Optimal glottal configuration for ease of phonation

Recent experimental studies have shown the existence of optimalvalues of the glottal width and convergence angle, at which the phonation threshold pressure is minimum. These results indicate the existence of an optimal glottal configuration for ease of phonation, not predicted by the previous theory. In this paper, the origin of the optimal configuration is investigated using a low dimensional mathematical model of the vocal fold. Two phenomena of glottal aerodynamics are examined: pressure losses due to air viscosity, and air flow separation from a divergent glottis. The optimal glottal configuration seems to be a consequence of the combined effect of both factors. The results agree with the experimental data, showing that the phonation threshold pressure is minimum when the vocal folds are slightly separated in a near rectangular glottis.     

On the relation between subglottal pressure and fundamental frequency in phonation

The change in fundamental frequency with subglottal pressure in phonation is quantified on the basis of the ratio between vibrational amplitude and vocal fold length. This ratio is typically very small in stringed instruments, but becomes quite appreciable in vocal fold vibration. Tension in vocal fold tissues is, therefore, not constant over the vibratory cycle, and a dynamic tension gives rise to amplitude-frequency dependence. It is shown that the typical 2-6 Hz/cm H2O rise in fundamental frequency with subglottal pressure observed in human and canine larynges is a direct and predictable consequence of this amplitude-frequency dependence. Results are presently limited to phonation in the chest register.     

A computational study of asymmetric glottal jet deflection during phonation

Two-dimensional numerical simulations are used to explore the mechanism for asymmetric deflection of the glottal jet during phonation. The model employs the full Navier-Stokes equations for the flow but a simple laryngeal geometry and vocal-fold motion. The study focuses on the effect of Reynolds number and glottal opening angle with a particular emphasis on examining the importance of the so-called "Coanda effect" in jet deflection. The study indicates that the glottal opening angle has no substantial effect on glottal jet deflection. Deflection in the glottal jet is always preceded by large-scale asymmetry in the downstream portion of the glottal jet. A detailed analysis of the velocity and vorticity fields shows that these downstream asymmetric vortex structures induce a flow at the glottal exit which is the primary driver for glottal jet deflection.     

Nonconscious control of fundamental voice frequency

The aim of this paper is to answer the question whether "perception-action" dissociation, which is well documented in vision, may also be found in auditory information processing. Trained singers were asked to produce vowel sounds into a microphone. The sound that each singer produced was fed back to their ears via headphones. Two seconds after the sound production had begun, the auditory feedback was shifted in pitch by a certain degree (9, 19, 50, or 99 cents in either direction). In every set of sounds, instances without any pitch shifts also appeared. After each trial, participants reported whether they were aware of a pitch change or not. It was found that even though the participants were unaware of subtle pitch changes, the fundamental frequency of their vowel production was found to shift slightly in the opposite direction to the pitch shift. These results show that auditory information is processed by two separate systems: one for perception and one for action. They also show that the function of the auditory control system differs from the visual control system. The latter is used to control bodily movements while the function of the former is a nonconscious, instant control of vocalization.     

Phonatory control in male singing: A study of the effects of subglottal pressure, fundamental frequency, and mode of phonation on the voice source

This article describes experiments carried out in order to gain a deeper understanding of the mechanisms underlying variation of vocal loudness in singers. Ten singers, two of whom are famous professional opera tenor soloists, phonated at different pitches and different loudnesses. Their voice source characteristics were analyzed by inverse filtering the oral airflow signal. It was found that the main physiological variable underlying loudness variation is subglottal pressure (Ps). The voice source property determining most of the loudness variation is the amplitude of the negative peak of the differentiated flow signal, as predicted by previous research. Increases in this amplitude are achieved by (a) increasing the pulse amplitude of the flow waveform; (b) moving the moment of vocal fold contact earlier in time, closer to the center of the pulse; and (c) skewing the pulses. The last mentioned alternative seems dependent on both Ps and the ratio between the fundamental frequency and the first formant. On the average, the singers doubled Ps when they increased fundamental frequency by one octave, and a doubling of the excess Ps over threshold caused the sound pressure level (SPL) to increase by 8–9 dB for neutral phonation, less if mode of phonation was changed to pressed. A shift of mode of phonation from flow over neutral to pressed was associated with a reduction of the peak glottal permittance i.e., the ratio between peak transglottal airflow to Ps. Flow phonation had the most favorable relationship between Ps and SPL.     

Physical mechanisms of phonation onset: a linear stability analysis of an aeroelastic continuum model of phonation

In an investigation of phonation onset, a linear stability analysis was performed on a two-dimensional, aeroelastic, continuum model of phonation. The model consisted of a vocal fold-shaped constriction situated in a rigid pipe coupled to a potential flow which separated at the superior edge of the vocal fold. The vocal fold constriction was modeled as a plane-strain linear elastic layer. The dominant eigenvalues and eigenmodes of the fluid-structure-interaction system were investigated as a function of glottal airflow. To investigate specific aerodynamic mechanisms of phonation onset, individual components of the glottal airflow (e.g., flow-induced stiffness, inertia, and damping) were systematically added to the driving force. The investigations suggested that flow-induced stiffness was the primary mechanism of phonation onset, involving the synchronization of two structural eigenmodes. Only under conditions of negligible structural damping and a restricted set of vocal fold geometries did flow-induced damping become the primary mechanism of phonation onset. However, for moderate to high structural damping and a more generalized set of vocal fold geometries, flow-induced stiffness remained the primary mechanism of phonation onset.     

The relationship among voice onset, voice quality, and fundamental frequency: a dynamical perspective

In dynamical motor theory, skill acquisition occurs as a modification of preexisting coordination patterns or attractor states. The purpose of this study was to assess how different levels of voice onset, voice quality, and fundamental frequency (F₀) combine to form the attractor states common to voice motor control. Three levels of voice onset (glottal, simultaneous, and breathy), voice quality (modal speech, mixed, and falsetto), and fundamental frequency (low, mid, and high) were manipulated by vocally untrained, female subjects. Percent correct of acquisition trials and self-report of effort were used as measures of stable phonations indicative of an attractor state. Using intensity as a covariate, the results provided support for two of the three predicted triads representing attractor states in female speakers: (1) glottal onset/modal speech quality/low F₀; and (2) breathy onset/falsetto quality/high F₀. The results of this study suggest that certain parameters of voice motor control, such as onset, quality, and F₀, exist as part of a dynamical system that can be identified and manipulated in voice motor acquisition and learning.     

Direct measurement of onset and offset phonation threshold pressure in normal subjects

Phonation threshold pressures were directly measured in five normal subjects in a variety of voicing conditions. The effects of fundamental frequency, intensity, closure speed of the vocal folds, and laryngeal airway resistance on phonation threshold pressures were determined. Subglottic air pressures were measured using percutaneous puncture of the cricothyroid membrane. Both onset and offset of phonation were studied to see if a hysteresis effect produced lower offset pressures than onset pressures. Univariate analysis showed that phonation threshold pressure was influenced most strongly by fundamental frequency and intensity. Multiple linear regression showed that these two variables, as well as laryngeal airway resistance, most strongly predicted phonation threshold pressure. Two of the five subjects demonstrated a significant hysteresis effect, but one subject actually had higher offset pressures than onset pressures.     

Fundamental frequency and sound pressure level of phonation in pathological states

The fundamental frequency (F₀) for the habitual pitch (F_0HAB), F₀ for the lowest physiological tone (F_0L), F₀ for the highest physiological tone (F_0H), F₀ range of phonation (F₀ Rg), sound pressure level (SPL) for habitual loudness (SPL_HAB), SPL for the softest tone (SPL_S), SPL for the loudest tone (SPL_L), and SPL range of phonation (SPL Rg) were measured in 40 normal adult subjects and 1,563 voice patients with varying diseases. F_0H, F₀ Rg, SPL_L, and SPL Rg were decreased in many disease groups. F_0HAB and F_0L varied. SPL_HAB and SPL_S were increased in some disease groups. F₀-related parameters reflected effects of treatments in the cases with polyp, Reinke's edema, epithelial hyperplasia, carcinoma, and paralysis. Effects of treatments were manifested in SPL-related parameters in the cases with nodule, polyp, carcinoma, and paralysis.     

X-ray diffraction in AT-cut quartz single crystal at acoustic excitation at the fundamental frequency

X-ray diffraction on different atomic planes of an AT-cut quartz crystal is studied experimentally in the Laue geometry in case of excitation by acoustic waves at the first resonant (fundamental) frequency. Acoustic waves lead to an increase in the integral intensity of the reflection-diffracted beam. The amplification coefficients in reflection are measured in dependence on the amplitude of a.c. voltage applied to the crystal at the resonant frequency. The frontal distributions of the intensity of the beam diffracted in the reflection direction are obtained for different atomic planes.     

Perceptual learning of fundamental frequency discrimination: effects of fundamental frequency, harmonic number, and component phase

Thresholds (F0DLs) were measured for discrimination of the fundamental frequency (F0) of a group of harmonics (group B) embedded in harmonics with a fixed F0. Miyazono and Moore [(2009). Acoust. Sci. & Tech. 30, 383386] found a large training effect for tones with high harmonics in group B, when the harmonics were added in cosine phase. It is shown here that this effect was due to use of a cue related to pitch pulse asynchrony (PPA). When PPA cues were disrupted by introducing a temporal offset between the envelope peaks of the harmonics in group B and the remaining harmonics, F0DLs increased markedly. Perceptual learning was examined using a training stimulus with cosine-phase harmonics, F0 = 50 Hz, and high harmonics in group B, under conditions where PPA was not useful. Learning occurred, and it transferred to other cosine-phase tones, but not to random-phase tones. A similar experiment with F0 = 100 Hz showed a learning effect which transferred to a cosine-phase tone with mainly high unresolved harmonics, but not to cosine-phase tones with low harmonics, and not to random-phase tones. The learning found here appears to be specific to tones for which F0 discrimination is based on distinct peaks in the temporal envelope.     

The perception of fundamental frequency declination

A series of experiments was carried out to investigate how fundamental frequency declination is perceived by speakers of English. Using linear predictor coded speech, nonsense sentences were constructed in which fundamental frequency on the last stressed syllable had been systematically varied. Listeners were asked to judge which stressed syllable was higher in pitch. Their judgments were found to reflect normalization for expected declination; in general, when two stressed syllables sounded equal in pitch, the second was actually lower. The pattern of normalization reflected certain major features of production patterns: A greater correction for declination was made for wide pitch range stimuli than for narrow pitch range stimuli. The slope of expected declination was less for longer stimuli than for shorter ones. Lastly, amplitude was found to have a significant effect on judgments, suggesting that the amplitude downdrift which normally accompanies fundamental frequency declination may have an important role in the perception of phrasing.     

Two-fold mode-locking by amplitude modulation at neighbouring harmonics of the laser-cavity fundamental frequency

A model is presented for the pulse-shaping dynamics in an actively mode-locked laser in which the losses are AM modulated at two harmonic frequencies differing by the cavity fundamental mode spacing and is applied to the case of third and fourth harmonics. Coupling to eight side modes is demonstrated. Computer simulations are implemented for a linear resonator which show the effects of modulation and gain for different initial conditions of field-amplitude and phases. This revised version was published online in November 2006 with corrections to the Cover Date.     

On the difference between negative damping and eigenmode synchronization as two phonation onset mechanisms

Negative damping and eigenmode synchronization as two different mechanisms of phonation onset are distinguished. Although both mechanisms lead to a favorable phase relationship between the flow pressure and the vocal fold motion as required for a net energy transfer into the vocal folds, the underlying mechanisms for this favorable phase relationship are different. The negative damping mechanism relies on glottal aerodynamics or acoustics to establish before onset and maintain after onset the favorable phase relationship, and therefore has minimum requirements on vocal fold geometry and biomechanics. A single degree-of-freedom vocal fold model is all that is needed for self-oscillation in the presence of a negative damping mechanism. In contrast, the mechanism of eigenmode synchronization critically depends on the geometrical and biomechanical properties of the vocal folds (at least 2-degrees-of-freedom are required), and has little requirement on the glottal aerodynamics other than flow separation. The favorable phase relation is established once synchronization occurs, regardless of the phase relationship imposed by glottal aerodynamics before onset. Unlike that of the negative damping mechanism, initiation of eigenmode synchronization requires neither a velocity-dependent flow pressure nor an alternating convergent-divergent glottis. The clinical implications of the distinctions between these two mechanisms are discussed.     

The dependency of timbre on fundamental frequency

The dependency of the timbre of musical sounds on their fundamental frequency (F0) was examined in three experiments. In experiment I subjects compared the timbres of stimuli produced by a set of 12 musical instruments with equal F0, duration, and loudness. There were three sessions, each at a different F0. In experiment II the same stimuli were rearranged in pairs, each with the same difference in F0, and subjects had to ignore the constant difference in pitch. In experiment III, instruments were paired both with and without an F0 difference within the same session, and subjects had to ignore the variable differences in pitch. Experiment I yielded dissimilarity matrices that were similar at different F0's, suggesting that instruments kept their relative positions within timbre space. Experiment II found that subjects were able to ignore the salient pitch difference while rating timbre dissimilarity. Dissimilarity matrices were symmetrical, suggesting further that the absolute displacement of the set of instruments within timbre space was small. Experiment III extended this result to the case where the pitch difference varied from trial to trial. Multidimensional scaling (MDS) of dissimilarity scores produced solutions (timbre spaces) that varied little across conditions and experiments. MDS solutions were used to test the validity of signal-based predictors of timbre, and in particular their stability as a function of F0. Taken together, the results suggest that timbre differences are perceived independently from differences of pitch, at least for F0 differences smaller than an octave. Timbre differences can be measured between stimuli with different F0's.     

Hydrogenic systems,frequency standards and fundamental constants

Hydrogenic (two-body) systems are the only atomic systems for which uncertainties in calculations of the energy levels approach the current state of the art in frequency measurement. This article discusses progress in the theory and measurement of transition frequencies in hydrogenic systems. These studies have relevance to the determination of fundamental constants and the testing of physical theories, especially quantum electrodynamics. A set of high accuracy calculable frequency standards could also be realized by using hydrogenic systems.     

Comparison of speaking fundamental frequency in English and Mandarin

To determine if the speaking fundamental frequency (F0) profiles of English and Mandarin differ, a variety of voice samples from male and female speakers were compared. The two languages' F0 profiles were sometimes found to differ, but these differences depended on the particular speech samples being compared. Most notably, the physiological F0 ranges of the speakers, determined from tone sweeps, hardly differed between the two languages, indicating that the English and Mandarin speakers' voices are comparable. Their use of F0 in single-word utterances was, however, quite different, with the Mandarin speakers having higher maximums and means, and larger ranges, even when only the Mandarin high falling tone was compared with English. In contrast, for a prose passage, the two languages were more similar, differing only in the mean F0, Mandarin again being higher. The study thus contributes to the growing literature showing that languages can differ in their F0 profile, but highlights the fact that the choice of speech materials to compare can be critical.     

The pitch of short-duration fundamental frequency glissandos.

Pitch perception for short-duration fundamental frequency (F0) glissandos was studied. In the first part, new measurements using the method of adjustment are reported. Stimuli were F0 glissandos centered at 220 Hz. The parameters under study were: F0 glissando extents (0, 0.8, 1.5, 3, 6, and 12 semitones, i.e., 0, 10.17, 18.74, 38.17, 76.63, and 155.56 Hz), F0 glissando durations (50, 100, 200, and 300 ms), F0 glissando directions (rising or falling), and the extremity of F0 glissandos matched (beginning or end). In the second part, the main results are discussed: (1) perception seems to correspond to an average of the frequencies present in the vicinity of the extremity matched; (2) the higher extremities of the glissando seem more important; (3) adjustments at the end are closer to the extremities than adjustments at the beginning. In the third part, numerical models accounting for the experimental data are proposed: a time-average model and a weighted time-average model. Optimal parameters for these models are derived. The weighted time-average model achieves a 94% accurate prediction rate for the experimental data. The numerical model is successful in predicting the pitch of short-duration F0 glissandos.     

Formant frequency analysis of children''s spoken and sung vowels using sweeping fundamental frequency production

High-pitched productions present difficulties in formant frequency analysis due to wide harmonic spacing and poorly defined formants. As a consequence, there is little reliable data regarding children's spoken or sung vowel formants. Twenty-nine 11-year-old Swedish children were asked to produce 4 sustained spoken and sung vowels. In order to circumvent the problem of wide harmonic spacing, F₁ and F₂ measurements were taken from vowels produced with a sweeping F₀. Experienced choir singers were selected as subjects in order to minimize the larynx height adjustments associated with pitch variation in less skilled subjects. Results showed significantly higher formant frequencies for speech than for singing. Formants were consistently higher in girls than in boys suggesting longer vocal tracts in these preadolescent boys. Furthermore, formant scaling demonstrated vowel dependent differences between boys and girls suggesting non-uniform differences in male and female vocal tract dimensions. These vowel-dependent sex differences were not consistent with adult data.