Biomechanical modeling and bifurcation theory are applied to study phonation onset and register transition. A four-mass body-cover model with a smooth geometry is introduced to reproduce characteristic features of chest and falsetto registers. Sub- and supraglottal resonances are modeled using a wave-reflection model. Simulations for increasing and decreasing subglottal pressure reveal that the phonation onset exhibits amplitude jumps and hysteresis referring to a subcritical Hopf bifurcation. The onset pressure is reduced due to vocal tract resonances. Hysteresis is observed also for the voice breaks at the chest-falsetto transition. Varying the length of the subglottal resonator has only minor effects on this register transition. Contrarily, supraglottal resonances have a strong effect on the pitch, at which the chest-falsetto transition is found. Experiment of glissando singing shows that the supraglottis has indeed an influence on the register transition.
REFERENCES
1.
Adachi
, S.
, and Yu
, J.
(2005
). “Two-dimensional model of vocal fold vibration for sound synthesis of voice and soprano singing
,” J. Acoust. Soc. Am.
117
, 3213
–3224
.2.
Alipour
, F.
, Berry
, D. A.
, and Titze
, I. R.
(2000
). “A finite-element model of vocal-fold vibration
,” J. Acoust. Soc. Am.
108
, 3003
–3012
.3.
Berry
, D. A.
, Herzel
, H.
, Titze
, I. R.
, and Krischer
, K.
(1994
). “Interpretation of biomechanical simulations of normal and chaotic vocal fold oscillation with empirical eigenfunctions
,” J. Acoust. Soc. Am.
95
, 3595
–3604
.4.
Berry
, D. A.
, Herzel
, H.
, Titze
, I. R.
, and Story
, B. H.
(1996
). “Bifurcations in excised larynx experiments
,” J. Voice
10
, 129
–38
.6.
Fant
, G.
(1960
). The Acoustic Theory of Speech Production
(Moulton
, The Hague, The Netherlands
).7.
Gömmel
, A.
, Butenweg
, C.
, and Kob
, M.
(2008
). “Calculation model of the influence of the vocal fold shape and the ventricular folds on the laryngeal flow
,” in Proceedings of the 6th International Conference on Voice Physiology and Biomechanics
, Tampere, Finland, pp. 194
–196
.8.
Guckenheimer
, J.
, and Holmes
, P.
(1983
). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
(Springer-Verlag
, New York
).9.
Hatzikirou
, H.
, Fitch
, W. T.
, and Herzel
, H.
(2006
). “Voice instabilities due to source-tract interactions
,” Acta Acust.
92
, 468
–475
.10.
Henrich
, N.
, d’Alessandro
, C.
, Doval
, B.
, and Castellengo
, M.
(2005
). “Glottal open quotient in singing: Measurements and correlation with laryngeal mechanisms, vocal intensity, and fundamental frequency
,” J. Acoust. Soc. Am.
117
, 1417
–1430
.11.
Hirano
, M.
(1974
). “Morphological structure of the vocal cord as a vibrator and its variations
,” Folia Phoniatr (Basel)
26
, 89
–94
.12.
Hirano
, M.
, and Kakita
, Y.
(1985
). “Cover-body theory of vocal cord vibration
,” in Speech Science
, edited by R. G.
Daniloff
(College Hill Press
, San Diego, CA
), pp. 1
–46
.13.
Hirano
, M.
, Vennard
, W.
, and Ohala
, J.
(1970
). “Regulation of register, pitch, and intensity of voice
,” Folia Phoniatr (Basel)
22
, 1
–20
.14.
15.
Horáček
, J.
, Švec
, J. G.
, Veselý
, J.
, and Vilkman
, E.
(2004
). “Bifurcations in excised larynges caused by vocal fold elongation
,” in Proceedings of the International Conference on Voice Physiology and Biomechanics
, edited by A.
Giovanni
, P.
Dejonckere
, and M.
Ouaknine
, Laboratory of Audio-Phonology
, Marseille, France
, pp. 87
–89
.16.
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
.18.
Kelly
, J. L.
, and Lochbaum
, C.
(1962
). “Speech synthesis
,” in Proceedings of the 4th International Congress on Acoustics
, Paper No. G42, pp. 1
–4
.19.
Liljencrants
, J.
(1985
). “Speech synthesis with a reflection-type line analog
,” Ph.D. thesis, Royal Institute of Technology
, Stockholm, Sweden.20.
Lous
, N. J.
, Hofmans
, G. C.
, Veldhuis
, R. N. J.
, and Hirschberg
, A.
(1998
). “A symmetrical two mass vocal fold model coupled to vocal tract and trachea, with application to prothesis design
,” Acta Acust.
84
, 1135
–1150
.21.
Lucero
, J. C.
(1998
). “Subcritical Hopf bifurcation at phonation onset
,” J. Sound Vib.
218
, 344
–349
.22.
McCandless
, S.
(1974
). “An algorithm for automatic formant extraction using linear prediction spectra
,” IEEE Trans. Acoust., Speech, Signal Process.
22
, 135
–141
.23.
Mergell
, P.
, Herzel
, H.
, and Titze
, I. R.
(2000
). “Irregular vocal fold vibration—High-speed observation and modeling
,” J. Acoust. Soc. Am.
108
, 2996
–3002
.24.
Miller
, D. G.
, Švec
, J. G.
, and Schutte
, H. K.
(2002
). “Measurement of characteristic leap interval between chest and falsetto registers
,” J. Voice
16
, 8
–19
.25.
Pelorson
, X.
, Hirschberg
, A.
, van Hassel
, R. R.
, Wijnands
, A. P. J.
, and Auregan
, Y.
(1994
). “Theoretical and experimental study of quasi-steady flow separation within the glottis during phonation
,” J. Acoust. Soc. Am.
96
, 3416
–3431
.26.
Riede
, T.
, and Zuberbühler
, K.
(2003
). “Pulse register phonation in Diana monkey alarm calls
,” J. Acoust. Soc. Am.
113
, 2919
–2926
.27.
Roubeau
, B.
, Chevrie-Muller
, C.
, and Arabia-Guidet
, C.
(1987
). “Electroglottographic study of the changes of voice registers
,” Folia Phoniatr (Basel)
39
, 280
–289
.28.
Salomão
, G. L.
, and Sundberg
, J.
(2008
). “Relation between perceived voice register and flow glottogram parameters in males
,” J. Acoust. Soc. Am.
124
, 546
–551
.29.
Sciamarella
, D.
, and d’Alessandro
, C.
(2004
). “On the acoustic sensitivity of a symmetrical two-mass model of the vocal folds to the variation of control parameters
,” Acta Acust.
90
, 746
–761
.30.
Shipp
, T.
, Robert
, E.
, and McGlone
, R. E.
(1971
). “Laryngeal dynamics associated with voice frequency change
,” J. Speech Hear. Res.
14
, 761
–768
.31.
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
.32.
Steinecke
, I.
, and Herzel
, H.
(1995
). “Bifurcations in an asymmetric vocal fold model
,” J. Acoust. Soc. Am.
97
, 1874
–1884
.34.
35.
Story
, B. H.
(1995
). “Physiologically-based speech simulation using an enhanced wave-reflection model of the vocal tract
,” Ph.D. thesis, University of Iowa
, Iowa City, IA.36.
Story
, B. H.
, Laukkanen
, A. -M.
, and Titze
, I. R.
(2000
). “Acoustic impedance of an artificially lengthened and constricted vocal tract
,” J. Voice
14
, 455
–469
.37.
Story
, B. H.
, and Titze
, I. R.
(1995
). “Voice simulation with a body-cover model of the vocal folds
,” J. Acoust. Soc. Am.
97
, 1249
–1260
.38.
Sundberg
, J.
, and Gauffin
, J.
(1979
). “Waveform and spectrum of the glottal voice source
,” in Frontiers of Speech Communication Research
, edited by B.
Lindblom
and S.
Oehman
(Academic
, London
), pp. 301
–320
.39.
Švec
, J. G.
, and Pešák
, J.
(1994
). “Vocal breaks from the modal to falsetto register
,” Folia Phoniatr (Basel)
46
, 97
–103
.40.
Švec
, J. G.
, Schutte
, H. K.
, and Miller
, D. G.
(1999
). “On pitch jumps between chest and falsetto registers in voice: Data from living and excised human larynges
,” J. Acoust. Soc. Am.
106
, 1523
–1531
.41.
Švec
, J. G.
, Sundberg
, J.
, and Hertegård
, S.
(2008
). “Three registers in an untrained female singer analyzed by videokymography, strobolaryngoscopy and sound spectrography
,” J. Acoust. Soc. Am.
123
, 347
–353
.42.
Tembrock
, G.
(1996
). Akustische Kommunikation bei Säugetieren (Acoustic Communication in Mammals)
(Wissenschaftliche Buchgesell
, Darmstadt, Germany
).44.
Titze
, I. R.
(1988
). “The physics of small-amplitude oscillation of the vocal folds
,” J. Acoust. Soc. Am.
83
, 1536
–1552
.45.
Titze
, I. R.
(2000
). Principles of Voice Production
, 2nd ed. (National Center for Voice and Speech
, Iowa City, IA
).46.
Titze
, I. R.
(2006
). Myoelastic Arodynamic Theory of Phonation
(National Center for Voice and Speech
, Iowa City, IA
).47.
Titze
, I. R.
(2008
). “Nonlinear source-filter coupling in phonation: Theory
,” J. Acoust. Soc. Am.
123
, 2733
–2749
.48.
Titze
, I. R.
, Riede
, T.
, and Popolo
, P.
(2008
). “Nonlinear source-filter coupling in phonation: Vocal exercises
,” J. Acoust. Soc. Am.
123
, 1902
–1915
.49.
Titze
, I. R.
, and Story
, B.
(2002
). “Rules for controlling low-dimensional vocal fold models with muscle activation
,” J. Acoust. Soc. Am.
112
, 1064
–1076
.50.
Tokuda
, I.
, Zemke
, M.
, and Herzel
, H.
(2008
). “Biomechanical modeling of voice registers and their transitions
,” in Proceedings of the 6th International Conference on Voice Physiology and Biomechanics
, Tampere, Finland, pp. 98
–100
.51.
Tokuda
, I. T.
, Horáček
, J.
, Švec
, J. G.
, and Herzel
, H.
(2007
). “Comparison of biomechanical modeling of register transitions and voice instabilities with excised larynx experiments
,” J. Acoust. Soc. Am.
122
, 519
–531
.52.
Vilkman
, E.
, Alku
, P.
, and Laukkanen
, A.
(1995
). “Vocal-fold collision mass as a differentiator between registers in the low-pitch range
,” J. Voice
9
, 66
–73
.53.
Wilden
, I.
, Herzel
, H.
, Peters
, G.
, and Tembrock
, G.
(1998
). “Subharmonics, biphonation, and deterministic chaos in mammal vocalization
,” Bioacoustics
9
, 171
–196
.54.
Zaccarelli
, R.
, Elemans
, C. P. H.
, Fitch
, W. T.
, and Herzel
, H.
(2006
). “Modelling bird songs: Voice onset, overtones and registers
,” Acta Acust.
92
, 741
–748
.55.
Zañartu
, M.
, Mongeau
, L.
, and Wodlicka
, G. R.
(2007
). “Influence of acoustic loading on an effective single mass model of the vocal folds
,” J. Acoust. Soc. Am.
121
, 1119
–1129
.56.
Zemke
, M.
(2008
). “Biomechanical-aerodynamical modeling of register transitions of the human voice
,” Diploma thesis, Humboldt University of Berlin
, Berlin, Germany.57.
Zhang
, Z.
(2009
). “Characteristics of phonation onset in a two-layer vocal fold model
,” J. Acoust. Soc. Am.
125
, 1091
–1102
.58.
Zhang
, Z.
, Neubauer
, J.
, and Berry
, D. A.
(2006
). “The influence of subglottal acoustics on laboratory models of phonation
,” J. Acoust. Soc. Am.
120
, 1558
–1569
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