Direct observations of nonstationary asymmetric vocal-fold oscillations are reported. Complex time series of the left and the right vocal-fold vibrations are extracted from digital high-speed image sequences separately. The dynamics of the corresponding high-speed glottograms reveals transitions between low-dimensional attractors such as subharmonic and quasiperiodic oscillations. The spectral components of either oscillation are given by positive linear combinations of two fundamental frequencies. Their ratio is determined from the high-speed sequences and is used as a parameter of laryngeal asymmetry in model calculations. The parameters of a simplified asymmetric two-mass model of the larynx are preset by using experimental data. Its bifurcation structure is explored in order to fit simulations to the observed time series. Appropriate parameter settings allow the reproduction of time series and differentiated amplitude contours with quantitative agreement. In particular, several phase-locked episodes ranging from 4:5 to 2:3 rhythms are generated realistically with the model.

1.
Alipour-Haghighi
,
F.
, and
Titze
,
I. R.
(
1991
). “
Elastic models of vocal fold tissues
,”
J. Acoust. Soc. Am.
90
,
1326
1331
.
2.
Bergé, P., Pomeau, Y., and Vidal, C. (1984). Order within Chaos (Hermann and Wiley, Paris).
3.
Bloss, H., Backert, C., and Raguse, A. (1993). CAMSYS high speed camera system. Fraunhofer Gesellschaft IIS, Erlangen, Germany.
4.
Colton, R. H., and Woo, P. (1995). “Measuring vocal fold function,” in Diagnosis and Treatment of Voice Disorders, edited by J. S. Rubin, R. T. Sataloff, G. S. Korovin, and W. J. Gould (Igaku-Shoin, New York, Tokyo), pp. 290–315.
5.
Dolansky
,
L.
, and
Tjernlund
,
P.
(
1968
). “
On certain irregularities of voiced-speech waveforms
,”
IEEE Trans. Audio Electroacoust.
AU-16
,
51
56
.
6.
Eysholdt
,
U.
,
Tigges
,
M.
,
Wittenberg
,
T.
, and
Pröschel
,
U.
(
1996
). “
Direct evaluation of high-speed recordings of vocal fold vibrations
,”
Folia Phoniatr.
48
,
163
170
.
7.
Fee
,
M. S.
,
Shraiman
,
B.
,
Pesaran
,
B.
, and
Mitra
,
P. P.
(
1998
). “
The role of nonlinear dynamics of the syrinx in vocalizations of a songbird
,”
Nature (London)
395
,
67
71
.
8.
Glass, L., and Mackey, M. (1998). From Clocks to Chaos (Princeton University Press, Princeton).
9.
Herzel
,
H.
,
Berry
,
D. A.
,
Titze
,
I. R.
, and
Steinecke
,
I.
(
1995
). “
Nonlinear dynamics of the voice: Signal analysis and biomechanical modeling.
Chaos
5
,
30
34
.
10.
Herzel, H. (1996). “Possible mechanisms of vocal instabilities,” in Vocal Fold Physiology: Controlling Complexity and Chaos, edited by P. J. Davies and P. J. Fletcher (Singular, San Diego).
11.
Ishizaka
,
K.
, and
Flanagan
,
J. L.
(
1972
). “
Synthesis of voiced sounds from a two-mass model of the vocal cords
,”
Bell Syst. Tech. J.
51
,
1233
1268
.
12.
Ishizaka
,
K.
, and
Isshiki
,
N.
(
1976
). “
Computer simulation of pathological vocal-cord vibration
,”
J. Acoust. Soc. Am.
60
,
1193
1198
.
13.
Isshiki
,
N.
,
Tanabe
,
M.
,
Ishizaka
,
K.
, and
Broad
,
D.
(
1977
). “
Clinical significance of asymmetrical vocal cord tension
,”
Ann. Otol.
86
,
58
66
.
14.
Kohler, K. J. (1996). “Articulatory reduction in German spontaneous speech,” in Proceedings of the 4th Speech Production Seminar (Autrans), edited by ESCA (Singular, San Diego), pp. 1–4.
15.
Liljencrants, J. (1991). “Numerical simulation of glottal flow,” in Vocal Fold Physiology: Acoustics, Perception and Physiological Aspects of Voice Mechanisms, edited by J. Gauffin and B. Hammarberg (Singular, San Diego), pp. 99–104.
16.
Lucero
,
J. C.
(
1999
). “
A theoretical study of the hysteresis phenomenon at vocal fold oscillation onset–offset
,”
J. Acoust. Soc. Am.
105
,
423
431
.
17.
Mazo, M., Ericson, D., and Harvey, T. (1995). “Emotion and expression: Temporal data on voice quality in Russian lament,” in Vocal Fold Physiology: Voice Quality Control, edited by O. Fujimura and M. Hirano (Singular, San Diego), pp. 173–178.
18.
Mende
,
W.
,
Herzel
,
H.
, and
Wermke
,
K.
(
1990
). “
Bifurcations and chaos in newborn cries
,”
Phys. Lett. A
145
,
418
424
.
19.
Mergell
,
P.
,
Herzel
,
H.
,
Wittenberg
,
T.
,
Tigges
,
M.
, and
Eysholdt
,
U.
(
1998
). “
Phonation onset: Vocal fold modeling and high-speed glottography
,”
J. Acoust. Soc. Am.
104
,
467
470
.
20.
Mergell
,
P.
,
Fitch
,
W. T.
, and
Herzel
,
H.
(
1999
). “
Modeling the role of nonhuman vocal membranes in phonation
,”
J. Acoust. Soc. Am.
105
,
2020
2028
.
21.
Nowicki
,
S.
, and
Capranica
,
R. R.
(
1986
). “
Bilateral syringeal interaction in vocal production of oscine bird sound
,”
Science
231
,
1297
1299
.
22.
Riviere
,
C. N.
,
Rader
,
R. S.
, and
Thakor
,
N. V.
(
1998
). “
Adaptive canceling of physiological tremor for improved precision in microsurgery
,”
IEEE Trans. Biomed. Eng.
45
,
839
846
.
23.
Robb
,
J. B.
, and
Saxman
,
J.
(
1988
). “
Acoustic observations in young children’s vocalizations
,”
J. Acoust. Soc. Am.
83
,
1876
1882
.
24.
Sirviö
,
P.
, and
Michelsson
,
K.
(
1976
). “
Sound-spectrographic cry analysis of normal and abnormal newborn infants
,”
Folia Phoniatr.
28
,
161
173
.
25.
Smith
,
M. E.
,
Berke
,
G. S.
,
Gerrat
,
B. R.
, and
Kreiman
,
J.
(
1992
). “
Laryngeal paralyses: Theoretical considerations and effects on laryngeal vibration
,”
J. Speech Hear. Res.
35
,
545
554
.
26.
Steinecke
,
I.
, and
Herzel
,
H.
(
1995
). “
Bifurcations in an asymmetric vocal fold model
,”
J. Acoust. Soc. Am.
97
,
1878
1884
.
27.
Svec
,
J. G.
, and
Schutte
,
H. K.
(
1995
). “
Videokymography: High-speed line scanning of the vocal fold vibration
,”
J. Voice
10
,
201
205
.
28.
Titze
,
I. R.
,
Horii
,
Y.
, and
Scherer
,
R. C.
(
1987
). “
Some technical considerations in voice perturbation measurements
,”
J. Speech Hear. Res.
30
,
252
260
.
29.
Titze, I. R. (1994). Principles of Voice Production (Prentice-Hall, Englewood Cliffs, NJ).
30.
Titze, I. R. (1996). “Coupling of neural and mechanical oscillators in control of pitch, vibrato, and tremor,” in Vocal Fold Physiology: Controlling Complexity and Chaos, edited by I. R. Titze (Singular, San Diego), pp. 47–62.
31.
Wilden
,
I.
,
Herzel
,
H.
,
Peters
,
G.
, and
Tembrock
,
G.
(
1998
). “
Subharmonics, biphonation, and deterministic chaos in mammal vocalization
,”
Bioacoustics
9
,
171
196
.
32.
Wittenberg
,
T.
,
Moser
,
M.
,
Tigges
,
M.
, and
Eysholdt
,
U.
(
1995
). “
Recording, processing and analysis of digital high-speed sequences in glottography
,”
Mach. Vision Appl.
8
,
399
404
.
33.
Wittenberg, T. (1998). Wissensbasierte Bewegungsanalyse von Stimmlippenschwingungen anhand digitaler Hochgeschwindigkeitsaufnahmen. Ph.D. thesis (Shaker Verlag, Aachen).
34.
Wong
,
D.
,
Ito
,
M. R.
, and
Cox
,
N. B.
(
1991
). “
Observation of perturbations in a lumped-element model of the vocal folds with application to some pathological cases
,”
J. Acoust. Soc. Am.
89
,
383
394
.
35.
Woodson
,
G. E.
(
1993a
). “
Configuration of the glottis in laryngeal paralysis. I. Clinical study.
Laryngoscope
103
,
1227
1234
.
36.
Woodson
,
G. E.
(
1993b
). “
Configuration of the glottis in laryngeal paralysis. II. Animal experiments.
Laryngoscope
103
,
1235
1241
.
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