃approaches␈α⊃leading␈α∩to␈α⊃a
␈↓ α∧␈↓␈↓ αdgreat increase in research productivity.

␈↓"∧␈↓ α∧␈↓␈↓ αdWe␈α≠experienced␈α≠further␈α≠problems␈α~when␈α≠digitizing␈α≠the␈α≠original␈α~music
␈↓ α∧␈↓␈↓ αdinstrument␈α
tones.␈α
Since␈α
the␈α
tones␈α
were␈α
first␈α
recorded␈α
on␈α
audio␈α
tape,␈α∞then␈α
fed
␈↓ α∧␈↓␈↓ αdinto␈αthe␈αcomputer␈αvia␈αan␈αanalog-to-digital␈αconverter,␈αour␈αoriginal␈αdigitizations
␈↓ α∧␈↓␈↓ αdwere␈αalready␈αcontaminated␈αwith␈αhiss,␈αprint-through,␈αand␈αdropout.␈αWe␈αfeel␈αit␈α
is
␈↓ α∧␈↓␈↓ αdmost␈α∩important␈α⊃to␈α∩feed␈α⊃the␈α∩signals␈α⊃directly␈α∩into␈α⊃the␈α∩computer␈α∩without␈α⊃the
␈↓ α∧␈↓␈↓ αdintervention␈α
of␈αaudio␈α
tape.␈α
This␈αrequires␈α
that␈α
an␈αacoustically␈α
isolated␈αbooth␈α
be
␈↓ α∧␈↓␈↓ αdpresent␈α∩near␈α∪the␈α∩computer.␈α∩This␈α∪is␈α∩especially␈α∩important␈α∪because␈α∩computer
␈↓ α∧␈↓␈↓ αdenvironments␈α
are␈α
typically␈α
very␈α
noisy.␈α Such␈α
an␈α
acoustically␈α
isolated␈α
booth␈αis,
␈↓ α∧␈↓␈↓ αdof␈α∩course,␈α∪␈↓↓absolutely␈↓␈α∩necessary␈α∪for␈α∩conducting␈α∪auditory␈α∩experiments␈α∪in␈α∩the
␈↓ α∧␈↓␈↓ αdcomputer environment.

␈↓"∧␈↓ α∧␈↓␈↓ αdA␈α∂general␈α∞purpose␈α∂computer␈α∞is␈α∂necessary,␈α∞of␈α∂course,␈α∞for␈α∂running␈α∂the␈α∞on-line
␈↓ α∧␈↓␈↓ αdexperiments,␈α∀doing␈α∀statistical␈α∃data␈α∀analysis,␈α∀multidimensional␈α∃scaling,␈α∀tone
␈↓ α∧␈↓␈↓ αdanalysis␈α⊗by␈α∃heterodyne␈α⊗filter␈α∃and␈α⊗other␈α∃techniques,␈α⊗and␈α⊗an␈α∃uncountable
␈↓ α∧␈↓␈↓ αdnumber␈αof␈αother␈αtasks.␈αA␈αlarge␈αdisk␈αis␈αstill␈αnecessary␈αfor␈αbulk␈αstorage␈αrelating
␈↓ α∧␈↓␈↓ ε%12␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdto␈α⊃support␈α∩for␈α⊃the␈α∩computer,␈α⊃storage␈α⊃of␈α∩sounds␈α⊃to␈α∩be␈α⊃analysed,␈α∩storage␈α⊃of
␈↓ α∧␈↓␈↓ αdanalysis␈α
data,␈α
storage␈α
of␈α
experimental␈α
results,␈α
storage␈α
of␈α
programs,␈α
and␈α
many
␈↓ α∧␈↓␈↓ αdmore.

␈↓"∧␈↓ α∧␈↓␈↓ αdComputer␈α⊗graphics␈α↔are␈α⊗of␈α⊗primary␈α↔importance␈α⊗for␈α⊗gaining␈α↔insight␈α⊗into
␈↓ α∧␈↓␈↓ αdexperimental␈α∞results.␈α∞All␈α∞of␈α∞the␈α∞figures␈α∞in␈α∞our␈α∞NSF␈α∞Proposal␈α∞were␈α
originally
␈↓ α∧␈↓␈↓ αdgraphics␈αwhich␈αwe␈αhave␈αmade␈αinto␈αhard␈αcopy.␈αFor␈αinstance,␈αwe␈αhave␈αreal-time
␈↓ α∧␈↓␈↓ αdinteractive␈α∂3D␈α∞rotation␈α∂routines␈α∂which␈α∞allow␈α∂the␈α∞experimenter␈α∂to␈α∂examine␈α∞a
␈↓ α∧␈↓␈↓ αdconfiguration␈αproduced␈αby␈αthe␈αmultidimensional␈αscaling␈αfrom␈αany␈αangle.␈α
 This
␈↓ α∧␈↓␈↓ αdcapacity␈αhas␈α
been␈αinvaluable␈αin␈α
helping␈αus␈αto␈α
interpret␈αthe␈αaxes.␈α
 The␈αability
␈↓ α∧␈↓␈↓ αdto␈αdisplay␈αanalyses␈αin␈αa␈αvariety␈αof␈αforms␈αhas␈αgiven␈αus␈αgreat␈αaid␈αin␈αvisualizing
␈↓ α∧␈↓␈↓ αdthe␈α
differences␈α
among␈α
the␈α
physical␈α
parameters␈α
of␈α
the␈α
different␈α
timbres␈αused,␈α
as
␈↓ α∧␈↓␈↓ αdwell␈α
as␈α
in␈α
exploring␈α
the␈α
varying␈α
implications␈α
of␈α
different␈α
types␈α∞of␈α
perceptual
␈↓ α∧␈↓␈↓ αddata analyses.

␈↓"∧␈↓ α∧␈↓␈↓ αdIn␈α∀summary,␈α∀each␈α∪component␈α∀of␈α∀our␈α∪hardware␈α∀configuration␈α∀was␈α∪chosen
␈↓ α∧␈↓␈↓ αdbecause␈α∩of␈α⊃its␈α∩extreme␈α∩importance␈α⊃in␈α∩our␈α⊃work␈α∩to␈α∩date.␈α⊃We␈α∩feel␈α∩that␈α⊃the
␈↓ α∧␈↓␈↓ αdcomputer␈α∪is␈α∪an␈α∪ideal␈α∪vehicle␈α∀for␈α∪research,␈α∪and␈α∪that␈α∪this␈α∀configuration␈α∪is
␈↓ α∧␈↓␈↓ αdessential␈α∂to␈α∂continue␈α∂our␈α∂present␈α∂course␈α∂of␈α∂investigation.␈α∂In␈α∂fact,␈α∂our␈α∂system
␈↓ α∧␈↓␈↓ αdrepresents in some ways the minimum system with which we can continue.


␈↓"∧␈↓ α∧␈↓␈↓ αd␈↓
G. Applications to Related Perceptual Research

␈↓"∧␈↓ α∧␈↓␈↓ αdThere␈α
exists␈αa␈α
wide␈αrange␈α
of␈αresearch␈α
areas␈αin␈α
musical␈αperception␈α
which␈αwill
␈↓ α∧␈↓␈↓ αddirectly␈α∞benefit␈α∞from␈α∞the␈α∞development␈α∞of␈α∞a␈α∞model␈α∞for␈α∞timbre␈α∞perception␈α
and
␈↓ α∧␈↓␈↓ αdcomputer simulation.  We will briefly discuss a few of these areas below.

␈↓"∧␈↓ α∧␈↓␈↓ αdTimbre␈α
perception␈α
research␈α
will,␈α
of␈α
course,␈α
directly␈α
benefit␈α
from␈α
data␈α
reduction
␈↓ α∧␈↓␈↓ αdmodeling␈α␈↓↓vis-a-vis␈↓␈αtimbre␈αmodeling.␈α Researchers␈αinterested␈αin␈αvarious␈αscalings
␈↓ α∧␈↓␈↓ αdof␈α∨general␈α∨perceptual␈α∨dimensions,␈α∨including␈α multidimensional␈α∨scaling,
␈↓ α∧␈↓␈↓ αdexplorations␈α
of␈α
timbral␈α
analogies,␈αand␈α
investigations␈α
of␈α
categorical␈αperception
␈↓ α∧␈↓␈↓ αdin␈αtimbre␈α
(besides␈αourselves,␈α
D.␈αL.␈αWessel;␈α
R.␈αPlomp;␈α
L.␈αWedin␈α
&␈αG.␈αGoude;␈α
J.
␈↓ α∧␈↓␈↓ αdC.␈α⊂Risset;␈α⊂J.␈α⊂E.␈α⊂Cutting␈α⊂&␈α⊂B.␈α⊂S.␈α⊂Rosner)␈α⊂could␈α⊂find␈α⊂stimuli␈α⊂produced␈α⊂by␈α∂a
␈↓ α∧␈↓␈↓ αdperceptually-related␈αsimulation␈α
model␈αto␈α
be␈αvery␈α
advantageous␈αin␈αmany␈α
phases
␈↓ α∧␈↓␈↓ αdof␈α
research.␈α
 Rigorous␈α
specification␈α
of␈α
perceptually␈α
salient␈α
features␈α
in␈α
timbral
␈↓ α∧␈↓␈↓ αdstimuli␈α≠drastically␈α≤reduces␈α≠the␈α≤problems␈α≠of␈α≤evaluating␈α≠the␈α≤results␈α≠of
␈↓ α∧␈↓␈↓ αdexperiments␈α!in␈α!terms␈α!of␈α!psychophysical␈α!relationships.␈α! The␈α!further
␈↓ α∧␈↓␈↓ αddevelopment␈α∪of␈α∪interpolation␈α∩algorithms␈α∪depends␈α∪upon␈α∩the␈α∪existence␈α∪of␈α∩a
␈↓ α∧␈↓␈↓ αdperceptual␈α
model␈α
for␈α
timbre␈α
synthesis;␈α
categorical␈α
perception␈α
research␈α
in␈α
turn
␈↓ α∧␈↓␈↓ αddepends␈α⊂upon␈α⊂this␈α∂latter␈α⊂development␈α⊂(see␈α∂pg␈α⊂127␈α⊂for␈α∂a␈α⊂discussion␈α⊂of␈α∂such
␈↓ α∧␈↓␈↓ αddevelopments).
␈↓ α∧␈↓␈↓ ε%13␈↓ 
d

␈↓"∧␈↓ α∧␈↓␈↓ αdStill␈α∂other␈α∂forms␈α∂of␈α∂research␈α∂that␈α∂could␈α∂be␈α∂more␈α∂feasible␈α∂as␈α∂a␈α∂result␈α∂of␈α∞our
␈↓ α∧␈↓␈↓ αdmodeling␈α⊂would␈α⊂be␈α⊂investigations␈α⊂of␈α⊂the␈α⊂perceptual␈α⊂correlates␈α⊂to␈α⊂combining
␈↓ α∧␈↓␈↓ αdtimbres,␈α⊂such␈α⊂as␈α⊃timbral␈α⊂dominance.␈α⊂ The␈α⊃effects␈α⊂of␈α⊂timbral␈α⊃parameters␈α⊂on
␈↓ α∧␈↓␈↓ αdpitch␈α
perception␈α
could␈α
be␈α
more␈α
rigorously␈α
approached␈α
given␈α
our␈α
techniques,␈α
as
␈↓ α∧␈↓␈↓ αdcould␈α⊃be␈α⊂an␈α⊃investigation␈α⊃of␈α⊂the␈α⊃relationships␈α⊂between␈α⊃timbre␈α⊃and␈α⊂musical
␈↓ α∧␈↓␈↓ αdscales and tuning preferences.

␈↓"∧␈↓ α∧␈↓␈↓ αdThe␈αdevelopment␈αof␈αa␈αdata␈αreduction␈αmodel␈αbased␈αon␈αperceptual␈αprocessing␈αis
␈↓ α∧␈↓␈↓ αda␈α∂prerequisite␈α∂for␈α∂the␈α∂ability␈α⊂to␈α∂investigate␈α∂the␈α∂higher-level␈α∂␈↓↓prosidic␈α⊂cues␈↓␈α∂in
␈↓ α∧␈↓␈↓ αdmusical␈α∞behavior,␈α∞especially␈α∞for␈α∞perception.␈α∞ We␈α∞are␈α∞referring,␈α∞by␈α∞analogy␈α∞to
␈↓ α∧␈↓␈↓ αdspeech,␈α⊂to␈α⊃the␈α⊂cues␈α⊃of␈α⊂articulation␈α⊃and␈α⊂phrasing␈α⊃found␈α⊂in␈α⊃musical␈α⊂streams.
␈↓ α∧␈↓␈↓ αdThe␈α∞ability␈α∞to␈α∞model␈α∞such␈α∞cues␈α∞depends␈α∞upon␈α∞first␈α∞modeling␈α∞the␈α∞more␈α∞basic
␈↓ α∧␈↓␈↓ αdacoustical␈α⊂elements␈α⊂of␈α⊂timbre.␈α⊂ This␈α⊂reasoning␈α⊂makes␈α⊂what␈α⊂we␈α⊂feel␈α⊂to␈α⊂be␈α⊂a
␈↓ α∧␈↓␈↓ αdvalid␈α
presupposition:␈α
that␈α∞an␈α
investigation␈α
of␈α
higher-level␈α∞musical␈α
perception
␈↓ α∧␈↓␈↓ αdmust␈α∞satisfy␈α∞lower-level␈α
requirements.␈α∞ For␈α∞instance,␈α
it␈α∞is␈α∞difficult␈α∞to␈α
evaluate
␈↓ α∧␈↓␈↓ αdthe␈α⊂total␈α⊂musical␈α⊂significance␈α⊂of␈α⊂studies␈α⊂on␈α⊂higher-order␈α⊂musical␈α⊂perception
␈↓ α∧␈↓␈↓ αdwhich␈α∃use␈α∃sawtooth␈α∃waveforms␈α∃for␈α∃controlled␈α∃acoustical␈α∃stimuli,␈α∃as␈α∀most
␈↓ α∧␈↓␈↓ αdcontemporary␈α∩work␈α∪does.␈α∩ Our␈α∩development␈α∪of␈α∩the␈α∩potentiality␈α∪of␈α∩directly
␈↓ α∧␈↓␈↓ αdusing␈α∂musical-acoustic␈α∂materials␈α∂in␈α∂higher-order␈α∂contexts␈α∂will␈α⊂eliminate␈α∂such
␈↓ α∧␈↓␈↓ αddifficulties.

␈↓"∧␈↓ α∧␈↓␈↓ αdThere␈α∩are␈α∪several␈α∩closely-related␈α∪areas␈α∩of␈α∩research␈α∪which␈α∩share␈α∪this␈α∩same
␈↓ α∧␈↓␈↓ αdbenefit␈α∃and␈α∀are␈α∃opened␈α∀to␈α∃more␈α∀extensive␈α∃investigation␈α∃using␈α∀computer-
␈↓ α∧␈↓␈↓ αdgenerated␈α∃musical␈α∃timbres.␈α∀ A␈α∃general␈α∃area␈α∀of␈α∃study␈α∃which␈α∃is␈α∀becoming
␈↓ α∧␈↓␈↓ αdincreasingly␈α⊃important␈α⊃is␈α⊃the␈α⊂examination␈α⊃of␈α⊃cognitive␈α⊃processes␈α⊃in␈α⊂melody
␈↓ α∧␈↓␈↓ αdperception␈α(W.␈αJ.␈αDowling;␈αD.␈αHarwood;␈αT.␈αBever;␈αand␈αothers).␈α Such␈α
research
␈↓ α∧␈↓␈↓ αdincludes␈α
the␈α
perceptual␈α∞segmentation␈α
of␈α
melodies␈α
with␈α∞respect␈α
to␈α
a␈α∞variety␈α
of
␈↓ α∧␈↓␈↓ αdfactors.␈α
We␈αfeel␈α
that␈αnot␈α
only␈αwould␈α
this␈αresearch␈α
benefit␈αfrom␈α
the␈αexistence␈α
of
␈↓ α∧␈↓␈↓ αda␈αtimbre␈αmodel␈αthat␈αrelates␈αto␈αsimulation␈α-␈αby␈αincreasing␈αthe␈αmusical␈αrelevance
␈↓ α∧␈↓␈↓ αdof␈α∂stimuli␈α∂-␈α∂but␈α∂it␈α∂would␈α∂also␈α∂be␈α∂opened␈α∂to␈α∂an␈α∂investigation␈α∂of␈α⊂many␈α∂more
␈↓ α∧␈↓␈↓ αdfactors␈αthat␈αmay␈αcome␈αinto␈αplay␈αon␈αthe␈αtimbral␈αlevel␈αwith␈αpitch,␈αloudness␈αand
␈↓ α∧␈↓␈↓ αddurational parameters.

␈↓"∧␈↓ α∧␈↓␈↓ αdIn␈α
short,␈α
we␈α
feel␈α
that␈α
the␈α
area␈α
of␈α
musical␈α
perception␈α
research␈α
would␈α
benefit␈α
not
␈↓ α∧␈↓␈↓ αdonly␈α⊂in␈α⊂the␈α⊂domain␈α⊂of␈α⊂theory␈α⊂from␈α⊂our␈α⊂contributions␈α⊂towards␈α⊃a␈α⊂perceptual
␈↓ α∧␈↓␈↓ αdmodel␈α
for␈α
timbre,␈α
but␈α
it␈α∞would␈α
also␈α
derive␈α
significant␈α
practical␈α∞benefits␈α
from
␈↓ α∧␈↓␈↓ αdour work on the related simulation techniques.