## 2 Models and Methods
### Onset Detection: Methodology  
The subglottal onset pressure (threshold pressure) was determined with the following systematic procedure similarly used [35]: pressure recordings began as the mass flow generator reached a flow rate  
Figure 5: Schematic diagram of the supraglottal channel that allows for the variation of the lateral displacement D (distances are in millimeters). Figure 6: Segmented vocal tract model used to vary the length of the vocal tract (distances are in millimeters). near 65 L/min. Then, the flow rate was increased uniformly to about 120 L/min in 11.9 s. Subsequently, the flow rate was decreased uniformly to less than 65 L/min in the same time interval. The subglottal pressure readings are shown by the rapidly oscillating black curve of Figure 7.  
The key to interpreting these data is the moving average subglottal pressure \(P^{\Delta t}_{sub}(t_{m})\) (equivalent to introducing a low-pass filter) defined in a time interval about \(t_{m}\) as follows [17; 36]:  
\[\overline{P}_{sub}^{\Delta t}(t_{m})=\frac{1}{q}\ \sum\
olimits_{l=m-\frac{q}{2}+1}^{m +\frac{q}{2}}P_{sub}(t_{l}), \tag{10}\]  
where \(q=\Delta t\,f_{\mathrm{s}}\) = 10,000 counts the number of points in the sample. The time interval \(\Delta t\) is set to 0.23 s, so that the sum of Equation (10) includes pressure values from 32 oscillations for Model 113 and 25 oscillations for Model 114. The pressure \(P^{\Delta t}_{sub}(t_{m})\) is represented by the thick yellow curve of Figure 7. When the pressure is near 3.5 kPa, the character of the pressure oscillations changes because of a noticeable change of amplitude. This qualitative difference may be used to define the onset pressure. The change in the amplitude of the oscillations near the threshold is apparent, although the size of this amplitude is less than 100 Pa, which is about 3% of the size of the total pressure signal near the threshold. Pressure oscillations of this size are consistent with one's expectation for small amplitude oscillations near the threshold. At the onset, the corresponding oscillation amplitude of the vocal folds is much smaller--less than 1 mm, as indicated in [PERSON] et al. [36]. Furthermore, the typical convergent-to-divergent glottal duct shape evolution during an oscillation cycle is visible but less pronounced at the onset pressure. A second qualitative change in the oscillation amplitude is observable between 10-11 s. This change defines the transition to a second type of oscillation, where the amplitude has become large enough so that the vocal folds close during the cycle. However, it is the pressure of the first type of oscillation at onset conditions that is the focus of this work [37; 38]. Past 11 s, the amplitude of the pressure oscillation decreases at a more or less uniform rate, until it drops abruptly to a much smaller amplitude between 20-21 s, which is a signal that the vocal fold oscillations have ceased. This point of change is used to define a pressure offset, and one can see that it is lower than the onset threshold. The offset pressure values observed by [PERSON] et al. were always smaller than the corresponding onset pressure [3; 5]. The difference in oscillation onset and offset pressure is often described as a hysteresis phenomenon [39]. Figure 7: (Color online) Subglottal pressure (black), its moving average (yellow), and its standard deviation (red) during one cycle of the variable flow rate. In order to define the pressure onset, it is convenient to introduce the moving standard deviation as a measure of the size of the oscillations about the moving average, whose square is given by:  
\[\left(\sigma_{sub}^{At}\right)^{2}=\ \frac{1}{q-1}\ \sum\
olimits_{l=m-\frac{ 2}{4}+1}^{m+q/2}\left(P_{sub}(t_{l})-\ \overline{P}_{sub}^{At}(t_{m})\right)^{2}. \tag{11}\]  
This quantity is represented by the red curve in Figure 7, where its magnitude is given by the scale on the right side of the figure. For the smaller oscillations that occur when \(t<5.0\) s, \(\sigma_{sub}^{At}\) is between 10-15 Pa.