Mammalian laryngseal air sacs add variability to the vocal tract impedance: Physical and computational modeling
Schematic of the subglottal parts of the experimental apparatus (numbers indicate distance in cm).
(Color online) Schematic of the two-layer vocal fold fabrication process, including computer model generation, rapid prototyping, and casting of the different layers. Shown at lower left is an image of the cross section of the vocal fold model.
(Color online) Schematic illustrations of the physical model configurations. Whereas no vocal tract is attached to the vocal fold physical model in (A) the following vocal tract models are attached to the vocal fold model in (B)–(F). (B) Single uniform tube as main vocal tract. (C) Main vocal tract with closed uniform tube side branch (“tube-SB”). (D) Main vocal tract with open tube-SB. (E) Main vocal tract with tube-SB and rigid cavity of variable volume (“bulla”). The volume is regulated by the water cavity level. (F) Main vocal tract with tube-SB and inflatable air sac (“air sac”). The inflation is regulated by “closing the mouth,” i.e., inserting a plug to close the aperture of the vocal tract as if the lips are closed.
Subglottal pressure–flow rate relationship of the vocal fold physical model during phonation. Data for the physical model with no vocal tract, data with a uniform tube as the vocal tract, and data with all other tested vocal tract models are combined. Note that the pressure-flow rate relationship is identical for different vocal tracts.
Sound pressure level (SPL)—subglottal pressure relationship of the vocal fold physical model during phonation. (A) Without and with a long tube as a vocal tract. (B) 20 cm long tube with tube-SB. Side branch is closed and mouth is open. Three side branches were tested; each has length with different inner diameters (inner diameters, IDs: 0.4, 0.8, 1.3, and ). (C) 20 cm long tube with tube-SB. A rigid cavity of variable size is added to the SB tube. Results for three cavity sizes are shown (cavity sizes: 1.0, 0.6, and ). The same trendlines as in Fig. 5(a) are drawn (lower line: physical model without vocal tract; upper line: uniform tube vocal tract).
Spectra and linear predictive coding (LPC) envelopes for different physical models. The vocal tract model is schematized in the top right corner of each spectrum. (A) No vocal tract [as in Fig. 3(A)], (B) uniform tube vocal tract [as in Fig. 3(B)], (C) uniform tube vocal tract with closed side branch [as in Fig. 3(C)] (arrow indicates additional pole), (D) uniform tube vocal tract with closed side branch [as in Fig. 3(D)], (E) uniform tube vocal tract with rigid cavity ( volume) [as in Fig. 3(E)], (F) uniform tube vocal tract with large rigid cavity ( volume) [as in Fig. 3(E)]. Note that the additional zero in the vocal tract with the open side branch overlaps with the fourth formant [arrow in panel (D)].
Experiment with a continuous change in rigid cavity volume attached to the main vocal tract. During the experiment, the cavity was gradually filled with water. Note the aphonic regime when the resonant frequency crossed F0. Phonation started again slowly after the resonance moved beyond from F0. The SPL reached a higher level after the crossing.
Dependence of phonation threshold pressure (PTP) on the volume of the rigid cavity attached to the main vocal tract.
(A) Spectrograms of the vocal tract model stimulated by sweep tones ranging from . As indicated above each spectrogram, the cavity volume was changed from . The arrows indicate the location of a pole (vocal tract resonance peak) introduced by the cavity; “no SB” stands for no side branch. (B) Pole-cavity size relationship. For each sweeptone, an averaged FFT was calculated. The pole shows up as a peak in the FFT spectrum.
Sound wave form (top panels), its spectrogram (second panels), and two spectra (third and fourth panels) from vocal fold physical model with inflatable bladder cavity (A) and from a siamang vocalization (B). Spectra are calculated from segments indicated with arrows “1” and “2.” Note that the formant structure of the open-mouth vocalization with a collapsed air sac [vocal tract model as schematized in Fig. 3(F)] resembles that of the closed side branch [see Fig. 6(c)]. “o”—open mouth or tube; “c”—closed mouth or tube.
Spectrogram of sweep tone transmitted through a tube vocal tract system with an inflatable air sac. Two situations are examined; first, a completely collapsed sac, up to about (arrow 1); second, continual deflation from air sac volume of about to complete deflation (from arrow 1 to end of sound). Arrow 2 indicates the location of zero frequency around (which corresponds to zero frequency produced by the open side branch of length). Arrows 3 and 4 indicate locations of zero frequency at about 1500 and (which correspond to zero frequency produced by the closed side branch of length). Note that during the deflation process (approximately between 9 and ), another zero-like structure appears at approximately , decreasing to .
Transfer functions obtained by the computational model that simulates the vocal tract without a side branch and the vocal tract with an open or a closed uniform side branch. Depending on whether the side branch is closed or open, an additional pole/zero pair of a uniform side branch is located differently, at approximately for closed side branch (left arrow) and at approximately for open side branch (right arrow). The position of the pole/zero pair behaves according to a quarter-wavelength resonator when the side branch is closed and to a half-wavelength resonator when the side branch is open.
(A) Transfer functions obtained by the computational model that simulates two rigid cavities (50 and volume). Note that the first formant is affected by the pole/zero pair located in the low frequency range. The uniform tube that connects the main vocal tract and the rigid cavity introduces another pole/zero pair around (arrow), which resembles that of an open side branch. (B) Dependence of the pole/zero location on the cavity volume of the rigid cavity attached to the main vocal tract.
Dependence of the input impedance of the vocal tract with a rigid cavity on the cavity volume. As an input signal to the vocal tract, reference sound measurement from the vocal fold physical model without a vocal tract is utilized. Since the input impedance is one of the key parameters that determine the PTP, the curve can be compared to the curve in Fig. 9.
Overview of four different anatomical designs of air sacs and bulla reviewed by Bartels (1905), Starck and Schneider (1960), and Hayama (1970). Further references on species-specific anatomy can be found in those three sources. A fifth design with lateral air sacs extending from the ventricles [like in (A)] with the addition of a cranial medial air sac [like in (B)] is described in detail in Hayama (1970).
Phonation threshold pressure (PTP) and flow rate at voice onset point for different vocal tract (VT) physical models. Values are averaged over three trial measures; the standard deviations in all cases are less than 0.5%. For uniform tube side branches (tube-SBs), two measurements are given: one for a closed side branch and the other for an open side branch.
Resonant frequencies obtained from measurements of different vocal tract (VT) models with closed and open side branches (SB: side branch; no SB: long tube without side branch; cSB: closed side branch; oSB: open side branch; SB-0.8: side branch with inner diameter of ). The nth resonant frequency is denoted as Fn. The term “pole” stands for an additional resonant frequency introduced by a side branch or cavity. Values in parentheses show deviations in percentage from the resonant frequencies of the long tube without a side branch.
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