The Fusion and Layering of Noise and Tone: Implications for Timbre in African Instruments
Author(s): Cornelia Fales and Stephen McAdams
Source: Leonardo Music Journal, Vol. 4 (1994), pp. 69-77
Published by: The MIT Press
Stable URL: http://www.jstor.org/stable/1513183
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4
SOUNDING
THE
A B S T RA C T
MIND
The
Fusion
and
Tone:
Implicatons
African
Instruments
in
and
Layering
of
Noise
for
Timbre
Cornelia
Fales
and StephenMcAdams
From theirfirstcontactwithAfricanmusic,Western ethnomusicologistshaveremarkedon the predilectionof
Africanmusiciansto "layer"(or superimpose) musical and
non-musicalsound until the distinctionbetweenthem is lost
[1]. In particular,it has been observed that Africanmusic
showsa specialfascinationwith 'Cnoise''-thetransformation
of ordinary,mundane sounds into the substanceof music.
And while the manufactureof classicalinstrumentsand the
performancepracticeof Westernmusicianshas aimedtoward
reducingthe amountof extraneousnoise producedby an instrument,Africanmusiciansaugment the naturalnoise potentialof their instrumentby attachingnoise-makerssuch as
rattlingseeds or bottle caps on which the vibrationsof the
main resonatoroperate.The effect is a complicatedlayering
of sound, rich in aperiodiccomplexity.
One of the motivationsfor our studywas the realization
that the combination of noise and musical elements, traditionallydescribedby ethnomusicologistsas "layering,"
actually takesat least two perceptualforms. Either the sound is
trulylayered,and listenershear twoor more perceptuallydiF
tinct sounds concurrently,or the physicallysuperimposed
sounds are perceptuallyfused, so that listenershear a single
sound a blend of the twosounds neither of whichis identifiable as the primar-yor the superimposedsound. A more
commonlyrecognized example of this distinctionis the difference betweena voice speakingthroughor in the presence
of noise (layerednoise and voice) and a hoarsevoice speaking (noisyvoice).
The directionof our researchhas involvedboth perceptual
experimentand acousticanalyses.Like manypsychoacoustic
studies,the first (experimental)part of our investigationinvolved the use of artificialstimuli, reduced to controllable
acoustic variables. To complement this part, an acoustic
analysisof real African instrumentsin which noise plays a
prominent part was essential to verifythe relevance of our
experimental results to sounds actuallyproduced by those
instruments.In particular,our experimentswere geared to-
Since their earliest explorations of Africanmusic, Western researchers have noted a fascination
on the part of traditionalmusicians
for noise as a timbralelement. The
authors present the results of perceptual and acoustic investigations
of the fusion and "layeringnof
noise and tone. These results have
implicationsfor pitch and timbre in
both traditionaland non-traditional,
acoustic and synthesized music.
The results define possible perceptual relations between noise and
tone and reveal that the construction of noise devices should follow
relativelyprecise acoustic rules involving the frequency, the bandwidth and the level of the noise
relativeto those of the tone. The
results also exemplifythe fusion of
wardestablishingthe parameters
twoextremelydifferenttimbres,
of noise and tone that influence
withimplications
forthe blendingof
the perceptual relation between
instrumental
timbresinan orchestralsethng.Theexpenments
them. We consldered three posshouldbe of interesttocomposers
sible relationsbetweennoise and
whosynthesizemixturesof noise
tone: (1) fusion (the noise and
andperiodicsoundandforwhom
tone are perceptuallyintegrated
the controlof suchmixturesrb
mains problemabc.
lnto a slngle sound event, both
contributing to the perceptual
qualityof the event), (2) laymng
(the two components are perceptuallysegregated into disiinct percepts,each withits own perceptualqualities)and (3)
maskingoftone by noise (the more intense noise "coversup"
the tone that can thus no longer be heard andhas no perceptual effect on the noise component). Layering is distinguished from fusion and maskingin that a layeredtone can
be heardseparatelyfrom the noise. Whilea tone that is fused
with a noise cannot be heard separately,it still contributesto
the timbralqualityof the noise; a maskedtone has no such
effect, because it has been perceptually"eradicated."
These
three perceptualphenomenaappearto depend on variations
of three acousticparameters:(1) the relativeintensitylevels
of the two components, (2) the bandwidthof the noise and
(3) the center frequency of the noise band relative to the
tone frequency.Since informalpilot testsshowedthat, in addition to these parameters,the perceptualrelationbetween
Fig. 1. Intensity series: Means (filled circles) and standard deviations (SD) (vertical bars indicate i 1 SD) of responses for each intensity difference between tone and noise for high register stimuli
with a 100-Hz band of noise centered on a 400-Hz tone.
INTENSllY SERIES,highregister
6-
'e
g:
V)
3
Cornelia Fales (ethnomusicologist), Institut de Recherche et Coordination
Acoustique/Musique (IRCAM), 1 place Stravinsky, F-75004 Paris, France.
2
Stephen McAdams (experimental psychologist), Laboratoire de Psychologie
Experimentale (CNRS), Universite Rene Descartes, EPHE, 28 rue Serpente, F-75006
Paris, France.
Manuscript solicited by Kathryn Vaughn.
Received 11 May l994.
K)1995 ISAST
-2s
-1s
-s
s
1S
Difference in noise and tone level (dB)
25
LEONARDO MUSIC JOURNAL, Vol. 4, pp. 69-77, 1994
69
-
-t
|
INTENSll Y SERIES,low register
.
.
.
.
.
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6"
3
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tC
1
,
25
.
.
.
,
5
-5
-15
15
innoiseandtone1eLevel(dB)
Difference
-25
-in which the noise center frecywas tested relative to the tone
Lency-the tone varied as described
in high and low registers, and the
rfrequency of the noise was offset
the tone by up to 200 Hz in the low
terand up to 400 for the high regThe noise in this last series had a
bandwidth of 100 Hz.
a given trial in one of the series, a
W
/noise stimulus was presented
times in succession. Each stimulus
00msec in duration and the onsets
ffsets of the noise and tone compo,were synchronous. The tone was
nted at a mean level of 57 dB SPL
ingrandomly by + 9 dB around this
on a trial-to-trial basis), and the
level was determined with respect
islevel for each trial.
e perceptual research was peredat Institut de llecherche et CoorionAcoustique/Musique (IRGAM),
sic research institute in Paris. We
fore were initially constrained in
stenerswe could readily test, being
ed primarily to Europeans and
noise and tone was greatly affected by
the pitch register of the two elements,
each of the three parameterswere varied for stimuliconstructedaroundboth
high and low registers (centered at
1,000 Hz and 400 Hz, respectively).
PERCEPrUAL RESEARCH
GeneralMeffiod
The experiments were organized in
three series, each testing the effect of a
different acoustic parameteron tone/
noise fusion. In the Intensity Series,
pure tones (sinusoidal waveform) in
high and low registerswere combined
with band-filteredwhite noise havinga
bandwidthof 100 Hz and a center frequencycoincidingwiththe frequencyof
the tone. For this series, the intensity
level of the tone variedrandomlywithin
a given range, while the noise level was
offset from the tone level by specificincrements.Forthe BandwidthSeries,this
procedure was repeated for several
noise bandwidths ranging from 50 to
200 Hz. For the Center FrequencySe-
Fig. 3. Bandwidthseries: Means(filled circles) for response categories 3 and 4 (indicatingfusion) for each bandwidthas a function of
level difference between tone and noise for high register.Vertical
axis shows amplitudedifference between tone and noise; horizontal axis indicatesbandwidth.
highregister
SERIES,
BANDWIDTH
|
|
6
|
|
|
Fig. 2. Intensity series: Means (filled
circles) and standard deviations
(SD) (vertical bars
indicate + 1 SD) of
responses for each
intensity difference
between tone and
noise for low regis
ter stimuli with a
100-Hz band of
noise centered on a
l,OOO-Hztone.
l
g
North Americans.Since the aim of this
part of the work was to establish some
basic psychoacousticthresholdsand because psychoacousticphenomenaat this
level are generallythought to be a function of the human hearing apparatus
(whichis essentiallythe same for all human beings), we considered the results
obtained from this study to reflect universal properties of auditory perception althoughthis assumptionwarrants
verificationin future research.Froman
ethnomusicologicalpoint of view,however,it is noteworthythat informalpilot
testswiththese subjectsrevealedthatthe
notion of fusion betweendissimilartimbreswasa difficultconceptto graspintellectuallyand, even moreso, perceptually.
Initially,subjectswere askedto rate on a
continuum the "degreeof fusion"demonstratedby a seriesof stimuli,but it became evident that the subjectswere unclear as to the definition of the
perceptualphenomenon that they were
askedto judge. Therefore,as an alternative, the subjectswere askedwhetherthe
acoustic components comprisedone or
two sounds,since fusion transformsmultiple elements into a single unitarypercept. Subjects were asked, in other
words, to rate the degree to which the
tone could be heard separatelyfrom the
noise in each trial.
Twenty-three listeners (all but one
had had some musical training; none
were professional musicians) were instructed to decide whether they heard
the tone separately from the noise or
not and to rate their certaintyby selecting one of six buttons as follows: (1)
"Toneheard separately:I am sure";(2)
"Tone heard separately: I am fairly
sure";(3) 'Woneheard separately:I am
not sure";(4) "ToneNOT heard sepa-
Fig. 4. Bandwidthseries: Means (filled circles) for response categories 3 and 4 (indicatingfusion) for each bandwidthas a function of
level diSerence between tone and noise for low register.Vertical
axis shows amplitudedifference between tone and noise; horizon- tal axis indicatesbandwidth.
BANDWIDTHSERIES,low register
|
r
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lS0
125
lQ0
Noise bandwidth(Hz)
175
200
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75
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125
150
175
200
Noise bandwidth (Hz)
70
Fales and Mc24dams,The Fusion and Layering of Noise and Tone
sO
7s
'
O.
/
..........
BANDWIDTH SERIES,high register
......................
X
s
=
X
Z
..
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BANDWIDTH SERIES,low register
6S
s
a
6
S-
sz
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-240
-40
160
360
Offset of noise centerfrequencyfrom tone frequency
Fig. 5. CenterFrequencySeries:Means (filled circles) of responses
for high registerstimuliin whichcenter frequencyof noise bandwidth is offset from tone frequencyby up to 400 Hz. Verticalaxis
shows response, horizontalaxis shows offset of noisocenter fro
quencyfrom tone.
rately:I am not sure";(5) 4'ToneNOT
heard separately:I am fairly sure";(6)
'4Tone NOT heard separately: I am
sure." We call these judgments "tone
separationratings."For the final Center
FrequencySeries,listenerswere alerted,
in addition,that the rangeof perceptual
differences might be changed, since
there might no longer be a condition in
which the tone was not heard at all, as
occurredin the firsttwo seriesof trials.
IntensitySeries
Tone separationratingswere made for
11 intensity differences between tone
and noise varyingfrom -25 to +25 dB in
5dB increments.Eachconditionwasrepeated five times for each listener.
These responses were then averaged
across listeners and repetitions. The
mean responses and their standarddeviations (a measure of variationacross
responses for a given condition) for
each intensity difference are shown in
Figs 1 and 2 for high and low registers,
respectively.Note thatwhen the noise is
weakcomparedto the level of the tone,
low ratingsare given (tone heard separately) and when the noise is intense,
high ratingsare given (tone not heard
separately).The curves for both registerssuggesta gradualprogressionof the
perceptfrom separationthroughfusion
to masking.
Presumingthat high ratings (5-6) indicate that the tone may be masked by
the noise and thatlow ratings(1-2) indicate that the tone is heard separately
fromthe noise, we takeintermediateratings (3 4) as indicativeof the conditions
under which the tone and noise are beginning to fuse. Figures 1 and 2 show
that the degree of noise-tonerelationin
-120
-20
80
180
Offsetof noisecenterfrequencyfromtonefrequency
Fig. 6. CenterFrequencySeries:Means (filled circles) of responses
for low registerstimuliin whichcenter frequencyof noise bandwidth is offset from tone frequencyby up to 200 Hz. Verticalaxis
shows response, horizontalaxis shows offset of noise-centerfrequencyfrom tone.
the high and low registers differs most were averagedacrosssubjectsand plotdramatically on the high intensity-differ- ted in Figs 3 and 4 for the low and high
ence end of the curve. For the low regis- registers,respectively.This comparison
ter, when the noise exceeds the tone by shows that the difference in level bemore than about 4 dB, the tone begins to tween tone and noise at the fusion
lose audibility;when the noise intensity is thresholddecreasesslightlyfor both the
less than the tone by about 15 dB, the high and low registersas the bandwidth
tone separates and the sound is layered. increases from 50 to 75 and then reBased on intermediate ratings, a Elrstes- mains relatively constant for larger
timation of the necessary intensity rela- bandwidths.
tion between noise and tone, therefore,
puts the fusion region between -7 and Center FrequencySeries
-1 dB, noise relative to tone. For the high In this experimental series, a constant
register, fusion appears to occur when the bandwidth(100 Hz) and noise-intensity
intensity level of the noise is between -3 level (65 dB with respect to the tone
and +4 dB, relative to the tone. There level) were maintained, while varying
would appear, therefore, to be a differ- the difference between the center freence between high and low registers, fu- quency of the noise and the tone fresion occurring at a slightly higher inten- quency from -200 to +200 Hz in incresity difference (about 3 dB) for the high ments of 20 Hz for the low registerand
register than for the low register.
from -400 to +400 Hz in incrementsof
BandwidthSeries
Tone separation ratings were made for
11 intensity differences as in the previous series, but here they were performed for each of five noise bandwidths varying from 50 to 200 Hz in
5SHz increments. The noise bands were
created with a second-order bandpass
filter. Each condition was repeated three
times for each listener. These responses
were then averaged across listeners and
repetitions. For this series, the same
types of mean response curves resulted,
with the same difference in registers, as
were seen for the first series with a noise
bandwidth of 100 Hz. In order to compare the intensity differences between
noise and tone in the fusion region (responses 3-4) across the different bandwidths, the intensity differences corresponding to mean responses of 3 and 4
40 Hz for the high register.It is important to note that for the stimuli in this
series, there was no condition in which
the noise maskedthe tone, since the intensitylevel of the noise remainedconstant at a level difference found to be
within the fusion response area for a
bandwidthof 100 Hz in the firstexperimental series. Thus, for this series, response category 6 (Tone NOT heard
separately:I am sure) wastaken to indicate the greatest degree of fusion, and
response category 5 (Tone NOT heard
separately:I am fairlysure) was considered the fusion threshold.In this series,
in other words,judgments of non-separation were taken to indicate fusion
rather than masking, given the signal
parametersused.
Mean responses across listeners and
repetitions as a function of the frequency difference are shown in Figs 5
Fales and McAdams,The Fusion and Layering of Noise and Tone
71
20
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2000
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4000
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5000
6000
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7000
8000
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9000
10000
Fig. 7. Narrowband spectrum of harmonic elements of flute tone of fundamental frequency 1,032 Hz. The horizontal axis corresponds to frequency (in Hz), and the vertiical
axis to amplitude (in dB). The fundamental frequency is approximately 1,032 Hz.
de
--
-
Discussion of the Perceptual
Experiments
--+
-
-
Hz
Fig. 8. Narrowband spectrum of noise elements of flute tone of fundamental frequen
1,032 Hz. The horizontal axis corresponds to frequency (in Hz), and fhe vertical axis CYor
responds to amplitude (in dB). Note fhe similarity in envelope (outline of peaks) of Jd
he
noise spectrum to fhe harmonic spectrum above, indicating fhat noisebands are rouglhly
centered on primary harmonics.
de
Hz
Fig. 9. Narrowband spectrum of flute tone (complete) of fundamental frequency 1,032!Hz
The horizontal axis corresponds to frequency (in Hz), and the vertical axis to amplitude
(in dB). Note presence of a second set of Zharmonics," which are marked by arrows. Note
I
also that the width of noisebands sulsounding fundamental and second two harmonic sare
roughly as large as the bandwidfhs of the auditory filters centered on these componen 8
72
and 6 for both registers. These curves
demonstrate that fusion is affected by
the way the auditory system Ellters the
incoming sound into frequency bands
in a manner similar to that shown for
masking by a vast body of psychoacoustic
research. The peripheral auditory system can be considered to be a bank of
overlapping bandpass filters (called "auditory filters'') whose center frequencies
cover the audible frequency range and
whose bandwidths (often called "critical
bandwidths") vary systematically with
the center frequency, being smaller at
low frequencies and larger at high frequencies. Thus, as the center frequency
of the noise moves away from the tone
frequency and its energy starts to fall
outside the auditory filter center on the
tone, the degree of fusion decreases.
This effect gives rise to the bell-shaped
curves in Figs 5 and 6.
Eales and McAdams,The Fusion and Layering of Noise and Tone
From an ethnomusicological point of
view, a primary interest of the results obtained so far resides in the relatively
small range of the acoustic parameters
that determine fusion. While we have
not yet tested the three parameters as
they might operate for fusion with complex tones, we can hypothesize that if a
musician were to construct an ideal
noise device intended to fuse with a continuum of pure tones that made up the
pitch inventory (an altogether unrealistic scenario), the device would produce
noise having the following characteristics: (1) a bandwidth as large or larger
than that of an auditory filter centered
on the highest pitch of the instrument;
(2) a center frequency as close as possible to the frequency of the tone with
which it is to fuse, but with a frequency
offset small enough to still allow the required noise power to enter an auditory
filter centered on the lowest frequency
produced by the instrument; and (3) an
intensity level that allows the required
noise power to enter the auditory filter
centered on the highest frequency produced by the instrument, given the chosen bandwidth of the noise. Informal
testing of laboratory stimuli has demonstrated that the fusion of noise with a
more realistic complex tone is more
complicated than fusion with a pure
tone. It is not a simple matter of surrounding each harmonic with noise or
adding a single block of noise with
bandwidth equal to the bandwidth of
the complex tone. However, though
confirmationwill only be possible with
continued experimentation,we suggest
that to the extent that the noise phenomena of fusion and masking are related, then our resultson the fusion of a
pure tone might be relevantto complex
tones as well. Since there are indeed instruments (such as the sanza of Southern, CentralSand West Africa, an exampleof whichwe will discussbelow) in
whicha unitarynoise devicecontributes
a cross-frequency
i'buzz"to the timbre,it
is probable that the invention of such
devices is neither haphazard nor
epiphenomenal. It does not appear to
be the case that the use of fused noiseS
at anz7rate,is simplyanotherexampleof
the Africanpredilectionfor layeredtextures. Rather, as demonstrated below,
sllch devlcesmustbe carefullychosen or
constructed in order to achieve a desired effect.
AGOUSTIGANALYSES
The second part of our study aims to
complement the perceptual research
withacousticanalysesof noise devicesin
Africanmusicalinstruments.The analyses whose results are presented here
were done using two kindsof digitalsignal processing software developed at
IRCAM.The firstof these (whichwe will
call Znoise-separation")separates the
non-periodic part of the signal (the
noise) from the periodic part (harmonic tone). The second is a filtering
program that allows very fine pass- or
stopbandfiltering by literally"drawing
ins'the desiredfilter on a spectrum.We
present the results from three instruments, a traditional bamboo flute, a
sanza [2] with a single level of metal
mellae
(tonglles) and a musical bow
[3]. All three intruments are from
Bllrundi and were chosen for analysis
because the first two demonstratefused
noise and tone} and the last demonstrateslayerednoise and tone.
Regardingthe fused instrumentssthe
flute has a relativelysimple spectrum
while the sanza is more complicated.
Perceptually,the flute timbreis characterized by breathiness or air noise,
which- although weaker in regard to
fusion than the noise in our synthesized
examplesemonstrates severalparameters of concern in our fusion experiments. The sanzanoise is produced by
beer bottle capsthathavebeen attached
to the resonator of the instrument.
Noise-tonefusion in the case of this instrumentis perceptuallymuch stronger
than for the flute. For the musicalbow,
which demonstratesunfused noise and
tone and whose spectrum is also relativelycomplicated,noise is producedby
metal isclackers'attached to the gourd
resonator,producinga metallicjingling
sound superimposedover the sound of
the struckcord.
Ironically,the majorproblemencountered in noise analysis of real instruments is exactly the result of the phenomenon that is the object of our
research:both acousticallyand perceptually,noise is intertwinedwith other elements of the music with tremendous
complexity.Whetherthe noise is layered
or fused,the resultingacousticsignal,of
course, includes both noise and tonal
components and the distinction between them is difficult to detect. The
noise-separationsoftwarethat we used
operates on the assumption that the
constituentnoise elements are lower in
amplitude within a given frequencyregion than the harmonicelements. The
results of our perceptual experiments
show that it is possible to achieve perceptual fusion of noise and tone even
when the noise is at a higher level than
the tone. Indeed the last instrumentwe
will discuss-the musical bow- shows
noise elements that are more intense
than periodic elements in some frequencyregions.In the case of the musical bow then, the noise-separationsoftwarewas unable to distinguishperiodic
from aperiodic elements, and we used
filtering softwareto isolate noise from
the harmonicelements.Evenin the case
of the flute and sanzaewhere the noise
separation program was 1lsed the
sampleshad to be resubmittedfor processing severaltimes, in order to separate noisy from periodic elements as
much as possible.
Wewilllook firstat the instrumentsin
which noise and tone fuse. Figures7-12
below show spectra of the flute and
sanza.In the Elrstgroup of three Fig. 7
shows the harmonic elements only of
the flute tone with a fundamental frequency of 1,032 Hz; Fig. 8 shows the
aperiodiccontent of the same tone; Fig.
9 shows the entire conglomerate The
second three figures show,respectively,
the harmonic structure (Fig. 10) the
aperiodiccontent (Fig. 11) and the entire sanza tone (Fig 12) with a fundamentalfrequencyof 285 Hz. The figures
for both instrumentsshowthat primary
harmonics are surrounded by noise.
Both noise spectra,in factyappearto follow the harmonic spectra of their respective instruments,so that the envelope of just the noise portion of each
signalresemblesthe envelope of the re-
lated harmonic portion, though at a
loweramplitude.
Flute Analyses
For the flute, the width of the noise
band surroundingthe fundamentaland
the second two harmonicsis at least as
large as the bandwidthsof the auditory
filters centered on these components
(for the fundamentalfrequencyat 1,032
Hz, the noise bandwidth must be approximately136 Hz; for the second [4]
harmonic at 2,016 HzSthe bandwidth
must be approximately241 Hz, for the
third harmonic at 3,105 HzSthe bandwidth mustbe 349 Hz). In addition,the
noise in the frequencyregionof the fundamental and third harmonic has the
highest level, correspondingto the fact
that these are the strongestharmonics.
Therefore,for the perceptionof the entire complex conglomerateSthe auditory filters in the region of the fundamental and the third harmonicare the
most stimulatedby the noise. In the case
of the higher harmonics,it is difficultto
determine where the noise bandwidth
beginsSsince the noise level flattensout
considerablyaboure
about 55000Hz.
We can make several other observations based on the spectra,as well as on
the sound of the signalwe are analyzing.
As mentioned above,the noise element
in the timbre of this flute is slight, as
might be predictedfrom the level of the
noise. If the fusion of noise with a complex tone has some relation to noisepure tone fusion}then, accordingto our
experiments, the difference in noise
and tone level here ought to make this
combination difficult to fuse And yet,
they arefusing, as is evidenced by the
sound of the entire signal as well as the
sound of the separate noise and tone
signals (both of which are noticeablyaltered by their isolation from one another). Fromthisexample,we can arrive
at one of twoconclusions.It maybe that
noise fusion in the case of a complex
tone differsmarkedlyfrom noise fusion
witha pure tone. However,insofaras the
noise phenomena of fusion and masking are related,Moore'sobservation[5]
that the maskingof a complex tone by
noise is predictablefrom the detectability of the most prominent harmonics
may be equally applicable to fusion.
Therefore,our resultson the fusionof a
pure tone oughttobe relevant to complex tones as well.
An alternativeexplanationof the failure of the flute example to conform
more exactlyto our experimentalresults
is that these resultsmayneed to be rein-
FaZesand MsAdams,The Fusion and Layering of Noise and Tone
73
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of fusion.
terpretedto accountfor degrees
In order to do this, we need to establish
a definition of fusion that accounts for
the varyingstrengthsof listeners'sensations.Does "weakfusion"occurwhen the
noise accompanyinga periodic tone is
dB
i
_
t
l
J
20
|
__
J
l_
i
I
F
-|--[
11 }
4
I
10
°O '
ig.
1000
10.
Fi
285
l
1 20001
3000
The
4000
of
(in
Note
dB).
distribution
the
the
across
r
5000
harmo?zi&
ax}s
horizontal
}
of
8000
sanza
of
(in
Hz),
partials,
as
from theto
tone
sonly
t by
suchofa itdegree
senis contributing
the that
a part
1I
10000
9000
tone
frequency
of
2
I
7i0
to
(,
11
J
!
elements
axis
1
1I
5000
composition of the timbre?And does
thatmean thatthe n) se it elfmustbe at
lowlevel?Or can tl oi e be relatively
i tense, butwithits c ter equencyoff-
y
w5
inharmonicity
frequency
:
I
corresponds
relative
,
ll
t9
-
0-
spectrum
Hz.
>amplitude
ven
- - tNarrowband
uency
t
t
i
^
1
L|
fre-
fundamental
and
vertical
the
by
indicated
axis
their
un-
*
dB
I
j
|
||\
01
}
be consideredto reflecta less strongdegree of fusion thus provoking a less
|
|
F
1
I
|
|
y
r
8
10
q
|
'
i
1000
30iOo
2000
4000
6000
60'00
7000
8000
9000
of
fundamental
10000
Hz
Fi ig.
11.
Narrowband
uency
285
Hz.
) amplitude
um
to
The
(in
the
of
spectrum
axis
horizontal
Notice
dB).
the
notse
of
elements
corresponds
above,
in
tone
(in
(outline
envelope
that
indicating
sanza
frequency
to
similarity
spectrum
harmonic
M
Hz),
of
and
noisebands
are
frevertical
the
peaks)
of
roughly
spec-
centered
on
pl rimaryharmonics.
ds
1lil
4D
E
I
1
1 1
,1 1
}t1111 l i V
2 A 18 4
r
,1 1
rotf T
{
21
11 |I
i L
- --
i
I
I I
o0 I I
1000
3000
2000
0
s \r N
l{"2|
-_
6000
1l
1l|
111
t
; I
5000
|
i
I
8000
r
It|ll
W 1F
I 11
mutualinfluenceofthetwocomponents
1
10000
9000
HZ
'ig.
T Nhe
in
Inly
12.
Narrowband
horizontal
dB).
axis
Here
starting
spectrum
noise
at
the
of
sanza
corresponds
to
bandwidths
begin
fifth
tone
frequency
to
(complete)
(in
approximate
Hz),
of
and
the
fundamental
the
size
of
harmonic.
285
frequency
vertical
respective
axis
to
lutual influence of the noise and tone
conditions are met: (1) the overalltimbre of the sound must demonstratethe
,1dl^M
1
11 11
7000
pe ceptual d stlnCtve e s o t e st
lntact [7] . Somethlng of the same distinction might well be relevant here,
where the flute timbreis augmentedby
the presenceof noise, althoughthe noise
itself is not sufElcientlyintense to produce the kind of emergenttimbretested
for in our experimentation. With the
fuexample,
it appears
flute
as an to
be defined
from a that
percep5 on ought
I
it
102
Tr
!
4000
I
_ 1
j
|
- | --I -
s
*
*t
axis
noise
the
^
nlerencc ol tl e Et robe ween "emergent"timbre, produced
by the perceptual fusion of the entire
spectraof two separateinstruments,and
timbre,producedby the fu"augmented"
sion of severalharmonicsfrom one instrumentwith the entire spectrumof a
second instrument, thus changing the
timbre of the second while leaving the
peAttI
I
II
°O
sation offusion? If the second arrangement of noise and tone is allowed as a
kind of fusionwithonly partof the noise
fusing, then can noise both fuse and
layer with the tone it accompanies?In
our experiments,we have consideredall
responses
4 to be
stimuli
provoking
to
perhaps
response32or
ought
fused, but
Eiz.
amplitude
auditory
filters
(so that in the case of two of the instruments representedhere, we have a noisy
flute and a noisy sanza,as opposed to a
flute and sanzain the presenceof noise),
and (2) when the soundis analyticallydivided into its two components,both the
noise alone and the tone strippedof the
noise must sound discernibly different in
the absence of the other.
The second observation we can make
from the flute spectra is that while the
74
FaZesand McAdams,The Fusion and Layering of Noise and Tone
1 1, 1 11111, ,1 .,1
noise envelopedoes followthe harmonic
envelope,beginningwiththe secondharmonic, it is actuallyshiftedslightly,such
that noise peaksare higher in frequency
than harmonicpeaks.Furthermore,Fig.
9 whichincludesspectraof both the harmonics and the noise, shows what appears to be a second set of harmonics,
beginningbelowthe fundamentalv
whose
peaks are in fact as regular as the real
harmonics. Our noise-separation programassignsmost of these peaks to the
noise component. However,their regulariqrmade us suspiciousof the accuracy
of this assignmentuniil we matchedthe
pitch of the tone and found it in fact to
correspondto a frequencyof about1,030
Hz. These regularpeaks, then, become
the peaks of the noise, which are themselves quite regular harmonically.The
shift of the noise center frequency is
greater than that predicted by our experiments on the coincidence of tone
frequencywith the center frequencyof
the noise which may contribute to the
weaker influence of the noise on the
flute timbre.At the same time, the real
partials of this traditional flute are remarkablyinharmonicfor a flute [8] although not so much in comparison to
the sanzadiscussedbelow.If the partials
were ideally harmonic, their values
would lie somewherebetween their actual peaksand the harmonicallyregular
peaksof the noise that surroundsthem.
Moore [9] and others have shown that
especiallywithin the first six harmonics
of a complex tone inharmonicpartials
tend to pull the sense of pitch awayfrom
that indicated by the frequency of the
fundamental in the direction of the
inharmonicity.If this is true, then a possible effect of the regularnoise peakslocatedabovethe trueharmonicsmightbe
the undoing of the tendency of the
flute's (inharmonic)partialsto pull the
sense of pitch downward,by addingwhat
mightalmostbe considereda second set
of partials,each paired with one of the
real harmonics,but offset in a direction
opposite to the real harmonics' inharmonicity.Indeed,in comparisonwith
the complete tone (noise and harmonic
frequencies) the harmonic-onlysignal
(withoutnoise) soundslower.Evenstronger confirmationof the role of noise in
undoing the pitch effects of
inharmonicityis heard in a comparison
of the harmonic-only signal with the
noise-and-harmonicsignal when both
havebeen filteredto exclude all but the
firstthree harmonics.Informallistening
to these soundsproducedgeneralagreement among listenersthat not only was
dB
___.
40
:
30
+
-
--
-
= a
20 h't -
...
&
4000
5000
t---
R
t!ltlll l I
i
3000
-
-
'
6000
1ll11'''11
'/1lpll
x
7X0
,
8000
i
!
SO00 10000 11000 120X 13000
)
18000
Hz
Fig. 13. Narrowband spectrum of musical bow tone (comptete) of fundamental frequenc
302 Hz. The horizontal axis corresponds to frequency (in Hz), and khe vertical axis correu
sponds to amplitude (in dB). Notice the presence of two kinds of noise (see text): noise
khat surrounds primary harmonics, as in sanza and flute tones, and high frequency noise
(above about 6,000 Hz) that appears to produce the layering audible in its timbre.
dB
i
a
°o
;
I q##ts-
jl---
1000 2000 3000 4000 5000 6000 7000 8000 gO00 100001100012000 1300014000 1500016000 1700018000
Hz
Fig. 14. Narrowband spectrum of high frequency noise filtered from spectrum. The horizontal axis corresponds to frequency (in Hz), and the vertical axis to amplitude (in dB).
Notice the relative formlessness of fhe noise in comparison with the noise in the remaining
signal (shown in Fig. 16).
dB
Hz
Fig. 15. Narrowbandspectrumof portion of signal remaining(after high frequencynoise
was filtered from spectrum)with noise removedby noise4eparationprocess. The hoxizontal axis correspondsto frequency(m Hz), and {he verticalaxis correspondsto amplitude
(in dB).
Fales and McAdams,The Fusion and Layering of Noise and Tone
75
dB
30
20
.lll
10
os
)
7000
8000
9000 10000 11000 12000 13000 14000 15000 16000 17000 18000
Fig. 16. Narrowbandspectrumof portion of signalremaining(afterhigh frequencynoise
was fflteredfrom spectrum)with noise only, isolated by noise-separationprocess. The
horizontalaxis correspondsto frequency(in Hz), and the verticalaxis correspondsto amplitude (in dB). Note, for this portion of the signal, the similarityin envelope (outline of
peaks) of the noise spectrumto the harmonicspectrumabove, indicatingthat noisebands
are roughlycenteredon primaryharmonics.
noise-separationprocess,of course,cannot distinguishbetweenthe twosources.
This is alwaysa problemwhen there is a
supplementarynoise device acting on
an instrument.Forthe analysisof overall
noise content, it probablymakes little
Sanza Analyses
The spectra for the sanza are remark- differencewhere the noise originates,as
ably complex when comparedwith the long as it is discerniblyfusing or layerflute spectra.The partialsof the sanza ing. However,when discussingthe reachave so inconsistenta relationship(the tion of supplementarynoise deviceson
distancebetweenthemvaryingfrom 212 the "natural"timbre of the instrument,
to 320 Hz, with a quasi-fundamentalof it is importantto distinguishnoise pro285 Hz) that it is difficult to decide duced in the absenceof the devicefrom
noise producedby the device.Thus,havwhichpeaksare legitimateharmonicseven though the sample was run ing suggested a possible "function"of
through the noise-separation process the sanza noise, we also point out that
three times to eliminate as much noise propositions as to noise devices that
as possible.Here again, the noise enve- "compensate"
for inharmonicity,for exlope follows the spectralenvelope. Un- ample, must remaintentativeas long as
like the flute, however,the noise band- there is no sample of the same
widths surrounding the harmonics instrument's sound with its inherent
begin to approximatethe size of the re- noise and withoutthe externalnoise despective auditory filters only with the vice- that is, as long as there is no pure
fifth harmonic.Further,with the excep- sample of what it is that the noise comtion of the fundamental, the intensity pensatesfor.
level of the noise relative to the harmonic it surroundsis high enough that Musical Bow Analyses
the total noise power entering each fil- As mentioned earlier, the musical bow
ter appearsto exceed the noise-to-har- example differs from the other instrumonic rationecessaryfor fusion.
ments describedhere in that it demonA problemin the noise analysisof the strates layered rather than fusedsanza(whichdid not arisein the case of tone and noise. When we tried our
the flute) is that, in all likelihood, the noise-separationprocess on samplesof
instrumentused for analysishere actu- the bow,we found that the softwareleft
ally contains more than one noise so much noise in the frequencyregion
source.We have mentioned alreadythe above 6,000 Hz that a spectrumof what
use of bottle caps attached to the reso- was meant to be harmonic-only elenator of the instrument. At the same ments looked quite similarto the spectime, there is probablysome degree of trumfor the entire tone. Whenwe next
noise producedby the instrumentitself, bandpass-filtered
this extractedsignalto
as it is traditionally performed. The leaveonly the region above6,000 Hz, we
the pitch higher for the reduced noisy
complex,but the "roughness"
or "graininess" of the noiseless complex was reduced by the presenceof noise.
76
Fales and McAdams,The Fusion and Layering of Noise and Tone
were unable to hear any periodic elements whatsoever;it was evident from
this result that the bow was an example
of an instrument on which our noiseseparation process is ineffective, since
the noise elements in part of the spectrum appearto be louder than the harmonic elements in the same regions.
Thus the software'schoice of the highest intensitypeaks as harmonicswas inappropriatein the case of the musical
bow. However, having filtered out the
frequency region above 6,000 Hz, we
could then apply the noise-separation
process to the sample that remained.
Figures 13-16 are spectraof the entire
bow tone (Fig. 13), the high-intensity
noise region removedby filtering (Fig.
14), the remainingsignalwith noise extracted (Fig. 15), and the noise only of
the remainingsignal (Fig. 16).
If we look firstat the spectraof the signal remainingafter filtering out all frequencies above 6,000 Hz, we see something of the same patternof noise-tone
relationas we sawin the flute and sanza.
The noise followsthe harmoniccontent
of the tone, forming noise bands surrounding each formant peak. Again,
when we furtherfiltered this part of the
signal to leave only the first four harmonics, those harmonics were inharmonic to the extent thattheywereheard
to be so weaklyfused that, ratherthan a
single, unified sound with a discernible
pitch, almostall listenersheard a collection of three or four pitches, none of
which appearedto be the same pitch as
the entire tone. When we combined
these four harmonicswith the highfrequencynoise(Fig. 13), the resultingpercept was of the separate pitches of the
harmonicswith noise superimposedor
layeredabove.Evidentlythe noise above
6,000 Hz contributedneither to the fusion of the harmonicsnor to the sense of
pitch but, rather,added an additional,
layeredsound. When we mixed back in
the noise below6,000 Hz (Fig. 17), however, listeners reported that the same
four harmonicsfusedinto a slightlynoisy
tone and yielded a sense of pitch matching that of the entire tone. Again,it appears that only the noise surrounding
harmonicsof the bow could aid in their
fusion and the resulting pitch perception, and further,that this noise wasalso
adding a slight noisy quality comparable in intensityto the noisy qualityof
the flute. When we then mixed back in
the high frequency noise (above 6,000
Hz), the resulting percept was almost
identicalto the entire tone as it occursin
performance,with a unified pitch and
timbre-senseand an additionalnoise layered over this complex.
Thusnlt appearsthat,in fact, the musical bow recorded for this sample produces two kinds of noise: one of lower
frequencyand intensity that fuses with
the tones it surroundsand that contriS
utes to their fusion and pitch sense and
another of higher frequencyand intensity that produces the layeringof noise
audibleabovethe tone. As in the case of
the sanza,there is no wayof knowingif
both kindsof noise arisefrom the noise
device attached to the instrumentor if
the fusingnoise is inherentto the instrument,whilethe layerednoise is the result
of the "metal clackers."Whatever the
sourcesof the noise, theirconfigurations
as revealed by the spectra above are
again in agreement with the results of
our experiments.The fusing noise centers roughly on prominent harmonics
while the layering noise is well set off
fromaudibleperiodicelementsand is of
sufficientintensitythatit masksanyperiodic elements that lie in the same frequencyregion.
One of the intriguing aspects.of the
studydescribedin this paper-although
it is one whose implicationscan only be
speculated occurred in informal responses from listeners describing the
fused noise-tone percept. Four comments that were repeated frequentlyby
subjectswere that the noise-tonefusion
(1) seemed to '4spreadout" the pitch
(2) gavethe sensationof more than one
pitch, (3) left listeners unsure of the
pitch7 and (4) caused the illusion of
asyrlchrony
betweenthe noise and tone.
Vincent Oehoux of the Departmentof
Ethnomusicologyin the laboratory of
the Langues et CivilisationsTraditionnelles Oralesof the CentreNationalde
Recherche Scierltifique ( LACITOCNRS)in Paristells the storyof being in
the presence of two sanza musicians
from the CentralAfricanRepublicwho
had been workingfor some time to tune
their instruments together for a duet
they were to perform. After a finalsunsuccessfulattempt they gave up the effort, deciding instead simply to attach
still more bottle caps to the resonators
of their instruments.And, said Dehous
[10], whatever the mechanismS the
bottle-cap trick appeared to work. It is in
stories such as this one that the analytical and experimental parts of our noise
fusion study come together. Anyone who
is familiar with the noisy timbre of a
bottle-cap-laden sanza such as the one
described above will recognize that the
level of the noise could not have been
nearly sufflcient to maskthe mismatched
intonation of the two sanzas. If there is
any validity to our earlier suggestion that
the noise described above counteracts
the inharmonicity of the instruments
that produce it-and if we consider the
comments of our experimental subjects
concerning the "spreading out of pitch
as an effect of noise-then it is possible
that a similar phenomenon is working
for the Central Mrican sanza musicians
to compensate for the imperfect intonation between the two instruments by
blending one intonation into the other.
hferences and Notes
CONCLUSION
7. Gregory Sandell, 'iAnalysis of Concurrent Timbres with an Auditory Model,s' paper presented at
the Third International Conference for Music Perception and Cognition (ICMPC), hosted by the European Society for the Gognitive Sciences of WIusic
(ESCONI), Liege Belgium, 23-27July 1994.
Verification of hypotheses concerning
the perceptual effects of noise in regard
to faulty tuning, inharmonicity or ambiguous pitch sensation will require further, extensive laboratory research. Verifying that such perceptual effects are
intentional on the part of musicians will
require additional extensive field research. Similarly an investigation of the
intended effect of noise fusion and layering-of whether one was more desirable
or productive of the illusion than the
other-will also require inventive field research The use of other noise phenomena, such as auditory restoration effects
might also contribute to the intended effects of noise in African music. From the
perspective of ethnomusicology, in order
to combine the controlled results of laboratory research with the richness of uncontrolled musical behavior experimentation of the kind described here must
consist of equal parts of laboratory research acoustic analyses of the instruments and field research.
1. See, for example, J*H. Kwabena Nketia, Muszcof
Afrzvs(New York:W.W. Norton, 1973).
2. The sanza, also called mbtruin parts of Africa, is a
small, handheld lamellophone with a rectangular
shallow box resonator and a clavier of wooden or
metal lamellae that are "pluckedt with the thumbnails. In some regions of AfricaXthe sanza may be
put inside a larger calabasse for extra resonance. In
the United States, the instrument is colloquially
called a zithumbpiano.t
3. The musical bow is a struck string instrument resembling the bow o£ a bow-and-arrowwith a gourd
resonator attached to the wooden bow part of the
instrument. This gourd is held against the
musician's chest cavitwfor further resonance while
he or she strikes the string with a short baton.
4. For musicians5 whose system begins counting
harmonics a£ter the fundamental frequency7 this
will be the first harmonic or overtone.
5. B.C.J. Moore, An Int;roductionto the Psychologyof
Hearzng(London: Academic Press, 1989).
6. I)egree of £usion was an issue of concern in factS
in the original design of the experiment, but the
intial difficulty encountered in proposing the notion of noise fusion to subjects made the proposition of degreesof fusion unrealistic.
8. Personal communication, Marc Pierre Merge (instrument acoustician, IRCAh4) concer ning inharmonicity of flute-like instruments, March 1994.
9. Moore [5].
10. Personal communicatiesnx see also Vincent
Dehoux, Les Chnts a Penser(Paris: SELAF,Place de
la Sorbonne, 1992) .
Bbliography
A.S. Bregman and S. Pinker 'Auditory Streaming
and the Building of Timbret Cvnadian Journst of
(1978) pp. 19-31.
P$ychobe32
B.R Glasberg and B CJ. Moore "Derivation of Auditory Filter Shapes from Notched Noise
Data,BHearznghsesrch47 (1978) ppw10>138.
B.C.J. Moore "The Perception vf Inharmonic
Complex Tones, in W. Yost and C. Watson, eds.}
Sounds (Hillsdale, :
AuditoryProcessingof Complenc
Lawrence Erlbaum Associates, 1987).
B.C.J. Moore, B. Glasberg and R. Peters, 'Relative
Dolninance of Individual Partials in Determining
the Pitch of Complex Tones,l' Journal of theAcousticat Soczet of America77, (1985) pp. 1853-1866.
B+C.J.Moore, R. Peters and R.W. Peters, Thresholds for the Detection of Inharmonicity in Complex TonesnJournat of theAcxs6cat icst of Amsa
77 (1985) pp. 1861-1867.
Acknowledgments
This research was funded in part by National Science Foundation and Fyssen Foundation grants to
the first author and by a grant from the French Ministry of Research and Space to the second author.
Fales
and M%cAda7rJ
The Fusion and Layering of Noise and Tone
77