Chapter 1 How Air Keeps the Vocal Folds Moving

Muscle sets the stage, air does the work

The vocal folds are two layered bands of muscle, ligament and soft mucosa stretched across the larynx. Muscles bring them together, set their length and stiffness and shape their edges; but they do not pull the folds open and shut two hundred times a second. That work is done by the air. This is the core of the myoelastic–aerodynamic theory of phonation: the folds vibrate because the airflow and the elastic tissue together form a self-sustaining oscillator, with the muscles setting its parameters (Titze 1994).

What the Bernoulli effect does and does not explain

Air from the lungs speeds up as it squeezes through the narrow glottis, and by Bernoulli’s principle its pressure falls where it moves fastest. Many textbooks once said that this suction pulls the folds together and so drives the vibration. That is only half right.

Evidence

A steady pressure that simply pulls the folds together on every cycle cannot feed energy into an oscillation: whatever it does on the way in, it undoes on the way out. Titze showed that self-sustained vibration needs the pressure on the folds to differ between the opening and the closing halves of the cycle. This happens because the folds do not move as rigid blocks: a wave travels upward along their soft cover, the mucosal wave, so the glottis is convergent (wider at the bottom) while it opens and divergent (wider at the top) while it closes (Titze 1988, 1994).

Calculation

The jet speed through the glottis, and the mean pressure on the folds for convergent, straight and divergent shapes, from Titze’s expression $P_g = P_s(1 – a_{\text{exit}}/a_{\text{entry}})$ , with the pressure above the glottis taken as zero.

import math

RHO = 1.14          # kg/m³, warm humid air
Ps = 800.0          # Pa, subglottal pressure (about 8 cm H2O, moderately loud singing)

# Bernoulli: the air speeds up through the narrow glottis, v = √(2Ps/ρ).
v = math.sqrt(2 * Ps / RHO)
print(f"jet speed through the glottis ≈ {v:.0f} m/s")

# Intraglottal pressure for a glottis whose entry and exit areas differ
# (Titze 1988, pressure above the glottis taken as zero): P = Ps · (1 − a_exit/a_entry).
def p_intra(a_entry, a_exit):
    return Ps * (1 - a_exit / a_entry)

for shape, ae, ax in (("convergent (opening)", 0.20, 0.10), ("straight", 0.15, 0.15),
                      ("divergent (closing)", 0.10, 0.20)):
    print(f"{shape:22s} entry {ae:.2f} cm², exit {ax:.2f} cm²: "
          f"mean pressure on the folds {p_intra(ae, ax):+5.0f} Pa")

# The folds open while the glottis is convergent (pushed apart) and close while it is
# divergent (pulled together): the force is in step with the motion in both halves of
# the cycle, so the air does net work on the tissue. A straight glottis gives no such
# difference, which is why Bernoulli suction alone cannot sustain vibration.
swing = p_intra(0.20, 0.10) - p_intra(0.10, 0.20)
print(f"pressure swing between opening and closing ≈ {swing:.0f} Pa, in step with the motion")
# jet speed through the glottis ≈ 37 m/s
# convergent (opening)   entry 0.20 cm², exit 0.10 cm²: mean pressure on the folds  +400 Pa
# straight               entry 0.15 cm², exit 0.15 cm²: mean pressure on the folds    +0 Pa
# divergent (closing)    entry 0.10 cm², exit 0.20 cm²: mean pressure on the folds  -800 Pa
# pressure swing between opening and closing ≈ 1200 Pa, in step with the motion

The convergent glottis is pushed apart while it opens; the divergent glottis is pulled together while it closes. In both halves of the cycle the force acts in the direction the tissue is already moving, so the airflow does net work on it, like a hand pushing a swing at the right moment. The Bernoulli effect is part of this, but the key is the asymmetry made by the mucosal wave.

The phonation threshold pressure

The smallest lung pressure that starts the folds vibrating is the phonation threshold pressure (PTP). It is a useful number for singers because it measures how easily the voice starts: a voice with a low threshold speaks or sings softly without effort, and one with a high threshold needs a push.

Evidence

For a simplified glottis, Titze derived

$P_{\text{th}} = \frac{k_t\,B\,c\,\xi_0}{T},$

where $k_t$ is a pressure coefficient close to 1, $B$ the damping of the tissue, $c$ the speed of the mucosal wave, $\xi_0$ the half-width of the glottis before vibration starts, and $T$ the thickness of the folds (Titze 1988; Zhang 2010). In healthy speakers the threshold is a few centimetres of water, and it rises with pitch (Titze 1992). Experiments have found that it rises when the vocal folds are less hydrated (Verdolini et al. 1994) and after prolonged loud voice use (Solomon and DiMattia 2000).

Calculation

The formula with a baseline normalised to 0.30 kPa (about 3 cm H₂O), and the effect of changing one factor at a time.

# Phonation threshold pressure from Titze's small-amplitude model (1988),
# for a glottis of equal upper and lower half-width ξ0:
#     Pth = k_t · B · c · ξ0 / T
# k_t transglottal pressure coefficient, B tissue damping, c mucosal-wave speed,
# ξ0 prephonatory half-width, T vocal-fold thickness.
def pth(B=1.0, c=1.0, xi0=1.0, T=1.0, kt=1.1):
    return kt * B * c * xi0 / T

base = pth()
scale = 0.30 / base                     # normalise the baseline to 0.30 kPa (about 3 cm H2O)
cases = [("baseline", {}),
         ("damping ×1.5 (e.g. dry, fatigued tissue)", {"B": 1.5}),
         ("stiffer cover, mucosal wave 1.3× faster", {"c": 1.3}),
         ("glottis 1.5× wider before onset", {"xi0": 1.5}),
         ("thinner folds (T × 0.7, high pitch)", {"T": 0.7}),
         ("stiffer + more damped together", {"B": 1.5, "c": 1.3})]
for name, kw in cases:
    p = pth(**kw) * scale
    print(f"{name:42s} Pth ≈ {p:.2f} kPa = {p * 10.2:.1f} cm H2O")
# baseline                                   Pth ≈ 0.30 kPa = 3.1 cm H2O
# damping ×1.5 (e.g. dry, fatigued tissue)   Pth ≈ 0.45 kPa = 4.6 cm H2O
# stiffer cover, mucosal wave 1.3× faster    Pth ≈ 0.39 kPa = 4.0 cm H2O
# glottis 1.5× wider before onset            Pth ≈ 0.45 kPa = 4.6 cm H2O
# thinner folds (T × 0.7, high pitch)        Pth ≈ 0.43 kPa = 4.4 cm H2O
# stiffer + more damped together             Pth ≈ 0.59 kPa = 6.0 cm H2O

Each factor has a physical meaning. More damping, as in dry or fatigued tissue, means more energy lost per cycle, so more pressure is needed to keep going. A stiffer cover carries the mucosal wave faster, and the threshold rises with it. A wider glottis before onset lets air escape without setting the folds moving. Two moderate changes together raise the threshold two to three times as much as either does alone.

Tension, cracks and pitch

Singers who “push” usually do several things at once: they press the folds together harder, raise the larynx, tighten the muscles of the neck and jaw, and drive more air. Some of these move the parameters of the formula in the wrong direction; others, such as pressing the folds together, take the voice outside the small-amplitude regime the formula describes, into a regime of strong collision. A voice working far above threshold has less room to adjust: fine changes in pitch need fine changes in stiffness and pressure together, and voice breaks (sudden jumps between registers) are known to occur when the vibrating system passes a point at which two patterns of vibration compete (Titze 1994).

Hypothesis · not established

Not established. Excess activity of the neck and jaw muscles around the larynx raises the phonation threshold pressure in singers, by stiffening the vocal-fold cover and increasing damping. The hypothesis predicts that, measured with the same equipment on the same day, a singer’s phonation threshold pressure at a fixed pitch is higher when surface EMG shows high activity of the muscles around the larynx than after a short relaxation routine that lowers that activity. It would be refuted if, in a pre-registered within-singer study, threshold pressure did not change when the surface EMG did.

Note

Measuring phonation threshold pressure properly needs an oral pressure tube or a flow mask and a trained operator. Chapter 8 uses simpler measures that any teacher can take with free software.

References

Solomon, N. P., and M. S. DiMattia. 2000. “Effects of a Vocally Fatiguing Task and Systemic Hydration on Phonation Threshold Pressure.” Journal of Voice 14 (3): 341–62.

Titze, Ingo R. 1988. “The Physics of Small-Amplitude Oscillation of the Vocal Folds.” Journal of the Acoustical Society of America 83 (4): 1536–52.

Titze, Ingo R. 1992. “Phonation Threshold Pressure: A Missing Link in Glottal Aerodynamics.” Journal of the Acoustical Society of America 91 (5): 2926–35.

Titze, Ingo R. 1994. Principles of Voice Production. Prentice Hall.

Verdolini, K., I. R. Titze, and A. Fennell. 1994. “Dependence of Phonatory Effort on Hydration Level.” Journal of Speech and Hearing Research 37 (5): 1001–7.

Zhang, Zhaoyan. 2010. “Dependence of Phonation Threshold Pressure and Frequency on Vocal Fold Geometry and Biomechanics.” Journal of the Acoustical Society of America 127 (4): 2554–62.

Fan, Y. (2026). The Biomechanics of Phonation and Attentional Shift: Myoelastic-Aerodynamic Theory, the Singer's Formant, Auditory-Motor Feedback and External Focus of Attention [发声的生物力学与注意力转移] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23719625 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).