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Audio Engineering Society
Convention Paper
Presented at the 123rd Convention
2007 October 5–8 New York, NY, USA
The papers at this Convention have been selected on the basis of a submitted abstract and extended precis that have been peer
reviewed by at least two qualified anonymous reviewers. This convention paper has been reproduced from the author's advance
manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents.
Additional papers may be obtained by sending request and remittance to Audio Engineering Society, 60 East 42nd Street, New
York, New York 10165-2520, USA; also see www.aes.org. All rights reserved. Reproduction of this paper, or any portion thereof,
is not permitted without direct permission from the Journal of the Audio Engineering Society.
Vibrato experiments with bassoon sounds
by means of the digital pulse forming
synthesis and analysis framework
Michael Oehler1 and Christoph Reuter2
1 University for Music and Drama, Hanover, Germany
kontakt@michaeloehler.de
2 University of Cologne, Musicological Institute, Cologne, Germany
info@chr-reuter.de
ABSTRACT
The perceived naturalness of real and synthesized bassoon vibrato sounds is investigated in a listening test. The
stimuli were generated by means of a currently developed synthesis and analysis framework for wind instrument
sounds, based on the pulse forming theory. The framework allows controlling amplitude and frequency parameters
at many different stages during the sound production process. Applying an ANOVA and Tukey HSD test it could be
shown that timbre modulation (a combined pulse width and cycle duration modulation) is an important factor for the
perceived naturalness of bassoon vibrato sounds. Obtained results may be useful for sound synthesis as well as in the
field of timbre research.
1. INTRODUCTION
The vibrato experiments with bassoon sounds were
realized using a currently developed synthesis and
analysis framework for woodwind instrument sounds.
Therefore the basic functionality of the framework will
be discussed in (2). As the system is based on the pulse
forming theory, first of all this specific explanation of
woodwind sound production will be explained in (2.1),
followed by a section dealing with the digital realization
of the pulse forming (2.2) and the further development
to an analysis and synthesis system. In consideration of
the pulse forming theory, the vibrato experiments are
finally discussed in (3).
2. SYNTHESIS AND ANALYSIS FRAMEWORK
2.1. The pulse forming theory
The pulse forming principle as a synthesis method for
wind instrument sounds was developed in the 1970ies at
the Musicological Institute at the University of Cologne,
Germany, by Jobst Fricke and Wolfgang Voigt. The
Oehler
&
central
i
instrume
n
excitatio
n
fundame
n
principle
Principl
e
Fricke ([
2
generati
n
stable f
o
excitatio
n
Cons
t
lips are
indepen
d
the fund
a
have to
r
are sev
e
cyclical
s
of the
modifica
audible
c
A co
m
domain
w
show, th
a
determin
Having
a
the spec
t
correspo
n
formant
the nece
s
spectral
of a con
s
frequenc
i
b
y the s
o
small fo
r
Figur
e
In fig.2
illustrate
d
pulse wi
d
b
e found
&
Reute
r
AE
i
dea of that
n
t sound ca
n
n
pulses,
n
tal tone alw
a
s, and in
w
e
s of Timbre
2
]) and Voig
t
n
g wind inst
r
o
rmant areas
n
pulses of d
o
t
ant opening
o
the basic co
n
d
ent of the p
u
a
mental freq
u
r
emain the sa
m
e
ral other f
a
s
pectra (see [
4
pulse width
tion of the r
e
c
hange of tim
b
m
parison of
t
w
ith correspo
n
a
t the ratio o
f
es the spectr
a
a
pulse width
t
ral gaps at t
h
n
ds to Karl
areas: Indepe
s
sity of any
b
minima and
m
s
tant width o
f
i
es a low pas
s
o
un
d
-hole or
r
the radiation
e
1a. Constant
resultin
g
the pulse f
o
d
using an i
s
d
th of τ and
a
at the partial
s
E
S 123rd C
principle i
s
n
basically
b
which ind
e
a
ys behave a
c
w
hich Karl
are reflecte
d
t
([3]) discov
e
r
ument-like
s
and spectral
o
uble-reeds or
o
r closing ti
m
n
dition for s
t
u
lse frequenc
y
u
ency may v
a
m
e. Besides t
h
a
ctors, influe
n
4
] and [5]).
R
or the p
u
e
levant spectr
u
b
re.
t
he excitatio
n
n
ding spectr
a
f
the pulse wi
d
a
l gaps in th
e
of τ and a cy
c
h
e partials n·(
T
Erich Schu
m
ndent from t
h
b
andpass filte
r
m
axima rem
a
f
the excitatio
n
s
filter effect
c
bell, which i
of the lowest
pulse width (
g
spectral en
v
o
rming princi
p
s
osceles tria
n
a
cycle of T
t
s
2n·(T/τ) wit
h
onvention,
s
, that ever
y
b
e put dow
n
e
pendently
o
c
cording to t
h
Erich Sch
u
d
(see [1]). I
e
red the princ
s
pectra with
gaps evoked
lips.
m
es of the re
e
t
able forman
t
y
. That mean
s
a
ry, the pulse
h
e pulse widt
h
n
cing the r
e
R
ather small
c
u
lse form c
a
u
m and there
w
n
pulses in t
h
a
in fig.1a an
d
d
th τ and the
e
frequency
d
c
le of T one
c
T
/τ) with n
∈
N
m
ann’s princ
h
e pitch and
w
r
, the positio
n
a
in constant
b
n
pulses (onl
y
c
an be found,
n many case
s
frequencies).
τ/T =1/10) a
n
v
elope.
p
le is sche
m
n
gle pulse. H
a
t
he spectral g
a
h
n
∈
N.
New York,
Page 2 of 8
y
wind
n
to its
o
f the
h
e same
u
mann’s
n 1975
iples of
typical
by the
e
ds and
t
areas,
s
, while
widths
h
, there
e
sulting
c
hanges
a
use a
w
ith an
h
e time
d
fig.1b
cycle T
d
omain.
c
an find
N
. This
iple of
w
ithout
n
of the
b
ecause
y
at low
caused
s
is too
n
d the
m
atically
a
ving a
a
ps can
F
i
If
sp
e
is
o
|C
k
de
a
m
[3
]
T
h
ex
A
u
of
sp
e
fa
l
T
h
pr
o
d
u
V
ibrato
e
NY, US
A
,
2
Figure 1b. C
o
r
e
i
gure 2. Cons
t
the res
u
T
/
τ is no inte
e
ctral distri
b
o
sceles triang
l
(1)
(2)
k
| is the ampl
i
scribes the
o
m
plitude beco
]
).
h
is demonstra
t
act pulse fo
r
u
hagen suppl
i
f
pulse width
a
e
ctral gaps,
b
l
ling edges as
Figu
r
h
at way, tria
n
o
duce spectr
a
u
ration of o
n
e
xperiment
s
2
007 Octob
e
o
nstant pulse
e
sulting spect
r
t
ant triangle
p
u
lting spectral
ger, the follo
w
b
ution of en
e
l
e pulses (2).
i
tude of parti
a
o
rdinal numb
e
mes a mini
m
t
es the spectr
a
r
m. Concern
i
i
ed evidence,
a
nd cycle du
r
b
ut the partit
i
shown in fig.
r
e 3. Triangle
n
gle pulses
w
a
with the s
n
e edge as a
s
with bass
o
er 5–8
width (τ/T =
1
r
al envelope.
p
ulse width (τ
/
envelope (se
e
w
ing functio
n
e
rgy for sq
u
a
l k, F the pul
e
r, for whic
h
m
um for the
f
a
l gaps’ depe
n
i
ng triangle
that not the
d
r
ation is resp
o
i
on ratio of
t
3 (see [6]).
pulses (see [
6
w
ith different
ame spectral
common d
i
o
on sound
s
1
/5) and the
/
T =1/10) and
e
[3]).
n
s describe th
e
u
are (1) an
d
.
se area and
k
o
h
the partial’
s
f
irst time (se
e
n
dency on th
e
pulse chains
d
escribed rati
o
o
nsible for th
e
t
he rising an
d
6
]).
widths coul
d
gaps, if th
e
i
visor is kep
t
s
e
d
o
s
e
e
,
o
e
d
d
e
t
Oehler
&
constant.
as it is s
h
Figure 4
an
d
Playing
a
rising a
n
transitio
n
reeds a
n
when pl
a
played t
o
played
t
promine
n
Figure
With ot
h
pulses, t
h
partials.
T
more th
e
at the hi
g
of shifti
n
Erich Sc
h
Whe
n
pulse f
o
concerni
n
influenc
e
real vib
r
frequenc
y
and [8])
,
appropri
a
sounds.
&
Reute
r
AE
If
t
1
≠ t
2
-t
1
,
t
h
own in fig.4
(
. Triangle pul
d
the resultin
g
a
tone on a
d
n
d falling edg
n
from openi
n
n
d vice versa
,
a
ying a tone i
n
o
ne has not o
n
t
one, but th
e
n
t than in the
s
5. Constant p
u
and the res
u
h
er words: T
h
h
e stronger
a
T
he shorter t
h
e
spectral gap
s
g
her partials.
n
g and skipp
i
h
umann.
n
summing
u
o
rming prin
c
n
g the vib
r
e
of an even
s
r
ato mostly
y
, amplitude
,
the pulse f
o
a
te method
t
E
S 123rd C
t
he gaps are
u
(
see [6]).
se (t
2
= 1/2,7
T
g
spectral env
e
d
ouble reed
i
es of the pul
n
g to closin
g
,
are less s
m
n
pp
. As can
b
n
ly a more ro
u
e
higher pa
r
s
pectrum of a
u
lse width (τ/
T
u
lting spectral
h
e more squa
r
a
re the ampl
i
h
e width of th
e
s
and forman
t
This corresp
o
i
ng formant
a
u
p the descri
b
c
iple, anothe
r
r
ato experi
m
s
mall pulse c
h
consists of
and timbre
o
rming princ
i
t
o synthesiz
e
onvention,
u
nequally dist
r
T
and t
2
-t
1
=
1
e
lope (see [6]
)
i
nstrument in
ses, represen
t
g
movements
m
ooth than t
h
b
e seen in fig
u
nded shape t
h
r
tials are al
s
ff
tone.
T
=1/10) pla
y
envelope.
r
ed the shap
e
i
tudes of the
e
constant pu
l
t
areas can b
e
o
nds to the p
r
a
reas found
b
b
ed features
r
important
m
ents is the
h
ange on ti
mb
a combina
t
modulation
(
i
ple seems t
o
e
woodwind
New York,
Page 3 of 8
r
ibuted,
1
/6,2 T)
)
.
ff
, the
t
ing the
of the
h
ey are,
.5, a
pp
h
an a
ff
s
o less
y
ed
pp
e
of the
higher
l
ses, the
e
found
r
inciple
b
y Karl
of the
aspect
direct
mb
re. As
t
ion of
(
see [7]
o
be an
vibrato
2.
2
T
h
p
o
pr
i
b
a
m
o
he
fo
l
S
e
V
a
th
e
In
F
o
fi
r
ci
r
w
e
se
c
us
e
fr
a
p
u
2.
3
T
h
a
n
pi
t
in
s
ill
u
V
ibrato
e
NY, US
A
,
2
2
. Digital p
u
h
e electronic
o
tential and
i
nciples and
h
a
sed on elect
r
o
dulated by a
created the
l
lowed by t
h
e
rialized by
t
a
riophon is t
h
e
basis of this
Figure 6
a recent pro
j
o
undation (D
F
r
st step digit
a
r
cuit simulat
i
e
ll as Nativ
e
c
ond step, th
e
e
d to devel
o
a
mework for
u
lse forming t
h
3
. The s
y
nt
h
h
e synthesis
a
n
alyzing the
p
t
ch and dyn
a
s
trument mo
u
strated for t
h
e
xperiment
s
2
007 Octob
e
u
lse formin
g
technician
possibilities
h
e began to
d
r
onic pulse c
h
breath contr
o
first prototy
p
h
e Variopho
t
he Euskirch
e
h
e first and o
n
natural pulse
. Variophon
w
j
ect, supporte
d
F
G), the ana
l
a
lly rebuil
t
b
i
on software
e
Instrument
s
e
core of the
c
o
p a combin
e
wind instru
m
h
eory.
h
esis and a
n
a
nd analysis
p
ulse width
a
a
mics of se
v
dules. In fi
h
e bassoon in
s
s
with bass
o
er 5–8
g
Jürgen Sch
m
of these p
u
d
evelop a wi
n
h
ains with c
o
o
ller. Using th
a
p
e in 1977, t
h
o
n in 1979
e
n Realton
C
n
ly synthesiz
e
forming pro
c
w
ith supplies
(
d
by the Ger
m
l
ogue Variop
h
b
y means of
SwitcherCA
D
s
Reaktor (s
e
c
onstructed i
n
e
d synthesis
m
ent sounds
n
al
y
sis s
y
s
t
system was
a
nd height d
e
v
eral analog
u
g. 7 this i
s
s
trument mod
u
o
on sound
s
m
itz saw th
e
u
lse formin
g
n
d synthesize
r
o
nstant width
s
a
t technology
h
e Martinetta
(see fig. 6)
C
ompany, th
e
e
r working o
n
c
ess.
(
1979).
m
an Resea
r
c
h
h
on was in
a
the analogu
e
D
/LTspice a
s
e
e [9]). In
a
n
strument wa
s
and analysi
s
based on th
e
t
em
developed b
y
e
pendency o
n
u
e Variopho
n
s
graphicall
y
u
le.
s
e
g
r
s
,
,
.
e
n
h
a
e
s
a
s
s
e
y
n
n
y
Oehler & Reuter Vibrato experiments with bassoon sounds
AES 123rd Convention, New York, NY, USA, 2007 October 5–8
Page 4 of 8
Figure 7. Pulse widths and heights of the Variophon
bassoon module.
The pulse width gradually changes with the dynamic
value but there are only 3 pitch registers, where
different pulse widths could be found. A low register
from A1 to C#3, a mid register from D3 to G#3 and a
high one from A3 to E4. The pulse height was constant
around 4,5V for every pitch and dynamic value. The
exact structure of the functions determines the timbre
gradient and therefore the specific character of the
instrument sound. The oboe for example has only two
registers with completely different pulse widths for the
corresponding dynamic values.
By applying a polynomial regression for the
measured values of every register, one got the following
manageable set of functions (3,4,5) for the low register
(f(x)low), the mid register (f(x)mid) and the high register
(f(x)hig) for 1 <= x <= 23 and x being the dynamic
value.
(3) f(x)low = – 0,00009x3 + 0,0053x2 – 0,1292x + 2,457
(4) f(x)mid = – 0,00001x3 + 0,0011x2 – 0,0419x + 1,483
(5) f(x)hig = – 0,000004x3 + 0,0004x2 – 0,0213x + 1,083
A generalized form of the equation is given in (6),
where i is the pulse width in ms, c is the pitch range in
cent (for example c=3100 for a pitch range from A1 to
E4), y is the played pitch in cent with the lowest pitch
within the defined pitch range as 0 cent and k is an
exponent for defining the kind of pitch dependency (for
example a logarithmic or exponential dependency).
(6) ,,, ·
.
Besides the central pulse forming core the system
consists of a module for onset behaviour, breath noise
and several other auxiliary units (see fig. 8). A more
detailed description of the system and every single
module can be found in [10].
Figure 8. Structure of the analysis and synthesis framework in NI Reaktor based on the Variophon bassoon module.
Variophon - Bassoon
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
2600
2700
2800
2900
3000
3100
3200
dynamic dependent voltage from breath controller (mV)
V / ms
pulse width low register (in ms)
pulse width mid register ( in ms)
pulse width high register (in ms)
pulse height low register (in V)
pulse height mid register ( in V)
pulse height high register (in V)
Oehler & Reuter Vibrato experiments with bassoon sounds
AES 123rd Convention, New York, NY, USA, 2007 October 5–8
Page 5 of 8
3. VIBRATO EXPERIMENTS
3.1. Background
In several experiments it was shown, that vibrato is an
important factor for the perceived naturalness in wind
instrument sounds ([11], [12], [13], [14]). The main
perspective in many studies is either phenomenological
([15], [16]), physiological ([17]), historical ([18]),
aesthetical ([19]) or performance related ([20]). In the
following study however, vibrato and micro-
modulations were investigated from a source oriented
perspective along the natural sound generating process.
Using the developed analysis and synthesis framework
for wind instrument sounds, it is possible to control
amplitude and frequency parameters at many different
stages during the sound production.
3.2. Aims
This approach seems to be promising, because besides
the existing useful results concerning vibrato rate,
extent, intonation and central pitch, a deeper insight into
the typical shape and behavior of the modulation of
wind instrument sounds as well as a better
understanding of the relevance of each individual
vibrato parameter can be provided. Based on
preliminary experiments it is therefore suggested, that
timbre modulation is an often underestimated factor for
the perceived naturalness of vibrato sounds.
According to Fricke & Blens ([21]) it is supposed
that the often used frequency and/or amplitude
modulation at the rather end of the signal path is no
adequate way to synthesize natural woodwind vibrato
sounds. Instead by using timbre modulation as a
combined pulse width and cycle duration modulation in
the synthesizing process it should be possible to create a
more natural sounding woodwind vibrato. Within the
pulse forming theory such kind of timbre modulation is
an integral part of the elementary processes of sound
production (see 2.1).
3.3. Methods
Modulated bassoon sounds were synthesized be means
of the described synthesis and analysis framework for
wind instrument sounds (see [22] and [10]). Based on
the pulse forming principle (see [12]), realistic source-
oriented pulse width and cycle duration modulations as
well as more unnatural but often used AM and FM-
modulations could be produced.
First of all different vibrato sounds were played by a
professional bassoon player in an anechoic room and
digitally recorded (96 kHz/24 bit). Together with the
bassoon player himself two musicians as well as two
musicologists selected instrument typical natural
sounding samples in the high and low register. After
comparing the selected sounds with the values of other
vibrato experiments (i.e. [13] and [23]) the final samples
for the listening test were chosen as follows. Low
register: 0 98 , vibrato rate 4,9 ,
vibrato extent 22 and amplitude modulation
14 . High register: 0 392 , vibrato
rate 4,6 , vibrato extent 25 and
amplitude modulation 19 . The duration of
each sample was three seconds. Only the stable parts of
the samples without onset sequence were used.
For the production of the different sound examples
by means of the synthesis and analysis framework the
modulation parameters should be similar to the
originally recorded sounds. To obtain reliable
comparisons with the original sounds it was first of all
necessary to extract the modulation parameters of the
recorded sounds. This was done using the analysis
software Melodyne. The proper dynamic und pitch
modulations were finally exported numerically in a
MIDI file, which later could be used to control the
synthesis and analysis system.
To verify the influence of every single vibrato
parameter on the perceived naturalness of the sound
examples, the following set of synthesis variations was
chosen:
(i) Pulse width modulation
(ii) Cycle duration modulation
(iii) Pulse width and cycle duration modulation
(iv) Amplitude modulation
(v) Frequency modulation
(vi) Amplitude and frequency modulation
Whereas (i), (ii) and (iii) are source oriented
modulations, because of having a direct impact on the
pulse chain and therewith on timbre, (iv), (v) and (vi)
are methods that impress the modulation after the main
sound generation process. As can be seen exemplarily in
fig. 9a and 9b the different kind of modulations can be
easily realized and controlled using the developed
analysis and synthesis framework (figures are taken
from the oboe experiments, but the structure is exactly
the same for the bassoon experiments. Solely the
functions in the pulse forming core unit “pulse forming”
are different).
Oehler & Reuter Vibrato experiments with bassoon sounds
AES 123rd Convention, New York, NY, USA, 2007 October 5–8
Page 6 of 8
Figure 9a. Structure of the analysis and synthesis framework for pulse width and cycle duration modulation.
Figure 9b. Structure of the analysis and synthesis framework for AM and FM modulation..
Realizing the source oriented modulation (iii), the
extracted pitch and dynamic values from the recorded
bassoon sound are fed into the system at the ports
“Mod” (pitch fluctuations) and “Dynamic” (dynamic
fluctuations). Both have instantaneous impact on the
central pulse forming process in the modules “pulse
forming”, “tau to ratio” and “pulse constant” (see fig.
9a). In the combined AM and FM modulation (vi) in fig.
9b however the central pulse forming unit is not
influenced by the input modulation signal. The module
“Mod” directly controls the frequency modulation after
the pulse forming process as well as the module
“Dynamic” influences exclusively the pulse height. That
means: there is no timbre modulation existent.
Including the real bassoon sounds, 7 stimuli in the
low register and 7 stimuli in the high register were rated
in a listening test by 60 subjects (28 female, 32 male, M
= 32.53, SD = 10.586) on a 6-digit scale from natural to
unnatural. Additionally a second experiment with the
same set of stimuli was convoluted with the pulse
response of a chamber music room, because it was
supposed that reverberation influences the general
judgment of the different sets of stimuli (according to
Meyer ([13] and [24]) the stimuli should be perceived
more natural) but does merely influence the judgment
between the different kinds of modulation.
Oehler & Reuter Vibrato experiments with bassoon sounds
AES 123rd Convention, New York, NY, USA, 2007 October 5–8
Page 7 of 8
3.4. Results
In fig. 10 the qualitative results of the experiments are
shown. Whereas (a) and (c) represent the low register,
(b) and (d) represent the high one. The convoluted
sound examples are represented by (a) and (b), (c) and
(d) show the characteristics of the non-convoluted
stimuli. The figure illustrates what in two independent
samples t-tests could be approved. It can be concluded
(p < .01) that the convoluted stimuli are perceived more
natural (M = 3.15, SD = 1.479) than the non-convoluted
ones (M = 3.63, SD = 1.507) as well as the high register
samples are rated significantly (p < .01) better (M =
3.13, SD = 1.51) than the low register sounds (M =
3.64, SD = 1.473). It looks like the different kind of
experiments (with and without convolution, low and
high register) solely result in an general shift of the
functions on the ordinate, the in-between ratings of the
different modulation types remain approximately the
same.
Figure 10. Qualitative results of the listening
experiments.
A conducted ANOVA showed (p < .01) that the
different types of modulation significantly affect the
perceived naturalness of the vibrato sounds. According
to the subsequently performed Post-Hoc Tukey HSD
test the example with combined pulse width and cycle
duration modulation (iii) is perceived as natural as the
original bassoon sound (group A). In the second group
(B) pulse width modulation (i), cycle duration
modulation (ii) and the combined AM and FM-
modulation (vi) are all perceived significantly less
natural than group A (p < .01). The third group (C)
consists of discrete AM (iv) and discrete FM-
modulation (v) and is perceived significantly less
natural than group B (p < .01).
The approximately parallel curve progression in fig.
10 indicates that there is no interaction between the
factors register and convolution resp. between the four
experiments and the different modulation types. A 3-
factorial ANOVA shows that the interaction effects
convolution * register, modulation * convolution and
modulation * convolution * register are effectively not
significant (p < .01).
4. CONCLUSIONS
The results support the hypothesis, that source-affected
timbre modulation is an important factor for the
perceived naturalness of bassoon vibrato sounds. The
use of the currently constructed pulse forming based
synthesis and analysis framework for wind instrument
sounds is an alternative method to analyze modulation
effects. Further investigations may be useful for
exploring new sound synthesis algorithms as well as for
other experiments in the field of timbre research.
5. ACKNOWLEDGEMENTS
This work was financially supported by the German
Research Foundation (DFG).
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