A theoretical study of f0-f1 interaction with application to resonant speaking and singing voice

An interactive source-filter system, consisting of a three-mass body-cover model of the vocal folds and a wave reflection model of the vocal tract, was used to test the dependence of vocal fold vibration on the vocal tract. The degree of interaction is governed by the epilarynx tube, which raises the vocal tract impedance to match the impedance of the glottis. The key component of the impedance is inertive reactance. Whenever there is inertive reactance, the vocal tract assists the vocal folds in vibration. The amplitude of vibration and the glottal flow can more than double, and the oral radiated power can increase up to 10 dB. As F0 approaches F1, the first formant frequency, the interactive source-filter system loses its advantage (because inertive reactance changes to compliant reactance) and the noninteractive system produces greater vocal output. Thus, from a voice training and control standpoint, there may be reasons to operate the system in either interactive and noninteractive modes. The harmonics 2F0 and 3F0 can also benefit from being positioned slightly below F1.     

Measures of spectral slope using an excised larynx model

Spectral measures of the glottal source were investigated using an excised canine larynx (CL) model for various aerodynamic and phonatory conditions. These measures included spectral harmonic difference H1-H2 and spectral slope that are highly correlated with voice quality but not reported in a systematic manner using an excised larynx model. It was hypothesized that the acoustic spectra of the glottal source were significantly influenced by the subglottal pressure, glottal adduction, and vocal fold elongation, as well as the resulting vibration pattern. CLs were prepared, mounted on the bench with and without false vocal folds, and made to oscillate with a flow of heated and humidified air. Major control parameters were subglottal pressure, adduction, and elongation. Electroglottograph, subglottal pressure, flow rate, and audio signals were analyzed using custom software. Results suggest that an increase in subglottal pressure and glottal adduction may change the energy balance between harmonics by increasing the spectral energy of the first few harmonics in an unpredictable manner. It is suggested that changes in the dynamics of vocal fold motion may be responsible for different spectral patterns. The finding that the spectral harmonics do not conform to previous findings was demonstrated through various cases. Results of this study may shed light on phonatory spectral control when the larynx is part of a complete vocal tract system.     

Glottal source-vocal tract interaction

The problem of glottal source-vocal tract interaction is treated. The effect of the first formant load on the waveform of glottal volume flow is investigated by solving a nonlinear differential equation which describes the variation of pressure drop across the first formant load. The glottal volume flow is calculated under the influence of supraglottal and subglottal formant loads. The estimation of the glottal area function is discussed as an application of the theory developed.     

Influence of acoustic loading on an effective single mass model of the vocal folds

Three-way interactions between sound waves in the subglottal and supraglottal tracts, the vibrations of the vocal folds, and laryngeal flow were investigated. Sound wave propagation was modeled using a wave reflection analog method. An effective single-degree-of-freedom model was designed to model vocal-fold vibrations. The effects of orifice geometry changes on the flow were considered by enforcing a time-varying discharge coefficient within a Bernoulli flow model. The resulting single-degree-of-freedom model allowed for energy transfer from flow to structural vibrations, an essential feature usually incorporated through the use of higher order models. The relative importance of acoustic loading and the time-varying flow resistance for fluid-structure energy transfer was established for various configurations. The results showed that acoustic loading contributed more significantly to the net energy transfer than the time-varying flow resistance, especially for less inertive supraglottal loads. The contribution of supraglottal loading was found to be more significant than that of subglottal loading. Subglottal loading was found to reduce the net energy transfer to the vocal-fold oscillation during phonation, balancing the effects of the supraglottal load.     

Dependence of phonation threshold pressure on vocal tract acoustics and vocal fold tissue mechanics

Analytical and computer simulation studies have shown that the acoustic impedance of the vocal tract as well as the viscoelastic properties of vocal fold tissues are critical for determining the dynamics and the energy transfer mechanism of vocal fold oscillation. In the present study, a linear, small-amplitude oscillation theory was revised by taking into account the propagation of a mucosal wave and the inertive reactance (inertance) of the supraglottal vocal tract as the major energy transfer mechanisms for flow-induced self-oscillation of the vocal fold. Specifically, analytical results predicted that phonation threshold pressure (Pth) increases with the viscous shear properties of the vocal fold, but decreases with vocal tract inertance. This theory was empirically tested using a physical model of the larynx, where biological materials (fat, hyaluronic acid, and fibronectin) were implanted into the vocal fold cover to investigate the effect of vocal fold tissue viscoelasticity on Pth. A uniform-tube supraglottal vocal tract was also introduced to examine the effect of vocal tract inertance on Pth. Results showed that Pth decreased with the inertive impedance of the vocal tract and increased with the viscous shear modulus (G") or dynamic viscosity (eta') of the vocal fold cover, consistent with theoretical predictions. These findings supported the potential biomechanical benefits of hyaluronic acid as a surgical bioimplant for repairing voice disorders involving the superficial layer of the lamina propria, such as scarring, sulcus vocalis, atrophy, and Reinke's edema.     

An aerodynamic study of Korean stop consonants: measurements and modeling

Measurements were made of intraoral air pressure and oral flow of ten native speakers uttering word pairs contrasting Korean fortis and lenis voiceless stop consonants in initial position. The production of fortis stops was found to be characterized by a higher intraoral pressure before release, yet a lower oral flow after release, than corresponding lenis stops. Possible reasons for this difference were explored with the use of a computer implemented aerodynamic model, giving an output of air pressure and flow. Input parameters were adjusted in accordance with known or hypothesized variations in glottal area function, vocal tract wall tension, respiratory muscle force, and supraglottal cavity volume, as given in the literature. In addition to the previously known differences in glottal area, it is inferred from the results of the modeling experiment that fortis stops are produced with greater vocal tract wall tension than lenis stops. Speaker-specific production strategies such as larynx lowering and heightened subglottal pressure during fortis stops and differences noted between word pairs are also discussed.     

A framework for the study of vocal registers

Register transitions are divided into two classes, periodicity transitions and timbre transitions. Periodicity transitions refer to changes in vocal quality that occur whenever glottal pulses are perceived as individual events rather than as a continuous auditory stimulus. Timbre transitions refer to changes in vocal quality associated with changes in spectral balance. Physiologically, these can be quantified with an abduction quotient. The singing registers appear to be based on timbre transitions resulting from subglottal resonances that interfere with the vocal fold driving pressure. Four of the major singing register shifts are predicted (in frequency and relative importance) on the basis of the first subglottal formant. Strategies for register equalization are proposed on the basis of supraglottal formant tuning (vowel modification) and adjustments in glottal adduction.     

Measurement of formant frequencies and bandwidths in singing

That singers under certain circumstances adjust the articulation of the vocal tract (formant tuning) to enhance acoustic output is both apparent from measurements and understood in theory. The precise effect of a formant on an approaching (retreating) harmonic as the latter varies in frequency during actual singing, however, is difficult to isolate. In this study variations in amplitude of radiated sound components as well as supraglottal and subglottal (esophageal) pressures accompanying the vibrato-related sweep of voice harmonics were used as a basis for estimating the effective center frequencies and bandwidths of the first and second formants.     

马铁菊头蝠声道声学特性的数值分析

采用有限元数值计算得到了马铁菊头蝠声道内部的声场分布,给出了马铁菊头蝠声道内几种特殊的腔体结构在蝙蝠发声过程中的作用。通过微型CT扫描并经过三维重构得到了马铁菊头蝠声道的三维立体模型用于有限元数值计算,通过在声门处放置单位声源计算得到了整个声道内部以及鼻孔周围的声压分布。结果表明,马铁菊头蝠声道包含了鼻腔结构后声波在声门上方的声压幅度明显大于不含鼻腔结构的情况,从传输曲线来看,声门上方鼻腔的存在使得系统对声波传输在二次谐波频率处呈现低阻抗效果,同时鼻腔的改变还可影响二次谐波的位置。而声门下方的气管空腔主要影响声波的背向转播,声门下方的气管空腔的存在可明显降低蝙蝠发声时声场在声道声门下方的声压幅度,同时抑制声音背向传播时二次谐波成分的强度。      

An anatomically based, time-domain acoustic model of the subglottal system for speech production

A time-domain model of sound wave propagation in the branching airways of the subglottal system is presented. The model is formulated as an extension to an acoustic transmission-line modeling scheme originally developed for simulating the supraglottal system in the time-domain during speech production [Maeda (1982). Speech Commun. 1, 199-229; Mokhtari et al. (2008). Speech Commun. 50, 179-190]. The approach allows for predictions of time-varying acoustic pressure and volume velocity at any point along the various generations of subglottal airways from trachea to alveoli. In addition, the model can be configured so that its overall structure simulates different geometric forms, including airways that branch in a symmetric or asymmetric pattern. Three subglottal configurations, two symmetric and one asymmetric, were represented based on reported anatomical dimensions of the subglottal airways. Estimates of the acoustic input impedances of these subglottal configurations revealed resonant characteristics similar to those found in the previous studies. Simulations of voiced sound propagation into the subglottal airways, achieved by coupling the subglottal model to a two-mass vocal fold model and a supraglottal tract configured for different vowels, yielded predictions of time-domain sound pressure waveforms below the vocal folds that compare favorably to previous measurements in human subjects.     

On subglottal formant analysis

When subglottal pressure signals which are recorded during normal speech production are spectrally analyzed, the frequency of the first spectral maximum appears to deviate appreciably from the first resonance frequency which has been reported in the literature and which stems from measurements of the acoustic impedance of the subglottal system. It is postulated that this is caused by the spectrum of the excitation function. This hypothesis is corroborated by a modeling study. Using an extended version of the well-known two-mass model of the vocal folds that can account for a glottal leak, it is shown that under realistic physiological assumptions glottal flow waveforms are generated whose spectral properties cause a downward shift of the location of the first spectral maximum in the subglottal pressure signals. The order of magnitude of this effect is investigated for different glottal settings and with a subglottal system that is modeled according to the impedance measurements reported in the literature. The outcomes of this modeling study show that the location of the first spectral maximum of the subglottal pressure may deviate appreciably from the natural frequency of the subglottal system. As a consequence, however, the comfortable assumption that in normal speech the glottal excitation function is constant and zero during the "closed glottis interval" has to be called into question.     

Voice source characteristics in six premier country singers

Voice source characteristics as derived from inverse filtering were analyzed in 6 country singers' speech and singing. Results showed that the closed quotient varied systematically with vocal loudness, and that glottal compliance (the ratio between transglottal AC volume displacement and subglottal pressure) decreased with increases in fundamental frequency but remained unaffected by vocal loudness. No striking differences were found in source characteristics between speech and singing within subjects. The degree of phonatory press, as judged by a panel of 19 expert listeners, appeared related to the range in which the singer was singing and to the sound pressure level gain from a doubling of subglottal pressure.     

Glottal flow through a two-mass model: comparison of Navier-Stokes solutions with simplified models

A new numerical model of the vocal folds is presented based on the well-known two-mass models of the vocal folds. The two-mass model is coupled to a model of glottal airflow based on the incompressible Navier-Stokes equations. Glottal waves are produced using different initial glottal gaps and different subglottal pressures. Fundamental frequency, glottal peak flow, and closed phase of the glottal waves have been compared with values known from the literature. The phonation threshold pressure was determined for different initial glottal gaps. The phonation threshold pressure obtained using the flow model with Navier-Stokes equations corresponds better to values determined in normal phonation than the phonation threshold pressure obtained using the flow model based on the Bernoulli equation. Using the Navier-Stokes equations, an increase of the subglottal pressure causes the fundamental frequency and the glottal peak flow to increase, whereas the fundamental frequency in the Bernoulli-based model does not change with increasing pressure.     

Acquisition of detailed laryngeal flow measurements in geometrically realistic models

Characterization of laryngeal flow velocity fields is important to understanding vocal fold vibration and voice production. One common method for acquiring flow field data is particle image velocimetry (PIV). However, because using PIV with models that have curved surfaces is problematic due to optical distortion, experimental investigations of laryngeal airflow are typically performed using models with idealized geometries. In this paper a method for acquiring PIV data using models with realistic geometries is presented. Sample subglottal, intraglottal, and supraglottal PIV data are shown. Capabilities and limitations are discussed, and suggestions for future implementation are provided.     

Medial Surface Dynamics as a Function of Subglottal Pressure in a Canine Larynx Model

During vocal fold vibration, there may be a mucosal wave in the superior-inferior (vertical) direction, resulting in a convergent shape during opening and a divergent shape during closing. Most of our understanding of the converging/diverging shape of the glottis has come from studies in a hemilarynx model. Previous work has shown that vibratory patterns in the full excised larynx are different than the hemilarynx. This study characterized the dynamics of the medial glottal wall geometry during vibrations in the full excised canine larynx model. Using particle image velocimetry, the intraglottal geometry was measured at the midmembranous coronal plane in an excised canine larynx model. Measurements of the glottal area were taken simultaneously using high-speed imaging. The results show that skewing of the glottal area waveform occurs without the presence of a vocal tract and that the phase-lag of the superior edge relative to the inferior edge is smaller than reported and depends on the subglottal pressure. In addition, it shows that the glottal divergence angle during closing is proportional to the magnitude of the acoustic intensity and the intraglottal negative pressure. This preliminary data suggests that more studies are needed to determine the important mechanisms determining the relationship between intraglottal flow, intraglottal geometry, and acoustics.     

On the role of glottis-interior sources in the production of voiced sound

The voice source is dominated by aeroacoustic sources downstream of the glottis. In this paper an investigation is made of the contribution to voiced speech of secondary sources within the glottis. The acoustic waveform is ultimately determined by the volume velocity of air at the glottis, which is controlled by vocal fold vibration, pressure forcing from the lungs, and unsteady backreactions from the sound and from the supraglottal air jet. The theory of aerodynamic sound is applied to study the influence on the fine details of the acoustic waveform of "potential flow" added-mass-type glottal sources, glottis friction, and vorticity either in the glottis-wall boundary layer or in the portion of the free jet shear layer within the glottis. These sources govern predominantly the high frequency content of the sound when the glottis is near closure. A detailed analysis performed for a canonical, cylindrical glottis of rectangular cross section indicates that glottis-interior boundary/shear layer vortex sources and the surface frictional source are of comparable importance; the influence of the potential flow source is about an order of magnitude smaller.     

Acoustic analysis of trill sounds

In this paper, the acoustic-phonetic characteristics of steady apical trills--trill sounds produced by the periodic vibration of the apex of the tongue--are studied. Signal processing methods, namely, zero-frequency filtering and zero-time liftering of speech signals, are used to analyze the excitation source and the resonance characteristics of the vocal tract system, respectively. Although it is natural to expect the effect of trilling on the resonances of the vocal tract system, it is interesting to note that trilling influences the glottal source of excitation as well. The excitation characteristics derived using zero-frequency filtering of speech signals are glottal epochs, strength of impulses at the glottal epochs, and instantaneous fundamental frequency of the glottal vibration. Analysis based on zero-time liftering of speech signals is used to study the dynamic resonance characteristics of vocal tract system during the production of trill sounds. Qualitative analysis of trill sounds in different vowel contexts, and the acoustic cues that may help spotting trills in continuous speech are discussed.     

高速摄影成像分析声带振动发声的前后不对称性

高速摄影成像直接观察到声带振动的前后不对称性。将11个离体狗喉声带进行发声实验,设置3组声门下压分别为10 cm H₂O,20 cm H₂O和30 cm H₂O,利用高速摄像仪和传声器,分别记录不同声门下压的声带振动图像和声信号.对高速摄影成像与同步采集的声信号基频进行定量分析和比较,基频均随声门下压的增大而增加。此外,对两种测量方法得到的基频进行相关分析比较,得到在同一声门下压下两种方法的基频相关系数均大于0.9,表明高速摄影成像得到的基频与声信号的基频具有高度相关性。高速摄影成像能直观地测量声带振动行为,对研究声带振动发声机理提供了有价值的测量手段。高速摄影获得的声带线性结构上25%,50%,75%位置处的振动幅度,显示了声带前后振动不对称且声门下压较低时振动不对称较明显。      

Pressure measurements during speech production using semiconductor miniature pressure transducers: impact on models for speech production

It appears that temperature instabilities are a major obstacle hindering the use of semiconductor strain gauge pressure transducers in speech research, especially when absolute pressure data are mandatory. In this paper a simple and reliable method for an in vivo calibration of this kind of transducer is described. The most important error source, the drift of the zero pressure level due to temperature changes, is discussed, and an estimation of the measurement accuracy which can be obtained is given. Moreover, some registrations of subglottal, supraglottal, and transglottal pressure are presented. It is shown that the pressure recordings allow us to obtain estimates of the volume flow in the trachea and pharynx. Analysis of those waveforms appears to lead to new insights into the physical processes underlying voice production. Specifically, an independent glottal contribution to the skewing of the glottal flow pulses is identified.     

In Vivo Quantification of the Intraglottal Pressure: Modal Phonation and Voice Onset

Intraglottal pressure is the driving force of vocal fold vibration. Its time course during the open phase of the vibratory cycle is essential in the mechanics of phonation, but measuring it directly is difficult and may hinder spontaneous voicing. However, it can be computed from the in vivo measured transglottal flow and glottal area (hence the air particle velocity) on the basis of the Bernoulli energy law and the interaction with the inertance of the vocal tract. As to sustained modal phonation, calculations are presented for the two possible shapes of glottal duct: convergent and divergent, including absolute calibration in order to obtain quantitative physical values. Whatever the glottal duct configuration, the calculations based on measured values of glottal area and air flow show that the integrated intraglottal pressure during the opening phase systematically exceeds that during the closing phase, which is the basic condition for sustaining vocal fold oscillation. The key point is that the airflow curve is skewed to the right relative to the glottal area curve. The skewing results from air compressibility and vocal tract inertance. The intraglottal pressure becomes negative during the closing phase. As to the soft (or physiological) voice onset, a similar approach shows that the integrated pressure differences (opening phase − closing phase) actually increase as the onset progresses, and this applies to the results based on Bernoulli's energy law as well as to those based on the interaction with the inertance of the vocal tract. Furthermore and similarly, the phase lead of the pressure wave with respect to the glottal opening progressively increases. The underlying explanation lies in the progressively increasing skewing of the airflow curve to the right with respect to the glottal area curve.