␈↓␈↓ ε.1␈↓ (

␈↓␈↓ ∧W␈↓	B. RESEARCH APPLICATIONS

␈↓␈↓AUDITORY PERCEPTION

␈↓Our␈αproposed␈αresearch␈αwill␈αhave␈αsignificant␈αcontributions␈αto␈αseveral␈αareas␈αof␈αscientific
␈↓investigation␈α⊂of␈α⊂both␈α⊂a␈α∂theoretical␈α⊂and␈α⊂practical␈α⊂nature.␈α∂ The␈α⊂most␈α⊂apparent␈α⊂field␈α∂to
␈↓be␈α⊗encompassed␈α⊗by␈α∃our␈α⊗work␈α⊗is␈α∃that␈α⊗of␈α⊗psychoacoustics,␈α∃the␈α⊗study␈α⊗of␈α∃auditory
␈↓perception.␈α∂ Here␈α∞our␈α∂work␈α∞will␈α∂make␈α∂contributions␈α∞both␈α∂to␈α∞the␈α∂state␈α∂of␈α∞fundamental
␈↓knowledge␈α⊂in␈α⊂this␈α⊂area,␈α⊂and␈α⊂to␈α⊂the␈α⊂development␈α⊂of␈α⊂tools␈α⊂and␈α⊂approaches␈α⊂which␈α⊂will
␈↓make␈α_possible␈α→the␈α_study␈α→of␈α_the␈α_more␈α→complex␈α_issues␈α→in␈α_hearing.␈α→The␈α_current
␈↓capacities␈α⊂of␈α∂instrumentation␈α⊂pose␈α∂quite␈α⊂definite␈α∂limitations␈α⊂to␈α∂the␈α⊂range␈α⊂of␈α∂stimulus
␈↓control␈α→and␈α→complexity␈α~that␈α→can␈α→be␈α~generated␈α→for␈α→experimental␈α~research.␈α→The
␈↓development␈α⊗of␈α⊗our␈α⊗proposed␈α⊗real-time␈α⊗digital␈α⊗signal␈α⊗processing␈α⊗system,␈α⊗and␈α∃its
␈↓application␈α⊂in␈α⊂our␈α⊂investigation␈α⊂of␈α⊂certain␈α⊂complex␈α⊂issues␈α⊂for␈α⊂auditory␈α⊂research,␈α⊂will
␈↓represent␈α∩a␈α∪major␈α∩breakthrough␈α∩in␈α∪research␈α∩approaches.␈α∩ In␈α∪what␈α∩follows,␈α∪we␈α∩will
␈↓enumerate␈α∃a␈α∃number␈α∀of␈α∃the␈α∃theoretical␈α∃issues␈α∀which␈α∃our␈α∃proposed␈α∃research␈α∀will
␈↓address,␈α
including␈α
the␈α
perception␈α∞of␈α
complex␈α
tones,␈α
reverberant␈α
spaces,␈α∞and␈α
localized
␈↓and␈α∪moving␈α∀sound␈α∪sources,␈α∀and␈α∪also␈α∪mention␈α∀the␈α∪great␈α∀potential␈α∪of␈α∀our␈α∪proposed
␈↓computer␈α⊂research␈α⊂system␈α⊂in␈α∂these␈α⊂and␈α⊂such␈α⊂other␈α∂areas␈α⊂of␈α⊂psychoacoustics␈α⊂as␈α∂the
␈↓perception␈αof␈αpitch,␈αloudness,␈αand␈αduration␈αof␈αcomplex␈αtones.


␈↓␈↓∧complex␈α
tones␈↓

␈↓Directly␈αtouched␈αby␈αour␈αproposed␈αwork␈α
will␈αbe␈αmatters␈αof␈αbasic␈αtheoretical␈α
concern␈αin
␈↓the␈α∩study␈α⊃of␈α∩the␈α⊃perception␈α∩of␈α⊃complex␈α∩signals,␈α⊃which␈α∩in␈α⊃our␈α∩research␈α∩will␈α⊃include
␈↓signals␈α⊂that␈α∂actually␈α⊂occur␈α∂in␈α⊂nature.␈α∂ Despite␈α⊂over␈α∂a␈α⊂century␈α∂of␈α⊂dedicated␈α∂scientific
␈↓research␈α
on␈α
this␈α
subject,␈αthe␈α
state␈α
of␈α
knowledge␈αfor␈α
the␈α
perception␈α
of␈α
complex␈αtones
␈↓remains␈α⊃in␈α⊃an␈α⊃infant␈α⊃condition.␈α⊃ A␈α⊃primary␈α⊂cause␈α⊃of␈α⊃this␈α⊃has␈α⊃been␈α⊃the␈α⊃limitations␈α⊂of
␈↓equipment␈α∪to␈α∀provide␈α∪an␈α∪adequate␈α∀means␈α∪of␈α∪producing␈α∀and␈α∪controlling␈α∀the␈α∪stimuli
␈↓needed␈α∪for␈α∪studying␈α∪complex␈α∪tones.␈α∪Several␈α∩of␈α∪the␈α∪basic␈α∪problems␈α∪posed␈α∪for␈α∩the
␈↓computer␈α
simulation␈α
of␈α
realistic␈α
music␈α
instrument␈α
tones␈α
are␈α
just␈α
those␈α
which␈α
have␈αnot
␈↓been␈α⊗solved␈α↔in␈α⊗auditory␈α↔theory.␈α⊗ Therefore␈α↔we␈α⊗will␈α↔be␈α⊗involved␈α↔in␈α⊗fundamental
␈↓research␈αmatters␈αfor␈αpsychoacoustics.

␈↓The␈α∞first␈α∞important␈α∞question␈α∞which␈α∞we␈α∞will␈α∞address␈α∞concerns␈α∞the␈α∂perceptually␈α∞salient
␈↓features␈α∞of␈α∞instrument␈α∞tones.␈α∞ Computer␈α∞analysis␈α∞of␈α∞real␈α∞tones␈α∞has␈α∂revealed␈α∞degrees
␈↓of␈α↔physical␈α↔waveform␈α↔complexity␈α↔that␈α↔would␈α↔seem␈α↔to␈α↔far␈α↔exceed␈α↔the␈α_limits␈α↔of
␈↓perceptual␈α∩processing.␈α∩ We␈α∩have␈α⊃abundant␈α∩information␈α∩from␈α∩the␈α∩speech␈α⊃perception
␈↓literature␈α~which␈α~does␈α~suggest␈α~that␈α~not␈α~all␈α~of␈α~the␈α~acoustical␈α~complexities␈α~are
␈↓␈↓ ε.2␈↓ (

␈↓psychologically␈αimportant.␈α The␈αtwo␈αlines␈α
of␈αapproach␈αto␈αtonal␈αsimualtion␈αwhich␈α
we␈αare
␈↓following,␈α∩additive␈α∩synthesis␈α∩based␈α∩upon␈α∪the␈α∩analysis␈α∩of␈α∩real␈α∩tones,␈α∪and␈α∩frequency
␈↓modulation␈α∪synthesis,␈α∀are␈α∪both␈α∪converging␈α∀on␈α∪a␈α∪more␈α∀general␈α∪model␈α∀for␈α∪computer
␈↓simulation.␈α⊂ This␈α⊂research␈α⊂is␈α⊂also,␈α⊂necessarily,␈α⊂converging␈α⊂on␈α⊂a␈α⊂perceptual␈α⊂model␈α⊂for
␈↓the␈α
salient␈α
features␈α
of␈α
these␈α
complex␈α
tones.␈α
 The␈α
additive␈α
synthesis␈α
approach,␈α
where
␈↓the␈α∪results␈α∀of␈α∪analysis␈α∀are␈α∪progressively␈α∀simplified␈α∪and␈α∀the␈α∪perceptual␈α∀effects␈α∪of
␈↓simplifications␈α↔are␈α↔measured,␈α_is␈α↔directly␈α↔aimed␈α↔at␈α_the␈α↔question␈α↔of␈α↔how␈α_far␈α↔the
␈↓waveform␈α≡may␈α≡be␈α≡simplified.␈α≥ The␈α≡frequency␈α≡modulation␈α≡synthesis␈α≥technique,
␈↓originated␈α
at␈α
our␈α
lab,␈α
has␈α
brought␈α
to␈α
the␈α
surface␈α
a␈α
very␈α
important␈α
and␈α∞salient␈α
feature
␈↓of␈α
several␈α
instrumental␈α
tones,␈α
the␈αevolution␈α
of␈α
bandwidth␈α
through␈α
time.␈α
 The␈αresearch
␈↓that␈α∂we␈α∂propose␈α∂to␈α∂undertake␈α⊂should␈α∂provide␈α∂much␈α∂of␈α∂the␈α∂fundamental␈α⊂data␈α∂needed
␈↓to␈α
construct␈α
informed␈α
models␈α
for␈α∞the␈α
perceptual␈α
processing␈α
of␈α
auditory␈α∞signals␈α
whose
␈↓complexity␈αmatches␈αthat␈αof␈αnatural␈αsounds.

␈↓In␈αaddition␈α
to␈αthe␈αabove␈α
planned␈αresearch,␈α
the␈αdigital␈αsystem␈α
which␈αis␈α
proposed␈αwould
␈↓enable␈α_scientific␈α_investigators␈α_to␈α_explore␈α_a␈α_host␈α_of␈α_topics␈α_concerned␈α_with␈α_the
␈↓perception␈α≡of␈α≡complex␈α≡tones␈α≡which␈α≡are␈α≡now␈α≡impractical␈α≡to␈α≡impliment.␈α≡ The
␈↓preservation␈α⊂of␈α⊂timbre␈α⊂with␈α⊂changes␈α⊂in␈α∂pitch,␈α⊂the␈α⊂complex␈α⊂nature␈α⊂of␈α⊂the␈α∂interactive
␈↓contributions␈α⊂from␈α⊂various␈α∂spectral␈α⊂regions␈α⊂to␈α⊂the␈α∂perception␈α⊂of␈α⊂the␈α⊂complex␈α∂signal,
␈↓the␈αinteraction␈α
of␈αthe␈α
perceptual␈αweightings␈αof␈α
various␈αdimensions␈α
of␈αa␈α
complex␈αsignal
␈↓with␈α⊃its␈α⊃duration,␈α⊃ the␈α⊂influence␈α⊃of␈α⊃critical␈α⊃bandwidth␈α⊂in␈α⊃the␈α⊃perception␈α⊃of␈α⊂different
␈↓sorts␈α∩of␈α∩complex␈α∩tones,␈α∩and␈α∩numerous␈α∩other␈α∩complex␈α∩aspects␈α∩of␈α∩perception␈α∩which
␈↓demand␈α⊃a␈α⊃highly␈α⊃flexible␈α⊃and␈α∩controlled␈α⊃stimulus␈α⊃source␈α⊃could␈α⊃easily␈α⊃be␈α∩dealt␈α⊃with.
␈↓Many␈α⊂other␈α∂examples␈α⊂will␈α∂be␈α⊂given␈α∂in␈α⊂the␈α∂following␈α⊂pages␈α∂of␈α⊂the␈α⊂possibilities␈α∂which
␈↓are␈α⊃opened␈α⊂to␈α⊃the␈α⊂investigator␈α⊃of␈α⊃auditory␈α⊂perception␈α⊃by␈α⊂our␈α⊃proposed␈α⊃system␈α⊂for
␈↓the␈αexamination␈αof␈αhighly␈αcomplex␈αstimuli␈αand␈αauditory␈αcontexts.


␈↓␈↓∧reverberant␈α
spaces␈α
and␈α
spatial␈α
perception␈↓

␈↓Our␈α∞work␈α
in␈α∞the␈α
computer␈α∞simulation␈α∞of␈α
reverberant␈α∞spaces␈α
also␈α∞requires␈α∞much␈α
initial
␈↓research␈α~that␈α→will␈α~bear␈α~on␈α→auditory␈α~theory.␈α~ Although␈α→there␈α~have␈α~been␈α→many
␈↓investigations␈α∂of␈α⊂the␈α∂physics␈α∂of␈α⊂room␈α∂reverberation,␈α∂very␈α⊂little␈α∂work␈α∂has␈α⊂been␈α∂done
␈↓to␈αdate␈α
on␈αthe␈αimportant␈α
perceptual␈αqualities␈αof␈α
rooms.␈α Systematic␈αexploration␈α
of␈αthe
␈↓perceptual␈α∂properties␈α∞of␈α∂digital␈α∞reverberation␈α∂networks␈α∞and␈α∂optimal␈α∞speaker-channel
␈↓arrangements␈α
will␈α
quantitavely␈α
pinpoint␈αthe␈α
salient␈α
physical␈α
features␈α
that␈αcharacterize
␈↓rooms␈α∂in␈α∞such␈α∂perceived␈α∞attributes␈α∂as␈α∞size,␈α∂shape,␈α∞tonal␈α∂"coloration",␈α∂"liveliness"␈α∞and
␈↓"transparency".␈α∩ We␈α∪will␈α∩also␈α∩examine␈α∪the␈α∩important␈α∩physical␈α∪cues␈α∩which␈α∪give␈α∩the
␈↓listener␈α∞information␈α∞about␈α∞where␈α∞he␈α∞is␈α∞located␈α∞with␈α∞respect␈α∞to␈α∞the␈α∞sound␈α∞source␈α∞and
␈↓the␈αboundaries␈αof␈αthe␈αroom.
␈↓␈↓ ε.3␈↓ (

␈↓Another␈α⊂important␈α⊂area␈α⊂of␈α⊂study␈α⊂which␈α⊂demands␈α⊂further␈α⊂research␈α⊂includes␈α⊂the␈α⊂tonal
␈↓effects␈α∞of␈α∞delay␈α∞times␈α∞in␈α∞reverberation␈α∞due␈α∞to␈α∞the␈α∞distances␈α∞which␈α∞the␈α∞signal␈α∞travels
␈↓along␈αthe␈αvarious␈αpaths,␈αfrom␈αthe␈αsource␈αto␈αdifferent␈αboundary␈αpoints␈αand␈α
in␈αreflection
␈↓back␈α_to␈α↔the␈α_listener.␈α↔ We␈α_are␈α↔quite␈α_interested␈α↔in␈α_following␈α↔up␈α_Bekesy's␈α↔work
␈↓concerning␈αtwo␈αimportant␈αperceptual␈αeffects␈α
linked␈αto␈αdelay:␈αthe␈αtemporal␈α
inhibition␈αof
␈↓a␈αtonal␈α
image,␈αand␈αthe␈α
perceived␈α"volume"␈α
of␈αa␈αsound␈α
source.␈α Another␈α
related␈αmatter
␈↓which␈α≠will␈α~be␈α≠investigated␈α~is␈α≠the␈α~perceptual␈α≠distortion␈α~of␈α≠timbre␈α≠by␈α~colored
␈↓reverberation,␈αwhere␈αone␈αof␈αour␈α
goals␈αis␈αthe␈αimplementation␈αof␈α
colorless␈αreveberation
␈↓networks,␈α⊃using␈α∩both␈α⊃the␈α⊃first-order␈α∩all-pass␈α⊃design␈α⊃of␈α∩Schroeder␈α⊃and␈α∩the␈α⊃second-
␈↓order␈αall-pass␈αdesign␈αdeveloped␈αat␈αour␈αlab.

␈↓An␈α∀important␈α∀aspect␈α∀of␈α∀the␈α∃development␈α∀of␈α∀the␈α∀above␈α∀simulation␈α∃techniques␈α∀and
␈↓perceptual␈α⊂models,␈α⊂in␈α⊂conjunction␈α⊂with␈α⊂the␈α⊂development␈α⊂of␈α⊂a␈α⊂real-time␈α⊂digital␈α⊂signal
␈↓processor,␈α⊂is␈α⊂the␈α⊂possibilities␈α⊂opened␈α⊃for␈α⊂the␈α⊂investigation␈α⊂of␈α⊂spatial␈α⊃perception.␈α⊂ A
␈↓number␈α∩of␈α∩studies␈α∩have␈α∩been␈α∩done␈α∩in␈α∩the␈α∩past␈α∩which␈α∩indicate␈α∩that␈α∩blind␈α⊃listeners,
␈↓specifically,␈α
are␈α
able␈α∞to␈α
perform␈α
quite␈α
amazing␈α∞perceptual␈α
fetes␈α
with␈α
respect␈α∞to␈α
their
␈↓use␈α∩of␈α∩cues␈α∩in␈α⊃the␈α∩surrounding␈α∩auditory␈α∩environment.␈α⊃ This␈α∩includes␈α∩cues␈α∩for␈α⊃self-
␈↓localization␈α∂in␈α⊂the␈α∂surrounding␈α⊂space,␈α∂and␈α∂also␈α⊂for␈α∂various␈α⊂types␈α∂of␈α⊂judgments␈α∂which
␈↓can␈αbe␈αmade␈αabout␈αthe␈α
contents␈αof␈αthe␈αspace.␈α Our␈α
facilities␈αcould␈αbe␈αused␈αto␈α
focus␈αin
␈↓on␈α⊂the␈α⊃various␈α⊂elements␈α⊃of␈α⊂such␈α⊃perceptual␈α⊂fetes,␈α⊃and␈α⊂to␈α⊃study␈α⊂its␈α⊃development␈α⊂in
␈↓sighted␈α⊂listeners.␈α⊂ We␈α⊂also␈α⊃suggest␈α⊂below␈α⊂the␈α⊂use␈α⊃of␈α⊂facilities␈α⊂like␈α⊂ours␈α⊃to␈α⊂actually
␈↓train␈αblind␈αpeople␈αhow␈αto␈αdevelope␈αsuch␈αskills.


␈↓␈↓∧localization␈α
with␈α
multiple␈α
speaker-channels␈↓

␈↓The␈α⊃algorithms␈α⊃which␈α⊃have␈α⊃been␈α⊃designed␈α⊃at␈α⊃our␈α⊃lab␈α⊃for␈α⊃the␈α⊃simuation␈α∩of␈α⊃localized
␈↓sound␈α∂sources␈α⊂manipulate␈α∂the␈α∂perceived␈α⊂angle␈α∂and␈α∂distance␈α⊂of␈α∂a␈α∂signal␈α⊂through␈α∂time
␈↓using␈α∞four␈α∞speaker-channels.␈α∂ They␈α∞are␈α∞largely␈α∞based␈α∂on␈α∞the␈α∞well␈α∂studied␈α∞perceptual
␈↓cues␈α∞for␈α∞angular␈α∞localization␈α∞and␈α∞the␈α∞lesser␈α∞studied␈α∞cues␈α∞for␈α∞distance␈α∞perception␈α∞in␈α∞a
␈↓reverberant␈α∪environment.␈α∪ We␈α∪have␈α∀found␈α∪no␈α∪other␈α∪research␈α∪on␈α∀localization␈α∪using
␈↓more␈αthan␈αtwo␈αspeaker-channels,␈αor␈αon␈α
the␈αsimultaneous␈αmanipulation␈αof␈αa␈αset␈α
of␈αcues
␈↓for␈αauditory␈αlocalization␈αand␈αmotion␈αperception.

␈↓One␈α∀important␈α∪question␈α∀which␈α∀our␈α∪research␈α∀proposes␈α∀to␈α∪address␈α∀is␈α∀the␈α∪trade-off
␈↓between␈αthe␈α
number␈αof␈α
independent␈αspeaker-channels␈α
and␈αthe␈α
quality␈αof␈α
control␈αover
␈↓the␈αlocalization␈αcues.␈α Much␈α
of␈αour␈αwork␈αwill␈α
be␈αconcerned␈αwith␈αthe␈α
perceptual␈αscaling
␈↓of␈α∂the␈α∂various␈α∂cues␈α∂such␈α⊂that␈α∂their␈α∂interactive␈α∂relationships␈α∂will␈α∂be␈α⊂quantified.␈α∂ This
␈↓will␈α∀include␈α∀an␈α∃examination␈α∀of␈α∀the␈α∃following␈α∀relationships:␈α∀perceived␈α∃distance␈α∀and
␈↓amplitude;␈α~perceived␈α~distance␈α→and␈α~reverberation-to-direct␈α~signal␈α~ratio;␈α→absolute
␈↓␈↓ ε.4␈↓ (

␈↓amount␈α⊃of␈α⊃reverberation␈α∩and␈α⊃power␈α⊃of␈α⊃distance␈α∩cue;␈α⊃angular␈α⊃perceptual␈α∩acuity␈α⊃and
␈↓motion␈α∞perception;␈α
amount␈α∞of␈α
Doppler␈α∞shift␈α
and␈α∞perceived␈α
motion␈α∞with␈α
respect␈α∞to␈α
the
␈↓other␈αcontributing␈αcues.


␈↓␈↓∧pitch␈α
perception␈↓

␈↓The␈α
type␈α∞of␈α
real-time,␈α∞interactive,␈α
digital␈α∞signal␈α
processing␈α∞system␈α
which␈α∞we␈α
propose
␈↓to␈α⊃develope␈α⊂will␈α⊃make␈α⊂possible␈α⊃the␈α⊂examination␈α⊃of␈α⊂the␈α⊃perception␈α⊂of␈α⊃pitch␈α⊃in␈α⊂more
␈↓complex␈α∂instances␈α∂than␈α∂normally␈α∞studied.␈α∂ Pitch␈α∂perception␈α∂has␈α∞long␈α∂been␈α∂one␈α∂of␈α∞the
␈↓most␈α↔highly␈α_explored␈α↔areas␈α↔of␈α_auditory␈α↔research.␈α↔ There␈α_is␈α↔a␈α↔current␈α_trend␈α↔in
␈↓psychoacoustics␈α∞to␈α∞look␈α∂at␈α∞pitch␈α∞perception␈α∞with␈α∂quite␈α∞abnormal␈α∞stimuli,␈α∂for␈α∞example,
␈↓bandwidths␈α∀of␈α∪delayed␈α∀noise,␈α∪small␈α∀sets␈α∪of␈α∀upper␈α∪harmonics␈α∀produced␈α∀by␈α∪filtered
␈↓pulse␈α∪trains␈α∪or␈α∪by␈α∪modulation␈α∪of␈α∪a␈α∪carrier␈α∪frequency,␈α∪and␈α∪in␈α∪some␈α∪instances␈α∩such
␈↓stimuli␈α⊂are␈α∂examined␈α⊂in␈α∂a␈α⊂dichotic␈α∂condition.␈α⊂ Theories␈α∂are␈α⊂emerging␈α⊂which␈α∂postulate
␈↓more␈α∞central␈α∞pitch␈α
processing␈α∞than␈α∞was␈α∞generally␈α
held␈α∞with␈α∞the␈α∞traditional␈α
theoretical
␈↓approaches.␈α It␈αis␈αnot␈αaltogether␈αclear,␈αhowever,␈αjust␈αwhat␈αthe␈αrelative␈α
importances␈αof
␈↓these␈α⊂many␈α⊂atypical␈α⊂types␈α⊂of␈α⊂pitch␈α⊂perception␈α⊂are␈α⊂with␈α⊂respect␈α⊂to␈α⊂daily␈α⊂perceptual
␈↓phenomena.

␈↓We␈α∂therefore␈α∂suggest␈α∞that␈α∂our␈α∂system␈α∂could␈α∞be␈α∂applied␈α∂to␈α∞the␈α∂study␈α∂of␈α∂these␈α∞many
␈↓sorts␈α∂of␈α∂pitch␈α∞perception,␈α∂where␈α∂a␈α∞greater␈α∂degree␈α∂of␈α∞control␈α∂could␈α∂be␈α∂exerted␈α∞over
␈↓the␈α∃stimulus␈α∃space␈α∀than␈α∃is␈α∃normally␈α∃possible␈α∀with␈α∃analog␈α∃facilities.␈α∃ For␈α∀instance,
␈↓melodic␈α
lines␈α
could␈α
be␈α
constructed␈α
on␈α
the␈α
basis␈α
of␈α
the␈α
type␈α
of␈α
pitch␈α
phenomenon␈α
that
␈↓is␈α∞being␈α∞investigated.␈α∞ Comparisons␈α∞between␈α
various␈α∞pitch␈α∞phenomena␈α∞could␈α∞be␈α
made
␈↓directly,␈α∪with␈α∪the␈α∪same␈α∀laboratory␈α∪facilities.␈α∪ Several␈α∪unexplored␈α∀pitch␈α∪phenomena
␈↓which␈α∂have␈α∂only␈α∂been␈α∂suggested,␈α∂could␈α∂be␈α∂easily␈α∂examined,␈α∂such␈α∂as␈α∂the␈α∂possibilities
␈↓of␈α⊂the␈α⊃pitch␈α⊂of␈α⊃spectral␈α⊂zeros,␈α⊃and␈α⊂melodies␈α⊃based␈α⊂on␈α⊃the␈α⊂harmonics␈α⊃themselves␈α⊂(a
␈↓technique␈α∪now␈α∪being␈α∪explored␈α∪by␈α∩musicians␈α∪that␈α∪remains␈α∪highly␈α∪controversial␈α∩with
␈↓psychoacousticians).␈α∞ The␈α∞correlates␈α∞to␈α∞listeners␈α∞who␈α∞are␈α∞or␈α∞aren't␈α∞able␈α∞to␈α∞hear␈α
such
␈↓pitch␈α↔phenomena␈α↔could␈α↔also␈α↔be␈α↔investigated,␈α↔as␈α↔well␈α↔as␈α↔techniques␈α_for␈α↔training
␈↓listeners␈α⊂to␈α⊂hear␈α⊂such␈α⊂phenomena.␈α⊂ Given␈α∂the␈α⊂tools␈α⊂which␈α⊂we␈α⊂will␈α⊂develope␈α⊂for␈α∂the
␈↓simulation␈α
of␈α
natural␈α
instrument␈α
tones,␈α
comparisons␈α
could␈α
also␈α
be␈α
made␈α
with␈α
the␈αsorts
␈↓of␈α
pitch␈αphenomena␈α
found␈αin␈α
daily␈αlife.␈α
 In␈αfact,␈α
much␈αmore␈α
could␈αbe␈α
learned␈α
about␈αthis
␈↓latter␈α⊃type␈α⊃of␈α⊃pitch␈α⊃perception,␈α⊃on␈α⊃a␈α⊃psychoacoustic␈α⊃level,␈α⊃with␈α⊃the␈α∩possibilities␈α⊃of
␈↓manipulating␈αthe␈αsignals␈αin␈αreal␈αtime␈αgiven␈αby␈αour␈αsystem.


␈↓␈↓∧loudness␈α
perception␈↓
␈↓␈↓ ε.5␈↓ (

␈↓Another␈α∞phenomenon␈α∞which␈α∞has␈α∞attracted␈α∞considerable␈α∞attention␈α∞in␈α∞auditory␈α∞theory␈α
is
␈↓that␈α↔of␈α↔the␈α↔perception␈α↔of␈α↔loudness.␈α↔ Much␈α↔seems␈α↔to␈α↔be␈α↔known␈α↔about␈α⊗loudness
␈↓perception␈α≥with␈α≥simple␈α≥tones,␈α≥but␈α≥the␈α≥issue␈α≥at␈α≥present␈α≡appears␈α≥hopelessly
␈↓complicated␈α∩in␈α∩the␈α∩case␈α∩of␈α∪complex␈α∩tones,␈α∩especially␈α∩tones␈α∩which␈α∪have␈α∩temporally
␈↓dynamic␈α∪spectral␈α∪characteristics.␈α∪ We␈α∀suggest␈α∪that␈α∪our␈α∪system,␈α∪and␈α∀the␈α∪simulation
␈↓techniques␈α→here␈α→developed,␈α→would␈α_be␈α→of␈α→great␈α→use␈α_to␈α→the␈α→study␈α→of␈α_loudness
␈↓perception␈α∃in␈α∃the␈α∃more␈α∀complex␈α∃cases.␈α∃ In␈α∃that␈α∀no␈α∃system␈α∃for␈α∃the␈α∃prediction␈α∀of
␈↓loudness␈α∞induced␈α∞from␈α∞the␈α∞existing␈α∞body␈α∞of␈α∞psychoacoustical␈α∞data␈α∞has␈α∞been␈α∞generally
␈↓accepted,␈αan␈α
empirical␈αapproach␈α
to␈αthe␈α
question␈αmay␈α
uncover␈αa␈α
much␈αwider␈α
data␈αbase
␈↓from␈α
which␈α
to␈α∞induce␈α
models.␈α
 It␈α
is␈α∞clear␈α
that␈α
such␈α
a␈α∞wide␈α
data␈α
base␈α
must␈α∞include␈α
the
␈↓very␈α∞complex␈α∞stimuli␈α∞which␈α∞we␈α∞propose␈α∞to␈α∞model␈α∞and␈α∞simulate,␈α∞and␈α∞furthermore,␈α
that
␈↓the␈α⊃signal␈α∩processor␈α⊃would␈α⊃be␈α∩an␈α⊃ideal,␈α⊃if␈α∩not␈α⊃the␈α⊃only,␈α∩way␈α⊃to␈α⊃fully␈α∩explore␈α⊃such
␈↓complex␈α∃stimuli.␈α∃ We␈α∃have␈α∃no␈α∃reason␈α∃to␈α∃expect,␈α∃in␈α∃fact,␈α∃that␈α∃the␈α∃perception␈α∃of
␈↓loudness␈α
is␈αmuch␈α
less␈αcompicated␈α
than␈αthe␈α
perception␈αof␈α
timbre.␈α To␈α
the␈α
contrary,␈αour
␈↓preliminary␈α∂encounters␈α⊂with␈α∂the␈α∂effects␈α⊂of␈α∂loudness␈α∂on␈α⊂timbre␈α∂indicate␈α∂that␈α⊂the␈α∂two
␈↓phenomena␈α∩are␈α∩highly␈α∩interconnected␈α∩perceptually.␈α∩ This␈α∩should␈α∩be␈α∩the␈α∪case,␈α∩since
␈↓they␈αdo␈αboth␈αhave␈αmuch␈αto␈αdo␈αwith␈αthe␈αspectral␈αdistribution␈αof␈αenergy␈αthrough␈αtime.


␈↓␈↓∧duration␈↓

␈↓Another␈αaspect␈αof␈αaudition␈αwhich␈αcould␈α
be␈αstudied␈αwith␈αour␈αsystem␈αis␈αthat␈α
of␈αduration.
␈↓We␈αhave␈αalready␈αsuggested␈αthat␈αthe␈α
effects␈αof␈αduration␈αon␈αthe␈αvarious␈αaspects␈α
of␈αthe
␈↓perception␈α∃of␈α∀complex␈α∃tones␈α∀could␈α∃be␈α∀easily␈α∃examined␈α∀with␈α∃our␈α∃proposed␈α∀signal
␈↓processing␈α⊂system.␈α∂ For␈α⊂example,␈α∂investigators␈α⊂are␈α∂recently␈α⊂interested␈α∂in␈α⊂a␈α∂detailed
␈↓examination␈α∪of␈α∀the␈α∪interaction␈α∪of␈α∀critical␈α∪bandwidth␈α∪and␈α∀duration␈α∪for␈α∪a␈α∀number␈α∪of
␈↓stimulus␈α∀configurations,␈α∀duration␈α∀of␈α∀the␈α∀signal,␈α∪of␈α∀the␈α∀masking␈α∀noise,␈α∀of␈α∀the␈α∪delay
␈↓between␈α⊂noise␈α⊂and␈α⊂signal,␈α⊂and␈α⊂of␈α⊂the␈α⊂bandwidths␈α⊂of␈α⊂energy␈α⊃distribution.␈α⊂ Eventually
␈↓researchers␈α∞may␈α∞want␈α∞to␈α∞study␈α∞these␈α∞complex␈α∞interactions␈α∞with␈α∂time-varying␈α∞signals,
␈↓where␈α∂certain␈α⊂physical␈α∂parameters␈α∂actually␈α⊂change␈α∂over␈α∂time.␈α⊂ It␈α∂would␈α∂seem␈α⊂that␈α∂a
␈↓system␈α
like␈αthe␈α
one␈αwhich␈α
we␈αpropose␈α
provides␈αthe␈α
best␈αway␈α
to␈αgenerate␈α
stimuli␈αand
␈↓collect␈α∂data␈α∞in␈α∂such␈α∞experiments.␈α∂ There␈α∞are␈α∂several␈α∞other␈α∂examples␈α∞which␈α∂could␈α∞be
␈↓named␈α∞where␈α
the␈α∞influence␈α
of␈α∞signal␈α
duration␈α∞is␈α
of␈α∞interest,␈α
and␈α∞a␈α
flexible␈α∞system␈α
for
␈↓stimulus␈α∀production␈α∪and␈α∀presentation␈α∪would␈α∀be␈α∀of␈α∪great␈α∀use␈α∪in␈α∀carrying␈α∀out␈α∪such
␈↓research.

␈↓Another␈α⊗area␈α⊗which␈α⊗is␈α⊗closely␈α⊗related␈α∃to␈α⊗the␈α⊗above␈α⊗involves␈α⊗the␈α⊗perception␈α∃of
␈↓duration␈α↔itself.␈α↔ Here␈α_we␈α↔may␈α↔be␈α↔interested␈α_in␈α↔the␈α↔contributing␈α↔factors␈α_to␈α↔the
␈↓perceived␈α∩duration␈α∩of␈α∪a␈α∩complex␈α∩time-varying␈α∩signal␈α∪as␈α∩measured␈α∩with␈α∪respect␈α∩to
␈↓some␈α∀set␈α∀of␈α∀stimuli.␈α∀ The␈α∀time-varying␈α∀properties␈α∀of␈α∀the␈α∀set␈α∀of␈α∀stimuli␈α∀could␈α∀be
␈↓␈↓ ε.6␈↓ (

␈↓completely␈α∂specified␈α⊂with␈α∂our␈α⊂simulation␈α∂techniques,␈α∂and␈α⊂the␈α∂important␈α⊂effects␈α∂could
␈↓be␈α∂deduced.␈α∂ We␈α∂are␈α∞in␈α∂the␈α∂process␈α∂of␈α∞formulating␈α∂experimental␈α∂approaches␈α∂for␈α∞the
␈↓measurement␈α∂of␈α∂the␈α∂relative␈α∂perceived␈α∂onset␈α⊂and␈α∂offset␈α∂times␈α∂for␈α∂a␈α∂set␈α⊂of␈α∂complex
␈↓signals,␈α∞a␈α∞closely␈α∞related␈α∞matter.␈α∞ Again,␈α∞this␈α∞sort␈α∞of␈α∞measurement␈α∞is␈α∞very␈α∞impractical
␈↓unless␈α
one␈α
has␈αa␈α
real-time␈α
digital␈αsynthesis␈α
capacity␈α
where␈αthe␈α
listener␈α
has␈α
access␈αto
␈↓a␈α∞continuous␈α∂range␈α∞of␈α∂durations.␈α∞ Present␈α∞schemes␈α∂for␈α∞adjusting␈α∂durations␈α∞of␈α∂a␈α∞time-
␈↓varying␈α⊂complex␈α⊂signal␈α⊂require␈α∂the␈α⊂preparation␈α⊂of␈α⊂a␈α∂large␈α⊂number␈α⊂of␈α⊂discrete␈α∂cases
␈↓which␈α⊃may␈α∩be␈α⊃randomly␈α⊃accessed␈α∩by␈α⊃the␈α∩listener␈α⊃in␈α⊃the␈α∩experiment,␈α⊃a␈α∩very␈α⊃costly
␈↓approach,␈αand␈αone␈αwhich␈αnecessitates␈αa␈αlarge␈αdigital␈αstorage␈αcapacity.